Bandwidth versus Keying Speed

eHam.net Home | FAQ | Log In Help | Please Subscribe

Welcome Anonymous Become a member or Login

New to Ham Radio?
My Profile

Community
Articles
Forums
News
Reviews
Friends Remembered
Strays
Survey Question

Operating
Contesting
DX Cluster Spots
Propagation

Resources
Calendar
Classifieds
Ham Exams
Ham Links
List Archives
News Articles
Product Reviews
QSL Managers

Site Info
eHam Help (FAQ)
Support the site
The eHam Team
Advertising Info
Vision Statement
About eHam.net

Bandwidth versus Keying Speed

Mickey Cox (K5MC) on May 26, 2007
View comments about this article!

Bandwidth versus Keying Speed

Introduction

A popular article on this reflector says that it is a "misconception" that the "bandwidth" of a CW transmitter is a function of the keying speed. On the other hand, The ARRL Handbook says that the keying speed is a factor in determining the bandwidth "occupied" by a CW signal. What's going on here?

Although there are a variety of potential pitfalls when discussing this topic, the most obvious one is the meaning of the word "bandwidth" itself. Many definitions of bandwidth exist and it is important that the precise definition or type of signal bandwidth be made clear early on.

Fourier Analysis of Signals

I will focus here on the "power" bandwidth of a CW transmitter when keyed by a long string of dits. According to Couch [1], the power bandwidth is f₂ - f₁, where f₁ < f < f₂ defines the frequency band in which 99% of the total average power resides. Note that this definition is similar to the FCC's definition of "occupied" bandwidth:

Occupied bandwidth. The frequency bandwidth such that, below its lower and above its upper frequency limits, the mean powers radiated are each equal to 0.5 percent of the total mean power radiated by a given emission [2].

In studying the specific waveforms presented here, I have used classical Fourier analysis as described in practically all of the communication systems and signal analysis textbooks written over the past 50 years or more.

Let's start with a very good keying wave shape, a sinusoidal-shaped pulse with identical rise and fall times of 5 milliseconds as shown in Figure 1. Now let's assume we form a periodic signal using these shaped pulses with a duty cycle of 50% to represent a long string of dits. Since we want to maintain the same rise/fall characteristics (shapes and times) regardless of speed, we will only vary the time duration of the constant amplitude portion of each pulse (designated as tc) to increase or decrease the number of dits sent per second. I have chosen two specific speeds here, 2.4 words per minute (wpm) and 30 wpm. These speeds were convenient choices mathematically and are also considered to be reasonably representative of the speed range employed by many hams. The value of tc is 0.490 seconds and 0.030 seconds for 2.4 wpm and 30 wpm, respectively. (These values of tc were found by first determining that the number of dits per second is 1 and 12.5 for 2.4 wpm and 30 wpm, respectively.)

Once the exact keying waveform has been decided, the detailed Fourier analysis can begin. If a periodic pulse signal is assumed for the keying waveform, one can calculate its Fourier series and the resulting average power (on a 1-ohm basis) for each discrete frequency component. Once the frequency characteristics of the keying waveform (which is the modulating signal) are known, the frequency characteristics of the radiated CW signal (which, mathematically, is binary ASK) can be found via trigonometric identities because the output signal is the product of the modulating signal and the high frequency carrier.

It turns out that the 99.1% power bandwidth of the 2.4-wpm CW/ASK signal is 34 Hz for the 5-ms sinusoidal-shaped keying waveform. (That is, 99.1% of the total power in the 2.4-wpm CW signal is contained by the carrier and the first 17 sideband pairs.) However, the 99.1% power bandwidth of the 30-wpm CW signal is 150 Hz. (99.1% of the total power in the 30-wpm CW signal is contained by the carrier and the first 6 sideband pairs.) Even though both signals have exactly the same rise and fall characteristics, Fourier analysis indicates that the 99.1% power bandwidth of the 30-wpm CW signal is over four times as large as that of the 2.4-wpm signal!

0x01 graphic

Figure 1. Sinusoidal keying waveform with symmetrical rise and fall times

Now suppose our keying waveform is changed from the very good one described above to one having zero rise and fall times. "Square-wave" keying is quite a bit easier to examine mathematically than sinusoidal keying and it will yield a "worst-case" value of power bandwidth for a given speed. As before, the speed of the dits is set so that we are sending at a rate of either 2.4 wpm or 30 wpm. In the case of square-wave keying, the 99.1% power bandwidth for our CW signal is 42 Hz and 525 Hz when sending dits at 2.4 wpm and 30 wpm, respectively. Once again we see that the power bandwidth increases significantly in going from 2.4 to 30 wpm. In fact, since both the rise and fall times of this keying waveform are zero, the power bandwidth ratio will be exactly equal to the speed ratio (12.5 to 1 in this specific example). Of course, we also expected the power bandwidth to increase significantly in going from sinusoidal keying to square-wave keying at the same speed. At 2.4 wpm, the 99.1% power bandwidth ratio is 1.24 for the two keying waveforms, but at 30 wpm the ratio is a whopping 3.50. The results are summarized in Table 1 below.

	2.4 words per minute	30 words per minute
Sinusoidal keying (5 ms)	34 Hz	150 Hz
Square-wave keying	42 Hz	525 Hz

Table 1. 99.1% power bandwidth for CW/ASK transmitter for periodic signaling

I have purposely avoided cluttering this article with the mathematical details used to obtain the values shown in Table 1. If anyone is interested, I will be glad to post the details in a follow-up article or via email. Although I have carefully checked all of my calculations, in some cases by both time-domain and frequency-domain approaches, there is always the possibility of some computational errors. However, these answers appear to be quite consistent with my expectations and with such sources as The ARRL Handbook.

Summary

The concept of "bandwidth" commonly used in electrical engineering (and certainly used by the FCC in its definition of occupied bandwidth) is a "time averaged" quantity. As shown in Table 1, 99.1% of the total mean (average) power of the 30-wpm signal resides in a wider bandwidth as compared to the 2.4-wpm signal. A crucial point to be made here is that the concept of occupied bandwidth does not say that the strength of the individual key clicks generated by a poorly designed transmitter is reduced when the sending speed is decreased! The information provided by the occupied bandwidth is exactly that described in its definition. In closing, however, I do want to point out that if I have to be subjected to key clicks when operating CW, I would much prefer that the offending transmitter send at a speed of 1 word per 20 minutes rather than 20 words per minute!

References

[1] Leon W. Couch, Digital and Analog Communication Systems, 7th ed., Pearson

Prentice Hall, 2007.

[2] FCC Rules and Regulations, 47 CFR 2.202

http://www.access.gpo.gov/nara/cfr/waisidx_06/47cfr2_06.html

Member Comments:

This article has expired. No more comments may be added.

Bandwidth versus Keying Speed

by SM0AOM on May 26, 2007 Mail this to a friend!

By a substantially identical reasoning, the ITU/CCIR
once formulated the "necessary bandwidth" formulas
in the Radio Regulations.

For A1A emission or "on/off telegraphy" it reads

Bn = BK

where Bn = necessary bandwidth in Hz
B = keying speed in Bauds
K = factor to accommodate the number of keying sidebands necessary to recreate the shapes of the signal elements. K is usually assumed to be 3 for
"non-fading circuits" or "soft keying", 5 for
"fading circuits" or "hard keying"
It is further assumed that the keying envelope functions are close to optimal.

Using the above formula,
a 20 WPM (16,66 Baud) A1A signal has a necessary bandwidth of 84 Hz for "hard keying" and 50 Hz for "soft keying".

For an in-depth discussion by W9CF of the optimum keying envelope function see
http://fermi.la.asu.edu/w9cf/articles/click/index.html

73/

Karl-Arne
SM0AOM

RE: Bandwidth versus Keying Speed

by W6TH on May 26, 2007 Mail this to a friend!

.
Very interesting.

Bandwidth versus Keying Speed versus my 250 Hz cw Filter.

Very interesting.

W6TH

.:

Bandwidth versus Keying Speed

by N0CTI on May 26, 2007 Mail this to a friend!

Looking at the results in the table I conclude that bandwidth is used more efficiently with soft keying rather than hard keying. Also, with hard keying the bandwidth per word-per-minute is constant; bandwidth is directly proportional to speed. With soft keying, faster speeds use bandwidth more efficiently than slow speeds.

Interesting. Thanks for the article.

Dave K0DCH (eham database is not quite up to date.)

RE: Bandwidth versus Keying Speed

by N4DSP on May 26, 2007 Mail this to a friend!

Congratulations to eHam and the authors of these articles. Its about time. Great learning experience for all. Who said there are no longer any elmers.

73
john-n4dsp

Bandwidth versus Keying Speed

by W8AD on May 26, 2007 Mail this to a friend!

This a great informative article. This is the kind of thing we need on E-HAM. The quality of this article should encourage hams, both new and experienced, that there are very knowledgeable and nice folks out there who make this a great hobby!

Thank you,

Don, W8AD (hope the trolls stay under the bridge on this one!)

RE: Bandwidth versus Keying Speed

by N6XL on May 26, 2007 Mail this to a friend!

OUT-STANDING, we could use more articles like this.

73's
Paul

RE: Bandwidth versus Keying Speed

by W6TH on May 26, 2007 Mail this to a friend!

.
K5MC Mickey,

"Quote Mickey"

In closing, however, I do want to point out that if I have to be subjected to key clicks when operating CW, I would much prefer that the offending transmitter send at a speed of 1 word per 20 minutes rather than 20 words per minute!
................................................

Well my friend, back in the "old days", key clicks never bothered us and speeds were well above 35 wpm just using a bug. Believe me with a few hundred volts across our bugs many time caused key clicks just keying the cathodes of the crystal oscillators. So I say the key clicks never was a problem.

We, back then, wanted very hard keying and not the soft kind as at the softer, higher speeds, (50 wpm) the words were run much closer together and sounded as though there were no spacing. Another thing we copied by the sound of the words and not by characters as is taught today.

So all in all, I still enjoy the hard keying and especially at speeds at 50 and above for nice copy, regardless of key clicks or not.

It was very easy to soften the cw as all we did was to put a 100 ohm resistor in series with the bug and a 1 Mfd capacitor across the resistor and go lower until the op on the other enjoyed the sound.

Key clicks were told to the operator and he worked on the keying until all was accomplished.

Nice article Mickey and hope we get more to elmer the new Amateur Radio Operators, but remember old days used logic and were creative.Now, "Thats Brother Hood".

73, W6TH
.:

RE: Bandwidth versus Keying Speed

by W7ETA on May 26, 2007 Mail this to a friend!

Wow!

A three fer: great prose, coherent, and concise.

Thanks

73
Bob

Bandwidth versus Keying Speed

by K6YE on May 26, 2007 Mail this to a friend!

Mickey,

I echo the other posts. Great article!!!

Semper Fi,

Tommy - K6YE
DX IS

RE: Bandwidth versus Keying Speed

by W8JI on May 26, 2007 Mail this to a friend!

Hi Mickey,

nice article but the bandwidth is actually set by the rise and fall times and shapes, not by the keying speed.

The keying speed only controls the number of times the offending sidebands repeat.

You can see detailed explanations of this on my web page at:

http://www.w8ji.com/keyclicks.htm

This page includes links to W9CF's site and a page with a white paper by Mark Amos.

73 Tom

RE: Bandwidth versus Keying Speed

by W8JI on May 26, 2007 Mail this to a friend!

By the way, most important is the link to W9CF's website where he shows the power distribution of keyclicks (the sidebands) of a CW signal.

Link:

http://fermi.la.asu.edu/w9cf/articles/click/index.html

If you look at the bandwidth distribution you will find the overall shape of the sidebands (attenuation vs. frequency as you tune off higher or lower) is identical with all keying speeds. The only thing that happens is nulls and peaks move around inside that overall shape, but the receiver doesn't know the difference since its filter always has to be wide enough to pass all the sidebands.

The W9CF and other pages and papers dispell the common misconception that overall bandwidth changes with speed. The badwidth ALWAYS has to be wide enough to pass the rising and falling edges of the envelope.

73 Tom

RE: Bandwidth versus Keying Speed

by AA4PB on May 26, 2007 Mail this to a friend!

Tom, is that because the keying speed on any normal CW signal is slow enough that the shape of the rise and fall times is the major contributor to bandwidth? As the speed countinues to rise (as in 300 baud, for example) then the speed becomes a major contributor to bandwidth? Otherwise it seems that we could run some very high baud rates on HF without worrying about occupied bandwidth.

RE: Bandwidth versus Keying Speed

by W6TH on May 26, 2007 Mail this to a friend!

.
Not much to really discuss on this post because there are two types of key clicks that I remember...One type that was within a few Hz of center frequency and the other type that was up and down the center frequency a few Khz.

Another, we may call it a third one was using a RF amplifier and was caused by poor neutralization of the final amplifier.

I enjoy the keying of a very fast rise time and a slower falloff time, guess it is up to the receiver and the human ear as many have looked good on the osciloscope and yet did not seem to sound so good.

Radios of today are as close as one can get as the majority sound exceptionally good.The outboard keyers also do help the keying even with a different dot to dash ratio.Then again most say the semi breakin sounds better than the full breakin.

..............................Tasters Choice.........

.:

RE: Bandwidth versus Keying Speed

by KE3HO on May 26, 2007 Mail this to a friend!

<<< "is that because the keying speed on any normal CW signal is slow enough that the shape of the rise and fall times is the major contributor to bandwidth?" >>>

Look at it this way: Consider Figure 1 above. The CW keying waveform as shown has three parts, the rise time, the period where the RF output is constant (tc), and the fall time.

During the rise time, the RF output is a time varying signal - in other words, it is a modulated signal. This time-changing signal produces sidebands. The sidebands produced are determined solely by the rise time and the shape of the keying function during the rise time.

During the "tc" period, the RF output is constant - in other words, it is a pure unmodulated carrier. During this period no sidebands are produced. The width of the carrier is set by the stability of the rigs oscillator, power supply stability, etc.

During the fall time, once again the signal is time-varying, so once again sidebands are produced.

How does keying speed play into this? Consider the rise time period. The keying waveform and the rise time are fixed - they do not depend on keying speed. If you don't believe this, they ask yourself the following question: "When I put down the key, how does the rig know how long I am going to hold it down?" See what I am saying? The only way that the rise time and keying waveform could change with keying speed would be if the rig somehow knew how long you were going to hold down the key. It can't. Period. Same goes for the fall time. The fall time and keying waveform are fixed.

Looking at the waveform again, as keying speed increases, the only thing that changes is the middle period, tc. As keying speed increases, tc becomes shorter. However, this is the period where the rig is producing as close to a pure unmodulated carrier as it can. The rise time period and fall time period are not affected by keying speed, so the sidebands that they produce do not change with keying speed.

73 - Jim

RE: Bandwidth versus Keying Speed

by W8JI on May 26, 2007 Mail this to a friend!

by AA4PB on May 26, 2007 Tom, is that because the keying speed on any normal CW signal is slow enough that the shape of the rise and fall times is the major contributor to bandwidth? >>

Picture it this way. When we key the transmitter the waveshape of the envelope changes. That waveshape has a rise time and a fall time, and a slope rate within that time.

With a perfect sine shaped rise and fall time each of .005 seconds, the full cycle takes .01 seconds. It is a 1/.01 = 100Hz sine wave modulating the carrier. This means we have a sideband 100Hz above and 100Hz below the carrier every time the key is closed and every time the key is opened. (This assumes an identical rise and fall waveform.)

We cannot possibly have a narrower signal, or we must lengthen the rise and fall times. As a matter of fact if we ran that signal through a perfect 100Hz bandwidth filter the rise and fall times would simply change to .010 seconds at the output!!!

I've cleaned up transmitters by doing just that.

Even if I just send a single rising edge it will make a sideband above and below the carrier, and the maximum frequency distance away from the carrier would be determined by the rate of change in that rising carrier. It is nothing but AM, an amplitude modulated DSB transmission. The occupied spectrum is always the same if it is one change a second or one change an hour, because the rate and slope of change determines the ultimate bandwidth. The only thing that happens when I send faster is the sidebands appear more often.

The sidebands ALWAYS have to be out further than the keying rate because the keying rate has to always be slower than the rise and fall frequency. You can NEVER send faster than the rise and fall time alolows the carrier to turn off or on!!! That's just common sense.

Because of that, the only thing keying speed does is make it appear like sidebands are moving around inside that spectrum....but that is an illusion of time. Your receiver...just like your ears....has no memory of the leading and trailing edges. Now a storage device, either in mathematical analysis or spectral display, will show those ripples inside the primary shape....but that is because we are looking at time domain modulation of the high frequency sidebands caused by a very low frequency keying signal. It really has no effect on our receiver or our ears.

Doug Smith rewrote the ARRL Handbook's incorrect section on keying. I think Doug Smith KF6DX also has a white paper on the web that explains exactly the same thing as I just described.

The incorrect Handbook information may well have been the reason Yaesu and others put out terrible CW transmitters for many years. Either that or the engineers at those companies misused the fourier analysis and assumed the WIDEST part of the signal was determined by the CW speed. If I send 2 WPM with an unmodified FT1000D you would hear me clicking up and down about 1kHz, and if I sent 50 WPM it would be the same. The clicks would just become more frequent.

Picture a light swicth in your house. You turn it on and you hear a click in an AM radio at 1500kHz. The "carrier" frequency of the light switch is 60 Hz. The sideband is at least 1500kHz away. It's there (and everywhere in between) no matter how fast the light switch is turned off and on. But if we looked at it in a time domain that was much longer than the off and on times it would appear like there were ripples moving around inside the bandwidth, although the overall response would be exactly the same.

A drawing is worth 1000 words, and Dr. Schmidt's (W9CF) analysis shows drawings of what happens. My web page has pictures, or anyone with a storage spectrum analyzer can see the very same thing. Anyone with a receiver can hear the very same thing also.

I really wonder, since everyone can see and hear the same thing, why this same misconception keeps popping up. Especially since the ARRL has now corrected the Handbook and there are so many white papers by so many different unrelated people appearing that explain the same exact result. It is also simple basic logic. A transmitter that requires a certain bandwidth to allow the carrier to turn off and on can become wider or narrower just because we use it once a day, once a minute, once a second, or once every 50 milliseconds. It can only change if we try to turn it off and on faster than the rise and fall allows.

If a transmitter HAS to generate a sideband at least the 1/time of the complete envelope rise and fall cycle above and below the carrier to allow the carrier to move, why do some insist the bandwidth of that transition that causes all the problems suddenly is narrower if we send one dit an hour?

It occurs less frequently, but the sideband is the same bandwidth. You close the key, the signal is so wide during the rise because of the rise modulation of the envelope. You open the key, the sidebands are so wide with such an amplitude based on the fall time and shape. You send faster and it happens more often, but the shape where the trash is generated remains the same and so does the overall bandwidth of the trash.

The CW receiver that it bothers by definition CANNOT remember and store the last rise or fall and add or subtract that energy over enough keying transitions to make the ripples appear. If it did it would never be able to pass the off and on tone, and it would not be useful as a CW receiver.

The flaw in the idea that speed sets bandwidth of a transmitter is the CW keying rate is so much slower than the rise and fall time that it simply doesn't affect what we hear on a receiver. We hear the same click at the same distance regardless of speed so long as the envelope rise and fall doesn't change time or slope, we simply hear it more or less often.

73 Tom

RE: Bandwidth versus Keying Speed

by W8JI on May 26, 2007 Mail this to a friend!

KE3HO,

Thank you Jim.

That's a fresh and correct contribution.

Changing the part of the waveform that is NOT producing sidebands cannot change the width of the sidebands. Very good and very simple.

There are a dozen ways to look at this, but the results are always the same.

73 Tom

Bandwidth versus Keying Speed

by VE3MFN on May 26, 2007 Mail this to a friend!

Very clear and concise, and the great thing is I could read it without feeling like I was about to 'blow out a frontal lobe' on some of the math....!! Great article....

Rick VE3MFN (QRQ nut)

Bandwidth versus Keying Speed

by K5MC on May 27, 2007 Mail this to a friend!

I'm sorry to see that W8JI continues to misunderstand the concept of "power" or "occupied" bandwidth. The mathematical meaning of power bandwidth is quite clear; I was also quite clear in my article that I was reporting on the 99.1% power bandwidth of the various keying waveforms that I considered.

W9CF's conclusion at http://fermi.la.asu.edu/w9cf/articles/click/index.html appears to be ". . . the keying speed does not effect (affect?) the overall bandwidth." I don't believe the term "overall" bandwidth is defined by W9CF or, for that matter, anybody else. I certainly don't recall seeing that term defined in any reputable signal analysis or communications textbook. If W9CF means the "absolute" bandwidth when he says the "overall" bandwidth, then he's clearly wrong, at least according to Fourier analysis. All signals that are limited in time have an absolute bandwidth of infinity.

Now that I've mentioned the article by W9CF, I'm afraid that while his mathematics may appear to be quite impressive, he also appears to not understand a fundamental limitation of Fourier transforms! The basic functions used in Fourier analysis are sine waves and cosine waves; these waves are precisely located in frequency but exist for all time. The frequency information of a signal calculated by the classical Fourier transform is an average over the entire time duration of the signal. (I've basically just quoted a couple of sentences from an engineering journal paper written by one of my graduate students and myself from about 10 years ago.)

If you calculate the Fourier transform of a single square-wave pulse, for example, you will clearly find that the "bandwidth" of that signal varies inversely with its time duration. (This assumes we are using a consistent definition of bandwidth, other than the absolute bandwidth. One possible definition is the 99% energy bandwidth.) I chose to use periodic keying signals in my article rather than single pulses (as assumed by W9CF) because I wanted to illustrate the concept of power bandwidth (essentially the same thing as the FCC's occupied bandwidth.) A periodic keying waveform also allows us to approach the problem via Fourier series rather than Fourier transforms. (The concept of Fourier series is simpler than that of Fourier transforms.)

I welcome anyone with a signal analysis/communications background to check my mathematics. The signal analysis that I discussed in my article (99.1% power bandwidth!) is representative of what a good junior or senior electrical engineering student is able to do after completing a typical signal analysis/communications course. I should know this because I'm an electrical engineering professor and I've taught such courses for over 20 years now.

One final note: If W8JI truly believes that the concept of occupied bandwidth is terribly wrong, then he should come up with his own precise (that is, mathematical) definition of bandwidth for the FCC engineers to consider.

73,
K5MC, Ph.D., P.E.

RE: Bandwidth versus Keying Speed

by SM0AOM on May 27, 2007 Mail this to a friend!

This discussion has split into two parts.

We have the part regarding any emissions outside the "necessary bandwidth"("key clicks") caused by improper shaping of the rise and fall times of the signalling elements.

And another part that deals with the bandwidth necessary to pass the actual information.

It is perfectly acceptable to transmit radiotelegraphy
using sinusodially shaped signal elements (but the signals will be very difficult to read by ear).

In this special case we have 100% AM with a slow modulating waveform, creating a single pair of sidebands that are spaced +/- (keying rate in Baud)/2 [Hz]from the carrier or center frequency.

If the shaping is "perfect" [no discontinuites] the necessary bandwidth will be just the keying rate in Baud; no more , no less.

Convenient aural reception of telegraphy requires the
starting and ending of the signal elements to be more defined than the sinusodial shapes, and if we decrease the rise and fall times to make the elements more distinct, this will create higher order sidebands.

If an operator at the receiving end is satisfied with an element shape that results by incorporating 3 pairs of sidebands, the transmitter shaping can be set to this value and the "necessary bandwidth" becomes 3 times the keying rate in Baud.

"Key clicks" are a completely different matter.
They result from using a transmitter shaping that is not properly related to the signal element duration or keying rate.

The CCIR "necessary bandwidth" formulas have been derived assuming that the transmitter shaping is done in a proper way, and the virtues of using the Gauss Error Function as the shaping function have been known for decades in the professional world.

The spectral masks resulting from this shaping waveform have been used in i.a. type acceptance criteria for point-to-point and marine radio transmitters at least since the 60's.

73/

Karl-Arne
SM0AOM

RE: Bandwidth versus Keying Speed

by W8JI on May 27, 2007 Mail this to a friend!

The problem is some people wrong assume the NECESSARY bandwidth is the ACTUAL bandwidth.

There will always be a few who cling to that mistake no matter how logic and actual measurement or operation dictates otherwise. :-)

All the theory in the world can't change what we hear with our own ears or see with our own eyes with a spectrum analyzer.

73 Tom

RE: Bandwidth versus Keying Speed

by W8JI on May 27, 2007 Mail this to a friend!

http://www.doug-smith.net/cwbandwidth1.htm

Doug Smith says "Fig 2 is a spectral analysis of the waveform of Fig 1. Spectral occupancy is chiefly determined by the envelope shape and not by the keying speed. To be sure, keying such a waveform at high speed puts more energy into adjacent frequencies than at low speed; but the instantaneous amplitude of the keying sidebands is constant during the rise and fall times, regardless of keying speed."

http://fermi.la.asu.edu/w9cf/articles/click/index.html

W9CF says "This problem was brought to my attention by Tom Rauch, W8JI, who, in his note to me, had described his experience and correctly pointed out all the main features that govern the bandwith. These notes are an expanded version of my reply giving the mathematical explanation.
To fit the most CW signals into the available spectrum, we need to limit the bandwidth taken up by the signals. It is therefore useful to see how the energy in a dot or dash pulse is distributed around the carrier frequency. Here I give some notes on how to make this analysis. The main result is that the spectrum for many keying shapes is given by the product of the spectrum of a square pulse times the spectrum of the slope of the rise and fall behavior of the pulse.

It seems from my experience reading morse, that the rise time should be the main factor in producing code that can be read by ear comfortably. Since the rise time dominates the bandwidth for the usual CW signal, the analysis shows that to get a nearly optimal bandwidth to rise time, the keying pulse shape should have a gaussian slope.

In the next section I review basic Fourier analysis of amplitude modulation. I then calculate the spectrum of a pulse with an exponentially shaped rise and fall as would be produced by simple RC networks. The results suggest the more general analysis in the following section, with the conclusion that a pulse with gaussian slope, i.e. error function rise and fall shapes, will have an optimal bandwidth and rise time.

It seems likely that all of this would have been worked out by radio engineers in the early 1900s when CW signals were first employed. "

Both articles are good reading, and common sense will agree with the details in those articles.

73 Tom

Bandwidth versus Keying Speed

by K5MC on May 27, 2007 Mail this to a friend!

It certainly appears to me that W8JI and some other folks on this reflector are assuming that a sinusoid (a sine wave or cosine wave) of frequency f Hz having a finite time duration has its entire spectrum concentrated at f Hz. According to Fourier analysis, at least, such an assumption is wrong! For a sinusoid of finite duration T seconds, the Fourier spectrum is spread out on either side of f Hz by the factor 1/T. In other words, the spectrum (that is, the bandwidth) of a sinusoid is inversely proportional to its time duration.

For example, let's consider two sinusoids of equal amplitude, say 1 volt. Assume that s1 is a 1-kHz sine wave that lasts for exactly 1 second and s2 is a 1-kHz sine wave that lasts for exactly 2 seconds. Therefore, s1 will consist of 1000 successive sine waves, with each wave having an amplitude and period of 1 volt and 1 millisecond, respectively. Similarly, s2 will consist of 2000 successive sine waves, with each wave also having an amplitude and period of 1 volt and 1 millisecond, respectively. The 99% energy bandwidth (just to be specific on my definition of bandwidth here) of s1 will be exactly twice as much as that of s2. By my calculations, the 99% energy bandwidth of s1 is 20.6 Hz and the 99% energy bandwidth of s2 is 10.3 Hz.

The discussion above should remind everyone that the "bandwidth" of an FM signal is not simply equal to twice the maximum deviation. For example, if the maximum deviation of a commercial FM broadcast station is limited to plus or minus 75 kHz, the bandwidth of that FM station is certainly larger than 150 kHz.

I also want to point out that spectrum analyzers are based upon the very principles of Fourier analysis that I've been discussing! Spectrum analyzers provide an approximation of the "exact" Fourier analysis that I have tried to present here. In addition to teaching the theory of signal analysis, I have some modest experience in working with "real world" signals, including such examples as the transient analysis of power engineering waveforms caused by such items as arc furnaces (which are essentially random loads during the early part of a melting cycle) and power transformers (for example, transformer inrush currents).

73, K5MC

RE: Bandwidth versus Keying Speed

by W8JI on May 27, 2007 Mail this to a friend!

Mickey,

I don't know how to explain it any bettter than I and several others have already done.

1.) Bandwidth is required only when the carrier changes level. When at full power or zero power it has no bandwidth, it has no modulation.

2.) Assuming a stable carrier the rate of power level change controls the highest sideband frequency produced. The level change at that slope (or any angle of slope during the transition) controls the amplitude of the sidebands.

3.) The receiver by required function cannot store the repeating sidebands. It has to respond to the very shortest off and on period without dragging the response out or we could not hear the tones starting and stopping.

4.) When we are off frequency with a CW receiver we hear the same exact amplitude level of clicks at the same spacing no matter how fast or slow the signal is keyed. This is because the transmitter ALWAYS has to generate the same badwidth during the upward and downward transition or it simply cannot transmit the shape of the rise and fall!!!

5.) If we look at that over a long time and add the effects of the much lower frequency off and on keying, the effect is to cause ripples or peaks and valleys in the points where energy is distributed. The overall SLOPE of that sideband energy is exactly the same with one dit or a hundred dits per second, just as long as the keying rate does not approach the rise and fall rate.

6.) We cannot sort out those close spaced ripples with a receiver, so they are meaningless to the operator. We cannot sort them out because the bandwidth of the receiver has to be wider than the rise and fall frequency during the rising and falling transitions or the receiver will "mush" the transmitter by clipping sidebands. You can hear this effect as you crank in selectivity on a receiver to values below a few hundred Hz.

7.) A spectrum analyzer will store the signals and as it makes many sweeps will paint the ripples on the screen, but if we look at the envelope shape we will always find the roll off or attenuation with frequency will always match the shape required to produce the rise and fall shape of the keyed signal.

I can't say much more. All it takes is a few minutes with a receiver and a transmitter and you will see what I say above is true. The space we take up on a band with our keyclicks is entirely dependent on the shape of the rising and falling edges.

While it is true the clicks appear more frequently at higher speeds and have more average power over time at higher speeds, the overall shape of the area you bother remains exactly the same independent of keying speeds as long as those speeds are reasonable. Of course if I send one klick an hour no one would care, but if I was 1kHz away and you were sending 5-10 WPM or 50 WPM you would be placing the same energy at each off and on transition on my frequency.

Sending slower will not make this bandwidth go away.

Thinking otherwise is pobably what got Yaesu and others in big trouble. They assumed they could put out rigs with horrible ~1mS rise times.

That's why you can hear an FT1000MP clicking on CW 1kHz or more away, even when the guy is sending only 10 WPM.

I'd like to agree with you, but I can't change how the system works. I wish I could because the bands would be much cleaner and we would not need to shape the waveform of the rise and fall. All we would need to do is turn the keyer speed down.

Unfortunately CW transmitters and receivers do not behave that way, and we have to set the rise and fall times and shape carefully to avoid adjacent channel keyclicks.

It was somewhere around the 1900's we learned this, but like many core skills we have forgotten the basics.

73 Tom

RE: Bandwidth versus Keying Speed

by W6TH on May 27, 2007 Mail this to a friend!

.

Very interesting discussion brother hams, but remember this, when you qso me, remember to run a pure square wave and make that keying as hard as you can as it certainly makes good copy for my head at 50 to 70 wpm.

Guess you can't teach an old dog new tricks.

73, W6TH

.:

RE: Bandwidth versus Keying Speed

by AA4PB on May 27, 2007 Mail this to a friend!

Tom, how does the CW bandwidth issue compare with bandwidth of other data modes (FSK for example)? I think that is part of the confusion. We are accustomed to thinking in terms of a higher signaling rate requiring greater bandwidth and trying to apply that to CW. I don't think you are implying that 300 baud packet requires the same bandwidth as 1200 baud packet, for example.

RE: Bandwidth versus Keying Speed

by VA3NR on May 27, 2007 Mail this to a friend!

I have a question on the mathematical analysis: I think the analysis assumes periodic pulse trains at the two speeds. i.e a string of dits. How does the analysis change if the transitions instead occur at random times? i.e. dashes, spaces between characters, and spaces between words are NOT integer multiples of the dot length. In fact they are not even constant - they vary throughout the transmission.

Thanks, I appreciate the presentation and discussion. Fourier study was long time ago for me and I think I purged it immediately upon graduation.

73, Chris VA3NR.

RE: Bandwidth versus Keying Speed

by SM0AOM on May 27, 2007 Mail this to a friend!

For those that can read German, the ITU point of view
regarding the relation between A1A telegraphy keying rates and occupied or necessary bandwidths is elaborated on http://www.qsl.net/dk5ke/a1a.html#signal

I would be most surprised if the international
radio engineering community should have been wrong all the time on this subject.

The "key-clicks" or spurious emissions that poorly engineered equipment can generate are a separate subject.

73/

Karl-Arne
SM0AOM

RE: Bandwidth versus Keying Speed

by W6TH on May 27, 2007 Mail this to a friend!

.
The "key-clicks" or spurious emissions that poorly engineered equipment can generate are a separate subject.
..............................................
This I agree.

Actually it is not poor engineering and can be overlooked. All it amounts to is time constants of a capacitor and a resistor.

On my Icom 756 Pro III, I have tried the 2, 4, 6, and the 8 ms for wave shaping and on the actual testing on the air, the operators have not by ear noticed any change. All agreed it was clean and smooth.

With my two Icom 718 radios, I have yet to have a complaint with the one exception, at high speed keying the receiving operators wanted the semi breakin keying.
This do to the shortening of dits and dahs.

...Sometimes hams get carried away...

On cw, we do not need the 3 Khz bandwidth and the use of filters can shorten the bandwidth, fiddle dee dum.

.:

Bandwidth versus Keying Speed

by K5MC on May 27, 2007 Mail this to a friend!

I appreciate very much the nice comments from a number of hams regarding my article. Now I would like to respond to some comments from VA3NR and SM0AOM.

I chose a long string of dits as the keying waveform (a so-called deterministic signal) so that it would be "reasonably easy" to calculate the power bandwidth of the resulting CW signal. The keying waveform that VA3NR mentioned is a true random signal that cannot be described as a function of time and it is impossible to find its Fourier transform. The approach taken in the signal analysis world is to determine the autocorrelation function of the random signal from its statistical information; from that one can find the power spectral density (PSD) function. Finally, the power contributed by the spectral components over a specific frequency interval can be found by integrating the PSD over that frequency interval. The most difficult part in this process, as far as I'm concerned, is to determine the autocorrelation function of a random keying waveform. Although I have not pursued the professional literature on this specific topic, I would be pleasantly surprised if anybody has ever nailed down the autocorrelation function of a random Morse code keying waveform.

Assuming a long string of dits as the keying waveform pretty much assures that the "worst-case" power bandwidth is found for a given code speed and assumed rise/fall characteristics. For example, in my article I reported that the 99.1% power bandwidth of a CW transmitter using sinusoidal keying (5-ms rise/fall times) is 150 Hz at 30 wpm. The 99.1% power bandwidth of that transmitter sending a random message at 30-wpm would have to be somewhat less than 150 Hz.

Regarding SM0AOM's comments, unfortunately I cannot read German. (There's probably an English version of those ITU rules around somewhere, but I haven't looked for it.) I suspect that the ITU rules are an elaboration of what we find in Part 97, however. The FCC distinguishes between "spurious" emissions (such as harmonics), "out-of band" emissions (such as key clicks) and "necessary" bandwidth.

By the way, the so-called "necessary" bandwidth is essentially a "legal" definition in my view; it certainly isn't an engineering (that is, mathematically precise) definition compared to occupied bandwidth, power bandwidth, absolute bandwidth, null-to-null bandwidth, equivalent noise bandwidth, and several others discussed in the engineering literature. Part 2 of the FCC rules (which I referenced in my article) includes a table of necessary bandwidths for a variety of signals.

It is also interesting to note that the definition of bandwidth found in 97.3 is, in essence, the 99.75% power bandwidth. The definition actually says the following: "Bandwidth. The width of a frequency band outside of which the mean power of the transmitted signal is attenuated at least 26 dB below the mean power of the transmitted signal within the band." This is the 99.75% (that is, 0.9975) power bandwidth because

10 log (1-0.9975)/1 = 10 log 0.0025/1 = -26.02 dB

The 99.75% power bandwidth, of course, will be somewhat larger than the 99% power bandwidth (which is, in essence, the FCC's definition of occupied bandwidth) for a given signal.

In closing this round of my comments, I will once again attempt to point out to W8JI (as I did in my original article) that the concept of power bandwidth does not say that the key clicks heard from a poorly designed CW transmitter are reduced in strength if the keying speed is reduced. Some people try to read that conclusion into the concept of power bandwidth (along with the general subject of Fourier analysis!), but they are simply misreading the information provided by the power bandwidth. The power bandwidth represents the time average values of the powers contributed by the various frequency components of the CW signal. You can be sure that, regardless of what W8JI or some others might say, the "power" bandwidth (and the "occupied" bandwidth as defined by the FCC) of a CW signal does definitely vary with the keying speed as I reported in my article.

73, K5MC

RE: Bandwidth versus Keying Speed

by W6TH on May 27, 2007 Mail this to a friend!

.
K5MC,

You can be sure that, regardless of what W8JI or some others might say, the "power" bandwidth (and the "occupied" bandwidth as defined by the FCC) of a CW signal does definitely vary with the keying speed as I reported in my article.
..................................................

Thanks Mickey and looking back quite a few years, I have remembered somewhat the same as above mentioned.

.......I am on your side with this one, thanks for the post and the math that finally convinced me...Don't be too shy and come visit us again.

73, W6TH
.:

RE: Bandwidth versus Keying Speed

by W8JI on May 27, 2007 Mail this to a friend!

Well in closing all I can say is there are people who willtake the time to reason through the problem and understand it, or to actually perform an experiment to confirm their understanding.

In the other camp there are those who will misapply a good formula and make it apply to something it does not actually apply to.

For example our friend from Sweden says it is a transmitter "defect". But there are no transmitters I've ever seen that readjust the rise and fall times to fit the very minimum bandwidth theory dictates. I doubt anyone would want a transmitter that sounded softer and softer as speed was slowed, or that changed rise and fall times on every dot and again when a dash came along.

Indeed if we set that as the standard for a "good design", so the bandwidth actually does what a few people claim and changes with speed, then every transmitter in the world is defective.

Until the people who are misapplying the formula actually take the time to reason through the problem or get off their duffs and do a simple experiment almost any novice could do.... there will be no meeting of the minds.

73 Tom

RE: Bandwidth versus Keying Speed

by W9AC on May 27, 2007 Mail this to a friend!

Mickey:

I believe you are incorrectly mixing occupied bandwidth with time.

Certainly, the amount of total time of occupied bandwidth is greater under higher WPM conditions. Why? Consider a ten-second period of keying at slow and fast WPM rates. At very slow speed, the number of rise/decay sequences may only be a fraction of rise/fall sequences at a higher WPM rate.

If I key a transmitter once during a ten-second period, there is one bandwidth-consuming rise interval and exactly one bandwidth-consuming decay interval. By contrast, perhaps 30 or more rise/decay changes occur during that same ten second period under higher WPM conditions -- but the amount of occupied bandwidth remains exactly the same in each case.

True, there may be a perception of higher occupied bandwidth with the higher WPM rate -- only because banwidth-consuming transitions are occuring more often over any given time period. However, as others have shown, the bandwidth of a pure CW signal is developed during the transition between zero and full delivered power -- and again at the transition back to zero.

The repetitions associated with keying speed have no consequence on bandwidth except perhaps as some keying extreme when keying becomes so fast that the keying rate is actually faster than the rise/decay time of the waveform; a pretty unlikely scenario.

Paul, W9AC

Bandwidth versus Keying Speed

by W1YW on May 27, 2007 Mail this to a friend!

"... welcome anyone with a signal analysis/communications background to check my mathematics. The signal analysis that I discussed in my article (99.1% power bandwidth!) is representative of what a good junior or senior electrical engineering student is able to do after completing a typical signal analysis/communications course. I should know this because I'm an electrical engineering professor and I've taught such courses for over 20 years now"

-------------------------

Looks good. Thanks for contributing.

73,
Chip W1YW
(now retired from BU)

RE: Bandwidth versus Keying Speed

by W9AC on May 27, 2007 Mail this to a friend!

I should clarify my previous statement in that the application of time to bandwidth is necessary but it's the way time and bandwidth are being applied in the article that yield incorrect results.

Paul, W9AC

Bandwidth versus Keying Speed

by N0AH on May 27, 2007 Mail this to a friend!

I agree with the accomplished MFJ amateur radio operator..........just look at 160M. Acclaimed DXers will jump all over your attempt to DX on the topband next to their frequencies served (at table 10. 1.823MHz)You better make sure to make something perfect which cannot be made perfect. And adjusting your speed to keep within a given bandwidth is stupid. Now turning off your amplifier, (Negative QRO for you newbies), that will keep you within bandwidth more than speed. Wy no one has brought this part of the equation up is par for this course- . I still really like the article. I have it printed off and in the binder.

Bandwidth versus Keying Speed

by K5MC on May 27, 2007 Mail this to a friend!

The positive feedback from both W6TH and W1YW is gratefully acknowledged.

I just realized that I was rather sloppy in my last posting, however, with my algebra in demonstrating that the bandwidth definition in Part 97.3 of the FCC rules is equivalent to the 99.75% power bandwidth. Here's a better "proof" of that statement:

10 log (Po/Pi) = -26 dB

where Po is the mean (average) power in the "outside" frequency band of the signal and Pi is the mean power in the "inside" (within the) frequency band of the signal.

Solving the equation above by dividing both sides by 10 and then taking the antilog of both sides we have

Po/Pi = 10^(-2.6) = 0.002512

Po = 0.002512 Pi

Pt = Po + Pi = 1.002512 Pi

where Pt is the total average power of the signal

Therefore, Pi = Pt/1.002512 = 0.997494 Pt. Thus, the average power of the transmitted signal within the band is very nearly 99.75% of the signal's total average power.

73, K5MC

RE: Bandwidth versus Keying Speed

by AB0WR on May 27, 2007 Mail this to a friend!

For square pulses repeated at a specfic interval we can define two values.

"a" is the pulse width. T is the time measured from halfway between pulse 1 and pulse 2 to halfway between pulse 2 and pulse 3.

In essence, a/T is a measure of the duty cycle of the pulse train. If "a" is held constant and T goes up then the duty cycle gets less.

The Fourier serices coefficient "c" for such a series of pulses is defined as

(V)(a/T)[ sin(nwa/2) / (nwa/2) ]

where V is the amplitude of the pulse and w = 2pi/T

As T approaches infinity you sooner or later wind up with the inverse Fourier transform equation.

It would seem that this would mean that only your coefficient values would change, their relationship wouldn't. Thus your power bandwidth calculations would require the same number of terms giving you the same bandwidth. The power contained might not be the same.

tim ab0wr

RE: Bandwidth versus Keying Speed

by SM0AOM on May 27, 2007 Mail this to a friend!

"But there are no transmitters I've ever seen that readjust the rise and fall times to fit the very minimum bandwidth theory dictates"

In fact there are such transmitters.

One that I have used myself is the Telefunken
S Steu 676 + Tg 676 exciter. It contains several rise/fall time options (realized as multi-pole low-pass filtering of the keying waveform), one of which is chosen for a given A1A keying rate. It does however not adjust its rise and fall time for the length of every signal element.

The description [1961]of this function in the transmitter quotes the CCIR Recommendation 230 from 1959, so the whole concept appears to have been well known already then by the professional and regulatory world.

Finally, I believe that the FCC 2.202 bandwidth calculations come straight out of the ITU Radio Regulations.

73/

Karl-Arne
SM0AOM

Bandwidth versus Keying Speed

by W1YW on May 28, 2007 Mail this to a friend!

And adjusting your speed to keep within a given bandwidth is stupid.

----------------------

..amd yet the PHYSICS tells you the reality.

Actually, a related case comes up in SETI. It is presumed that narrow signal(s)will be transmitted at a very low bit rate, in part to keep the highest SNR: increasing bandwidth decreases the SNR for a given power.

The SNR will, in fact, decrease as your keying speed increases. Don't like that fact? Tough. And don't do moonbounce.

I am so grateful that W9AC put up a fun and informative piece, written for everyone to understand and enjoy--and refuses to be driven away just because he is smart, and worked hard to get that way.

73,
Chip W1YW

Bandwidth versus Keying Speed

by W1YW on May 28, 2007 Mail this to a friend!

Apologies to K5MC--

Obviously the august article author; whereas W9AC is a cordial and worthwhile commenter.

Let's see if I get my call straight:-)

73,
Chip W1YW

RE: Bandwidth versus Keying Speed

by W9OY on May 28, 2007 Mail this to a friend!

Paul writes:

"True, there may be a perception of higher occupied bandwidth with the higher WPM rate -- only because bandwidth-consuming transitions are occurring more often over any given time period. However, as others have shown, the bandwidth of a pure CW signal is developed during the transition between zero and full delivered power -- and again at the transition back to zero."

I find this statement a bit confusing. How is this perception realized? If a string of transitions are in fact causing this "perception" are you analyzing the wrong thing?

73 W9OY

RE: Bandwidth versus Keying Speed

by VA3NR on May 28, 2007 Mail this to a friend!

It is the issue of time-averaging the power spectrum that’s leading to the different viewpoints. The length of time over which the power is averaged is subjective. The presentation uses a relatively large window, such that the (small) bandwidth during the constant amplitude portion pulls the average down vs. the (large) bandwidth during the transitions.

Time-averaging over long period is not useful method of looking at key clicks. Consider a transmitter sending wide clicks at 100wpm for 10 seconds but then going key-down and sending a steady carrier for 50 seconds. The calculated 1-minute time-average bandwidth would give appearance of relatively small bandwidth because most of the time the bandwidth was very narrow.

The math to prove it has long since left me, but I suspect the time average bandwidth would be directly related to the number of transitions in the time window. So for a given (long) window, and periodic keying waveform, higher speed gives larger average.

For looking at clicks, it would be more useful to use relatively small window for time averaging the spectrum. I saw FCC reg.s just mentions “mean power” and doesn’t specify time interval. There is some guidance in mean power definition in US Federal Standard 1037C:

“mean power (of a radio transmitter): The average power supplied to the antenna transmission line by a transmitter during an interval of time sufficiently long compared with the lowest frequency encountered in the modulation taken under normal operating conditions. [NTIA] [RR] (188) Note: Normally, a time of 0.1 second, during which the mean power is greatest, will be selected.”

I suspect if in the analysis, a window of only 0.1 second were used to average power, and the worst case throughout the pulse trains were selected, it would more effectively capture the clicks produced during the transitions. I suspect wpm speed would have little effect over range where there were equal number of transitions in the window.

73, Chris VA3NR

___
For those interested, definition of bandwidth for Cdn. Amateur is worded differently and doesn’t use mention average or mean power. From Industry Canada RIC-2: “The bandwidth of a signal shall be determined by measuring the frequency band occupied by that signal at a level that is 26 dB below the maximum amplitude of that signal.”

RE: Bandwidth versus Keying Speed

by W9AC on May 28, 2007 Mail this to a friend!

"I find this statement a bit confusing. How is this perception realized? If a string of transitions are in fact causing this "perception" are you analyzing the wrong thing?"

Lee,

It's not that complicated. There is no "perception" being analyzed. More rise/decay transitions per unit of time will be more apparent to the listener.

Example: If someone sends a string of dits for ten seconds at 60 WPM from a transmitter generating moderate key clicks, and I listed to a weak DX station up a few hundred Hz, the interference caused by key clicks is more noticeable than locking down the key of the same transmitter for ten seconds where there is one CW rise period and one decay period. More rise/decay transitions per unit of time are more noticeable to a listener. This is the "perception" I spoke of earlier.

However, in this example, the occupied bandwidth remains the same whether the keys clicks are generated at 60WPM or 0.5 WPM.

Paul, W9AC

Bandwidth versus Keying Speed

by K5MC on May 28, 2007 Mail this to a friend!

I believe AB0WR has been reviewing some of his old EE textbooks! Tim's mathematical posting is the classic analysis of a train of rectangular pulses of amplitude V and duration "a" seconds, recurring periodically every T seconds. (I used the term "square-wave" rather than "rectangular" in my article.) Because I have my latest edition of Hayt and Kemmerly (one of the most classic EE circuits books around) handy, I will simply "borrow" some observations directly from it. The bandwidth of a filter that's designed to pass these periodic pulses is a function of the pulse width but not of the pulse period. The "required" bandwidth is approximately 1/a Hz. (This turns out to be essentially the "first null" bandwidth.) Because I assumed that my keying waveform was a "string of dits" having a constant duty cycle of 50%, both a and T change proportionally with speed such that a/T = 0.5. Therefore, I found that the power bandwidth varies directly with the speed in the case of square-wave (rectangular) keying, which is exactly consistent with the theory.

SM0AOM's comment about some CW transmitters from 45 years ago having variable rise/fall characteristics is very interesting. I am not surprised to learn that that is exactly the case. There are obviously some additional issues involved regarding the rise/fall characteristics of a CW signal versus speed when a human operator is involved (for example, "harder" keying to combat QSB/QRN), but if we ignore those issues, it would be desirable to increase the rise/fall times as we decrease our sending speed. Maintaining constant rise/fall characteristics regardless of speed is certainly not the norm in modern digital communication systems. (By the way, I've looked at the keying envelope generated by my Orion II. It looks approximately sinusoidal to me. Although the software setting says 8 ms, the rise/fall times look about 5 ms according to the scope.)

As W1YW as pointed out, we can improve our S/N ratio by slowing down. QRSS is an extreme example of this fact. Indeed, the fundamental relationships between bandwidth, S/N ratio, and channel capacity as expressed by Shannon's equation are quite fascinating!

73, K5MC

Bandwidth versus Keying Speed

by K5MC on May 28, 2007 Mail this to a friend!

VA3NR makes some very interesting comments. Fourier analysis can be misleading when used to study signal transients. As I pointed out earlier, the frequency information of a signal calculated by the classical Fourier transform is an average over the entire time duration of the signal. If there is a local transient over some small interval of time in the lifetime of the signal (such as the rise/fall times of a single keying pulse having a relatively long total time duration), the transient will contribute to the Fourier transform but its location on the time axis will be lost.

The "short-time" Fourier transform is one attempt to overcome this limitation, but a more recent mathematical approach to studying signal transients is "wavelet" analysis. Rather than using everlasting sinusoids, the wavelet functions are "local" both in time and frequency. There are many different families of wavelet functions, however, and choosing the most appropriate one to use for a specific signal isn't usually a trivial matter. Perhaps some day a manufacturer will develop a "wavelet" analyzer to study signal transients, but as far as I know, no such instrument is readily available and wavelet analysis remains more of a research tool. (Studying the transients generated by a variety of CW keying waveforms using wavelets would probably make an interesting research topic for my next graduate student!)

At times Fourier analysis strikes me as a very artificial way to study real signals. For example, an orchestra has a finite number of instruments, each of which that often starts and stops and starts again, with varying amplitudes and frequencies, while playing a particular piece of music over some particular time interval a < t < b. A Fourier transform can be determined for that particular piece of music. In effect, the Fourier "orchestra" consists of an infinite number of instruments (sinusoids), each one playing a very monotonous tone of constant amplitude and frequency, starting from time equal to negative infinity and continuing forever. The frequency of each instrument is infinitesimally smaller or larger than that of its adjacent instruments (continuous line spectrum). The amplitudes and phases of these sinusoids are such that they add up to the particular piece of music from a < t < b and add up to zero at all other times! Lathi [1] refers to this as the "marvelous balancing act" of Fourier transforms. It amazes me that Fourier analysis proves to be such a useful tool in the study of real signals and systems.

[1] B.P. Lathi, Modern Digital and Analog Communication Systems, 3rd ed., Oxford University Press, 1998.

73, K5MC

RE: Bandwidth versus Keying Speed

by W9OY on May 28, 2007 Mail this to a friend!

Paul

My point was that analyzing a transmitted signal is not quite the same as analyzing a received signal.

Guess I was a bit too subtle

73

RE: Bandwidth versus Keying Speed

by AB0WR on May 28, 2007 Mail this to a friend!

k5mc:"The "short-time" Fourier transform is one attempt to overcome this limitation, but a more recent mathematical approach to studying signal transients is "wavelet" analysis"

Are there any reasonably priced books you would recommend on this? This must be an analysis tool developed after I left school.

tim ab0wr

Bandwidth versus Keying Speed

by K4GLM on May 28, 2007 Mail this to a friend!

Nice work, Mickey
I think of the phenomenon as adding and subtracting the digital signal to the carrier. This produces sums and differences, that are greater when the digital signal is greater; hence more bandwidth.
I believe Claude Elwood Shannon mathematically defined this with Shannon's theorem. (Not me, maybe a cousin or something...)
Shannon Boal K4GLM

Ain't seen nothing yet!

by N4QA on May 29, 2007 Mail this to a friend!

And, if the no-coders of this world are frightened of communication via on-off keying of sinewaves, just wait 'til someone attempts to clue them in to the intricacies of the generation, modulation, transmission etc of the human voice!

CW forever!

72.
Bill, N4QA

Bandwidth versus Keying Speed

by K5MC on May 29, 2007 Mail this to a friend!

In response to AB0WR's question, two books I have at home that discuss short-time Fourier transforms are:

System Analysis and Signal Processing by Philip Denbigh (Addison-Wesley, 1998, ISBN 0-201-17860-5)
Signals and Systems by Simon Haykin and Barry Van Veen (Wiley, 2005, ISBN 0-471-70789-9)

I will look in my office at school later this week for some other books. Many of the books that discuss fast Fourier transforms (FFTs) may also include a discussion of short-time Fourier transforms.

As Denbigh points out in his book, to analyze a signal whose frequency content changes with time, the waveform is divided up into segments. Each of these segments is analyzed separately by means of the FFT to give a "short-time" Fourier transform (STFT) and then the resulting spectra are displayed side by side to generate a "spectrogram." Speech is probably the most common signal used to illustrate the concepts of STFTs and spectrograms. (BTW, Denbigh's book emphasizes the use of MATLAB, one of the most popular software packages used in electrical engineering these days, at least in academic circles.)

73, K5MC

RE: Bandwidth versus Keying Speed

by NI0C on May 29, 2007 Mail this to a friend!

K5MC wrote: "As W1YW as pointed out, we can improve our S/N ratio by slowing down. QRSS is an extreme example of this fact. Indeed, the fundamental relationships between bandwidth, S/N ratio, and channel capacity as expressed by Shannon's equation are quite fascinating!"

First of all, thanks for this article and discussion.

One comment I have with regard to Chip's observations on QRS is that, in order to realize the benefits of the improved s/n ratio, the person at the receiving end needs to respond by narrowing his/her receiver bandwidth.

73,
Chuck NI0C

RE: Bandwidth versus Keying Speed

by W9PMZ on May 29, 2007 Mail this to a friend!

K5MC - is it possible that W8JIs conclusions are based in the rise and fall times being much greater than the keying speed, and you have the opportunity to shape the envelope (rise and fall times); and you are discussing a generalized case?

What I believe that W8JI is doing is creating a matched filter on the transmit end (e.g. controlling the rise and fall times) to fit the performance of the receiver.

After all it doesn't make much sense to have a signal rising when it needs to be falling....

73,

Carl - W9PMZ

Bandwidth versus Keying Speed

by K5MC on May 29, 2007 Mail this to a friend!

As NI0C points out, the reason the SNR (signal-to-noise ratio) improves is because the receiver's bandwidth is reduced by the operator when copying very slow CW, thus reducing the average noise power. The average power of the transmitted CW signal is independent of the speed, but the "power" or "occupied" bandwidth varies with the sending speed when proportional spacing between the code characters is used. (I got somewhat "carried away" when I brought up Shannon's equation!)

Regarding W9PMZ's comments, I'm hesitant to speculate on exactly how W8JI reaches some of his conclusions. However, here's a quote from one of W8JI's posts earlier in this thread:

1. Bandwidth is required only when the carrier changes level. When at full power or zero power it has no bandwidth, it has no modulation. (W8JI)

W8JI makes this statement immediately after I had just discussed this very issue with my example of the 1-second and 2-second duration 1-kHz sine waves. As I pointed out, the 99% energy bandwidth of the 1-second duration 1-kHz sine wave is 20.6 Hz, whereas the 99% energy bandwidth of the 2-second duration 1-kHz sine wave is 10.3 Hz.

W8JI's error here is essentially that of the "pioneers" in the early days of radio broadcasting. (Lathi [1] discusses this interesting bit of history in his textbook.) Let's assume that the maximum and minimum carrier frequencies of an FM station are fc + m and fc - m, where fc and m denote the unmodulated carrier frequency and the amount of deviation, respectively. The pioneers assumed that a sinusoid of frequency f Hz has its entire spectrum concentrated at f Hz and, therefore, they reasoned that the spectrum of the FM signal would lie entirely within a bandwidth of twice that of the deviation (a value of 2m using my example), but this is incorrect because the bandwidth of a time-limited sine wave is not zero! For a sinusoid of finite duration T seconds, the spectrum (bandwidth) of the sinusoid is spread out on either side of its center frequency by 1/T Hz. The pioneers had overlooked this spreading effect as W8JI apparently continues to do.

[1] B.P. Lathi, Modern Digital and Analog Communication Systems (ISBN 0-19-511009-9)

73, K5MC

Bandwidth versus Keying Speed

by W8XR on May 29, 2007 Mail this to a friend!

Mickey,

I would like to see the mathematical details underlying the bandwidth calculations, either on the
forum or off (mark.amos@toast.net)

It would be instructive to compare actual sine wave keying bandwidth in the table in addition to the 5ms rise/fall calculations that you label "Sinusoidal keying".

For instance modulating a carrier at 25 Hz (50 elements per second) you get a 60 WPM modulation.

Since a carrier modulated by a sine wave results in a copy of the modulating waveform above and below the carrier - the sidebands - I would expect a 60 WPM (25Hz) sinewave modulation to require 50 Hz of bandwidth (25 for the lower sideband plus 25 for the upper bandwidth.) I assume that your math would corroborate this "degenerate case." It would be a good way to check the numbers, in any case.

A sinewave with a period of 10 ms (5 ms "rise" and 5 ms "fall") would demand 200 Hz of bandwidth (1/.01, or 100 Hz each for the upper and lower sidebands).

I should think that _any_ modulating wave that had sinusoidal rise and falls of 5ms would require a similar bandwidth, regardless of the pulse width. At least this should be the case for normal CW keying speeds (to the point where there wasn't time for a complete modulation cycle because of rise and fall time constraints - somewhere around 200 baud - 240 WPM.) To Tom's point: while the envelope is not changing, it can't be contributing any bandwidth.

I believe it's the case that the limiting factor determining bandwidth is the envelope shape rather than the period of the modulating waveform - at least at amateur speeds.

In any case, I'm hopeful that the underlying math will help clear this up.

Mark

RE: Bandwidth versus Keying Speed

by W6TH on May 29, 2007 Mail this to a friend!

.

Actually I would like to see the pulses pictured while in action, with the changing speed of from 10 wpm to 100 wpm.

As we all know:

Heaviside Step Function.......Of course, any monotonic function with constant unequal horizontal asymptotes is a Heaviside step function under appropriate scaling and possible reflection. The Fourier transform of the Heaviside step function is to be used.

The rise and fall times of the output pulses depend on the operating voltage and the time constant of R and C, but will be typically in
the order on tens of nanoseconds or to your own satisfaction. Fourier points it all out along with others, but am afraid the math is over most heads.

.:

Bandwidth versus Keying Speed

by K5MC on May 29, 2007 Mail this to a friend!

W8XR: I would like to see the mathematical details underlying the bandwidth calculations, either on the forum or off (mark.amos@toast.net)

Mark, I will be glad to forward you several pages of my math details.

Regarding your keying waveform, I think you are describing a half-wave rectified sine wave. In that case, to maintain proportional spacing as I assumed earlier with my "string of dits" (50% duty cycle) keying waveform with the same rise/fall times (5 ms), the speed will be 120 wpm (50 dits per second is 120 wpm). To send at 60 wpm using a half-wave rectified sine wave, the rise/fall times will each be 10 ms. Are these the keying waveforms that you are talking about?

W8XR: To Tom's point: while the envelope is not changing, it can't be contributing any bandwidth.

Mark, to clarify my understanding, I would like to know if you think there is any difference in the "bandwidth" of the following two signals:

s1 = sin (2000 pi)t for 0 < t < 1 second and s1 = 0 for all other values of t

s2 = sin (2000 pi)t for 0 < t < 2 seconds and s2 = 0 for all other values of t

73, K5MC

Bandwidth versus Keying Speed

by K5MC on May 29, 2007 Mail this to a friend!

K5MC: The average power of the transmitted CW signal is independent of the speed, but the "power" or "occupied" bandwidth varies with the sending speed when proportional spacing between the code characters is used.

My comment above concerning the average power is strictly true only if square-wave keying is assumed. For the sinusoidal keying waveform I used in my article, for example, the total average power of the 2.4-wpm signal is about 13% larger than that of the 30-wpm signal.

73, K5MC

RE: Bandwidth versus Keying Speed

by W8JI on May 30, 2007 Mail this to a friend!

The overall bandwidth of the transmitter using on and off keying relates entirely to the shape and duration of the rising and falling edges. Be definition it HAS to dominate the bandwidth since the keying speed requires a small fraction of the bandwidth required by the transitions.

The only thing sending faster does is make the pulses occur more frequently. This can make the overall time-averaged LEVEL of the sidebands change, but not the overall bandwidth or slope of bandwidth.

Any formula or theorem will give an incorrect answer when people apply the formula or theorem incorrecty or incompletely by failing to understand the actual problem. The acid test is if all the numbers fit what we observe.

People tend to forget the math or a theorem is simply a tool to help us explain what we observe, and it can't really alter what we onserve. Instead of sitting here arguing endlessly and using an incomplete or misapplied analysis to prove a point that simply isn't true, it would be a better idea to spend ten minutes with a receiver or spectrum analyzer and a transmitter. If you do, you will find what I and others say is EXACTLY true.

I know some of the brightest and most experienced people in communications engineering, real engineers who take the time to understand how things actually work and who work with things like this often. Not a single person disagrees with the statement that bandwidth of a CW transmitter is entirely dependent on the rise and fall time and shape of that transition, and the only thing speed does is vary how often the sidebands occur or create peaks and nulls distributed inside that bandwidth with the same overall shape to the slope of the sidebands regardless of speed.

Either spend a few minutes with a spectrum analyzer or a real receiver and a transmitter, or live in the dark.

73 Tom

RE: Bandwidth versus Keying Speed

by W8JII on May 30, 2007 Mail this to a friend!

Interesting little war we have going on here. Reminds me of the old bumblebee argument. Engineer says it's impossible for a bumblebee to fly. Wings can't provide enough lift for that big body. Can't convince the engineer otherwise. He proved it mathematically so he must be right. Right formulas----wrong application. The bumblebee flies!!!!!!!!!!!!!!

Seems to me Mr Rauch has a point get a spectrum analyzer an open your eyes and look--------------------It flies!!
73, ron

RE: Bandwidth versus Keying Speed

by W6TH on May 30, 2007 Mail this to a friend!

.
It is only a squarewave generator or are all confused with the Schmitt trigger or is it the relaxation oscillator.

Then again it may be a trapazoid oscillato/generator what all are commenting about.

Possibly under load the squarewave turns into a trapazoid, uhh, just kidding.

.:

Bandwidth versus Keying Speed

by K5MC on May 30, 2007 Mail this to a friend!

I continue to welcome any of W8JI's "experts" (including himself) to carefully examine the definition of power bandwidth (and occupied bandwidth) and to do the calculations themselves.

Now let me quote from page 9.7 in the 2006 edition of the ARRL Handbook:

"The bandwidth occupied by a CW signal depends on the keying rate (See the Mixers, Modulators and Demodulators chapter of this Handbook), with higher speeds requiring a wider filter to pass the sidebands. In addition, occupied bandwidth depends on the rise and fall time and the shape of the keyed RF envelope. That shape should be somewhat rounded (no abrupt transitions) in order to prevent "key clicks" - harmonics of the keying pulse. These can extend over several kHz and cause unnecessary interference. The ideal RF envelope of a code element would rise and fall in the shape of a sine wave."

The results I reported in my article are exactly consistent with what the Handbook says!

I hesitated to submit my article because I didn't want to get in a "shouting" match with W8JI and, yet, it appears that that's where we are at now. I had little hope of changing W8JI's opinion with my article, but I wanted other hams to know that the current editions of the ARRL Handbook are in agreement with the theory of Fourier analysis. I am also willing to wager a modest sum that the electrical engineers employed by the FCC will agree with my article over W8JI and his experts. As I've said many times now, the power bandwidth (and the occupied bandwidth as defined by the FCC) does vary with speed.

73, K5MC

RE: Bandwidth versus Keying Speed

by KE3HO on May 30, 2007 Mail this to a friend!

I am FAR from an expert on Fourier analysis. I took ONE undergraduate course on digital signal processing where we learned about Fourier analysis, Fourier transforms, etc. The last time I used any of that was the day I took the final exam in that class, and that was 24 years ago. So if any of my comments that follow are incorrect, please feel free to tell me where I have made an error. I will state up front that I may be wrong on any one or more points, and would welcome a chance to learn.

Fourier analysis is, fundamentally, for analyzing periodic waveforms, and that it is only mathematically exact for analyzing periodic waveforms that exist from t = -infinity to t = +infinity and only then if you include all of its frequency components out to f = infinity. That is not to say that it is useless for real world analysis. It is certainly useful for analyzing real world signals. Applying it to finite duration periodic waveforms certainly yields very good results. Not exact, but very good. Good enough to be useful in the real world.

Is it not true that the extension of Fourier analysis to NON-PERIODIC finite duration waveforms involves further assumptions that might make it unsuitable for analysis of certain types of signals as well as additional approximations that make the results less accurate than applying Fourier analysis to finite duration periodic waveforms? In addition, the mathematical calculations involved in this process offer varying degrees of accuracy depending on your choice of input parameters (such as window size, window offset, number of samples, etc). Is it not true that it is an approximation that is only as good as the inputs to the algorithm, and even then it can only be “so good”. I honestly don’t know the answers to these questions, as I have never studied this method, and I am simply asking if this is true.

I think that if you wanted to synthesize the waveform of a CW signal with the keying waveform that you show in Figure 1, then the Fourier analysis would give you the necessary frequency components and amplitudes to make a VERY GOOD APPROXIMATION to the original signal. I don’t believe that the analysis will give you the spectral content of the original signal, only the spectral content of the synthesized approximation to the original signal.

K5MC said:
<< Mark, to clarify my understanding, I would like to know if you think there is any difference in the "bandwidth" of the following two signals:

s1 = sin (2000 pi)t for 0 < t < 1 second and s1 = 0 for all other values of t

s2 = sin (2000 pi)t for 0 < t < 2 seconds and s2 = 0 for all other values of t >>

I’m not Mark, but I will comment on this. K5MC will say, based on Fourier analysis, that these two signals have different bandwidths. I am not going to argue the mathematical analysis with you, as I would not know where to start the argument (and would certainly loose the argument anyway). Mathematical analysis aside, I would like to understand where the change in bandwidth comes from. I’m not talking about a mathematical explanation based on Fourier analysis because, frankly, that is the part that I don’t believe in the first place. Where does the extra bandwidth come from? When I go key down, the transmitter won’t “know” when I am going to go key up until I let go of the key. So how and where is this extra bandwidth generated? In the trailing edge of the waveform? That is the only place where the transmitter "knows" how long I am going to key down, so that must be the only place where it can suddenly generate the extra bandwidth. What is the mechanism for generating this extra bandwidth on the trailing edge?

73 - Jim

RE: Bandwidth versus Keying Speed

by W6TH on May 30, 2007 Mail this to a friend!

.

... Even though the square wave generator swings the voltage output from plus to minus , the frequency does not depend upon this supply voltage. If you supplied it with a variable voltage, you could freely change the amplitude without changing the frequency. You could then make it a variable frequency source by making either C or R variable...

Good for ham use with those old xtal rigs. Less harmonics if run at 50%.

.:

RE: Bandwidth versus Keying Speed

by W8XR on May 30, 2007 Mail this to a friend!

Mickie,

Thanks, I'll look forward to seeing them.

Just to clarify, the keying waveform I described is not a half wave rectified sine, but a raised sine - an actual sine wave raised by a .5 amplitude DC component. "On" is (arbitrarily) defined as anything above half the amplitude of the sine wave and "off", anything below half the amplitude.

Of course this extreme case would be "difficult" to copy, but it really is the the softest possible envelope - basically a set of Gaussian curves strung together one after the other.

Here are the details on the two examples in tabular form (much easier to see than in the narrative I used above.)

In the first example I used a 25 Hz raised sine modulating waveform:
= 25 dits and 25 dit spaces
= 50 "elements" total per second
= 1 word per second
= 60 WPM
= two 25 Hz wide sidebands
= 50 Hz total bandwidth
= 20 ms rise time and 20 ms fall time
= 40 ms wavelength

In the second example, a 100Hz raised sine as a modulation envelope:
= 100 dits and 100 dit spaces
= 200 "elements" total per second
= 4 words per second
= 240 WPM
= two 100 Hz wide sidebands
= 200 Hz total bandwidth
= 5 ms rise time and 5 ms fall time
= 10 ms wavelength

If we modulate a carrier with this 100 Hz raised sine, we'll get the carrier plus an upper side band of 100 Hz and a lower sideband of 100 Hz width, yielding 200 Hz of bandwidth.

Or, put another way: convolving a sine wave carrier with a sine wave modulation source results in the carrier +/- the modulating waveform.

Now, in my limited experience I've seen that there may be FFT resolution problems, bin bleed through, etc., (or in real radios and amplifiers there could be some non-linearity in mixing) that would fatten up the peaks and yield a wider bandwidth.

However, I contend that 200 Hz is a reasonable description of the bandwidth required for this signal - since what we're looking at is a product of mixing two sine waves.

That's what the examples were about.

I further contend that if you used a 5 ms Gaussian rise and fall time with any well behaved modulating envelope you would get the same resulting bandwidth. A DC component of a modulating signal can't modulate the carrier at all - ie. it can't have an effect on the bandwidth. (This is likely where we disagree because of the power bandwidth question, below, and the pulse width issue.)

Yes, I agree that the instantaneous power when integrated over different lengths of time would yield a power bandwidth product that is larger over longer periods of time. And, of course, what you use as the bandwidth measure affects the results (of course the -60dB bandwidth of the signal will be much wider than the -3dB bandwidth.)

Certainly a practical consequence of this could be that higher speed CW is is likely to be more annoying than lower speed CW when you're listening nearby.

However, I contend that the difference between hard and soft keying has a much greater effect on this than does the keying speed.

RE: Bandwidth versus Keying Speed

by W8XR on May 30, 2007 Mail this to a friend!

Jim,

Good questions! I wished I'd asked them as well!

Mark

RE: Bandwidth versus Keying Speed

by WA0LYK on May 30, 2007 Mail this to a friend!

It may be time to review the definitions in Part 2 for necessary bandwidth and occupied bandwidth.

The mathematical work being done is trying to define the minimum bandwidths required for a cw signal. A good example of this is using a sine wave rather than a square wave to analyze the needed bandwidth. By definition, this is attempting to determine the necessary bandwidth.

The folks recommending using a spectrum analyzer are by definition determining the occupied bandwidth. Trying to arrive at a mathematically correct determination for the occupied bandwidth is difficult because of all the stages and components involved.

While the statement that the "rise time" determines the bandwidth, not the keying speed, may be correct for the observed occupied bandwidth, it doesn't explain what minimum bandwidth should be.

Why is this? The difference between necessary bandwidth and occupied bandwidth in this scenario is primarily determined by the overall system performance of non-ideal circuits and is quite naturally measured by the response to a step function. It only takes one amplifier that doesn't have sufficient bandwidth, i.e. slew rate, to cause the bandwidth to increase beyond the minimum when hit with a step function.

W8JI's comments seem to infer that the rise time determines the "necessary bandwidth" and that you can see this by watching signals with a spectrum analyzer. This just isn't correct. What you are seeing with a spectrum analyzer is implementation dependent and doesn't provide information about an "ideal" signal. It is only showing the system response of a non-ideal system. The math behind what he is saying is basically defining the system response of a real world device. However, this isn't the definition of necessary bandwidth.

So why worry about it? Necessary bandwidth calculations allow a comparison between different signal types based upon a common denominator, i.e. the ideal minimum bandwidth. Occupied bandwidth's on the other hand are implementation dependent, and are useless in comparing the characteristics of given signal types.

A good example is the psk31 signal. The accepted necessary bandwidth for this is 31 Hz. Yet one only has to watch a waterfall for a short time to see that the occupied bandwidths vary all over the place because they are implementation dependent.

Jim
WA0LYK

RE: Bandwidth versus Keying Speed

by W6TH on May 30, 2007 Mail this to a friend!

.
Now let me quote from page 9.7 in the 2006 edition of the ARRL Handbook:

Thanks Mickey, you are back in the game. The same is written in my 1966, The Radio Amateur's handbook. Also the wave shapes and form are shown. I will check my older books like in 1940, it may be there also.
.:

RE: Bandwidth versus Keying Speed

by W6TH on May 30, 2007 Mail this to a friend!

.
According to the ARRL handbooks and to abide by the FCC rules and regulation, there seems to have been problems with keying of radio transmitters. The common cause of interference was key clicks and how to eliminate this interference.

The way was to soften the wave form and to do so was by adding a 100 ohm resistor and a capacitor of 0.1 to 0.5 Mfd, or another device called a vacuum tube keyer. The cause of key clicks was from many causes such as poor voltage regulation, sparking at the key, parasitic radiation and oscillation, etc.

By adding a capacitor and resistor to soften the keying from a square wave slowed the rise and decay time of the so called square wave. This in turn widened the bandwidth. The correction was made to perform, to match the speed of the sending operator and each transmitter had to adjust to the requirements of each individual transmitter.

In my 1940 and earlier Amateur Radio Handbook has no mention of squarewaves, that came later in years, which of course now gives us all a better understanding of key clicks, operation of speed and the proper ratio of dits and dahs.

Lets not confuse ham radio along with the commercial industry as far as band width goes, but from all evidence these squarewaves can certainly make a lot of interference on my ham radios.

.:

RE: Bandwidth versus Keying Speed

by VA3NR on May 30, 2007 Mail this to a friend!

I think the answer to following question might clarify difference between infinite-time spectrum and practical spectrum measurement: Calculated by Fourier analysis, what would be the 99.1% power bandwidth of an FSK signal that continuously steps between 1 MHZ and 2 MHz in manner such that it sends a constant amplitude carrier at 1 MHZ 99.99% of the time, and the same amplitude carrier at 2 MHz remainder of the time? (I wish I could do the math - maybe I'll dig out my old textbooks too. Hopefully Mickey will help us find answer.) From looking at spectrum analyzer or listening with reciever I would say bandwidth of that signal is approximately 1 MHz, but I suspect Fourier says something different.

73, Chris.

RE: Bandwidth versus Keying Speed

by W6TH on May 30, 2007 Mail this to a friend!

.
Chris, try this and is easy to understand.

http://www.dattalo.com/technical/theory/sqwave.html

.:

RE: Bandwidth versus Keying Speed

by W3JJH on May 30, 2007 Mail this to a friend!

Ok, folks, here's my swing at the analysis ...

Consider a 30 word/min train of dits. It will have 1500 elements per minute or 25 per second. Half of the elements are marks and half are spaces, so we have a 12.5 Hz square wave. Harry Nyquist says that in order to reliably recover the signal, I'm gonna need a channel bandwidth at least twice that of the signal. That's 25 Hz.

Now, Morse radiotelegraphy is a double-sideband AM system, so I'll need that 25 Hz bandwidth on either side of the carrier. Thus, the minimum required bandwith for an ideal system would be 50 Hz. Practical systems (including those with a human ear as part of the decoding system) will need around two to four times the theortical minimum. Note that the "Necessary Bandwith" Table in the FCC rule [47 CFR 2.202 (g)] shows that 25 word/min requires 100 Hz of bandwidth for fading circuits. That would imply around 120 Hz for 30 word/min.

Of course, the occupied bandwidth of the transmitted signal will be much wider than the required receiver bandwidth. A 30 word/min dit train with hard rise times modulating a carrier will result in a occupied bandwidth of around 525 Hz (taking the FCC's 99.5 percent of radiated power definition). This is because the modulating waveform is rich in harmonics which will appear in the upper and lower sidebands.

Rolling off those harmonics by slowing down the rise and fall times will reduce the occupied bandwidth. This technique can allow a 30 word/min signal to fit in 200 Hz of bandwidth. The same rise and fall times will permit a 12 word/min signal to pass with essentially all of its switching harmonics intact. They will also allow for useable transmission of a 50 word/min signal.

Bandwidth versus Keying Speed

by K5MC on May 30, 2007 Mail this to a friend!

KE3HO: Is it not true that the extension of Fourier analysis to NON-PERIODIC finite duration waveforms involves further assumptions that might make it unsuitable for analysis of certain types of signals as well as additional approximations that make the results less accurate than applying Fourier analysis to finite duration periodic waveforms?

Jim, I think you are confusing Fourier series and Fourier transforms. Fourier analysis is a rather broad term that includes such tools as Fourier series, Fourier transforms, FFTs, STFTs, etc. Strictly speaking, we have to assume that a signal is periodic (that is, it repeats itself over and over again from time equal to negative infinity to time equal to positive infinity) to use the technique of Fourier series. A Fourier transform can be found for both periodic and non-periodic signals, but it is particularly useful when we are dealing with non-periodic signals such as a finite-duration pulse. The inverse relationship between a pulse's time duration and magnitude spectrum (bandwidth) illustrated by the Fourier transform is among the most fundamental aspects of Fourier analysis.

KE3HO: I’m not Mark, but I will comment on this. K5MC will say, based on Fourier analysis, that these two signals have different bandwidths. I am not going to argue the mathematical analysis with you, as I would not know where to start the argument (and would certainly loose the argument anyway). Mathematical analysis aside, I would like to understand where the change in bandwidth comes from. I’m not talking about a mathematical explanation based on Fourier analysis because, frankly, that is the part that I don’t believe in the first place. Where does the extra bandwidth come from? When I go key down, the transmitter won’t “know” when I am going to go key up until I let go of the key. So how and where is this extra bandwidth generated? In the trailing edge of the waveform? That is the only place where the transmitter "knows" how long I am going to key down, so that must be the only place where it can suddenly generate the extra bandwidth. What is the mechanism for generating this extra bandwidth on the trailing edge?

Jim's comments above are very interesting and I have also thought along these lines before. As I've tried to point out, Fourier analysis is an approximation to the real world; I'm amazed that it works as well as it does in modeling real signals and systems.

To be perfectly honest, I really don't know where the extra bandwidth comes from, but human logic would very likely say that the "bandwidth" is "generated" at the trailing edge for the reason you point out. If I ignore Fourier analysis and simply look at s1 and s2, I would probably believe that both signals have the same "bandwidth" because, in part, I wouldn't have a mathematically precise definition of bandwidth to start with! For that matter, shouldn't the "bandwidth" be zero Hz because s1 and s2 are sine waves that begin and end smoothly?

If we smoothly sweep the carrier frequency plus and minus 75 kHz about the center frequency using, for example, a 1-kHz sine wave as the modulating signal, shouldn't the spectrum of this FM signal lie entirely within a bandwidth of 150 kHz? After all, according to W8JI, the carrier amplitude isn't changing.

At the end of the day, I have to trust some mathematics to quantify such concepts as energy signals, power signals, harmonics, average power, and bandwidth. Unlike most concepts in signal analysis, there are many different definitions of "bandwidth" and that fact is what prompted me to post my article in the first place. I wanted some hams to understand that if one calculates the "power" bandwidth (which has a precise definition), then one definitely finds that the keying speed is a factor in determining that specific bandwidth.

By the way, if W8JI and W9CF mean "absolute" bandwidth when they use the terms "overall" and "actual" bandwidth, then I'm in perfect agreement with them. (The absolute bandwidth is defined to be f2 - f1, where the spectrum is zero outside the interval f1 < f < f2 along the positive frequency axis.) The absolute bandwidth of any finite-duration signal is equal to infinity and the sending speed is not a factor. All man-made signals, strictly speaking, are energy signals and have an infinite bandwidth according to Fourier analysis.

I also noticed that KF6DX (http://www.doug-smith.net/cwbandwidth1.htm) "hedges his bet" by writing that "Spectral occupancy is chiefly determined by the envelope shape and not by the keying speed." "Chiefly determined" doesn't exactly sound like "wholly determined" to me!

73, K5MC

Bandwidth versus Keying Speed

by K5MC on May 30, 2007 Mail this to a friend!

W8XR: Here are the details on the two examples in tabular form (much easier to see than in the narrative I used above.)

OK, Mark, I think I'm clued in now on your keying waveforms. You are actually talking about classic single-tone amplitude modulation (tone frequencies of either 25 Hz or 100 Hz), or DSB-AM. (Your modulation index happens to be 100%.) Therefore, ignoring all the imperfections in the hardware (which is what I did in my article), I agree that the bandwidth will be either 50 Hz or 200 Hz as you said. (These bandwidths would even be the so-called "absolute" bandwidths because, in practice, we are assuming these signals to be sufficiently long in duration so that the spectra of the sinusoids are essentially impulse functions.) As you also pointed out, I believe these signals would be rather difficult for a human operator to copy!

W8XR: Certainly a practical consequence of this could be that higher speed CW is is likely to be more annoying than lower speed CW when you're listening nearby. However, I contend that the difference between hard and soft keying has a much greater effect on this than does the keying speed.

Mark, I hope nobody thought I ever contended otherwise. I believe practically all of us agree that it is important to properly shape the keying waveform to avoid key clicks. I was also very careful to point out that the concept of occupied bandwidth does NOT say that the strength of the key clicks generated by a poorly designed transmitter is reduced when the sending speed is decreased. The focus of my article was simply to demonstrate the fact that the "power" bandwidth (or the "occupied" bandwidth as defined by the FCC) is a function of both the keying speed and the keying waveform. For the umpteenth time I welcome anyone having a good grasp of the theoretical/mathematical concepts involved (power bandwidth, average power, Fourier analysis, etc.) to either do the calculations themselves or to check mine.

73, K5MC

RE: Bandwidth versus Keying Speed

by W8JI on May 30, 2007 Mail this to a friend!

Hi Jim,

I am VERY clear in saying the rise and fall times set the actual sideband (keyclick) bandwidth of the transmitter, and that bandwidth that causes all the problems has NOTHING to do with the CW speed. The CW speed only determines how often the sidebands necessary to modulate the carrier repeats, so speed can contriool power over time, but the receiver by definition cannot have a memory of that time through the signal processing channel.

If the receiver did have energy storage over the time of Morse characters it could not produce the off and on tones. They would neither start or stop. They would blend.

This simply has to be true because the shape and level changes in the rising and falling edges require a certain spectrum, and that spectrum by definition is always much higher than the frequency of the off and on keying.

Some people will beat this to death in order to misuse or misapply a good formula, and never lift a finger to observe what they are attempting to define.

Others of a more curious mindset will send a series of dots with a transmitter and observe the results on a receiver or spectrum analyzer and see that I and many others who have thought this problem through (and the new Handbook where the errors were corrected) are correct.

W8XR is a person who went through this on his own and reached his own conclusions. You can read what people who actually thought this problem through or did experiments at the following links:

http://www.sm5bsz.com/others/occbw.htm

Doug was instrumental in developing the Ten Tec Orion CW transmitting system.

http://fermi.la.asu.edu/w9cf/articles/click/index.html

You can read about Kevin's work at this link:
http://physics2.asu.edu/people/atkes

and the list can go on and on.....

The fact is we cannot have the shape and duration of the rise and fall times without the signal occupying a bandwidth that allows that shape, and that is true no matter how fast or slow we send.

When claims or analysis do not fit actual results the best course is to correct the analysis, since the results already prove the flawed analysis without room for any argument.

Those who are truly curious will actually take the time to observe the real life actions of the transmitter, not what they imagine happens.

73 Tom

RE: Bandwidth versus Keying Speed

by W8XR on May 30, 2007 Mail this to a friend!

Thanks for providing the details of your calculations. I'm in the midst of some practical DSP work and hope to be able to make some sense of the discrepancy between the "intuitive" analysis that I've used and the mathematic analysis that you've performed.

The piece that really bothers me is that leading edge / trailing edge bit. I just can't fathom how bandwidth could possibly depend on the distance between them. Also, except for extreme speeds, the bandwidth required for even reasonable shapes should swamp any bandwidth required because of the keying speed.

However, I believe that the math SHOULD agree with experience. So, I come to one of several conclusions: there's something wrong with the application of the Fourier transform to this problem, or there's some piece of knowledge I'm missing that would invalidate the intuitive approach. If there is some problem with the application of the math, I think it will be very useful to understand why this is the case.

In any case, often, when there is controversy there is knowledge to be got - and I intend to get it.

This particular problem (the problem of the discrepancy between the math and experience) is just too interesting to let it go.

RE: Bandwidth versus Keying Speed

by W8JI on May 30, 2007 Mail this to a friend!

I think the problem here is Mickey is considering a transmitter that readjusts the rise and fall to match the CW speed.

If I'm not mistaken Mickey assumes the transmitter somehow adjusts the rise and fall times to the minimum reqired to allow a CW signal of a certain speed assuming a raised sinewave. This would be a wave that starts at the negative peak as a zero, and increases to the positive peak where it rolls over and flattens off during the on tie. A shape just like a sinewave except it starts at zero and goes up through maximum where it then turns downward to zero.

The problem is, and where we disagree is, I consider the CW genrated by a NORMAL transmitter of excellent design to have a fixed rise and fall duration. This the way every single CW transmitter that has every been built works. I'm looking at a real system.

I consider a POOR design to be a transmitter that has a shape like the ARRL Handbooks used to describe, like a CW signal generated through a R C filter, or one with otherwise good shaping that has needlessly fast rise and/or fall times.

This is probably the only difference between what Mickey is saying and what I (and others) say.

This is why in the very beginning I said Mickey is looking at the minimum bandwidth required and not the actual bandwidth used by transmitters.

Unless the transmitter somehow readjusts the envelope rise and fall to match the speed and the CW is sent with the softest possible rise and fall of perfect shape at every speed you can toss the formulas out the window.

It's important to note these differences between the REAL world and what humans accept as a good sounding signal than can make it through noise or fading conditions and a theoretical system that does not apply to communication systems and that everyone would find unusable.

73 Tom

RE: Bandwidth versus Keying Speed

by W3JJH on May 30, 2007 Mail this to a friend!

W8JI:

Tom, with a DSP-based radio it is not impossible to control the rise and fall time of the keying based on the the keyer dit speed. It's not even particularly hard with some analog radios. The necessary low-pass filtering can be made to track the keyer dit speed quite easily in a low-level system. I've designed such circuits for use in pulse-rate-modulation telemetry systems. Of course, linear amplification is required following the modulation, so high-efficiency power amps can't be used, but the finals in all my store-bought HF radios are class-AB these days.

73 de W3JJH
John

Bandwidth versus Keying Speed

by K5MC on May 30, 2007 Mail this to a friend!

W8JI: I think the problem here is Mickey is considering a transmitter that readjusts the rise and fall to match the CW speed.

No, I am not considering such a transmitter in my article!

W8JI: If I'm not mistaken Mickey assumes the transmitter somehow adjusts the rise and fall times to the minimum reqired to allow a CW signal of a certain speed assuming a raised sinewave.

No, I am not assuming any such thing!

W8JI: The problem is, and where we disagree is, I consider the CW genrated by a NORMAL transmitter of excellent design to have a fixed rise and fall duration. This the way every single CW transmitter that has every been built works. I'm looking at a real system.

I think we disagree on some things, but this particular item is not one of them!

K5MC: Since we want to maintain the same rise/fall characteristics (shapes and times) regardless of speed, we will only vary the time duration of the constant amplitude portion of each pulse (designated as tc) to increase or decrease the number of dits sent per second. (This is a direct quote from my article.)

Tom, I thought I went to great pains in my article to explain that my 5-ms sinusoidal keying waveform had a constant 5-ms rise time and a constant 5-ms fall time at both 2.4 wpm and 30 wpm. The only thing that changed in my sinusoidal keying waveform when the speed was changed from 2.4 wpm to 30 wpm was the "center" time of the pulses (dits) when the keying pulse amplitude was fixed at a constant value of 1. Please read my article again and look at the keying waveform as it is drawn. Again, the only thing that changes in my sinusoidal keying waveform when the speed of the string of dits is changed from 2.4 wpm to 30 wpm is the time duration denoted by "tc" in the waveform sketch. As you say above, this is how normal CW transmitters work and that is EXACTLY what I assumed!

For my second keying waveform, I assumed the rise and fall times of the keying waveform were zero and referred to it as "square-wave" keying.

73, K5MC

RE: Bandwidth versus Keying Speed

by KE3HO on May 30, 2007 Mail this to a friend!

W8XR: << The piece that really bothers me is that leading edge / trailing edge bit. I just can't fathom how bandwidth could possibly depend on the distance between them. Also, except for extreme speeds, the bandwidth required for even reasonable shapes should swamp any bandwidth required because of the keying speed. >>

This is where I have problems too. There is a huge disconnect between the theory presented and the physical processes involved (IMHO). The rise time and fall time and their shape are fixed and independent of keying speed . Those waveforms should produce sidebands and the spectral content of those sidebands should be independent of keying speed. During tc, the carrier is constant and unmodulated. Mickey is saying that the duration of tc affects the bandwidth of the transmitted signal. I have a big problem with this. What is the physical process by which this happens? During tc, you have an RF oscillator running at a fixed frequency and amplitude. Each cycle of the sine wave looks just like the one before it and just like the one after it. So what is the connection between duration and bandwidth? I just don't see it. If the duration of tc affects bandwidth, how is that physically produced? Once I go key down and get through the rise time to the start of the tc period, the length of tc is set by how long I hold the key down. But during tc, the RF oscillator and PA can't predict when I am going to go key up, so how can the bandwidth of the signal change? As I said earlier, the end of tc is defined by when I go key up which is the start of the fall time. The only way there could be some physical mechanism for the duration of tc to affect the bandwidth would be if somehow the duration of tc was somehow "remembered" by the rig and all of the "extra bandwidth" was created during the fall time. When I said this earlier, I was not seriously suggesting that this might be the case. Rather, I was trying to show this to be a paradox. I'm with you Mark, I just don't see the physical means to produce this extra bandwidth.

This has been a truly interesting thread, and I have read everything that everyone has said. I agree with Tom that the "obvious" thing to do is to take a spectrum analyzer and see what really happens with a real rig in the real world. I wish I had the equipment to do that.

Let me put forward one last idea for consideration. Mickey talks about the power bandwidth, and I wonder if that is somehow the source of our disagreement. Here is what I am getting at. It is my belief that, for a fixed rising and falling keying waveform, that the sidebands produced during the rise time and fall time are completely determined by the shape of the rising and falling keying waveform, and that these sidebands are independent of keying speed. I also believe that during tc, no sidebands are produced and that the bandwidth of the signal during tc is determined by the stability (in frequency and amplitude) of the transmitter. As keying speed changes, the only thing that changes in Figure 1 is the duration of tc. During the rise and fall times, you have an AM signal - the carrier modulated by the rising and falling keying waveforms. During these periods, you have 2/3 of your power in the carrier, and 1/3 divided between the two sidebands (I hope I remember the distribution of power correctly). During tc, 100% of the power is in the carrier alone. If you key faster, tc becomes shorter. When this happens, the amount of power in the sidebands during the rise and fall is the same, but the amount of power in the carrier during tc is less. The fixed amount of power in the sidebands becomes a larger fraction of your total power integrated over the entire transmitted pulse width. If the "power bandwidth" is determined by calculating the spectral width which contains 99.1% of your total integrated power, then I can see a connection between the keying speed and this "power bandwidth". If you key very slowly and tc is 1 second, then the power contained in the sidebands (generated during the rise time and fall time) is an insignificant part of your total integrated power. If you key so fast that tc goes to zero, then a full 1/3 of your total integrated power will be in these same sidebands. However, the spectral width of and the total power contained in these sidebands will nevertheless be the same at any keying speed.

I truly appreciate all of the effort that everyone has put into their contributions on this thread. This has been one of the most interesting threads here in a long time, and I will add that, IMO, the tone of the thread has been pretty pleasant also - it has not degraded into a playground fight like some of the threads have in the past. This has been a pleasure. Thank you everyone.

73 - Jim

Bandwidth versus Keying Speed

by AB7E on May 31, 2007 Mail this to a friend!

I think KE3HO is correct in his explanation of the differences in perspective here. It makes sense ... clearly rise and fall times are the only transition that take up spectrum, but making them happen more often would increase the time density ("power bandwidth"?) of that use of bandwidth. In practical terms we only hear that which the rise and fall times cause, but the keying speed affects the time-averaged percentage of where the power ends up spectrally.

I have a son (not a ham) who has an advanced math degree and works as a software development engineer with a company doing signal processing work for the government. I asked him to check this thread and he came to the same conclusion.

What I don't understand is how a university math professor can't figure out how to rationalize the math to match real life. How did this thread not converge days ago?

Bandwidth versus Keying Speed

by K5MC on May 31, 2007 Mail this to a friend!

W8XR: The piece that really bothers me is that leading edge / trailing edge bit. I just can't fathom how bandwidth could possibly depend on the distance between them.

Mark, the following four sentences are found on page 89 in Lathi's textbook [1]:

"Reciprocity of Signal Duration and Its Bandwidth - The scaling property implies that if g(t) is wider, its spectrum is narrower, and vice versa. Doubling the signal duration halves its bandwidth, and vice versa. This suggests that the bandwidth of a signal is inversely proportional to the signal duration or width (in seconds). We have already verified this fact for the gate (rectangular) pulse, where we found that the bandwidth of a gate pulse of width T seconds is 1/T Hz."

Most textbooks that discuss Fourier transforms will also discuss the various Fourier transform operations/properties, such as scaling, time shift, frequency shift, time convolution, and frequency convolution. I'm pretty sure that Fourier transforms, along with the various transform operations, are used by many practicing engineers as they go about designing and analyzing "real world" communication systems. I know for a fact that these topics are included in the typical undergraduate signal analysis/communication courses in electrical engineering.

By the way, when Lathi says that the "bandwidth" of a gate pulse of width T seconds is 1/T Hz, he is referring to the "first-null" bandwidth. However, his general statement regarding the inverse relationship between time duration and "bandwidth" is equally valid for almost every other type of bandwidth found in the literature, such as the 99% energy bandwidth (for energy signals) and the 99% power bandwidth (for power signals). The only type of "bandwidth" precisely defined in the professional literature in which Lathi's statement does not hold, as far as I know, is the absolute bandwidth. However, the absolute bandwidth is of little practical value when comparing real signals.

In closing here, I would like to remind everyone that if you want to increase the information rate (more information transmitted per unit of time) without increasing the signal power, the "bandwidth" must increase as well. (Let me hasten to say that the exchange of bandwidth and signal power is not possible in AM systems as it is in digital and FM/PM systems.) Mother Nature does not allow us a "free lunch" in this regard. This simple fact is another reason why nobody should be surprised that the "power" bandwidth of a CW signal varies with the keying speed as my article demonstrated. (Yes, even for keying waveforms that have identical rise/fall shapes and times!)

[1] B.P. Lathi, Modern Digital and Analog Communication Systems (ISBN 0-19-511009-9)

73, K5MC

Bandwidth versus Keying Speed

by K5MC on May 31, 2007 Mail this to a friend!

KE3HO: Those waveforms should produce sidebands and the spectral content of those sidebands should be independent of keying speed.

Jim, don't forget that the location of these sidebands along the frequency axis varies with speed. When sending the string of dits at 2.4 wpm, the fundamental frequency f1 of the keying waveform is exactly 1 Hz because the time period T between consecutive dits at this speed is exactly 1 second (T = 1/f1). However, when sending the string of dits at 30 wpm, the fundamental frequency of the keying waveform is exactly 12.5 Hz because the period between consecutive dits at this speed is exactly 80 ms.

KE3HO: If you key faster, tc becomes shorter. When this happens, the amount of power in the sidebands during the rise and fall is the same, but the amount of power in the carrier during tc is less.

Below are the first several Fourier coefficients for the sinusoidal keying waveforms I studied in my article. (I calculated these coefficients out to 7 decimal places to minimize round-off errors.)

For the 2.4-wpm keying waveform with 5-ms sinusoidal rise/fall times:

a0 = 0.4963662 V (dc or average value of keying waveform)
a1 = 0.6365602 V (fundamental frequency coefficient at 1 Hz)
a2 = 0.0072660 V (second harmonic coefficient at 2 Hz)
a3 = -0.2120282 V (third harmonic coefficient at 3 Hz)
etc.

For the 30-wpm keying waveform signal with 5-ms sinusoidal rise/fall times:

a0 = 0.4545775 V (dc or average value of keying waveform)
a1 = 0.6273706 V (fundamental frequency coefficient at 12.5 Hz)
a2 = 0.0878988 V (second harmonic coefficient at 25 Hz)
a3 = -0.1856182 V (third harmonic coefficient at 37.5 Hz)
etc.

The value of a0 is "responsible" for the amount of power in the carrier. Therefore, for the sinusoidal keying waveform, the amount of power in the carrier is less for the faster speed. However, the amount of power contained by the respective sidebands is also different for the two speeds. For example, the power of the first pair of sidebands in the 2.4-wpm CW signal is larger than that in the 30-wpm CW signal because the value of a1 for the slower keying waveform is larger than that of the faster keying waveform.

To calculate the average power of each frequency component, let's assume R = 1 ohm for convenience.

For the 2.4-wpm sinusoidal keying waveform we have the following average powers per frequency component:

At 0 Hz (DC) we have (0.4963662)2 = 0.2463794 W
At 1 Hz (fundamental) we have (0.6365602/1.414)2 = 0.2026045 W
At 2 Hz (second harmonic) we have (0.0072660/1.414)2 = 0.0000264 W
At 3 Hz (third harmonic) we have (-0.2120282/1.414)2 = 0.022478 W
etc.

(Remember to divide the amplitudes by the square root of 2 (shown above as 1.414) to obtain the rms values of the various cosine terms and then square the rms values to get the average powers on a 1-ohm basis.)

For the 30-wpm sinusoidal keying waveform we have the following average powers per frequency component:

At 0 Hz (DC) we have (0.4545775)2 = 0.2066407 W
At 12.5 Hz (fundamental) we have (0.6273706 /1.414)2 = 0.1967969 W
At 25 Hz (second harmonic) we have (0.0878988 /1.414)2 = 0.0038631W
At 37.5 Hz (third harmonic) we have (-0.1856182 /1.414)2 = 0.0172271W
etc.

The total average powers of the sinusoidal keying waveforms are as follows:

Pavg = 0.49500 W for 2.4-wpm keying signal at 5-ms sinusoidal rise/fall times

Pavg = 0.43750 W for 30-wpm keying signal at 5-ms sinusoidal rise/fall times

When you add up the average powers of the DC component and the first 17 harmonic components for the 2.4-wpm keying signal, you get 0.4906272 W, which is 99.12% of the total average power (0.49500 W). Therefore, the 99.12% bandwidth of the 2.4-wpm keying signal (5-ms rise/fall times) is 17 Hz. When you use this waveform to key a CW transmitter, the resulting 99.12% bandwidth of the output signal will be exactly twice as much, 34 Hz. (I rounded 99.12% to 99.1% in my article.)

When you add up the average powers of the DC component and the first 6 harmonic components for the 30-wpm keying signal, you get 0.4337106 W, which is 99.13% of the total average power (0.437500 W). Therefore, the 99.13% bandwidth of the 30-wpm keying signal (5-ms rise/fall times) is 75 Hz, since 6 X 12.5 Hz = 75 Hz. When you use this waveform to key a CW transmitter, the resulting 99.13% bandwidth of the output signal will be exactly twice as much, 150 Hz. (I rounded 99.13% to 99.1% in my article.)

The approach is the same for square-wave keying, but this is a "standard" waveform that is readily found in the textbooks. The Fourier series for the 2.4-wpm and 30-wpm periodic signals assuming square waves (50% duty cycle as before) are given by s1(t) and s2(t), respectively, as follows:

s1(t) = 0.5 + (2/pi)[cos(2 pi t) - 1/3 cos(6 pi t) + 1/5 cos(10 pi t) - . . . ]

s2(t) = 0.5 + (2/pi)[cos(25 pi t) - 1/3 cos(75 pi t) + 1/5 cos(125 pi t) - . . . ]

(I would like to point out here that the Fourier series for the 5-ms sinusoidal keying waveforms have both even and odd harmonic frequency components, but the square-wave keying waveforms only contain odd harmonics because the square-wave keying waveforms have so-called half-wave symmetry.)

The total average power of s1(t) is exactly the same as that of s2(t), 0.5000 W. If we add the average powers of the frequency components up through the 21st harmonic for the 2.4-wpm signal, we will have 0.495398 W, which is 99.08% of the total. (I rounded this up to 99.1% in my article.) Therefore, the 99.1% power bandwidth of the 2.4-wpm square-wave keying signal is 21 Hz; thus, the 99.1% power bandwidth of the CW signal will be 42 Hz.

Likewise, we need the frequency components up through the 21st harmonic for the 30-wpm signal to have 99.08% of the total. Therefore, the 99.1% power bandwidth of the 30-wpm square-wave keying signal is 21 X 12.5 Hz = 262.5 Hz; thus, the 99.1% power bandwidth of the CW signal will be 525 Hz.

KE3HO: However, the spectral width of and the total power contained in these sidebands will nevertheless be the same at any keying speed.

For the CW signal with square-wave keying, the distribution of the average powers is identical for the two speeds. However, since the fundamental frequency of the 30-wpm keying waveform is 12.5 times higher than that of the 2.4-wpm waveform, the 99.1% power bandwidth is likewise in that exact same ratio for the two speeds. However, as shown above, the distribution of the average powers is not identical for the sinusoidal keying waveforms because those two waveforms are not equal to each other by a simple scaling factor like the square-wave keying waveforms are.

KE3HO: If the "power bandwidth" is determined by calculating the spectral width which contains 99.1% of your total integrated power, then I can see a connection between the keying speed and this "power bandwidth". If you key very slowly and tc is 1 second, then the power contained in the sidebands (generated during the rise time and fall time) is an insignificant part of your total integrated power.

Jim, as you can see from my details above, you are getting extremely warm! I am very happy that you have "hung in" here on this somewhat esoteric topic/thread.

73, K5MC

Bandwidth versus Keying Speed

by K5MC on May 31, 2007 Mail this to a friend!

AB7E: I have a son (not a ham) who has an advanced math degree and works as a software development engineer with a company doing signal processing work for the government. I asked him to check this thread and he came to the same conclusion.

If your son doesn't have a background in signal analysis equivalent to that typically included in an undergraduate electrical engineering curriculum, then I'm not too surprised that he doesn't understand the concept of power bandwidth and the results I discussed in my article. If he does have such a background, then it appears that he needs to review the definition of power bandwidth, along with the other basic principles of Fourier analysis as applied to signals and systems. (If all of his degrees are in math, then I'm pretty sure that he doesn't have the background of which I speak.)

AB7E: What I don't understand is how a university math professor can't figure out how to rationalize the math to match real life. How did this thread not converge days ago?

If you want to take me to task for continuing to try to open the eyes of some hams, I think you should at least understand that I am an electrical engineering professor, not a math professor!

73, K5MC

Bandwidth versus Keying Speed

by K5MC on May 31, 2007 Mail this to a friend!

K5MC: At 0 Hz (DC) we have (0.4963662)2 = 0.2463794 W
At 1 Hz (fundamental) we have (0.6365602/1.414)2 = 0.2026045 W
At 2 Hz (second harmonic) we have (0.0072660/1.414)2 = 0.0000264 W
At 3 Hz (third harmonic) we have (-0.2120282/1.414)2 = 0.022478 W
etc.

I just noticed that the formatting screwed up when I posted my Word file to the eham site. The equations above involving the squared terms should look like this:

At 0 Hz (DC) we have (0.4963662)^2 = 0.2463794 W
At 1 Hz (fundamental) we have (0.6365602/1.414)^2 = 0.2026045 W
At 2 Hz (second harmonic) we have (0.0072660/1.414)^2 = 0.0000264 W
At 3 Hz (third harmonic) we have (-0.2120282/1.414)^2 = 0.022478 W
etc.

K5MC: At 0 Hz (DC) we have (0.4545775)2 = 0.2066407 W
At 12.5 Hz (fundamental) we have (0.6273706 /1.414)2 = 0.1967969 W
At 25 Hz (second harmonic) we have (0.0878988 /1.414)2 = 0.0038631W
At 37.5 Hz (third harmonic) we have (-0.1856182 /1.414)2 = 0.0172271W
etc.

Likewise, these intended equations are as follows:

At 0 Hz (DC) we have (0.4545775)^2 = 0.2066407 W
At 12.5 Hz (fundamental) we have (0.6273706 /1.414)^2 = 0.1967969 W
At 25 Hz (second harmonic) we have (0.0878988 /1.414)^2 = 0.0038631W
At 37.5 Hz (third harmonic) we have (-0.1856182 /1.414)^2 = 0.0172271W
etc.

The ability to post math equations on eham is rather limited!

73, K5MC

Bandwidth versus Keying Speed

by K5MC on May 31, 2007 Mail this to a friend!

K5MC: If you want to take me to task for continuing to try to open the eyes of some hams, I think you should at least understand that I am an electrical engineering professor, not a math professor!

I want to apologize to AB7E for all of my comments directed to him. After reading his post again, I believe that I misinterpreted much, if not all, of what he was saying. I will try very hard to avoid doing that again!

73, K5MC

RE: Bandwidth versus Keying Speed

by W8JI on May 31, 2007 Mail this to a friend!

I have limited time to follow this thread, but rereading some parts it looks like Mickey is using a long time period average power that includes many off and on cycles to determine bandwidth.

Everyone agrees or should agree as fixed shape and level pulses occur more and more frequently there are more of them in a given time period, twice as many at twice the speed. He then compares that long term accumulation of sidebands to the power in the transmitter.

This long term accumulation of enery in clicks is NOT what causes the problem on adjacent channels when we are operating CW. By definition neither our brains nor or receivers can accumulate or store that energy.

Our only perception is the clicks occur more often. As we look at them on the receiver they cause more frequent QRM but not stronger QRM, within limits or reasonable CW speeds.

The off and on transitions ALWAYS occupy the same overall bandwidth because they are caused by rise and fall periods, not the spaces between the rise and fall times.

The spaces between the rise and fall times cannot affect the bandwidth occupied by the rises and falls. The rises and falls are so brief they set the ultimate space occupied by the CW signal, not the much slower Morse rate.

I think the difference of opinion would go away if people considered how the system actually works.

You cando this by sending dots and tuning across the signal with a real receiver.

73 Tom

RE: Bandwidth versus Keying Speed

by WA0LYK on May 31, 2007 Mail this to a friend!

KE3HO
>>W8XR: << The piece that really bothers me is that
>>leading edge / trailing edge bit. I just can't fathom
>>how bandwidth could possibly depend on the distance
>>between them. Also, except for extreme speeds, the
>>bandwidth required for even reasonable shapes should
>>swamp any bandwidth required because of the keying
>>speed. >>

>>This is where I have problems too. There is a huge
>>disconnect between the theory presented and the
>>physical processes involved (IMHO). The rise time and
>>fall time and their shape are fixed and independent
>>of keying speed . Those waveforms should produce
>>sidebands and the spectral content of those sidebands
>>should be independent of keying speed. During tc, the
>>carrier is constant and unmodulated. Mickey is saying
>>that the duration of tc affects the bandwidth of the
>>transmitted signal. I have a big problem with this.
>>What is the physical process by which this happens?
>>During tc, you have an RF oscillator running at a
>>fixed frequency and amplitude. Each cycle of the sine
>>wave looks just like the one before it and just like
>>the one after it. So what is the connection between
>>duration and bandwidth? I just don't see it. If the
>>duration of tc affects bandwidth, how is that
>>physically produced?

First, what K5MC and AB0WR have been trying to describe is a periodic function. In other words, a keying waveform (i.e. a gate function) where the distance between the rising and falling edges ARE related by the keying speed used.

What you are describing is a keying waveform where the rise and fall times are non-periodic, i.e. NOT RELATED, and would require an analysis using step functions only.

Also, you are confusing time and frequency. The fact that a spectrum analyzer may show increased power in the sidebands at the start and end of a pulse doesn't tell you what those frequencies are or how they are energies are related. So be careful in describing the time related power and the frequency related power.

Here is a conundrum for you. You are saying the length of the pulse should have no effect on the sideband frequencies generated, only the rising and falling edges. This means the bandwidth would be constant out to about 120 wpm with 5 ms rise and fall times, i.e. when the pulse "width" would become zero. Yet even W8JI admits that at some higher speed the "percentage" of the rise and fall times become a significant portion of the pulse and therefore the bandwidth becomes dominated by the periodic analysis. I believe he indicates this occurs at around 50 wpm with 5 ms rise and fall times. This means that the transfer function would require at least two terms that describe bandwidth, some increasing and some decreasing (or remaining constant). They would cross over at about 50 wpm.

Can anyone do the math that describes this?

Jim
WA0LYK

RE: Bandwidth versus Keying Speed

by W8JI on May 31, 2007 Mail this to a friend!

Since I can't seem to get the theorists to actually measure the bandwidth of a transmitter, I've measured it for them.

Please review this new page on my website:

http://www.w8ji.com/occupied_bw_of_cw.htm

These measurements were made with currently certified equipment that directly measures occupied bandwidth.

CW speed does NOT affect the occupied BW of a CW transmitter unless it changes the rising and falling edges of the waveform.

73 Tom

RE: Bandwidth versus Keying Speed

by W8XR on May 31, 2007 Mail this to a friend!

Mickie,

Thanks for the Lahti reference - I'll see if I can find a used one (the retail is $117...) for additional reading.

My complaint with this reference and your general comment about other experts is that they don't provide an explanation of _why_ this should be the case - they merely corroborate your counter-intuitive assertion (or vice-versa.)

In order to make sense of the problem, I really need to have some concrete connection between theory and real systems. In many mathematic systems (at least the ones a typical engineer is likely to run across) you can make some exemplar transformations between formulae and the real world that they purport to model.

For example, a model of the operation of an inductor or oscillator feedback system describing electrons moving and accumulating and standing still provides a useful connection between the math used to describe the systems and the behaviour of the systems themselves. I'm sure as an educator, you appreciate the value of a good physical model to get your point across.

There should be such examples, or even some appropriate metaphors, that would help illustrate your assertions here.

Since many (perhaps most) hams will not be willing to dive into the math, it would be more effective for you to develop the math into some kind of physical model that they (we) can better understand.

Of course this is more about philosophy of science and epistomology (and pedagogy) than bandwidth... So, I'm going to quit, for now, disagreeing with your conclusions, as well informed as they may be.

Thanks to everyone for the broad and thought provoking comments, particularly those of you who illustrated my arguments better than I did!

Mark

RE: Bandwidth versus Keying Speed

by W8XR on May 31, 2007 Mail this to a friend!

Tom,

Great real-world illustration!

Mark

RE: Bandwidth versus Keying Speed

by AB0WR on May 31, 2007 Mail this to a friend!

K5MC:

Mickey,

You used a square wave for your analysis. Shouldn't you be using a gate function instead?

Use of a square wave assumes positive and negative peaks imposed as modulation on the carrier. A gate function would just be turning the carrier on and off which is what CW does.

It think you will get the same conclusion but the actual bandwidths may wind up being a little different. I've worked out the convolution of the gate function and the carrier graphically but I haven't yet finished the math or doing any actual calculations (too many things like the yard needing mowing and getting some sleep at night gets in the way!). I will keep working on them. My graph shows that you just get the sampling function waveform at the +/- carrier frequencies.

It would look to me like you would have a couple of terms involved. 1) if A is the amplitude of the pulse, tau is the length of the pulse, and T is the period between pulses then you would have a term like
(A * tau)/T. 2) you would also have a term that looks like
[sin (n * w * tau)/T] / [(n * w * tau)/T] where n is the number of the harmonic.

In other words the second function would be a sinx/x type of function with x being (n * w * tau)/T.

I'll get this all worked out sooner or later.

I know you pointed this out earlier but people seem to keep mixing up the time domain with the frequency domain. That is an easy thing to do. But once you have done a Fourier transform of a time domain function you lose the "time" placement information and everything gets shifted into the frequency domain.

In other words, in the frequency domain there is no "leading edge" or "trailing edge" of a pulse at a certain measureable point in time. There is only the pulse width and pulse period as "constants", if you will. Their unit is in seconds but all math in the frequency domain is done with respect to frequency in Hz and not time in sec so time is no longer a variable of concern in the frequency domain.

If the pulse width or period changes it will change the fundamental frequency w0, and the amplitude of the all the frequency components that make up the signal. But you still won't be able to tell where *in time* this all occurred.

For those that are interested, the actual rise time (or fall time) of a pulse really only tells you the bandwidth of the system response, i.e. how big "n" above can be. What you wind up with is a relationship that is basically
bandwidth * rise-time = pi or, for our purposes
bandwidth = pi/rise-time.

In other words the longer the rise time the lower the bandwidth the system has and this means the system will pass fewer harmonics of the fundamental frequency. A shorter rise time indicates that more harmonics can be passed. In the limit, as rise-time goes to zero, you wind up with a system that has infinite bandwidth. Using the relation above, a system which passes a square wave with a rise time of 5msec (.005sec) has a bandwidth of about 625hz. This means you can pass up to about 25 harmonics of a waveform with a fundamental frequency of 12.5hz (30wpm). I believe Mickey calculated 20 harmonics needed to reach the FCC bandwidth definition so a system with a 5ms rise time will be sufficient.

As Mickey pointed out there will be harmonics present out past his 20th harmonic. They may even be large enough to be seen on a spectrum analyzer. But you shouldn't see very many out past the 25th harmonic because of the system bandwidth limit.

If you take the transmitted bandwidth to include all harmonics that can pass through the system then you may very well take the bandwidth to be about 625hz for a CW signal. This seems to be a little excessive, however, for very slow keying speeds which have a much smaller fundamental frequency -- e.g. 5wpm with a 2hz fundamental would be able to get about 150 harmonics passed. The amplitude of the higher harmonics would probably be too small to be seen.

This also leads to the conclusion that 5ms rise time may very well be too long (i.e. the bandwidth may be too limited) to work well with faster keying speeds. Too many of the harmonics will begin to disappear to allow a good "perception" of when a pulse has actually been sent. That could very well be why some on here have said the "harder" keying pulse works better. The system providing the "harder" pulse would have a wider bandwidth (i.e. a shorter rise-time) and would pass more harmonics of the faster keying pulses allowing a better perception of the pulse.

I didn't mean to write a dissertation. I apologize for the length of the post. Guess I had a lot to say.

73,

tim ab0wr

RE: Bandwidth versus Keying Speed

by W8JI on May 31, 2007 Mail this to a friend!

Tim,

Unfortunately the measured occupied BW of a transmitter, either by using a receiver or a spectrum analyzer capable of measuring occupied BW, does not change with keying speed unless the keying speed affects the slope of the rise and fall.

See:

http://www.w8ji.com/occupied_bw_of_cw.htm

73 Tom

RE: Bandwidth versus Keying Speed

by KE3HO on May 31, 2007 Mail this to a friend!

WA0LYK: << What you are describing is a keying waveform where the rise and fall times are non-periodic, i.e. NOT RELATED, and would require an analysis using step functions only.

Also, you are confusing time and frequency. >>

Jim,

I am talking about the very same keying waveform that Mickey is talking about. A rising waveshape that is constant at all keying speeds, a steady state, followed by a falling waveform that also is constant at all keying speeds.

No, I am not confusing time and frequency. I do not believe for 5 ms that the keying speed affects the bandwidth of a CW transmitter. At the same time, I don't think Mickey is a fool of any sort. I have been trying to understand his analysis, and I was simply wondering if his "power bandwidth" might be some time weighted function - for example, like watt-seconds - key down for 1 second at 100 watts and you have 1 watt-second of power. If the "power bandwidth" somehow integrated the power at each frequency over the duration of the signal, then I could then see some connection between this "power bandwidth" and keying speed. Even if that is true, it only points to the fact that as keying speed increases the total watt-seconds that you transmit decreases. The power in the sidebands remains unchanged with keying speed, but the power in the sidebands becomes a more significant portion of your total watt-seconds as keying speed increases. Still, the bandwidth of the transmitted signal remains unchanged. Tom's measurements, along with others that he has cited here, show that.

73 - Jim

RE: Bandwidth versus Keying Speed

by WB2WIK on May 31, 2007 Mail this to a friend!

There has to be a relationship between sending speed and bandwidth.

I know there's a relationship between the speed I drive my car and it's width -- which explains why I can fit through a tollbooth lane at 10 mph just fine but when I try it at 100 mph, the car doesn't fit.

:-)

WB2WIK/6

RE: Bandwidth versus Keying Speed

by KE3HO on May 31, 2007 Mail this to a friend!

<< I know there's a relationship between the speed I drive my car and it's width -- which explains why I can fit through a tollbooth lane at 10 mph just fine but when I try it at 100 mph, the car doesn't fit. >>

Actually, it isn't your car that changes. The faster you drive, the smaller everything outside of your car gets. That's why when you drive faster you reach your destination soon - you have less distance to travel.

:-)

73 - Jim

RE: Bandwidth versus Keying Speed

by AB0WR on May 31, 2007 Mail this to a friend!

w8ji:"CW speed does NOT affect the occupied BW of a CW transmitter unless it changes the rising and falling edges of the waveform."

w8ji:"Unfortunately the measured occupied BW of a transmitter, either by using a receiver or a spectrum analyzer capable of measuring occupied BW, does not change with keying speed unless the keying speed affects the slope of the rise and fall."

Rather than telling us we are wrong you would be better advised to figure out why the CW signal from a 751a does not match what theory predicts.

Trust me, I have been down this road many, many times. The math is correct. Anyone with an audio program like Cool Edit can generate a square wave and use the frequency analysis window to see the odd-order frequency components making up the square wave. Modulation of a carrier, either by a linear system such as one using a Gain Transfer function or by a non-linear system such as a FET mixer, only shifts these frquency components to being sidebands around the +/- carrier frequencies. Again, the math is correct, it just doesn't lie.

Similarly, the slope of the rise time does not generate any frequency components. The slope of the rise time only indicates the bandwidth of the system passing a square wave or generating a square wave. As the slope approaches vertical it only indicates a system with a wider bandwidth and as the slope gets more horizontal it only indicates a system with a narrower bandwidth. The slope itself generates nothing.

A CW key closure is either on or off. That is a step function if it happens once (i.e from off to on), it is a gate function if the transition happens regularly (i.e. off to on to off to on .....). That gate function generates a waveform that has frequency components that basically go on to infinity. Once you get high enough in the harmonic order the amplitude approaches zero but never quite gets there. That is what generates all the frequency components.

If the system connected to that CW key winds up with a waveform that has a slope then it is indicative of a bandwidth limited system. If you wish I can email you the Fourier analysis that shows this. That is all that the slope tells you, nothing more and nothing less.

I have looked at the spectrum graphs you show. I'm not even sure where to begin analyzing them. The first display doesn't even begin to show any of the individual frequency components involved in a square wave. For a 10hz signal you would have frequency components at 10hz, 30hz, 50hz, 70hz, etc. First off, it appears that you did a 90sec collection of data using a 10hz resolution. I suspect that the frequency jitter of the PLL in a 751a over 90sec would be enough to smear the 10hz spaced frequency elements of the CW signal all over the place. It would either make the frequency output look like a continuous spectrum instead of fixed elements or it would leave the spectrum analyzer missing important elements on which to base the bandwidth calculation. I believe the 751a has a 10hz step built into its oscillator which would confirm this assumption. Sometimes a specfic frequency component might look like it is at 10hz and the next instant be at 20hz -- and that is assuming you have a perfectly stable oscillator in your spectrum analyzer that doesn't make the smearing even worse.

This is further confirmed by your displays for 25 dots per second and for 40 pulses per second. The harmonics in the first would be at 25hz, 75hz, 125hz, etc. The low side of the display shows approximately this but at least one frquency component is missing. The high side doesn't show any of these close in elements. For a 40hz square wave the harmonics in a square wave would be a 40hz, 120hz, 200hz, 280hz, etc. This is far enough apart that the jitter in the 751a along with your resolutino would tend to establish a fixed location for some of the frequency components. That is why the 40 dots per second display shows a pretty good display. It's actually surprising that the occupied bandwidth for a 40 dots per second display is not wider than 500hz when the calculated bandwidth for a 12.5hz square wave is 525hz. This leads me to believe that the rise time of the 751a is actually longer than 5ms indicating a bandwidth restricted to something less than 625hz.

Bottom line? I'm not sure I would trust your spectrum analyzer to measure anything less than a 400-500hz bandwidth from a 751a transmitter. There are too many frequency jitter issues at the low speeds we are speaking of to insure that a proper measurement is being taken. I would believe you if you said that a 400-500hz bandwidth is the lowest you can measure. But that wouldn't make the math wrong in any way.

tim ab0wr

Bandwidth versus Keying Speed

by KX0R on May 31, 2007 Mail this to a friend!

Perhaps it would clarify this discussion to remember that we don't hear "power bandwidth". We hear clicks, which are brief sounds associated with the sidebands produced by the transitions of a keying-modulated signal.

Regardless of what type of receiver we have, regardless of the filter, most of us listen with ears several khz wide. What we hear off-frequency from a clicking signal is something derived from those sidebands caused by the too-fast rise and fall of the keyed signal. In clicks we hear a mixture of the heterodyned click-sideband frequencies, receiver distortion products, intermod products, filter ringing, AGC effects, and numerous other transient byproducts. If the clicking signal is strong and the signal we wish to hear is weak, the effect on our relatively wideband ears and brain is severe. We do a lot of brain processing when we copy CW, and clicks from an interfering signal screw it up.

We don't really hear power bandwidth. I think that the author is correct that power bandwidth goes up with keying speed, for a constant modulation shape - but this is not very relevant when we're on the radio. The FCC's defintion is close to a power bandwidth definition, but that's not what we really care about on the bands when we're trying to copy a weak signal through key-click QRM.

W8JI is also right that the bandwidth (semi-instantaneous power bandwidth, not power bandwidth, fuzzy definition) is determined by the modulating function of the keying. Tom is talking about what exists on the spectrum (frequency domain) during the rise or fall of a keyed signal. What we hear with our wide-bandwidth ears is a whole bunch of almost instantaneous, complex junk that hinders our ability to concentrate on another station. This junk is much worse as the rise and fall times decrease.

Whether copy of high-speed signals is easier if they have faster (clicking) edges will be debated forever, but I think that W6TH is right that the sharp keying is easier to copy when the code speed is up high (with all its devastating clicks and QRM out several khz or more).

I have a switch for rise and fall time on the cathode keyer for one of my rigs. It's an RC circuit - technically imperfect. If copy is rough I sometimes sharpen my keying.

Every CW operator should look at his keyed output with a scope and decide if it represents what he wants to send all over the world.

You can also listen for clicks with a separate receiver, with your transmitter on a dummy load and minimal coupling to the receiver. The receiver must not be overloaded, and the AGC should be off. You can hear your clicks as you tune off-frequency with a narrow IF filter. It's easy to hear the clicks change as you make adjustments to your transmitter keying. If you get your rise and fall times longer than about 5 ms, you won't hear many clicks. The debate for all of us is whether keying like 1 or 2 ms is desirable, easier to copy through noise and QRM, etc. If you have a memory keyer, you can do tests to help decide for yourself. Some of us in the QRP ranks have been debating 1 or 2 ms keying vs the 5 ms "standard". A lot of folks think that sharp keying has an advantage and is "justified" with QRP. I think anything well under 2 ms is rude, unless you're a real fast op.

What we really need here is a reasonable compromise between theory and practical reality. A keyed CW signal with moderate shaping, even by an RC-derived modulation device, will greatly reduce interference caused by uncontrolled or defective shaping. It might be true that we need keying that is bit sharper, as well as a wider receiver filter, if we go real fast.

This is a real interesting topic, and thanks to the various super-sharp minds who have jumped into the fire here.

Bandwidth versus Keying Speed

by KX0R on May 31, 2007 Mail this to a friend!

Before long, the leading manufacturers of HF/CW transceivers will offer features for control of the CW keying modulation. It would inexpensive to offer rise and fall times that are mathematically derived. These times could optionally track the keying speed, so the instantaneous bandwidth of the signal would be more nearly ideal.

These features might be attractive to operators who take pride in the quality of their signals. We certainly don't need thousands of powerful rigs with poor engineering filling our spectrum with nasty sidebands.

Newer rigs like the Elecraft K3 might be able to offer keying control features with only a firmware upgrade, since the DSP is in the signal path on transmit. Every cool new feature is an inducement to buy!

RE: Bandwidth versus Keying Speed

by SM0AOM on May 31, 2007 Mail this to a friend!

I would recommend a through study of the
CCIR (ITU-R) Recommendation SM.328-10
"Spectra and Bandwidth of Emissions".

This Recommendation, as expected, quotes a "necessary bandwidth" for an A1A emission of K*B where K is the "hardness factor" of the telegraph signal elements (K= 3 or 5), and B is the modulation rate in Bauds.

Also, a semi-empirical expression for the A1A "occupied bandwidth" at the 1 percent out-of-band power level of L = B*((1/(0.05+a))-1)[Hz] is shown. "a" is the rise or fall time of the shortest signal element expressed as a fraction.

Note that all bandwidths are proportional to B.

"Plugging in" actual numbers for the IC-751 as read from the oscilloscope photo in the QST Jan 1985 review,(http://www.classicicom.com/product_reviews/pr8501.pdf)and taking the rise and fall times as the shortest of the asymmetrical envelope transitions (tr)about 3 ms, at a keying rate of 8 WPM or 6,66 baud (dot length of 150 ms)would result in a "necessary bandwidth" of 5 * 6,6 or 33 Hz and an "occupied bandwidth" of about 90 Hz.

Judging from the spectrum plots at http://www.w8ji.com/occupied_bw_of_cw.htm
the calculated "necessary bandwidth" of the IC-751 corresponds well to the main lobe width that can be seen on the 10 Baud (or dps) plot. The primary cause for the much wider "occupied bandwidth" appears to be deviation from the optimum Gaussian shape and the overshoot at the leading edge.

The ITU formulas corresponds also very well to actual spectral measurements made on ship's radiotelegraph transmitters by former colleagues at ITT/Standard Radio and Swedish Telecom Radio in the mid 70's. At that time type acceptance specifications often used the CCIR Gaussian keying function as the norm, and manufacturers became hard pressed to make equipment that had sufficiently good keying properties in order to present acceptable adjacent channel interference levels.

In the era of the DSP-based A1A or CW transceiver, it should not be too difficult to design adaptive keying shaping methods so that the ratios between "occupied" and "necessary" bandwidths are kept at a minimum.

The "bottom line" of this discussion may be that the amateur radio manufacturers should look into specification and design practices that the professionals accepted decades ago.

73/

Karl-Arne
SM0AOM

Bandwidth versus Keying Speed

by K5MC on May 31, 2007 Mail this to a friend!

AB0WR: You used a square wave for your analysis. Shouldn't you be using a gate function instead? Use of a square wave assumes positive and negative peaks imposed as modulation on the carrier. A gate function would just be turning the carrier on and off which is what CW does.

K5MC: Now suppose our keying waveform is changed from the very good one described above to one having zero rise and fall times. "Square-wave" keying is quite a bit easier to examine mathematically than sinusoidal keying and it will yield a "worst-case" value of power bandwidth for a given speed. (Quoted from my article directly under Figure 1)

Tim, I apologize for the confusion. I thought everyone would understand that the "square-wave" keying waveform I described in my article was similar to my "sinusoidal" keying waveform shown in Figure 1 except that the rise and fall times of my "square-wave" keying waveform are zero. What I have been calling "square-wave" keying from the very beginning is exactly the same waveform as the classic rectangular (or gate) pulse train (as first mentioned by AB0WR) of constant amplitude (1 V in my calculations) with a pulse width "a" and a pulse period T (and a/T = 0.50 at both 2.4 wpm and 30 wpm). In other words, my "square-wave" keying waveform is equal to 1 V 50% of the time and it is equal to 0 V the other 50% of the time. (In hindsight I should have included a second figure in my article showing my "square-wave" keying waveform.)

As I posted earlier, the trigonometric form of the Fourier series for the 2.4-wpm and 30-wpm "square-wave" keying waveforms are given by s1(t) and s2(t), respectively, as follows:

s1(t) = 0.5 + (2/pi)[cos(2 pi t) - 1/3 cos(6 pi t) + 1/5 cos(10 pi t) - . . . ] volts

s2(t) = 0.5 + (2/pi)[cos(25 pi t) - 1/3 cos(75 pi t) + 1/5 cos(125 pi t) - . . . ] volts

Compare the two equations above with the "classic" square pulse periodic signal s3(t) that has an amplitude of plus or minus 0.5 V (therefore zero average value) with a fundamental frequency of 1 Hz:

s3(t) = (2/pi)[cos(2 pi t) - 1/3 cos(6 pi t) + 1/5 cos(10 pi t) - 1/7 cos(14 pi t) + . . . ] volts

We note that s3(t) has zero average (DC) value because it only includes harmonically-related cosine terms and the average value of each cosine wave is zero. However, both s1(t) and s2(t) include the factor 0.5; in other words, the average or DC value of s1(t) and s2(t) is 0.5 V. Notice that s1(t) = 0.5 + s3(t). That is, my 2.4-wpm "square-wave" keying waveform is simply s3(t) with a constant 0.5 V term added to it. To change from 2.4 wpm to 30 wpm, each of the frequency coefficients in the cosine terms in s1(t) are multiplied by 12.5 to obtain the Fourier series for the 30-wpm "square-wave" keying waveform because 30/2.4 is equal to 12.5.

By the way, I promise you that if you properly set up a waveform generator to produce a square pulse periodic signal having an amplitude of plus or minus 0.5 V and a period of 1 second (by looking, for example, at the signal in the time-domain on an oscilloscope), you will see the discrete-line (magnitude) spectrum on a modern spectrum analyzer as implied by the Fourier series for s3(t) above. That is, the spectrum analyzer will display the same amplitude values (within experimental error) at the proper frequencies as indicated in the s3(t) equation. For example, if the vertical display of the analyzer is set on a linear scale, the amplitude of the seventh harmonic component (7 Hz) will be only 1/7 that of the fundamental frequency component (1 Hz). If the vertical display of the analyzer is set on a log scale rather than a linear scale, then you will see the following relationship between the fundamental and seventh harmonic components:

20 log (1/7) = -16.9 dB

That is, the amplitude of the seventh harmonic is 16.9 dB "down" from the fundamental frequency component.

How do I know all of this? Because I have done it in the laboratory where I teach! For example, I frequently use an HP 3561A "Dynamic Signal Analyzer" in our electric machinery/power systems lab to examine the spectrum of such signals as the exciting current drawn by an unloaded power transformer. I have also used the spectrum analyzer capabilities of the HP 8920A in the communications lab at my school. As I said in one of my earlier posts, spectrum analyzers are based upon Fourier analysis (Fourier series, Fourier transforms, FFTs, etc.). It helps if the person using the spectrum analyzer has a good understanding of Fourier analysis!

Now if you believe that the equations for s1(t) and s2(t) above are correct for my "square-wave" keying waveforms at 2.4 wpm and 30 wpm, then it should be fairly easy for me to convince you the rest of the way! The CW signal that results from these keying waveforms is found by multiplying either s1(t) or s2(t) by an everlasting sinusoid. For example, the 2.4-wpm CW signal as a function of time is

s1(t) * cos (2 pi fc t) where fc is the carrier frequency.

We can now use fairly simple algebra and trigonometry to determine the frequency-domain components of this CW signal. The frequency components of this 2.4-wpm CW signal will include the carrier term at the frequency fc, the first pair of sidebands located plus and minus 1 Hz from the carrier, the second pair of sidebands (which correspond to the third harmonic component in s1(t)) located plus and minus 3 Hz from the carrier, and so forth. The frequency components of the 30-wpm CW signal will include the carrier at fc, the first pair of sidebands located plus and minus 12.5 Hz from the carrier, the second pair of sidebands (which correspond to the third harmonic component in s2(t)) located plus and minus 25 Hz from the carrier, and so forth.

Finally, the average powers for the various frequency components are calculated as I described in my comments posted late last night and the definition of power bandwidth gives you the final results for the "square-wave" keying waveform that I included in my article.

In closing this round of comments, let me say a few things that perhaps I should have emphasized more in my article. I used the example of "square-wave" keying to further illustrate the point that the power bandwidth does vary with sending speed, along with the fact that the rise/fall characteristics of the keying waveform are also very definitely a factor. There is no doubt that the key clicks that would be generated by such a keying waveform would be horrendous. The FCC addresses the problem of key clicks in Part 97 by such statements as "Emissions outside the necessary bandwidth must not cause splatter or keyclick interference to operations on adjacent frequencies." The FCC understands (just as I do) that the definition of occupied (or power) bandwidth does not adequately address the problem of key clicks caused by improper wave shaping. I've repeatedly said that the definition of occupied bandwidth only means exactly what it says! However, I think it would be nice if hams have some appreciation of how electrical engineers at the FCC (and other electrical engineers, whether in academia or in the "real world") calculate or measure the "occupied" or "power" bandwidth of a CW signal. To be honest, at times the technical comments posted in this thread have made me cringe at the idea of amateur radio in this country changing from the current "mode" approach to a "bandwidth" approach.

73, K5MC

RE: Bandwidth versus Keying Speed

by AD5X on May 31, 2007 Mail this to a friend!

"Rather than telling us we are wrong you would be better advised to figure out why the CW signal from a 751a does not match what theory predicts."

Seems backwards to me. During my engineering career, I found that when I measured something other than what theory predicted, 99% of the time it was because the theoretical model was incorrect. You can certainly question the validity of the measurements, but you should also question the validity of the model.

Phil - AD5X

RE: Bandwidth versus Keying Speed

by WR8Y on May 31, 2007 Mail this to a friend!

W8JI said:
""""Since I can't seem to get the theorists to actually measure the bandwidth of a transmitter, I've measured it for them.""""

I was wondering when someone would throw the calculators and books away and actually MEASURE SOMETHING!

W8JI said:
""""Please review this new page on my website:

http://www.w8ji.com/occupied_bw_of_cw.htm

These measurements were made with currently certified equipment that directly measures occupied bandwidth.

CW speed does NOT affect the occupied BW of a CW transmitter unless it changes the rising and falling edges of the waveform.

73 Tom """"

Awwwwwwwwwwwwwwwwww, ya beat me to it. I went to the trouble of dragging a radio and keyer into the shop and trying this was an RF Spectrum Analyzer. It was hard to make out anything below 1 kHz of width with our equipment - but I saw no difference between 5 and 40 WPM.

So, I then used the narrow filter in the TS830 to listen to another rig as I adjusted the speed - and the TS830's filters showed no difference in occupied bandwidth again, from 5 to 40 wpm.

Again, to quote you:
""""CW speed does NOT affect the occupied BW of a CW transmitter unless it changes the rising and falling edges of the waveform. """"

Exactly. But I think that egos and the willingness to argue are what this thread is about - not taking actual measurments!

Makr

RE: Bandwidth versus Keying Speed

by W8JI on May 31, 2007 Mail this to a friend!

WR8Y Mark,

Thanks for taking the time to make some actual measurements. Many people take a hard position with verifying through experiment they are actually correct.

It was suggested I check my 751A to see why it does not follow some rules some people are applying.

The problem is I have measured at least a dozen different models of radios and NONE of them follow their theory either, and I know other people who have done the same.

I wonder what could really be wrong when measured results by multiple people on multiple pieces of gear using multiple methods consistantly do not match the prediction a few people present?

73 Tom

Bandwidth versus Keying Speed

by W1YW on May 31, 2007 Mail this to a friend!

If the measurement does not match the prediction of well-known physics, hoary in origins, then either the measurement is in error or there are other factors being measured beyond what the PHYSICS states.

There is nothing wrong with the physics. Mickey knows what he is talking about.

73,
Chip W1YW

RE: Bandwidth versus Keying Speed

by AB0WR on May 31, 2007 Mail this to a friend!

ad5x:"Seems backwards to me. During my engineering career, I found that when I measured something other than what theory predicted, 99% of the time it was because the theoretical model was incorrect. You can certainly question the validity of the measurements, but you should also question the validity of the model."

Please, this is nonsense. From designing trunk relays for 756 private branch exchanges to broadcast circuits using v-type amplifiers and a multiplicity of telephone cable types, when the circuit didn't behave the way the models showed it could be traced back to the physical implementation. From flat spring relays whose timings were out of spec to to improper options in the amps to cables contaminated with water, it wasn't the models that were wrong. If what you build doesn't do what your math say it should and your math follows established process then it can hardly be the model that is wrong.

The mathematics of the Fourier transforms, square waves, etc as well as modulation theory have been known since the turn of the 20th century.

If the physical implementation doesn't match the model then you need to look at the physical model.

Look at it this way. K5MC calculated the bandwidth of a 12.5hz signal to be about 525hz. That correlates *VERY* closely with the 490hz W8JI found for a 10hz signal.

The reason the bandwidth for the faster signals doesn't increase is because the system bandwidth is physically limited. The bandwidth of a 40hz signal should be much, much greater than a 12.5hz signal. Yet W8JI measures it to be about the same. Using the relationship that bandwidth * rise-time = pi that indicates a 40hz keying speed has the rise time of pi/bandwidth = 6.2 millisec for a 751a transmitter.

The slope of the waveform isn't what generates the harmonics, it is what *LIMITS* the number of harmonics the system can transmit. That seems to be what these displays are showing. Saying that slope of the waveform is what generates the harmonics is just plain incorrect. Saying that keying speed doesn't change the bandwidth is only correct for a bandwidth limited system where the input bandwidths are greater than the limited bandwidth the system can transmit.

What would be very interesting is to see what w8ji would measure for a 2 hz signal or even a 1hz signal. If the bandwidth still comes out to 500hz *then* it would be interesting to start digging into the 751a to see why.

WR8Y:"It was hard to make out anything below 1 kHz of width with our equipment - but I saw no difference between 5 and 40 WPM."

If it was hard to make out anything below 1000hz of width then how did you expect to make out something as small as a 10hz difference in the harmonic lobes? Considering that a 5wpm signal has harmonics at 6hz, 10hz, 14hz, etc. and a 40wpm signal has harmonics at 50hz, 83hz, 116hz, etc) seeing a 4hz or even a 33 hz difference between the lobes would seem to be a problem if it is hard to see anything below 1000hz width. Does your analyzer really have markings allowing reading down to the thousandths?

ALL:
I guess I would like for someone to explain to me just exactly how the math works that causes a 1hz square wave to have a bandwidth of 500hz when it is sent through a transmitter. You are saying that it does yet I have yet to see anyone explain it. I have the math to show that a rise time LIMITS bandwidth, it doesn't *cause* it. I don't have the math to show how a 1hz square wave can generate enough sidebands (at least out to the 249th harmonic) to have a 500hz bandwidth.

There are apparently enough people on here that believe this that *someone*, SOMEONE should be able to explain it mathematically.

And again, AGAIN, please don't tell me that the value of the slope of a square wave generates harmonics, it doesn't. It LIMITS the number of harmonics, it doesn't generate them! Anyone who wants the math showing this just let me know. I'll be glad to send it to you. Or you can go to http://zone.ni.com/devzone/cda/tut/p/id/2709, http://www.tek.com/Measurement/App_Notes/Technical_Briefs/bw_rt/55_18024_0.pdf, or even http://en.wikipedia.org/wiki/Rise_time for a description of how rise time indicates a bandwidth limited system.

So, is there anyone on here who can do more than quote the statement that "the slope of the rise time generates the bandwidth"? Is there anyone who can show the math for how a 1hz square wave can generate a 500hz bandwidth?

tim ab0wr

Bandwidth versus Keying Speed

by K5MC on May 31, 2007 Mail this to a friend!

Below is an email I received from W7AY, along with my initial response. As long as Chen is OK with my posting his email messages to eham, I will keep everyone informed.

73, K5MC

Chen W7AY,

Thanks very much for your message. I will definitely post your message below along with my return comments.

The fact that you studied under Bracewell certainly gets my attention! I will try to find a copy of Bracewell's book in my school's library. Unfortunately, I've never obtained a personal copy of it.

While I'm trying to do that and look over your details below, please let me know exactly what your definition of bandwidth is. At one point you refer to the "effective" bandwidth. Please let me know in a precise way what you mean by the "effective" bandwidth.

In referring to your J2A signal below, you say that "the effective bandwidth does not change by much either." Can you be more specific (how much more as
a function of speed?) and, again, what is your definition of "effective" bandwidth? I am particularly interested if you can tell me the values of the 99% power bandwidth for your J2A signal at different speeds. (BTW, the keying waveforms in my article employed proportional spacing at both 2.4 wpm and 30 wpm. I'm assuming that your J2A signal does likewise.) From an English language point of view, the fact that you admit that the "effective" bandwidth does increase with speed (even if not "by much"), then it appears to me that you must also say that the sending speed is a factor in determining the "effective" bandwidth of your J2A signal.

Turning to my examples now in my eham article in which I calculated the 99.1% power bandwidth, do you disagree with any of my numerical results? That is, based upon the keying waveforms that I assumed, along with the
definition of "power" bandwidth that I quoted from Couch's textbook (which is essentially equivalent to the FCC's definition of "occupied" bandwidth), do you disagree with my results?

I'm looking forward to your response.

73, Mickey K5MC

----- Original Message -----
From: "Kok Chen" <chen@mac.com>
To: <k5mc@arrl.net>
Sent: Thursday, May 31, 2007 3:29 PM
Subject: Re: Bandwidth versus Keying Speed

> Hi Mickey,
>
> I am replying to your article by email rather than on eham for various
> reasons...
>
> Imagine that we build a wave-shaped stream of dits from scratch.
>
> Let's start with a "prototype" wave-shaped pulse.
>
> The pulse can be constructed from a single square pulse that is convolved
> with a window function (which is narrower than the square pulse).
>
> From the Fourier Duality theorem, the Fourier transform of the shaped
> pulse must therefore be the product of the Fourier transform of the
> square pulse and the Fourier transform of the window.
>
> I.e.,
>
> F( p*w ) = F( p ) F (w )
>
> where * is the convolution operator, and F() is the Fourier transform, p
> is the time waveform of a single square pulse and w is the time waveform
> of the wave-shaping window.
>
> The transform of the single pulse is of course a sin(x)/x function.
>
> I will use a Gaussian window (since its Fourier transform is also a
> Gaussian and it is easier to describe things).
>
> So, the transform of the resultant shaped pulse is the product of a
> Gaussian and a sin(x)/x function.
>
> Notice that for any smooth function that you use as a window, it's
> Fourier transform will fall faster than the envelope of the sin(x)/s
> function -- i.e., for a reasonable wave-shaping, the Fourier transform of
> the Gaussian falls off faster than 1/f where f is frequency.
>
> Ergo, it is the wave-shaping function that is what governs the bandwidth
> of the shaped pulse, it is not the pulse width.
>
> Now, a sequence of dits is just a convolution of a comb of Dirac deltas
> with the fundamental shaped pulse.
>
> In his classic Fourier Transform book, Bracewell had called a comb of
> Dirac deltas to be a "Shah" function and showed that the Fourier
> transform of a Shah is just another Shah function (i.e., the Gaussian is
> not the only function that is its own transform).
>
> (I was fortunate to have Bracewell as a professor in both a Fourier
> Transform and an Interferometry grad class back at Stanford many decades
> ago).
>
> Again, from the Fourier Duality statement, the spectrum of a series of
> dits is just a product of the Fourier transform of the prototype shaped
> pusle and a comb in the frequency domain. Again, the spectrum of the
> "window" predominates and knocks out all the higher frequency components
> of the comb.
>
> I.e., as a first order approximation, the envelope of the spectrum of a
> series of dits is just the Fourier transform of the wave shaping window.
>
> In this sense, W8JI is correct in stating that it is rise and fall times
> that matters (i.e., it is the window function that matters) since the
> rise and fall times are defined by the window shape as I describe here.
>
> I have implemented CW transmission by using J2A modulation (instead of
> using A1A modulation) in a software modem for the MacOS. For the
> waveshaping function, I had used a modified Blackman window. You can see
> the spectrum of a series of dits here:
>
> http://homepage.mac.com/chen/cocoaModemPage/UsersManual/cwManual/
> index.html
>
> Just scroll down to Figure 5.
>
> As theory predicts, by using the constant Blackman window (i.e., rise
> time and fall time left invarient), what happens to the spectrum as you
> change keying speed is that the lobes under the envelope change spacings,
> but the envelope itself does not change -- and thus the effective
> bandwidth does not change by much either. When you increase the keying
> speed, the lobes under the envelope will be wider spaced (since in the
> time domain they become closer to one another -- another factoid from
> Fourier theory). Until your keying speed becomes so fast that there is
> only a single lobe under the window's envelope -- at that point the Morse
> will sound very "soft" to the ear (but with Blackman windows, will not
> "ring.").
>
> Please feel free to post this to eham if you wish.
>
> Vy 73
> Chen, W7AY

Bandwidth versus Keying Speed

by K5MC on May 31, 2007 Mail this to a friend!

AB0WR: Is there anyone who can show the math for how a 1hz square wave can generate a 500hz bandwidth?

Tim, I admit that I'm getting pretty confused trying to keep up with the comments from everyone. Can you give me a little more background on what you are talking about here?

73, K5MC

Bandwidth versus Keying Speed

by K5MC on June 1, 2007 Mail this to a friend!

W8JI: See: http://www.w8ji.com/occupied_bw_of_cw.htm

Tom, I've looked at your spectrum plots. I have some questions and comments regarding your results.

1. Did you also use an oscilloscope and see the actual envelopes of the CW signals (the exact same CW signals as fed into your spectrum analyzer) as functions of time? If you didn't, I think you need to. Otherwise, you are assuming too much.

2. Based upon your oscilloscope observations, did your Icom 751A actually send dits uniformly at the rate of 40 per second? That's 96 wpm! I find it pretty hard to believe that an unmodified 751A can achieve that speed without some serious shortcomings in the output signal. I also wouldn't be too surprised if it had some difficulty when keyed at 25 dits per second (60 wpm).

3. If you send a uniform string of dits for a "long" time, then the magnitude spectrum that you would have to see on an ideal analyzer would be essentially discrete because such a signal would be, for all practical terms, a periodic signal. It's true that it would take an infinite amount of time to achieve a perfect discrete line spectrum, but the fact that your spectrum plots are clearly not discrete and the spectrum plots for the signals in my article are discrete means that we are comparing, to some degree at least, apples and oranges.

4. Continuing with my comments from #3, can you make some adjustments on your particular analyzer so that your display will be more like what it should be for a long string of dits? I see that you are sweeping over an identical range of 3 kHz for all three speeds. If it's possible on your particular analyzer, I think you need to reduce the frequency span below 3 kHz, particularly at the slower speeds. (However, I've got a feeling that 3 kHz might be the smallest span your analyzer allows, at least at 3.5 MHz.)

5. Since the frequency span of your analyzer is set to 3 kHz, and the 99% power bandwidth at 24 wpm is probably around 150 Hz for the 751A (assuming it has reasonably good keying characteristics), your span is well over 10 times what is needs to be to capture essentially all of the signal's spectrum. If you could decrease your span to 150 Hz or so, for example, you would see a spectrum that is much closer to what it really is (essentially a discrete line spectrum). As your analyzer's frequency span increases, its spectrum resolution decreases and that is a major problem in your results.

73, K5MC

RE: Bandwidth versus Keying Speed

by W8JI on June 1, 2007 Mail this to a friend!

by K5MC on June 1, 2007

<<1. Did you also use an oscilloscope and see the actual envelopes of the CW signals (the exact same CW signals as fed into your spectrum analyzer) as functions of time? If you didn't, I think you need to. Otherwise, you are assuming too much.>>

Of course I've looked at the envelope! Looking at the envelope really doesn't yield much useful information other than when major changes in envelope shape occur. The things that cause adjacent channel problems can be very subtile, as you know.

The 751A starts to seriously modify the envelope at about 55 dits per second, but the only change at 40 dits per second is a small decrease in weight. The off time is a bit longer compared to on time, but the dot rate does NOT change and neither does peak envelope power.

I intentionally stayed well below the radio's speed limit.

<<2. Based upon your oscilloscope observations, did your Icom 751A actually send dits uniformly at the rate of 40 per second? That's 96 wpm! I find it pretty hard to believe that an unmodified 751A can achieve that speed without some serious shortcomings in the output signal. I also wouldn't be too surprised if it had some difficulty when keyed at 25 dits per second (60 wpm). >>

The 751A has a pretty fast rise and fall, and yes....it has no problems at all. It's my opinion radio manufacturers are crazy with speed limits and that's why keyclicks are such an issue. The bandwidth is horrable at any speed compared to necessary bandwidth.

<<3. If you send a uniform string of dits for a "long" time, then the magnitude spectrum that you would have to see on an ideal analyzer would be essentially discrete because such a signal would be, for all practical terms, a periodic signal. It's true that it would take an infinite amount of time to achieve a perfect discrete line spectrum, but the fact that your spectrum plots are clearly not discrete and the spectrum plots for the signals in my article are discrete means that we are comparing, to some degree at least, apples and oranges. >>

We are comparing what you predict and what actually happens Mickey, and respectfully that indeed is apples and oranges.

<<4. Continuing with my comments from #3, can you make some adjustments on your particular analyzer so that your display will be more like what it should be for a long string of dits? I see that you are sweeping over an identical range of 3 kHz for all three speeds. If it's possible on your particular analyzer, I think you need to reduce the frequency span below 3 kHz, particularly at the slower speeds. (However, I've got a feeling that 3 kHz might be the smallest span your analyzer allows, at least at 3.5 MHz.) >>

That setting depends on the assigned channel bandwidth, although I can manually override its control of span. The channel bandwidth really should be wide enough to see all the sidebands of the transmitter, and in this case I set it at 1kHz.

The analyzer BW is 10Hz, naturally requiring a very long sweep time. If I span 500Hz, the results are virtually identical. I've done that.

I think you are looking for the periodic frequency domain ripples that are predicted, and they do indeed occur IF the analyzer sweep is triggered in exact sync with the dot generator. Of course that does not change the occupied bandwidth, it remains essentially the same.

The only way I can change the occupied BW more than a few Hz from the ~500 Hz displayed is to change the rise and fall characteristics, not the speed.

<<5. Since the frequency span of your analyzer is set to 3 kHz, and the 99% power bandwidth at 24 wpm is probably around 150 Hz for the 751A (assuming it has reasonably good keying characteristics), your span is well over 10 times what is needs to be to capture essentially all of the signal's spectrum. If you could decrease your span to 150 Hz or so, for example, you would see a spectrum that is much closer to what it really is (essentially a discrete line spectrum). As your analyzer's frequency span increases, its spectrum resolution decreases and that is a major problem in your results. >>

Well, it has ten Hz resolution bandwidth now. Exactly how narrow does it have to be to display a 500Hz wide signal with reasonable accuracy? In my experience 2% of the transmitter's BW is pretty damn good.

I just let a 500Hz span with 10Hz selectivity run, and guess what? The same radio had 500Hz occupied bandwidth.

I really don't see what the problem is Mickey. I can duplicate the results using a Selective Level Meter that has peak power averaging, and a regular CW receiver with narrow filters pretty much agrees.

This pattern repeats from transmitter to transmitter. Some clicky Yaesus and a Ten Tec Omni C I tested have over 1kHz OBW and the bandwidth repeats at various speeds unless the speed affects the rise and fall shape or duration. They bother people on the air at ANY reasonable speed, I can hear them the same distance off frequency at any reasonable speed. They all have different bandwidths when the rises and falls are different times and shapes, but they all share in common the single fact bandwidth does not change substantially with speed.

You were openly critical of W9CF's abilities, but the fact is every single measurement I've ever made using good careful methods agrees 100% with W9CF and disagrees with Tim and your predictions.

Not only that some very experienced communications systems engineers, people I consider the top in the field (I've met about 5 people like that in the past 40 years) disagee with the way you and Tim are predicting bandwidth and agree with W9CF and others.

As a matter of fact if I syncronize the sweep trigger points with the dot generator time base, the picture on the analyzer looks exactly like the frequency domain Kevin predicts. This does not change the OBW that is measured, it simply changes the picture to make nulls and peaks appear.

If everyone else is wrong, why do direct measurements of at least a dozen rigs using multiple methods disagree with you and Tim? Are the other people AND the measurements all in error? If so why don't the actual systems, the receivers and transmitters, behave the way you predict on the air?

Why can I hear a FT1000MP or IC775DSP about the same distance away regardless of keying speeds? Why don't the clicks suddenly move in closer to the carrier frequency when only the speed is reduced?

73 Tom

RE: Bandwidth versus Keying Speed

by AD5X on June 1, 2007 Mail this to a friend!

ad5x:"Seems backwards to me. During my engineering career, I found that when I measured something other than what theory predicted, 99% of the time it was because the theoretical model was incorrect. You can certainly question the validity of the measurements, but you should also question the validity of the model."

AB0WR: "Please, this is nonsense. From designing trunk relays for 756 private branch exchanges to broadcast circuits using v-type amplifiers and a multiplicity of telephone cable types, when the circuit didn't behave the way the models showed it could be traced back to the physical implementation. From flat spring relays whose timings were out of spec to to improper options in the amps to cables contaminated with water, it wasn't the models that were wrong. If what you build doesn't do what your math say it should and your math follows established process then it can hardly be the model that is wrong."

I'm sorry, but I disagree. You must consider that either the model OR the measurement (or both) can be the problem. My experience is with QAM digital microwave communications designs (4-256 QAM) and DWDM lightwave designs operating at 10gb/s. We often had advanced technology groups of engineers working to try to resolve the differences between our measurements and the models - and the problems were almost always with the models. Don't get me wrong - errors were also made in measurements. But normally it was the accuracy of the models that was at issue. Over time our models would get better, but then we would introduce more complex modulation systems, higher data rates, more power, etc and find that there were new unknowns that made the models inaccurate. When there is a discrepancy between measurement and theory, you must look at both and try to resolve the discrepancy. You have to assume that either could be wrong. Automatically assuming that one is correct and the other isn't can lead you into months of effort working on the wrong thing. I've seen this too many times.

I am certainly enjoying this thread. Who knows, maybe we'll all learn something.

Phil - AD5X

Bandwidth versus Keying Speed

by W1YW on June 1, 2007 Mail this to a friend!

I'm sorry, but I disagree. You must consider that either the model OR the measurement (or both) can be the problem.

------------------------------

And again, you have those with the experience to disagree with this comment.

So let's push it further. Mickey has given a nice, simple (but elegant) analysis that establishes how extant physics reveals certain inherent bandwidth issues that relate to speed of transmission. He is NOT presenting this as a basis for testing the validity of the PHYSICS--no; he is presenting it as a guide for what to look for in APPLICATIONS.

Notice it is NOT presented as a PREDICTION of a THEORY. Why? Because the analysis includes no new physics.

Given that state, if you DON'T masure what Mickey SHOWS, then there are either ERRORS or UNCERTAINTIES in the measurement---or-- there are additional factors in the EQUIPMENT BEING MEASURED that go beyond the analysis being presented. In the latter, the ASSUMPTION being made is that no OTHER factors are affecting the MEASUREMENT.

IMO, hams would be better served for themselves if they used Mickey's analysis to understand the limits of measurement, and the transfer functions inherent to their equipment. That itself is interesting.

73,
Chip W1YW

RE: Bandwidth versus Keying Speed

by WR8Y on June 1, 2007 Mail this to a friend!

WR8Y:"It was hard to make out anything below 1 kHz of width with our equipment - but I saw no difference between 5 and 40 WPM."

AB0WR: "If it was hard to make out anything below 1000hz of width then how did you expect to make out something as small as a 10hz difference in the harmonic lobes? Considering that a 5wpm signal has harmonics at 6hz, 10hz, 14hz, etc. and a 40wpm signal has harmonics at 50hz, 83hz, 116hz, etc) seeing a 4hz or even a 33 hz difference between the lobes would seem to be a problem if it is hard to see anything below 1000hz width. Does your analyzer really have markings allowing reading down to the thousandths?"

Did you read the rest of my post? I then resorted to using the 170 hz filter in the 830 while listing to a stream of dits - adjusting the speed from 5 WPM to 40 WPM. NO BANDWIDTH CHANGE!

RE: Bandwidth versus Keying Speed

by W9AC on June 1, 2007 Mail this to a friend!

> http://www.w8ji.com/occupied_bw_of_cw.htm

If a picture is worth a thousand words, a well-documented spectrum plot is worth ten thousand.

Well done.

If Mickey's theory were correct, we should see at least *some* relevant level of increasing bandwidth as a function dits per unit of time, assuming all other variables remain constant as you have ensured -- even if (arguably) the spectrum analyzer mechanics do not completely track with mathematics.

Tom, one final test might be to temporarily disable ALC on the 751A to rule out the mid-speed ALC anomaly, just to satisfy any doubters.

RE: Bandwidth versus Keying Speed

by AB0WR on June 1, 2007 Mail this to a friend!

<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<

w8ji:"If everyone else is wrong, why do direct measurements of at least a dozen rigs using multiple methods disagree with you and Tim? Are the other people AND the measurements all in error? If so why don't the actual systems, the receivers and transmitters, behave the way you predict on the air? "

w9ac:"> http://www.w8ji.com/occupied_bw_of_cw.htm

If a picture is worth a thousand words, a well-documented spectrum plot is worth ten thousand.

Well done.

If Mickey's theory were correct, we should see at least *some* relevant level of increasing bandwidth as a function dits per unit of time, assuming all other variables remain constant as you have ensured -- even if (arguably) the spectrum analyzer mechanics do not completely track with mathematics.

Tom, one final test might be to temporarily disable ALC on the 751A to rule out the mid-speed ALC anomaly, just to satisfy any doubters. "

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

If you two would actually read what is being posted this is what you would find:

A square wave with a rise time of 5ms to 6ms indicates a system with a MAXIMUM bandwidth of 523hz 628hz. The rise time doesn't *generate* this bandwidth, it is a response to an *INPUT* signal. A signal with a smaller bandwidth will pass through relatively unaffected. A signal with a wider bandwidth will be limited to the system bandwidth while passing through the system.

You are shoving square waves at 10hz to 40hz, which should have bandwidths of 500hz and *GREATER*, into a bandwidth limited system (around 500hz to 600hz) and then saying that the keying speed doesn't determine the bandwidth of the keyed signal.

You are then extrapolating that to saying that *ANY* keying speed will have a 500hz bandwidth.

Do you see the disconnect? What you should be saying is that the system response limits the output response. Instead, you are trying to convince everyone that it limits the input.

If you put a keying speed of 1hz to 5hz into the system, both of which will have bandwidths of *less* than 500hz, do you really expect to still see a 500hz bandwidth output from the 751a?

If you want to show us something, show us how a string of dits at 2hz will generate a signal with a bandwidth of 500hz. Show us the math that shows that a 2hz square wave has a bandwidth of 500hz.

Mickey's analysis *is* correct. If you don't understand the inputs *to* the system you will never understand the outputs *from* the system. That fact that you have rise times on the outputs indicates that you have a bandwidth limited system reponse. If the input bandwidth is wider than the system response bandwidth you get exactly what Tom is showing in his displays. You have extrapolated that into saying that the system response will *ALWAYS* be that wide no matter what the input happens to be. Yet your displays only include inputs that are *wider* than the system response. Therefore you have not provided a full system test.

<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
w8ji:"If everyone else is wrong, why do direct measurements of at least a dozen rigs using multiple methods disagree with you and Tim? Are the other people AND the measurements all in error? If so why don't the actual systems, the receivers and transmitters, behave the way you predict on the air?"
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

Do they all have 500hz bandwidth outputs regardless of the input? Do they have 500hz bandwidths at keying speeds *LESS* than 10hz? You haven't shown us that yet. You are measuring the outputs of a bandwidth limited system using input responses with bandwidths equal to or greater than the system response and then are saying that the output response you see will *ALWAYS* be what you see regardless of the input. Show us that a system input at 2hz results in a 500hz bandwidth output and then we can actually discuss why that is.

tim ab0wr

RE: Bandwidth versus Keying Speed

by W8JI on June 1, 2007 Mail this to a friend!

W9AC Paul,

I've watched the waveforms on the scope and even measured a Viking Valiant and a Globe Scout of all things.

It absolutely is not an instrument artifact since I've used multiple measurement devices.

It behaves this way on a simple real receiver.

It behaves this way on a Selective Level Meter.

It isn't ALC because it behaves this way on radios without ALC and at any power setting on radios with ALC. As a matter of fact my FT1000MKV's were sometimes set so the ALC wasn't active. Didn't make a difference in them because the hold time was long enough to stabilize the gain.

73 Tom

RE: Bandwidth versus Keying Speed

by AB0WR on June 1, 2007 Mail this to a friend!

k5mc:"To be honest, at times the technical comments posted in this thread have made me cringe at the idea of amateur radio in this country changing from the current "mode" approach to a "bandwidth" approach. "

Me too. Using w8ji's and w9ac's claim that a cw keying waveform always has a 500hz bandwidth, regardless of how slow the keying speed is, and overlaying this on the ARRL's bandwidth segmentation plan, CW would always be restricted from using the narrow, 200hz bandwidth portion of the band. It would have to stay in the 1.5khz bandwidth portion and compete with all of the wider digital modes.

I would also like to point out that the analysis you received from the other ham speaking of the convolution of a comb input and a shaped window in the time domain is still nothing more than the classis Output(w) = Input(w)System-response(w) form of equation in the frequency domain. If the Input(w) is a true shaped comb input then that indicates a very wide bandwidth input (infinite perhaps?)together with a system response that is bandwidth limited. Of course the output response will be bandwidth limited. That is really all his analysis is saying.

On the other hand, if the Input(w) is a limited bandwidth signal that is smaller than the System-response(w) window, the System-response(w) window will have no affect at all on the Output(w).

Too many people here are trying to say that since the Output(w) response is bandwidth limited by the System-response(w) that the Output(w) response will *always* be the same bandwidth. They are ignoring the cases where the Input(w) signal has a lower bandwidth than the System-response(w) transfer function. It would seem that they are mistaking the system response bandwidth for both the input signal *and* the output signal and saying that they are all the same thing. That just isn't true.

Your (and the FCC's) definintion of the signal bandwidth puts a restriction of the bandwidth to be considered, even on a square wave with an infinite number (albeit progressively weaker) of harmonics. If that restriction results in the definition of a system input that is narrower than the system response function, the input should be seen in all its glory in the output, e.g. your analysis for a keying wave of 1hz speed. If a 1hz square wave keying waveform has a 99.1% power bandwidth of 42hz it should pass through a system with a 500hz system bandwidth response relatively unaffected. On the other hand, an input with a 525hz bandwidth (your 12.5hz square wave keying waveform) *will* be bandwidth limited to 500hz by the system response bandwidth window.

I would still like to see a spectrum analyzer display from Tom that shows the output bandwidth for a 1hz keying waveform. That would show the output response from an input signal that is narrower than the system response function. It will be very interesting to see if that would still show a 500hz bandwidth for the output response.

tim ab0wr

RE: Bandwidth versus Keying Speed

by AB0WR on June 1, 2007 Mail this to a friend!

w9ac:"If Mickey's theory were correct, we should see at least *some* relevant level of increasing bandwidth as a function dits per unit of time, assuming all other variables remain constant as you have ensured -- even if (arguably) the spectrum analyzer mechanics do not completely track with mathematics. "

How do you expect the Output response to vary in bandwidth if the Input signal always has a bandwidth wider than the System-response bandwidth?

output(t) <-> Output(w)

Output(w) = Input(w)System(w)

If Input(w) is always wider than System(w) why would you expect Output(w) to change in any way?

That's really all Tom's displays are showing us - an Output response from Input signals with a wider bandwidth than the system can pass. Of course they will always show the same bandwidth -- that of the system response.

How do you extrapolate this to also claiming that Input signals with bandwidths less than the System bandwidth will also cause Output responses equal to the System bandwidth?

tim ab0wr

RE: Bandwidth versus Keying Speed

by AB0WR on June 1, 2007 Mail this to a friend!

wr8y:"Did you read the rest of my post? I then resorted to using the 170 hz filter in the 830 while listing to a stream of dits - adjusting the speed from 5 WPM to 40 WPM. NO BANDWIDTH CHANGE!"

Exactly what did you expect to hear that would indicate a change in bandwidth?

Did you expect the sound you heard to change from a tone to a buzz if the bandwidth changed?

If what you heard didn't change, exactly how does that relate to the bandwidth not changing?

I would be very interested in knowing exactly what you would expect a change in bandwidth to "sound" like? Can you define what the different bandwidths would sound like if they, in fact, *did* change?

tim ab0wr

RE: Bandwidth versus Keying Speed

by W8JI on June 1, 2007 Mail this to a friend!

Tim,

I know how to tune a receiver and listen to signal levels, and I know how to read an S meter.

I can hear the clcks exactly the same distance from the carrier at any speed so lon as I don't have a speed that changes the envelope rise and fall.

I know we are all uncomfortable with and disagreement that disputes what we believe, but that's just a fact we can't change.

Secondly, I reduced the speed to 4dps. That's pretty darned slow. The Occupied BW is 465 Hz. That's right in line with all the other measurements.

We can probably all look forever, but what Chen posted agrees with Kevin W9CF and many other people. Chen explains it well. Like W9CF, the measured data I get looks exactly like the predictions of W9CF and many other people.

Let me repost the eHam posting it so perhaps you can think about where you went wrong:

> Imagine that we build a wave-shaped stream of dits from scratch.
>
> Let's start with a "prototype" wave-shaped pulse.
>
> The pulse can be constructed from a single square pulse that is convolved
> with a window function (which is narrower than the square pulse).
>
> From the Fourier Duality theorem, the Fourier transform of the shaped
> pulse must therefore be the product of the Fourier transform of the
> square pulse and the Fourier transform of the window.
>
> I.e.,
>
> F( p*w ) = F( p ) F (w )
>
> where * is the convolution operator, and F() is the Fourier transform, p
> is the time waveform of a single square pulse and w is the time waveform
> of the wave-shaping window.
>
> The transform of the single pulse is of course a sin(x)/x function.
>
> I will use a Gaussian window (since its Fourier transform is also a
> Gaussian and it is easier to describe things).
>
> So, the transform of the resultant shaped pulse is the product of a
> Gaussian and a sin(x)/x function.
>
> Notice that for any smooth function that you use as a window, it's
> Fourier transform will fall faster than the envelope of the sin(x)/s
> function -- i.e., for a reasonable wave-shaping, the Fourier transform of
> the Gaussian falls off faster than 1/f where f is frequency.
>
> Ergo, it is the wave-shaping function that is what governs the bandwidth
> of the shaped pulse, it is not the pulse width.
>
> Now, a sequence of dits is just a convolution of a comb of Dirac deltas
> with the fundamental shaped pulse.
>
> In his classic Fourier Transform book, Bracewell had called a comb of
> Dirac deltas to be a "Shah" function and showed that the Fourier
> transform of a Shah is just another Shah function (i.e., the Gaussian is
> not the only function that is its own transform).
>
> (I was fortunate to have Bracewell as a professor in both a Fourier
> Transform and an Interferometry grad class back at Stanford many decades
> ago).
>
> Again, from the Fourier Duality statement, the spectrum of a series of
> dits is just a product of the Fourier transform of the prototype shaped
> pusle and a comb in the frequency domain. Again, the spectrum of the
> "window" predominates and knocks out all the higher frequency components
> of the comb.
>
> I.e., as a first order approximation, the envelope of the spectrum of a
> series of dits is just the Fourier transform of the wave shaping window.
>
> In this sense, W8JI is correct in stating that it is rise and fall times
> that matters (i.e., it is the window function that matters) since the
> rise and fall times are defined by the window shape as I describe here.
>
> I have implemented CW transmission by using J2A modulation (instead of
> using A1A modulation) in a software modem for the MacOS. For the
> waveshaping function, I had used a modified Blackman window. You can see
> the spectrum of a series of dits here:
>
> http://homepage.mac.com/chen/cocoaModemPage/UsersManual/cwManual/
> index.html
>
> Just scroll down to Figure 5.
>
> As theory predicts, by using the constant Blackman window (i.e., rise
> time and fall time left invarient), what happens to the spectrum as you
> change keying speed is that the lobes under the envelope change spacings,
> but the envelope itself does not change -- and thus the effective
> bandwidth does not change by much either. When you increase the keying
> speed, the lobes under the envelope will be wider spaced (since in the
> time domain they become closer to one another -- another factoid from
> Fourier theory). Until your keying speed becomes so fast that there is
> only a single lobe under the window's envelope -- at that point the Morse
> will sound very "soft" to the ear (but with Blackman windows, will not
> "ring.").
>
> Please feel free to post this to eham if you wish.
>
> Vy 73
> Chen, W7AY

What Chen describes above is precisely what appears when we look at the spectrum. Mickey and you are unfortunately not right on this one Tim.

73 Tom

Bandwidth versus Keying Speed

by K5MC on June 1, 2007 Mail this to a friend!

I hope everyone will find these email messages between W7AY and myself to be of interest.

BTW, I appreciate some of the recent comments posted, particularly by Chip W1YW and Tim AB0WR, very much. There have been times during this thread when I have felt very lonely in trying to get my points across!

73, K5MC

Chen,

Thanks very much for your quick reply. I believe the end of this discussion
(at least the first phase of it) is now in sight. I am very happy to hear
you say that the results I presented in my article are "perfectly sound."
Regarding the "optimum" shaping factor for the keying waveform, I have no
doubt that my "sinusoidal" choice is not the optimum as you say. I was
careful to say it was a "very good" one, but with hindsight I probably
should have merely said it was much better than no shaping at all. I was
clearly thinking of the performance of the sinusoidal shape versus what I
called "square-wave" keying when I made that statement in my article.

I chose the sinusoidal shape primarily because I knew I could readily find
its Fourier series coefficients "exactly" by evaluating the integrals by
hand and then double checking my results using EXCEL. As I have some spare
time this summer, I might look at the other waveshapes you have mentioned
(raised cosine, etc.) and see how much difference there is in the 99% power
bandwidth at a given speed. Right now my gut feeling is that there is "not
much" (say, maybe 125 Hz for the "best" versus my 150 Hz at 30 wpm.)

Yes, I would very much appreciate a copy of VE3NEA's QEX article. I don't
suscribe to it and apparently everyone who has commented during this thread
are either in the same boat or they've forgotten about that particular
article.

Concerning your comment about what the "practical guys" are seeing on their
analyzers, I'm afraid I do disagree with you on that assessment at this
point. I believe that W8JI is simply being mislead by his analyzer! If you
will look at the spectrum plots that he presents at
http://www.w8ji.com/occupied_bw_of_cw.htm I think you will see what I mean.
I'm afraid the resolution of his analyzer is simply not great enough at 3.5
MHz to really see what's going on with the keying sidebands generated by
such a narrow CW/ASK signal as that produced by a string of dits at 24 wpm.

I've got to start teaching some classes today, but I will also see if I can
screw together some lab equipment that will actually show the keying
sidebands and the resulting "power" or "occupied" bandwidth as I described
in my article.

Thanks again very much.

73, Mickey K5MC

----- Original Message -----
From: "Kok Chen" <chen@mac.com>
To: "mcoxk5mc" <mcoxk5mc@bellsouth.net>
Sent: Friday, June 01, 2007 12:19 AM
Subject: Re: Bandwidth versus Keying Speed

> Hi again, Mickey,
>
> Please read the part last answer (No, you are **NOT** wrong) first and
> then you can read the top, HI HI.
>
> On May 31, 2007, at 9:16 PM, mcoxk5mc wrote:
>> In referring to your J2A signal below, you say that "the effective
>> bandwidth does not change by much either." Can you be more specific
>> (how much more as a function of speed?) and, again, what is your
>> definition of "effective" bandwidth?
>
> Basically, the "envelope" of the spectrum does not change. The only
> thing that changes is the spacing of the lines within that envelope. So,
> as you change the keying rate, the distribution of the energy _under_ the
> spectral envelope changes, but is upper bounded by the envelope itself.
> I.e., the envelope (i.e., a single pulse) is the upper bound of how wide
> the spectrum is.
>
>> I am particularly interested if you can tell me the values of the 99%
>> power bandwidth for your J2A signal at different speeds. (BTW, the
>> keying waveforms in my article employed proportional spacing at both 2.4
>> wpm and 30 wpm. I'm assuming that your J2A signal does likewise.)
>
> I don't design using 99% figures. IMO, it is much better to specify how
> many dB down at a certain frequency away.
>
> For example, take a distribution that is concentrated within 100 Hz for a
> center frequency, but has a -80 dB tail all the way out to 1 MHz away.
> The effective bandwidth is very wide in this case, but the signal is not
> likely to cause any interference to anybody.
>
>
>> From an English language point of view, the fact that you admit that the
>> "effective" bandwidth does increase with speed (even if not "by much"),
>> then it appears to me that you must also say that the sending speed is a
>> factor in determining the "effective" bandwidth of your J2A signal.
>
> The energy distribution under the spectral envelope changes and that will
> affect any "effective bandwidth". However, outside of the envelope all
> keying sidebands are attenuated by the spectral envelope.
>
> Basically, keying sidebands of a 20 wpm signal falls off at a faster rate
> than keying sidebands of a 10 wpm signal. I.e., the 10th keying sideband
> of a 20 wpm signal has as much energy as the 20th keying sideband of a 10
> wpm signal.
>
> Alex VE3NEA (another DSP type) had looked at CW keying envelope in the
> same manner. If you subscribe to QEX, you will find his article ("CW
> Shaping in DSP Software") that looks at a couple of different windows
> (Hamming, Raised Cosine, Gaussian, Blackman-Harris, etc) in the May/June
> 2006 issue of the bimonthly.
>
> I will be glad to scan and email the article (just 5 pages) for you if
> you don't have QEX handy.
>
>> Turning to my examples now in my eham article in which I calculated the
>> 99.1% power bandwidth, do you disagree with any of my numerical results?
>
> No, you are **NOT** wrong.
>
> I think your calculations are perfectly sound -- however, the window
> function that you are using is not the right one to use and therefore not
> attenuating the keying sidebands.
>
> If I am not wrong, your window function is equivalent to a cosine
> function between -pi/2 and +pi/2 and zero elsewhere. What this is
> equivalent to in the time domain is a cosine from -infinity to +infinitym
> that is multiplied by a pulse between -pi/2 and +pi/2.
>
> I.e., your window is
>
> w(t) = cos(t).pulse(t)
>
> where pulse(t) is 1 between -pi/2 and +pi/2, and is 0 elsewhere.
>
> Again, using the convolution theorem, the spectrum W(s) is therefore
>
> W(s) = F(cos(t))*F(pulse(t))
>
> where F() is the Fourier transform and * is the convolution operator.
>
> F(cos(t)) is just the Dirac delta, which is very narrow (theoretically
> infinitesimally narrow), but it is convolved with F (pulse) which is a
> sin(x)/x function.
>
> The problem is that sin(x)/x falls very slowly (envelope decays as 1/ x)
> and therefore does not fall off fast enough to attenuate the keying
> sidebands enough, so your effective bandwidth is very wide.
>
> From the mathematical viewpoint, the problem comes from the fact that
> there is a slope discontinuity when the pulse starts and another slope
> discontinuity when the pulse ends (even though there is no discontinuity
> in the function itself).
>
> So, even though f(t) is continuous, f'(t) is not and that is allowing the
> spectrum of the prototype pule to assume a very wide spectral shape.
>
> A better function souls be a *raised* cosine -- i.e., 1 + cos(x) -- that
> is starts at -pi (instead of -pi/2) and stops at +pi (instead of +pi/2).
> I.e., the leading edge of the prototype pulse slowly rises (instead of
> abruptly rises) and slowly tapes of to the top of the pulse. Ditto the
> trailing edge.
>
> I.e., instead of the function you'd used
>
> w(t) = cos(t) for -pi/2 < t < +pi/2
>
> use instead:
>
> w(t) = ( 1 + cos(t) )/2 for -pi < t < pi.
>
> In fact VE3NEA in his article specifically showed the example of the
> "sine shaping" (that is what he calls it) that you have used to show how
> slowly the spectrum decays.
>
> I am surprised that out of all those exchanges on eHam, no one had picked
> up this point! It is not your calculation that is wrong -- it is the
> fact that the prototype pulse that you had used to base the calculations
> on is not one that limits keying sidebands properly.
>
> I am sure that if you apply this second window function (raised cosine),
> everything will come out as the practical guys have measured on their
> spectrum analyzers. (a simple RC filter produces no slope discontinuity
> when a pulse is passed through the filter!)
>
> If you'd use a Blackman window, the far out spectrum would be even better
> than the raised cosine. But give the raised cosine above a shot first.
> I think it will prove my "slope discontinuity" point.
>
> Vy 73
>
> Chen, W7AY

RE: Bandwidth versus Keying Speed

by W8XR on June 1, 2007 Mail this to a friend!

Mickey,

Thanks for posting the Chen exchanges.

His "raised cosine" window is what I was trying to get at in my examples.

My amateur suggestion was that the peaks and troughs of the raised sine function could be "stretched" to provide a quiet keying waveform - one that was not dependent on the keying rate (up to the risetime/falltime limits.)

But, I had not considered using some other windowing function for the keying shape - I figured Gaussian was probably "good enough". Some of these should provide even better keying characteristics.

Mark

RE: Bandwidth versus Keying Speed

by AB0WR on June 1, 2007 Mail this to a friend!

w8ji:"Secondly, I reduced the speed to 4dps. That's pretty darned slow. The Occupied BW is 465 Hz. That's right in line with all the other measurements."

I would appreciate if you would copy the display and put it on your web site with the 10,25, and 40hz keying signals. I would like to see exactly what it shows at 4dps.

It shouldn't matter if this exercise is being done at 3.5Mhz or at 10khz. The mathematics for the modulation process is the same regardless of the carrier frequency. When I get time during summer break I am going to hook up my signal and function generators through an FET gate (i.e. one passing a 10khz sine wave that is biased on and off with a square wave) and see what the sound card shows for the spectrum at different keying rates using Cool Edit Pro. I can then add in RC low pass filters to limit the bandwidth of the square wave and see what that does to the output spectrum. We'll see if that matches what your spectrum analyzer shows. If it does, why then I'll have to take another look at the math. If it doesn't then we'll have to figure out exactly what the transmitters are doing that causes the system transfer function be different.

w8ji:"We can probably all look forever, but what Chen posted agrees with Kevin W9CF and many other people. Chen explains it well. Like W9CF, the measured data I get looks exactly like the predictions of W9CF and many other people."

What he posted agrees with a system whose InputFunction bandwidth is wider than the SystemResponseFunction which causes the OutputResponsefunction to look like the SystemResponseFunction. If you hang a big picture outside your house over a small windowpane all you can see of the picture is what the windowpane covers. If you then hang a small picture outside your house over the window pane, especially one that is smaller than the window pane, then you can see the entire picture.

If you start out with a small picture, i.e. a 4hz keying waveform, and it gets converted to a *big* picture by hanging it outside your house (i.e. a 500hz bandwidth), then either the hanging process or the window pane is *doing something* other than just being a window pane (i.e. an RC low-pass filter function). It is somehow affecting the input signal to make it different.

The square wave function depends on a 1/x amplitude relationship between the fundamental and the odd-order higher harmonics in order to retain the proper relationship and make the bandwidth what is calculated. If the system response is non-linear, i.e. the amplitude of the fundamental is being compressed (because a stage in the transmitter is being run into saturation) so that the amplitude relationship between the fundamental and the harmonics is changed from the input then all bets are off.

That is one possible explanation of why the bandwidth of a pulse train is not what is expected. But that still doesn't make the statement that the slope of the output wave generates the harmonics causing the bandwidth. The rise time is *STILL* an indicator of a limited bandwidth system response, nothing more. In essence, there would be two system response components that would have to be accounted for. In fact, what would be happening from a non-linear stage saturating on the fundamental would be a whole set of intermod products from the mixing of all of the harmonics of the input square wave. The result of that would be very complex to study but it would account for both the extended bandwidth as well as key clicks far removed from the fundamental carrier frequency.

I know that my old Globe Chief 90a also suffered from big power supply dropoff during a long CW pulse. In essence, it was like laying an exponential decay function on top of the system response. That alone would cause the system gain response to become non-linear thus generating all kinds of intermod products which would, in turn, make the OutputResponse function look much wider than it should.

Does anyone else have any ideas on what else would cause a transmitter to change the bandwidth of a 4hz input square wave to a 500hz power bandwidth?

The math that Mickey has used is correct. If it isn't then there any number of electrical, civil, mechanical, industrial engineers, and even biologists, all of whom use Fourier series and transforms to study various phenomena, including biological phenomena, who are alive today who need to be told that their all their knowledge and research needs to thrown in the dumpster because W8JI and W9CF say that the slope of a square wave generates harmonics rather then indicating a bandwidth limited system response to an input function.

I don't think that is going to happen. Therefore, it would behoove us to figure out why the 751a transmitter Tom is measuring has a system response function that causes the input bandwidth to be extended.

BTW, Tom, how do you hear key clicks out beyond 500hz from a system that is bandwidth limited to 500hz? Or are you saying that the bandwidth * rise-time = pi is also wrong for a square wave response?

tim ab0wr

tim ab0wr

RE: Bandwidth versus Keying Speed

by W8XR on June 1, 2007 Mail this to a friend!

I respectfully disagree with your assertion regarding rise time. The keying waveform isn't an indicator of limited bandwidth system response - it's merely the shape of the keying waveform in use. The steeper the leading and trailing edges of the keying waveform, the more high frequency harmonic components it contains. The more harmonics are mixed with the carrier to produce a wide bandwidth signal.

The use of any poorly formed keying waveform (one with steep sides or discontinuities) will result in a wide bandwidth signal. The use of a well formed keying waveform (one with slowly sloping sides and no discontinuities or abrupt transitions) will result in a narrower bandwidth signal.

I think Chen made this point rather well.

RE: Bandwidth versus Keying Speed

by W8XR on June 1, 2007 Mail this to a friend!

I hit send before the final edit... the second sentence has been edited, below.

I respectfully disagree with your assertion regarding rise time. The [rise time of the] keying waveform isn't an indicator of limited bandwidth system response - it's merely the shape of the keying waveform in use. The steeper the leading and trailing edges of the keying waveform, the more high frequency harmonic components it contains. The more harmonics are mixed with the carrier to produce a wide bandwidth signal.

The use of any poorly formed keying waveform (one with steep sides or discontinuities) will result in a wide bandwidth signal. The use of a well formed keying waveform (one with slowly sloping sides and no discontinuities or abrupt transitions) will result in a narrower bandwidth signal.

I think Chen made this point rather well.

RE: Bandwidth versus Keying Speed

by W9AC on June 1, 2007 Mail this to a friend!

AB0WR: "If you two would actually read what is being posted this is what you would find..."

Tim, please read Chen's analysis and get back to us.

Regards,

Paul, W9AC

RE: Bandwidth versus Keying Speed

by KE3HO on June 1, 2007 Mail this to a friend!

I think that it is interesting that Tom and Mickey both posted letters from Mr. Chen. It would appear that both Tom and Mickey hold Mr. Chen in high esteem and value his opinion.

Reading Mr. Chen’s letter to Tom, it seems to say that Tom is correct – the bandwidth of a CW signal is dominated by the shape of the leading and falling edges of the keying waveform, not by the pulse width (or keying speed).

Reading Mr. Chen’s letter to Mickey, it seems to say that Mickey’s *calculations* are correct, but that the difference between his calculated bandwidths and Tom’s measurements are due to Mickey’s choice of his window function, and that if he had used a raised cosine for his window function that his calculated bandwidths would agree more closely with Tom’s measurements.

The bottom line, IMHO, is that Mickey’s calculations are mathematically correct, but that the window function that he chose does not match the type of keying waveform found in typical transmitters, and that substitution of a different window function would give results matching real world measurements. If a transmitter were made with a keying function that matched Mickey’s window function, the transmitter would almost certainly perform just as Mickey has calculated.

You are all, of course, free to draw your own conclusions. You are also free to jump in here to comment on my above statements. However, rather than having a bunch of people on one side jump in here and say that I am right, and a bunch of people on the other side jump in and say that I am full of fertilizer, I would love for someone to ask Mr. Chen if my summary is correct. (Mr. Chen must feel like he just stepped in between the Hatfields and the McCoys)

73 - Jim

RE: Bandwidth versus Keying Speed

by WR8Y on June 1, 2007 Mail this to a friend!

wr8y:"Did you read the rest of my post? I then resorted to using the 170 hz filter in the 830 while listing to a stream of dits - adjusting the speed from 5 WPM to 40 WPM. NO BANDWIDTH CHANGE!"

Exactly what did you expect to hear that would indicate a change in bandwidth?

Did you expect the sound you heard to change from a tone to a buzz if the bandwidth changed?

If what you heard didn't change, exactly how does that relate to the bandwidth not changing?

I would be very interested in knowing exactly what you would expect a change in bandwidth to "sound" like? Can you define what the different bandwidths would sound like if they, in fact, *did* change?
------------------

Where the hell did I say I "heard" anything? I OBSERVED no change in bandwidth by sweeping across the transmitted signal with the '830's receiver. (Using narrow filter and tightening down the passband to ~170 hertz. It's not hard to do.

RE: Bandwidth versus Keying Speed

by WR8Y on June 1, 2007 Mail this to a friend!

OOPS. I did say "heard" - not a good choice of words. I can see how you read into my statement what you did!

What I did was what ANY HAM HERE CAN DO, I listened to a varying speed of dits from one transmitter on another receiver with a tight filter, sweeeping across the transmitted signal.

Using a stream of dits sent adjusted to 5 WPM, then a stream of dits at 40 WPM, I saw no change in bandwidth.

And I must say, I have never noticed that highspeed CW has any wider bandwidth than a novice at 5 wpm.

Anyone who has studied electronics in school has been required to do MORE than read a book and punch buttons on a calculator - time to do a lab demonstration, guys!

SHOW me your theory in a lab experiment.

RE: Bandwidth versus Keying Speed

by AD5X on June 1, 2007 Mail this to a friend!

W8RY: "SHOW me your theory in a lab experiment."

Bravo - This is what we always do in the real product development world. And this will validate your (K5MC) model. We've seen experiments run by W8JI and W8RY that indicate your model is not correct. I'm not talking about the math - I'm talking about the model that the math is applied to. Rather than criticize the measuremtns done, run your own experiments on real transmitters and show us. I just made some very simple measurements of my own. I transmitted with my IC-706MKIIG into a dummy load, and then looked at the signal with my Yaesu MKV using a 60HZ DSP filter (basically using the MKV as a selective level meter). The MKV has a shorted input RF connector (shorted through a relay) and also has 18dB of front end attenuation in-line which gives me an S9 reading on the S-meter when tuned exactly to the IC-706 frequency. Tuning the MKV in 50HZ increments, I wrote down the S-meter reading (looking at the peak-hold bar) using 6WPM and 30WPM. I ran these tests a bunch of times. I could not really see any difference, other than at -250Hz (data below):

IC-706G frequency = 21.030.000

Freq. 30WPM 6WPM
0 S9 S9
-50Hz S9 S9
-100Hz S8 S8
-150Hz S7 S7
-200Hz S5 S5
-250Hz S3 S2
-300Hz S0 S0

Of course, I have no idea how accurate the S-meter readings are, and eyeballing the bargraph S-meter on the MKV isn't the best thing in the world. But this relative test does indicate that BW does not vary with keying speed.

Phil - AD5X

RE: Bandwidth versus Keying Speed

by AB0WR on June 1, 2007 Mail this to a friend!

<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
w8xr:" respectfully disagree with your assertion regarding rise time. The keying waveform isn't an indicator of limited bandwidth system response - it's merely the shape of the keying waveform in use. "
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

I'm sorry, this just can't be. The keying waveform starts at your cw key. It is just a switch. It is either on or off. The keying waveform begins as a pure square wave (disregarding contact bounce and contact resistance). It just doesn't get any more square than this.

This square wave waveform goes into the black box that is your transmitter. That black box takes that square wave input, does what ever it does to the square wave, and provides an output response.

That black box has a system response function. Call it G(w), H(w), S(w) or whatever. I've seen it called a lot of different things in a lot of different places.

That system response function, coupled with the input signal, is what determines the output response. If that output response is a quare wave with a non-zero rise time then you know that the system response function does NOT provide an infinite bandwidth. The amount of the rise time will tell you the system response bandwidth.

Even in a DSP system where the output function is generated directly you will find the math derived from the very same roots. You start with a square wave with an infinite number of harmonics and then you apply a bandwidth-limited response function (it can be a simple loww-pass filter, a gaussian filter, a raised cosine filter, or whatever) to diddle with the harmonics to get the output response you want.

This is elementary. I gave you three web sites to go look at that explains this in detail. It isn't just something that I made up. From the Tektronics site to the Wikipedia site, they all say the same thing.

<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
w8xr:"The steeper the leading and trailing edges of the keying waveform, the more high frequency harmonic components it contains. The more harmonics are mixed with the carrier to produce a wide bandwidth signal. "
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

That keying waveform starts out as a square wave with an infinite number of harmonics (they may be impossible to measure in the higher numbered ones but they exist nonetheless). Unless the CW key you use is different than any key I have ever seen it is just an on-off switch. There is no shaping done by any key that I know of.

I do agree that the more harmonics the system will transmit the wider the bandwidth you will see. The smaller the rise time the higher the number of harmonics being sent. If, however, the input waveform has a smaller bandwidth than the system response bandwidth you will see the input response repeated in the output response with no degradation (assuming linear amps and all that). If the input waveform has a wider bandwidth than the system response then the output response will be a degraded copy of the input waveform.

w8xr:"The use of any poorly formed keying waveform (one with steep sides or discontinuities) will result in a wide bandwidth signal."

I have no disagreement with this.

w8xr:" The use of a well formed keying waveform (one with slowly sloping sides and no discontinuities or abrupt transitions) will result in a narrower bandwidth signal. "

And I have no disagreement with this.

w8xr:"I think Chen made this point rather well. "

We disagree on what his point is. The way I read it his point assumes an input waveform with a wider bandwidth (i.e. a comb function) than the system response bandwidth. Of course this will result in a shaped output response and the shaping will look exactly like the system response window in the frequency domain. It simply does not address the issue, however, of what happens when an input waveform has a *smaller* bandwidth than the system response function. An input waveform with a power bandwidth of 42hz should pass through a system with a system response bandwidth of 500hz with no change. The system response will *not* somehow magically stretch the input bandwidth to 500hz as long as it is only a bandwidth limiting response function. It's like running a chunk of 10 gauge copper through a 12 guage die. Copper is removed until its size is 12 guage. Look at the system response as that wire die and the copper wire as the input waveform. That input waveform will get stripped down to be no wider than the bandwidth of the system response function. On the other hand, if you run a 14ga wire through that 12 gauge die nothing happens to the wire. Thats just like running a 42hz bandwidth signal into a system with a 500hz bandwidth response. The 14ga wire doesn't get ballooned out to 12ga and the 42hz bandwidth shouldn't get ballooned out to 500hz.

The shah function that was mentioned by Chen is nothing more than an infinite train of impulses spaced at intervals of T. In other words, it is a VERY HIGH BANDWIDTH signal, effectively infinite in bandwidth. It is defined as the sum from negative infinity to positive infinity of e^jwt. You don't get any wider than this. Unless you have an infinite system response function, this input waveform is going to get modified in some manner. And that is all Chen is saying. It simply doesn't address the case of what happens when the input waveform has a smaller bandwidth than the system response function.

If you don't believe me, go look at the web sites I quoted. They explain exactly the same thing in exactly the same way. If you don't understand your inputs and you don't know what your system response is then there is little you can do to determine the system output response.

If Tom is correct that a 42hz bandwidth signal waveform, when input into a 751a transmitter, comes out as a 500hz bandwidth signal then something is going on in that 751a that is much, much more than a bandwidth-limiting system response function. It will be fun to find out exactly what that is. I can guarantee you that it is NOT the rise time of the output response that is "generating" bandwidth. Outputs waveforms don't generate anything. Inputs waveforms and system response functions *generate* output waveforms, not vice-versa.

tim ab0wr

RE: Bandwidth versus Keying Speed

by AB0WR on June 1, 2007 Mail this to a friend!

<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
w9ac:
AB0WR: "If you two would actually read what is being posted this is what you would find..."

Tim, please read Chen's analysis and get back to us.

Regards,

Paul, W9AC
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

Paul, I did read it, did you?

Do you know what a shah function is?

It is an infinite bandwidth signal. Of course an infinite bandwidth input waveform, when submitted to a system response function with a limited bandwidth response, is going to assume the shape of the system response function in the frequency domain.

Did you expect anything else?

This is nothing more than the elementary Fourier equation that the OutputResponse(w) = Input(w) x SystemResponse(w).

This still does not explain how an input signal that is *narrower* in bandwidth than the system response function gets stretched to almost 10 times the bandwidth in the output function. Something like a 400hz RC lowpass filter in the keying circuit to generate a bandwidth limited response function is NOT going to stretch an input signal with a 42hz power bandwidth out to an output response with a power bandwidth of more than 400hz.

If you can explain how a simple lowpass filter can acommplish this using the appropriate mathematics I would dearly *LOVE* to see it.

As Chen pointed out, Mickey's calculation of power bandwidths are correct for a bandwidth limited square wave. That means that a 1hz keying speed with a 5ms rise time has about a 42hz power bandwidth. I fail to see how that magically gets converted into a 500hz bandwidth in the output of a 751a transmitter unless that transmitter has more than a simple bandwidth-limiting system response function.

I have yet to see anyone show that Mickey's calculations are incorrect. If Tom's measurements are correct then *SOMETHING* more than a bandwidth-limited system response *HAS* to be in play. I have yet to see anyone explain what this is.

Saying that the slope of the output square wave "generates" harmonics is just plain incorrect. That slope is the *result* of a bandwidth limited system limiting the harmonics being passed, it is not the generator of harmonics.

I believe the 751a generates CW by keying a LO signal does it not? Then that keyed LO signal is mixed with the VFO signal to generate the actual output response, right? If that is true then I have no idea what all could be happening in any pre-mixer amplifiers, the mixer itself, any post-mixer amplifiers, the driver circuity, or the final amp itself. It is entirely feasible that a stage along the way is being driven into saturation thus generating all kinds of intermod products close in to the CW signal itself making the signal look much wider than it actually should be. In other words, the system response function may not be a simple bandwidth-limited response.

Instead of considering such possibilities you and Tom seem to want to insist that the math learned by all kinds of engineers, not just electrical engineers, has been wrong for more than 100 years.

You simply cannot look at the output of a black box and say that it invalidates all kinds of known physics without knowing in detail the input to the black box and the system response of the black box. Mickey has tried to explain the significance of the input signal. What is left is to characterize what is happening in the system response function.

You and Tom can ignore this process if you will and just continue to tell us that the simple math of square waves has to be wrong. If you do, however, you are just going to get left in the dust as the rest of us figure out what is going on.

tim ab0wr

RE: Bandwidth versus Keying Speed

by W8XR on June 1, 2007 Mail this to a friend!

I'm sorry, I misunderstood your use of the word "system".

I don't use a key, I use a software keyer that generates the keying waveform and I/Q signals that are then upconverted to RF. So for me "system" starts with two inputs: 1.) Keying Envelope and 2.) carrier. (As it turns out these are merely blackbox constructs - in the SDR environment this is all in software so there really isn't a keying envelope or carrier. But I still use these abstractions for discussion.)

My apologies for missing your point.

My point was that if you modulate a carrier with a well shaped keying envelope it doesn't matter how fast you transmit (within the limits of the rise/fall time of the envelope.) Hence, my assertion that the bandwidth of the output is constrained by the rise/fall of the keying envelope and not the sending speed (at least for a 5ms rise/fall and otherwise monotonous envelope at typical amateur speeds - up to about 200+ WPM where the rise/fall no longer provide adequate pulse length.)

Again, sorry for misinterpreting "system".

Mark
W8XR

RE: Bandwidth versus Keying Speed

by AB0WR on June 1, 2007 Mail this to a friend!

ke3ho:"The bottom line, IMHO, is that Mickey’s calculations are mathematically correct, but that the window function that he chose does not match the type of keying waveform found in typical transmitters, and that substitution of a different window function would give results matching real world measurements. If a transmitter were made with a keying function that matched Mickey’s window function, the transmitter would almost certainly perform just as Mickey has calculated. "

Jim,

This is from my Signals, Systems, and Communications textbook by B.P. Lathi, copyright 1965.

"Consider a system with the transfer function H(s). If r(t) is the response of the system to a driving function f(t) and if R(s) and F(s) are their respective transforms, then

R(s) = F(s)H(s) equation (10.1)"

The keying function, i.e. the "window" function, is the response of the system mentioned in the quote above, it is H(s). The driving function, f(t) is the square wave input from the CW key. The output of a CW key *has* to be a square wave, it can only be on or off.

The window functions Chen, as well as the rest of us, have been discussing are frequency response functions (i.e. H(s)) not frequency generation functions. Therefore they can only modifiy the input function. The "window" functions can't "generate" anything of their own.

I wish I could draw a picture of this but it really *is* like looking at a picture through a pane of glass with everything outside the pane covered up. You can have round panes, cosine shaped panes, raised cosine shaped panes, gaussian shaped panes, big panes, small panes, etc. Each will let you see different sizes and shapes of the picture (i.e. different bandwidths) but none can extend the picture beyond what is already there (i.e. the input "driving" function). If the picture is smaller than the pane then you can see it all, the input signal gets through with no bandwidth modification. If the picture is larger than the pane then you only get to see part of it, the bandwidth of the input signal is cut down to match that of the response function.

In order to change the power bandwidth of a square wave with a 5ms rise time from 42 hz to more than 400hz (a whole order of magnitude change), something more than a window function would be required inside that black box we know as a transmitter.

Professor Lathi goes on to say:

"The principles of frequency analysis of linear systems may be expressed succintly as follows:

1) the response of a linear time-invariant system to an external exponential signal e^st is given by H(s)e^st.

e^st <-> H(s)e^st

2. By means of frequency transforms, every driving function f(t) can be expressed as a continuous sum of exponential functions.

f(t) = (1/j2pi) Integral F(s)e^st ds

with integration limits of sigma + j(infinity) and sigma-j(infinity).

3, By the virtue of linearity, the principle of superposition applies, and the response r(t) is given by a continuous sum of the responses of the system to individual components.

r(t) = (1/j2pi) Integral H(s)F(s)e^stds"

Mickey has done No. 2. He has broken down the square wave driving function into its components. He has also attempted to accomplish No. 1 by defining the system response, H(s), as a bandwidth limiting response, i.e. a shaped square wave with a given rise time (think bandwidth = pi/rise-time for a square wave).

He has used these to calculate No. 3. W8JI and W9CF are trying to imply that these calculations must be wrong because they don't describe what they see. But the calculations *are* correct. There just isn't any question about it.

That means that Step No. 1 is the area that needs to be looked at. The system response function H(s) *must* be something other than a frequency response window function in most transmitters. It *has* to be if it is actually *generating* frequency components.

Tom and Paul would be better off trying to help explain what that system response function has to be rather than in continuing to say that all the math has to be wrong. Who knows, we might come up with a major modification for the 751a that will make it an even better CW rig!

We better hope that we can come up with something else or no CW will be allowed in the ARRL 200hz bandwidth segmentation areas. If the necessary bandwidth of a CW signal is 500hz, those really narrow areas will be reserved only for psk31, psk125, etc. Please also note that if the claim is made that the *real* necessary bandwidth for CW is actually less than 500hz then that is a tacit admission that something besides a frequency response window is going on inside the transmitter that is extending the necessary bandwidth to make it wider than needed.

tim abw0r

RE: Bandwidth versus Keying Speed

by W8JI on June 1, 2007 Mail this to a friend!

Tim,

You might as well give up on blaming the 751A. A Viking Valiant and a Globe Scout 65 and even a DX 60 act the same way. So does my two tube cathode keyed 6AG5 driving an 807. My Yaesu's and Ten Tec's do the same.

You made this statement:

"In order to change the power bandwidth of a square wave with a 5ms rise time from 42 hz to more than 400hz (a whole order of magnitude change), something more than a window function would be required inside that black box we know as a transmitter."

Where did that 42Hz come from? I can't find it.

73 Tom

RE: Bandwidth versus Keying Speed

by W9AC on June 1, 2007 Mail this to a friend!

AB0WR: "I have yet to see anyone show that Mickey's calculations are incorrect. If Tom's measurements are correct then *SOMETHING* more than a bandwidth-limited system response *HAS* to be in play. I have yet to see anyone explain what this is..."

Tim, I don't believe anyone is refuting K5MC's calculations -- what is being questioned is whether or not the correct theorem is being applied to a problem. See Chen's comments on this.

This from K5MC:

"I believe that W8JI is simply being mislead by his analyzer!"

That's a pretty strong statement. We're led to believe that measured data cannot possibly trump the mis-application of a theorem.

Let's start by proving that the claimed theorem is the right tool for the analytical application and that the analytical theorem offered by W9CF is in incorrect. Proof, please.

The reasonable explanation is that the spectrum analyzer is not the root-cause of the discrepancy. Rather, the analytical tool is not the right one for job. Tim, what is it about the SA samples you disagree with? The Res BW? The sweep time? Where do you want it?

> "BTW, Tom, how do you hear key clicks out beyond 500hz from a system that is bandwidth limited to 500hz? Or are you saying that the bandwidth * rise-time = pi is also wrong for a square wave response?"

This suggests a lack of understanding of the issue. Aside from a S/A, one can easily use a receiver and tune to either the side of a keyed, transmitted carrier and hear key clicks with any filter setting. If key clicks are generated 5 kHz from the carrier F, the ability to tune the Rx VFO into the upper transmitted spectrum is all that is necessary, even with a narrow filter. We can use a 250 Hz filter, a 2.8 kHz filter, or even a 6 kHz filter to detect the presence of key clicks -- it's done by moving the receiver's VFO to put the clicks into the receiver's filtered passband.

If I am using a 250 Hz filter and I hear clicks at 7.010 MHz and the interfering station is on 7.005 MHz, I'ved just proved that the clicks are present well beyond the limits of the filter's passband.

> "Does anyone else have any ideas on what else would cause a transmitter to change the bandwidth of a 4hz input square wave to a 500hz power bandwidth?"

Yes, it's the rise and decay function of the keyed waveform as we've been discussing all along -- and analyzed/documented by W9CF.

> "Professor Lathi goes on to say:.."

I have nothing but respect for Lathi, but can we leave the Wikipedia "copy and paste" out of this?

Regards,

Paul, W9AC

RE: Bandwidth versus Keying Speed

by AB0WR on June 1, 2007 Mail this to a friend!

w8xr:"My point was that if you modulate a carrier with a well shaped keying envelope it doesn't matter how fast you transmit (within the limits of the rise/fall time of the envelope.) Hence, my assertion that the bandwidth of the output is constrained by the rise/fall of the keying envelope and not the sending speed (at least for a 5ms rise/fall and otherwise monotonous envelope at typical amateur speeds - up to about 200+ WPM where the rise/fall no longer provide adequate pulse length.) "

Using a well-shaped keying envelope *will* limit the transmitted bandwidth. There just isn't any doubt about that.

And the *maximum* bandwidth of the output *is* constrained by the bandwidth of the system response function. That doesn't specify the minimum bandwidth of the system, however.

Look at it this way - an RC low pass filter with a cutoff of 600 hz would eliminate all of the harmonics of a 100hz square wave that are above 600hz. The 3rd harmonic would be at 300hz, the 5th harmonic would be at 500hz, and the 7th harmonic would be at 700hz. So you would wind up with a square wave consisting of only the fundamental and the 3rd and 5th harmonics. It's not going to look like a very good square wave.

If you apply a 5hz signal to that same filter, you will get odd harmonics all the way out to the 119th. A much better square wave will result.

If we assume that the harmonics tend to start getting unmeasurable around the 30th harmonic (if I remember this correctly, I could be off on this), the absolute bandwidth of the 5hz square wave would be 150hz compared to the absolute 500hz of the 100hz square wave. Thus you would have less interference to adjacent channels even though you might be sending a square wave with shorter rise times.

If your software defined radio has the same shape keying envelope, in the time domain I assume?, no matter what speed you send or what length of element you send then I would tell you that the radio is changing the filter reaponse to match your keying speed. If this is true, the actual bandwidths you send should change as you change keying speeds, the shouldn't stay constant.

This whole idea that the bandwidth of square waves is constant just floors me. If that were true the telephone companies could use T1 carrier (1.544Mhz) cable to send T2 carrier (6Mhz) signals since the square waves being used would have exactly the same bandwidth. This is exactly the same logic as saying a 4hz square wave results in exactly the same bandwidth as a 40hz square wave (an order of magnitude difference). And yet I know that T2 cable required a much higher cutoff bandwidth and needed special low-capacitance cable to provide this. T1 cable simply wasn't capable of carrying the T2 spectrum. That's a dead giveaway to me that square waves of different frequencies don't have the same bandwidth.

tim ab0wr

RE: Bandwidth versus Keying Speed

by AB0WR on June 1, 2007 Mail this to a friend!

"Where did that 42Hz come from? I can't find it. "

Look at the original message. It's a 2.4wpm, 1hz square wave power bandwidth.

If the power bandwidth of a square wave, that's a waveform with the maximum number of harmonics and zero rise time, is 42hz but the power bandwidth becomes *higher* when the wave is bandwidth limited, i.e. a rise time is appears on the wave, then the whole world is upside down. That means we could generate higher and higher bandwidths by using longer and longer rise times.

Either the power bandwidth is maximum when the rise time is zero or the power bandwidth is maximum when the rise time is NOT zero. It can't be both.

You and Paul seem to be trying to convince us that the power bandwidth is NOT maximum when the rise time is zero. That somehow the power bandwidth goes up when the rise time gets longer.

Now I suppose it could be that Mickey's calculations of power bandwidth for a square wave are wrong but I've yet to see anyone show just where. In fact, I have yet to see anyone actually say that they are wrong.

So that leaves us with the connundrum of how does the bandwidth of a square wave go up when the rise times get longer?

And please don't use the canard that the slope of the rise time generates the bandwidth. It doesn't, at least not if the response function of the system is a frequency domain filter window. Filter window response functions don't generate anything, they only modify inputs. And even the slope of a filter response function did generate harmonics that means that shorter rise times would give wider bandwidths which, in the limit, would mean that a zero rise time would give the widest bandwidth. But that is what you are saying is NOT happening since you are saying that a rise time on a 1hz CW signal will give a 500hz power bandwidth even when a perfect 1hz square wave has a 42hz power bandwidth. It's a form of argumentative fallacy called begging the question - i.e. using the conclusion as your premise. It's a vicious circle which provides no real answer.

tim ab0wr

RE: Bandwidth versus Keying Speed

by KE3HO on June 1, 2007 Mail this to a friend!

Tim,

I think that you are misinterpreting Chen’s comments. Also, with regards to the keying waveform, you are considering the open/close of the key as the keying waveform. That open/close is shaped by the rig to give it a smooth rising and falling wave shape. That shaped waveform is the keying waveform and is the input to the system.

When I read Chen’s analysis, I see the following. The keying waveform, which is the modulation to the RF stage, he describes as a square (or rectangular wave) that is convolved with a wave-shaping window function. The square/rectangular wave sets the overall pulse width while the convolution with the wave-shaping window function sculpts the rising and falling shape of the keying function. The convolution in the time domain is, as Chen points out, a simple multiplication in the frequency domain after the FT is taking of the square/rectangular wave and the wave-shaping window function.

In Chen’s own words:

“Notice that for any smooth function that you use as a window, it's Fourier transform will fall faster than the envelope of the sin(x)/s function -- i.e., for a reasonable wave-shaping, the Fourier transform of the Gaussian falls off faster than 1/f where f is frequency.

Ergo, it is the wave-shaping function that is what governs the bandwidth of the shaped pulse, it is not the pulse width.”

That seems pretty clear to me. It is the shape of the rising and falling edge of the keying waveform that dominates the bandwidth, not the pulse width.

Then Chen goes on to discuss what happens when you have a train of pulses rather than a single pulse. He describes the keying waveform as a comb function convolved with the prototype keying function he described above.

Once again, in Chen’s own words:

“Again, from the Fourier Duality statement, the spectrum of a series of dits is just a product of the Fourier transform of the prototype shaped pulse and a comb in the frequency domain. Again, the spectrum of the window predominates and knocks out all the higher frequency components of the comb.”

That also seems pretty clear to me. The shape of the rising and falling edges of the keying function dominates the bandwidth for a series of dits, not the width of the pulses.

Now, what did Chen have to say about Mickey’s calculations?

Chen: “I think your calculations are perfectly sound -- however, the window function that you are using is not the right one to use and therefore not attenuating the keying sidebands.”

Chen: “The problem is that sin(x)/x falls very slowly (envelope decays as 1/x) and therefore does not fall off fast enough to attenuate the keying sidebands enough, so your effective bandwidth is very wide.

From the mathematical viewpoint, the problem comes from the fact that there is a slope discontinuity when the pulse starts and another slope discontinuity when the pulse ends (even though there is no discontinuity in the function itself).

So, even though f(t) is continuous, f'(t) is not and that is allowing the spectrum of the prototype pulse to assume a very wide spectral shape.

I am sure that if you apply this second window function (raised cosine), everything will come out as the practical guys have measured on their spectrum analyzers.”

That too is pretty clear: Mickey’s calculations are *mathematically correct* - in other words, he did not make an error in calculation. However, Chen states very clearly that the problem is Mickey’s choice of his window function, which has a slope discontinuity, and it is this slope discontinuity that causes the prototype pulse to “assume a very wide spectral shape”. And finally, Chen is very clear that if Mickey were to use a more suitable window function, he is sure that the calculations will agree with the spectrum analyzer plots.

Personally, I think that Mickey did an excellent job in his analysis and in presenting the information here. I think that there was a fundamental flaw in the underlying assumptions that the analysis was based on, and Mr. Chen pointed out what that flaw was – the choice of window function. My conclusion from Mr. Chen’s comments: if Mickey had chosen a more suitable window function (i.e. a window function that more closely represents the leading and trailing wave-shaping of a typical CW transmitter) his calculations would agree with Tom’s measurements on the spectrum analyzer.

I am not attacking Mickey here. I have tremendous respect for Mickey, and I commend him on the work that he did in his analysis. I certainly would not have discovered the source of disagreement between his calculations and Tom’s measurements, and only through reading Mr. Chen’s comments do I finally understand where the difference comes from.

Mickey - have I unfairly summarized Chen's comments, or have I misunderstood them?

73 - Jim

RE: Bandwidth versus Keying Speed

by AB0WR on June 1, 2007 Mail this to a friend!

w9ac:"Tim, I don't believe anyone is refuting K5MC's calculations -- what is being

questioned is whether or not the correct theorem is being applied to a problem. See

Chen's comments on this. "

I have seen Chen's comments on this. I explained them to you. I have yet to see you

refute my explanation. Again, a shah function is an infinite bandwidth function. Do

you really expect this to result in anything except a shaped response when a filter

window is applied to it?

Do you expect a input driving function to EXPAND its bandwidth when it is also applied

to the same filter window? If so, please provide the math to show how this happens

since it violates all of the convolution rules for both the time domain and frequency

domain that I learned.

<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
This from K5MC:

"I believe that W8JI is simply being mislead by his analyzer!"

That's a pretty strong statement. We're led to believe that measured data cannot

possibly trump the mis-application of a theorem.

Let's start by proving that the claimed theorem is the right tool for the analytical

application and that the analytical theorem offered by W9CF is in incorrect. Proof,

please.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

You have been provided the proof in at least three messages now. You have yet to

respond to any of them. You just keep asking for proof over and over. You consider

this a valid discussion method?

Again, this is a fundamental theorem:

R(s) = F(s)H(s)

where R(s) is the transform of the output response, F(s) is the transform of the

driving response (i.e the input), and H(s) is the transform of the system response

function.

Question 1: Do you agree with this fundamental theorem?

The transmitter *IS* a system. Therefore it has a system response function. Our

analytical model assumes this system has a linear response and it is described by a

bandwidth limiting function since a perfect square wave input results in an output

response that is bandwidth limited, i.e. a square wave with a rise time.

Question 2: Do you agree with this assumption?

Question 3: If you do not agree then how would you characterize the system response

function for the black box that is a transmitter.

<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
The reasonable explanation is that the spectrum analyzer is not the root-cause of the

discrepancy. Rather, the analytical tool is not the right one for job. Tim, what is it

about the SA samples you disagree with? The Res BW? The sweep time? Where do you want

it?
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

Did you think my call is K5MC for some reason?

<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
> "BTW, Tom, how do you hear key clicks out beyond 500hz from a system that is

bandwidth limited to 500hz? Or are you saying that the bandwidth * rise-time = pi is

also wrong for a square wave response?"

This suggests a lack of understanding of the issue. Aside from a S/A, one can easily

use a receiver and tune to either the side of a keyed, transmitted carrier and hear

key clicks with any filter setting. If key clicks are generated 5 kHz from the carrier

F, the ability to tune the Rx VFO into the upper transmitted spectrum is all that is

necessary, even with a narrow filter. We can use a 250 Hz filter, a 2.8 kHz filter, or

even a 6 kHz filter to detect the presence of key clicks -- it's done by moving the

receiver's VFO to put the clicks into the receiver's filtered passband.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

If key clicks are generated 5khz away from a square wave with a 1hz frequency then you are hearing the 5000th harmonic. For a keying waveform with a 2hz frequency you would be hearing the 2500th harmonic. For a keying waveform of 4hz you would be hearing the 1250th harmonic. The 1250th harmonic would be something like -62db down from the fundamental.

Question 4. Just how strong of a signal are you putting out that you can hear the 1250th harmonic of a 4hz keying wave that is 62db down from the fundamental?

Question 5. If you can hear the 1250th harmonic of a 4hz keying wave how sure are you that you aren't nearing artifacts from an overloaded receiver?

<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
If I am using a 250 Hz filter and I hear clicks at 7.010 MHz and the interfering

station is on 7.005 MHz, I'ved just proved that the clicks are present well beyond the

limits of the filter's passband.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

The only thing I can say is -- So? You need to answer Questions 4 and 5 to further the discussion. I'll even add another question.

Question 6: How do you know that this key click that is 5000hz away, the 1250th harmonic of a 4hz keying wave is not being generated by intermod products somewhere in the transmitter chain? This is exactly what one would expect from a transmitter being driven into non-linearity somewhere. It is the exact same thing that one hears on SSB from someone over driving an amplifier and causing buckshot several kilohertz away from his operating frequency.

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
> "Does anyone else have any ideas on what else would cause a transmitter to change

the bandwidth of a 4hz input square wave to a 500hz power bandwidth?"

Yes, it's the rise and decay function of the keyed waveform as we've been discussing

all along -- and analyzed/documented by W9CF.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

Your analysis is doing nothing more than than calculating the bandwidth of an output response from a system. You calculate the bandwidth of an output response indicated by the rise time of that output response and then use it in a non-causual way to say that this output function will *always* be the output function no matter what the input driving function is or what the system response function is. You are analyzing an *OUTPUT* response and then are trying to say that it is both the input driving function as well as the system response function.

As I told Tom, this is called "begging the question". It is using the conclusion as a premise, i.e. the output will the output because it is the output.

You need to show in your analysis how the F(s) and H(s) terms result in your R(s) term. We know that the input to the system is a perfect square wave. A CW key cannot produce anything else. That leaves the H(s) system response function to be evaluated.
If we can't get from a 4hz square wave leaving the CW key on the desk to a 400hz output response then how will we ever be able to tell what is happening inside that black box we call a transmitter?

<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
> "Professor Lathi goes on to say:.."

I have nothing but respect for Lathi, but can we leave the Wikipedia "copy and paste"

out of this?
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

No, we can't. He is an accepted authority whereas I am not. When what he says confirms what I am saying, I will continue to use him as an authority. I'm sorry if that offends you but it's just the way it will be.

Now, can you answer the questions above?

Or are you going to continue to ignore them?

tim ab0wr

RE: Bandwidth versus Keying Speed

by AB0WR on June 2, 2007 Mail this to a friend!

ke3ho: "think that you are misinterpreting Chen’s comments."

That's always possible but I haven't seen it yet.

<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
Also, with regards to the keying waveform, you are considering the open/close of the key as the keying waveform. That open/close is shaped by the rig to give it a smooth rising and falling wave shape. That shaped waveform is the keying waveform and is the input to the system.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

The opening and closing of the key is not the keying waveform. It is the driving function. It is the system input. Everything done after that is a system response to that driving function. That driving functino is a square wave with a period and a duty cycle.

If that square wave is shaped by the rig then the rig is applying a system response against the driving function to come up with an output response.

With no key opening and closing how would the system have anything to respond to?

You are trying to change places between the chicken and the egg. In this case you have to have the egg to hatch before you can have a chicken to fry.

<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
When I read Chen’s analysis, I see the following. The keying waveform, which is the modulation to the RF stage, he describes as a square (or rectangular wave) that is convolved with a wave-shaping window function. The square/rectangular wave sets the overall pulse width while the convolution with the wave-shaping window function sculpts the rising and falling shape of the keying function. The convolution in the time domain is, as Chen points out, a simple multiplication in the frequency domain after the FT is taking of the square/rectangular wave and the wave-shaping window function.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

Let's think about what is being said here. The comb function is a series of impulses in the frequency domain, lets say an impulse every 10 hz at an amplitude of 1. Now, what does a low pass filter look like in the frquency domain? It looks like a box from -wf to +wf and lets say the gain of the function (i.e. the height of the box) is also 1. Lets say the bandwidth of our box is 500hz, i.e. from -250hz to +250hz around the center frequency. Now do the multiplication in the frequency domain. Impulses further away from the center than -250hz, i.e. from -260hz, -270hz, etc will be multiplied against a filter response that is zero. So we get zero for a result. From -250hz to +250hz we get an impulse of 1 every 10hz multiplied by a filter function that is 1 so we get impulses of 1. For frequencies higher than 250hz we get multiplications that are zero.

So what do we wind up with? We go from a comb driving function with impulses from negative infinity to positive infinity (i.e. infinite bandwidth) to a bandwidth limited response that only has impulses between -250hz and 250hz.

Now, lets go from that easy example to one with a square wave with impulses at every odd harmonic from negative infinity to positive infinity but whose amplitudes gradually decrease as 1/n. Assume the same filter function with a gain of 1. What do we get when the two are multipled together in the frequency domain? You get exactly the same thing as before. Any impulses outside the -250hz to +250hz bandwidths have multiplication results of zero and impulses inside the -250hz to +250hz bandwidth have the same amplitude as before the multiplication. The result? A square wave missing higher frequency harmonics which results in a bandwidth limited output response. It is a square wave but now with rise times caused by the bandwidth limiting.

Now, let's look at a raised cosine filter. In the time domain it looks kind of like a damped sine wave. In the frequency domain it looks like anything from a rectangular window to a mis-shaped partial cosine depending on the rolloff factor. The rolloff factors basically determine the bandwidth of the filter in the frequency domain and the amplitude of the filter when applied to impulses inside the filter bandwidth. If the rolloff factor is 1 you get the closest to a cosine shape so what do you get when you apply this to a square wave? Close in frequencies are not changed much, cos 0 = 1 so the fundamental and the 3rd harmonic are probably not changed much. As you go further out, the cosine approaches zero so those impulses near the filter cutoff get attenuated significantly. What's the result? Again, you wind up with an bandwidth limited output response that is a square wave with missing higher harmonics as well as harmonics that are still there but significantly attenuated.

Bottom line? None of these multiplications in the frequency domain result in any impulses being created further from the fundamental than were already there. The only way to increase the power bandwidth, at least that I can see, is for this multiplication in the frequency domain to somehow create frequencies that didn't exist in the driving function. In other words you have to have a system response function that is a generator as well as a filter. Do you know of any transmitter amplifiers or keying shaping circuits that are frequency generators as well as frequency filters?

<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
In Chen’s own words:

“Notice that for any smooth function that you use as a window, it's Fourier transform will fall faster than the envelope of the sin(x)/s function -- i.e., for a reasonable wave-shaping, the Fourier transform of the Gaussian falls off faster than 1/f where f is frequency.

Ergo, it is the wave-shaping function that is what governs the bandwidth of the shaped pulse, it is not the pulse width.”

That seems pretty clear to me. It is the shape of the rising and falling edge of the keying waveform that dominates the bandwidth, not the pulse width.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

The shape doesn't determine the bandwidth other than by limiting the frequencies that can be passed through the system response function. I hope my analysis above shows that. The frequencies that appear in the driving function, which is all that the wave shaping filter has to work with, *are* determined by the pulse width, at least insofar as the pulse width is an indicator of the fundamental frequency of the square wave. For a 50% duty cycle, periodic square wave, the fundamental frequency is easy to calculate and demonstrates the theory quite well.

Remember that the square wave is a sort of damped sine wave in the frequency domain - that is a sinx/x function. All that Chen is saying is that a good window will reduce the amplitudes of the impulses of the square wave that are far away from the fundamental frequency even faster than they already do decrease!

<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
Then Chen goes on to discuss what happens when you have a train of pulses rather than a single pulse. He describes the keying waveform as a comb function convolved with the prototype keying function he described above.

Once again, in Chen’s own words:

“Again, from the Fourier Duality statement, the spectrum of a series of dits is just a product of the Fourier transform of the prototype shaped pulse and a comb in the frequency domain. Again, the spectrum of the window predominates and knocks out all the higher frequency components of the comb.”
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

Yes, that is exactly what I have been saying. We agree totally. The window, i.e. the system response function, limits the bandwidth of the system. It takes the bandwidth of the driving function, i.e. a comb with an infinite frequency bandwidth, and *REDUCES* it. It doesn't make the bandwidth wider!

<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<,
That also seems pretty clear to me. The shape of the rising and falling edges of the keying function dominates the bandwidth for a series of dits, not the width of the pulses.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

Nope. The shape of the output response is only a function of the multiplication of the driving function and the system response function. Yes, the shape, which includes the rising and falling edges, is a result of the multiplication of the two frequency domain responses but it isn't the *cause*, per se, of the bandwidth. The bandwidth is determined by *both* the driving function and the system response function.

Let's take it that one more step further. Let's suppose we still have that ideal 500hz bandwidth low pass filter. But let's also suppose we have a driving function that is a 1hz square wave. That square wave is make up of impulses at 1hz, 3hz, 5hz, 7hz, 9hz, 11hz, ..... etc. Now, what will the amplitude of the harmonic impulses be at the 250hz bandwidth edges of the filter? 1/249 or .004 if we assume 1 as the normalized maximum amplitude. Pretty small eh? What do you suppose dominates the power bandwidth of this square wave? Is it the system response function? Probably not. If you assume that the first 30 harmonics are the main power components, it's not even close.

In this case how can you say the rising and falling edges of the system response function has any impact on the bandwidth of the system output at all?

<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<,
Now, what did Chen have to say about Mickey’s calculations?

Chen: “I think your calculations are perfectly sound -- however, the window function that you are using is not the right one to use and therefore not attenuating the keying sidebands.”

Chen: “The problem is that sin(x)/x falls very slowly (envelope decays as 1/x) and therefore does not fall off fast enough to attenuate the keying sidebands enough, so your effective bandwidth is very wide.

From the mathematical viewpoint, the problem comes from the fact that there is a slope discontinuity when the pulse starts and another slope discontinuity when the pulse ends (even though there is no discontinuity in the function itself).

So, even though f(t) is continuous, f'(t) is not and that is allowing the spectrum of the prototype pulse to assume a very wide spectral shape.

I am sure that if you apply this second window function (raised cosine), everything will come out as the practical guys have measured on their spectrum analyzers.”
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

Well, duh! What do you suppose the first derivative of a square wave is? It is a series of impulses. A series that extends from negative infinity to positive infinity in the frequency domain. This is nothing earth shattering. It *is* what makes a pure square wave output from a transmitter very wide, wider than it needs to be.

As I beleive Mickey pointed out, what he was doing was using an easily calculated example to demonstrate the theory. It is easier to start easy and gradually work your way into the harder stuff.

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
That too is pretty clear: Mickey’s calculations are *mathematically correct* - in other words, he did not make an error in calculation. However, Chen states very clearly that the problem is Mickey’s choice of his window function, which has a slope discontinuity, and it is this slope discontinuity that causes the prototype pulse to “assume a very wide spectral shape”. And finally, Chen is very clear that if Mickey were to use a more suitable window function, he is sure that the calculations will agree with the spectrum analyzer plots.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>.

No, that is not what Chen is saying. He is saying Mickey didn't pick a window function that will limit the bandwidth as much as it could be limited. If Mickey's calculations are right then they are right. What Chen is saying is that the bandwidth could be even SMALLER than what Mickey calculated, not *bigger*.

Again, you don't have a choice in the driving function, it is a square wave. It is an open and close switch operation. It is the system response to this driving function that determines the output response bandwidth.

Do you honestly believe that most people don't know that a square wave has a very wide spectral shape? And that they don't know that a real-world 6db rolloff low pass filter is not a very effective filter?

Nothing Chen speaks of will INCREASE the output response bandwidth, it will only reduce it from what Mickey has calculated. You seem to have a disconnect here. Remember, Chen said that Mickeys filter window is "not attenuating the keying sidebands". Yet Mickeys bandwidths are already narrower than what we are seeing the measurements show. Chen's advice will only further narrow the bandwidth and make the discrepancy between the calculations and the measurements even worse!

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Personally, I think that Mickey did an excellent job in his analysis and in presenting the information here. I think that there was a fundamental flaw in the underlying assumptions that the analysis was based on, and Mr. Chen pointed out what that flaw was – the choice of window function. My conclusion from Mr. Chen’s comments: if Mickey had chosen a more suitable window function (i.e. a window function that more closely represents the leading and trailing wave-shaping of a typical CW transmitter) his calculations would agree with Tom’s measurements on the spectrum analyzer.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

I agree Mickey did an excellent job! This is as good of a thread as I have seen for a long time!

Chen didn't point out any flaws, and I can't find any either. the only "flaw" might be that a simple low pass filter is not an efficient bandwidth shaper but I think everyone already knew that.

You still have the disconnect that Chen said Mickey could make the bandwidth smaller by using a different window and you are turning that into saying that Chen said Mickey could make the bandwidth WIDER by using a different window. Your conclusion and Chen's statements can't both be right.

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
I am not attacking Mickey here. I have tremendous respect for Mickey, and I commend him on the work that he did in his analysis. I certainly would not have discovered the source of disagreement between his calculations and Tom’s measurements, and only through reading Mr. Chen’s comments do I finally understand where the difference comes from.

Mickey - have I unfairly summarized Chen's comments, or have I misunderstood them?
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

I hope you will look closely at my explanation of the multiplication of a filter window and a square wave. I think you will find that the source of the difference between Mickey's calculations and Tom's measurements are still up in the air.

73,

tim ab0wr

RE: Bandwidth versus Keying Speed

by W8JI on June 2, 2007 Mail this to a friend!

by AB0WR on June 1, 2007 Look at the original message. It's a 2.4wpm, 1hz square wave power bandwidth.

If the power bandwidth of a square wave, that's a waveform with the maximum number of harmonics and zero rise time, is 42hz but the power bandwidth becomes *higher* when the wave is bandwidth limited, i.e. a rise time is appears on the wave, then the whole world is upside down. That means we could generate higher and higher bandwidths by using longer and longer rise times. >>

This explains why we have the difference of perception. I tried earlier to get everyone on the same page but was obviously unsuccessful.

Indeed if we look at the energy distribution of a very slow square wave, we find what you are saying.

As I have said before the problem is nothing in the system cares about what happens in the long term. It does not affect the receiver bandwidth, it does not affect the transmitter bandwidth so far as distributed power. We always have to consider how the system behaves.

The job of any mathematical analysis is to provide a shortcut or another way of explaining the system, not to change how the system works or how we perceive the system works. It works as it does. We hear and observe what we hear and observe.

When the application of a shortcut calls our observation of reality a liar, it's time to change the application or to just admit it doesn't apply to the real world we live in.

I built my first real transmitter and sent CW on the air in 1962 on 7175 kHz. Now in 2007 I'm transmitting a carrier again on 7175 kHz.

There are about 31.5 million seconds in a year. 1.42 billion seconds in 45 years. How can that very slow square wave with a period of 45 billion seconds produce a keyclick that causes problems 2 kHz away?

It seems to me on a lesser time scale we have the same problem. Of course the energy in the carrier, if we send slow enough, overwhelms or dwarfs the sidebands that cause problems.

That slowing does not change the communications system and the bandwidth that system occupies or requires. The bandwidth required is the bandwidth needed to pass the rise and fall without altering the shape of the rise and fall.

It doesn't matter to the CW receiver or the operator how many gallons of water the carrier can heat over a twenty minute period (or even a ten second period) compared to the long term accumulated energy in the sidebands. It only matters what the very short term level of the sidebands are compared to the peak envelope transmitter power, and that is relatively constant.

Neither the receiver nor the operator accumulate energy over an infinite time period, they don't even do it for milliseconds. It's a peak power problem.

73 Tom

Bandwidth versus Keying Speed

by K5MC on June 2, 2007 Mail this to a friend!

I believe I have a graduate student lined up this summer to help me calculate the power/occupied bandwidths of the various keying waveforms that W7AY has mentioned. Since the 5-ms rise time for the "sinusoidal" keying waveform in my article is the time required to go from 0% to 100% amplitude, we will use the same definition of rise time (rather than the more standard 10% to 90%) for the other keying waveforms we plan to study. Although I have no doubt that the power bandwidths of these other keying waveforms are more narrow than my "sinusoidal" waveform, I simply cannot believe that we will find that their power bandwidths remain "essentially" constant when the speed increases from 2.4 wpm to 30 wpm. Of course, we will report exactly what our calculations show.

Turning to the spectrum plots and occupied bandwidth data presented by W8JI, I continue to believe that the problem here is primarily the lack of frequency resolution by Tom's spectrum analyzer. I have seen that with my own eyes using spectrum analyzers as well as in computer simulations that approximate the Fourier transforms of signals.

For example, yesterday a couple of graduate students and I clearly observed the discrete line spectrum produced by a CW/ASK "transmitter" under "square-wave" keying. We used a Wavetek Model 180 function generator to produce a "raised" square-wave keying waveform just as I used in my calculations. The keying waveform from the Wavetek modulated the amplitude of a "high frequency" sinusoidal carrier wave produced by an HP 33120A signal generator. In addition to seeing the magnitude spectrum on the HP 3561A Dynamic Signal Analyzer, we observed the CW/ASK signal on a Tektronix 2445 oscilloscope. The fundamental frequency of the keying waveform was initially set to 10 Hz, giving us 10 dits per second or 24 wpm. The discrete spectrum we observed on the HP 3561A was exactly what the theory/mathematics says. When we increased the sending speed to 20 Hz (48 wpm), the frequencies of the respective sidebands moved out further from the carrier exactly as told by the Fourier series.

The carrier frequency was only 50 kHz when we saw these very nice looking discrete line spectra on the analyzer! Even though the HP 3561A is now over 15 years old, I believe it is still an excellent low frequency analyzer. According to the 3561A operating manual, with a frequency span of 2 kHz the analyzer's display resolution is 5 Hz. With a span of 100 kHz (the upper frequency limit of the 3561A), its display resolution is 250 Hz.

With the start and stop frequencies set to 49 kHz and 51 kHz, respectively, our display resolution was 5 Hz. Therefore, we were able to see the individual keying sidebands distinctly, starting with the first pair of sidebands plus and minus 10 Hz from the 50-kHz carrier! The noise levels between the various sidebands was probably 40 dB down or more, so there's no question that the "power" bandwidths for this particular "CW" transmitter using this particular spectrum analyzer would give results very close to my calculations.

We then set the carrier frequency to 3.5 MHz and observed the spectrum on an HP 8920A analyzer. With the frequency span of the 8920A set to 10 kHz (the lowest span available on the 8920A), we had to increase our sending speed up to around 2400 wpm (1,000 Hz modulating frequency or 1,000 dits per second) before we began to even see some distinct frequency components! At speeds below around 2400 wpm the analyzer's resolution was simply too low to properly display the actual discrete line spectrum being generated by the signal. I have also observed the very same effect when analyzing signals using MATLAB, a popular software package that estimates Fourier transforms via FFTs. If you do not have enough data points in your sampled waveform, the resulting spectrum calculated by the FFT will look very similar to what the students and I saw on the 8920A yesterday, both of which are very similar, in my opinion, to the plots posted by W8JI.

If every transmitter (from old tube rigs on up) ever tested by Tom with his spectrum analyzer indicates that the occupied bandwidth remains essentially constant no matter what the speed is, then obviously either the math model I assumed in my article is an extremely poor approximation to physical CW transmitters or there's something wrong in the measurement process. As I discussed above, I believe the problem is primarily due to the lack of frequency resolution in Tom's analyzer. Perhaps Tom can show us spectra displays from a tone-modulated AM transmitter. If I'm right, then the spectra displayed by his analyzer when testing an AM transmitter tone modulated using a sine wave at 10 Hz (corresponding to the fundamental frequency when sending 10 dits per second or 24 wpm), 25 Hz (60 wpm), and 40 Hz (96 wpm) will all look essentially the same when his analyzer is adjusted as he had it for his CW spectra plots. I believe this test should answer the question I have about Tom's spectrum analyzer. (I will do a similar test myself using the 8920A on Monday.) Hopefully everyone here will at least agree that an ideal analyzer under these conditions would display a distinct line spectrum corresponding to the carrier at 3.5 MHz, the upper sideband at either 10, 25, or 40 Hz above 3.5 MHz, and the lower sideband at either 10, 25, or 40 Hz below 3.5 MHz.

73, K5MC

RE: Bandwidth versus Keying Speed

by W8JI on June 2, 2007 Mail this to a friend!

by K5MC on June 2, 2007 I believe I have a graduate student lined up this summer to help me calculate the power/occupied bandwidths of the various keying waveforms that W7AY has mentioned.>>

It might be helpful to look at a radio first.

<< Since the 5-ms rise time for the "sinusoidal" keying waveform in my article is the time required to go from 0% to 100% amplitude, we will use the same definition of rise time (rather than the more standard 10% to 90%) for the other keying waveforms we plan to study. Although I have no doubt that the power bandwidths of these other keying waveforms are more narrow than my "sinusoidal" waveform, I simply cannot believe that we will find that their power bandwidths remain "essentially" constant when the speed increases from 2.4 wpm to 30 wpm. Of course, we will report exactly what our calculations show.>>

But we already know what your logic, thought process, and application of formulas describe Mickey. Repeating that process isn't necessary. The results will always be the same.

<<Turning to the spectrum plots and occupied bandwidth data presented by W8JI, I continue to believe that the problem here is primarily the lack of frequency resolution by Tom's spectrum analyzer. I have seen that with my own eyes using spectrum analyzers as well as in computer simulations that approximate the Fourier transforms of signals.>>

You can believe it all you want Mickey but the resolution bandwidth of the analyzer is 10 Hz. If I do a occupied power measurement of a steady carrier from the same rig the result is an occupied BW of 30 cycles. If I repeat it with a narrower and more selective Selective Level Meter the occupied BW of the carrier is 15Hz.

Both tell me it is about 400-500 Hz for a string of dots, and while a receiver hears the clicks for a wider bandwidth since it has a wider filter it also does not change with speed so long as the speed isn't at an extreme limit.

I have a question. My IC-751A's SSB transmitter has an occupied BW of about 2kHz with normal speech. If I talk slower does the transmitter become narrower?

73 Tom

RE: Bandwidth versus Keying Speed

by KE3HO on June 2, 2007 Mail this to a friend!

Tim,

If you choose a window function that is very broad in the frequency domain, it will intercept multiple teeth of the comb. As you key faster, it will intercept more and more teeth of the comb. You and Chen and I are all in agreement on this.

So what does that prove? It proves that if you choose a leading and trailing edge wave-shaping function in your CW transmitter that has a very broad FT then you have done nothing more than design the worlds best key-click generator. Chen pointed out that, mathematically, this is what Mickey has done. If you design your leading and trailing edge wave-shaping function so that it is narrow enough in the frequency domain that it only intercepts one tooth of the comb for the fastest keying speed that you are designing for, then your spectrum is the same at all keying speed - you only ever intercept one tooth of the comb. I can't put it any planer than that.

Yes, Mickey's analysis is exactly correct. His calculations are without error. The problem is that his analytical model is a model of an outstanding keyclick generator. This is what Chen is saying.

If Mickey had chosen a better window function, one that is narrower in the frequency domain, then the prototype pulse would only ever intercept one tooth of the comb for reasonable keying speeds and the spectrum would be completely independent of keying speed. Mickey chose a window function that was easy to calculate the FT of. Being easy to calculate is not a virtue if it does no represent something that you might actually use in the real world.

So why does Tom's 751 have a 500Hz signal at all keying speeds? Because that it the width of the sidebands generated by the leading and trailing edge pulse shaping function of the 751. The sidebands are generated by the leading and trailing edge pulse shape of the CW keying function, and are independent of keying speed so long as the FT of the pulse shaping window function is narrower than the spacing of the comb for your highest keying speed.

73 - Jim

RE: Bandwidth versus Keying Speed

by AB0WR on June 2, 2007 Mail this to a friend!

w8ji:"Indeed if we look at the energy distribution of a very slow square wave, we find what you are saying"

Let me get this straight. You are saying that a rise time on a square wave indicates a higher bandwidth signal instead of a lower bandwidth signal?

I just want to be extremely clear on this point.

tim ab0wr

Bandwidth versus Keying Speed

by W7AY on June 2, 2007 Mail this to a friend!

HI all,

I apologize if this adds more flames to the fire. (eHam finally allows me to post; I had not been registered earlier).

IMHO, KE3HO hits the nail right on the head.

A Fourier window is nothing more and nothing less than a low-pass filter which has a finite duration in the time domain.

You simply need to choose a window whose spectrum falls faster than both the spectrum of the sin(x)/x of the square wave pulse and the spectrum of a comb from the repetitive pulses.

Here is an experiment: tune in to a nice 35 wpm CW signal. Now crank your filter down to 150 Hz. Still perfectly copyable, no?

Which means that if I were to apply a 150 Hz brick-wall filter to the transmit signal, the other end will also be able to copy my 35 wpm CW fine, too.

Further, this 150 Hz filter would cut off any higher spectral components, whether they come from the sin(x)/x of the original square wave pulse, or from a comb.

I.e., you do not need to transmit all that wideband stuff to pass aural Morse information. Waveshaping the pulse is just one way to limit said bandwidth.

If you have a Macintosh, you can easily do this experiment using cocoaModem, since it transmits using J2A emission mode (audio CW that is translated to RF with an SSB transmitter) and it has a risetime slider. Send the output to the computer's speakers and listen to the generated Morse.

Just set the transmit Morse speed at some suitably high speed and then go to the configuration panel to adjust the rise time slider.

Even better, if you have a second Macintosh, just run that audio output of the first computer into a second computer that watches the spectrum of the signal in a cocoaModem spectrum window (which measures down to -100 dBFS).

In cocoaModem I had use a Blackman window to shape the prototype pulse. The risetime slider adjusts the width of the window so that the function rises from 10% to 90% to the stated risetime. For the default, I had used a 5 msec risetime, which seems to work well.

In Fourier transforms, first order discontinuities cases wide spectra, but second order discontinuities (slope discontinuities) also causes wide spectra.

That is why "good" window functions that DSP folks use are attempts to be maximally smooth and yet have finite duration.

For an example where slope discontinuity is harmful, take a look at John Grebenkemper's modification of the K2 here

http://home.pacbell.net/johngreb/improving_elecraft_keyingmod.pdf

Scroll down to the first figure and you can see that the original keying pulse (in red) has a bad slope discontinuity at the onset of the rising edge. John's modification creates a more gradual change. Several plots later, he shows the spectra for the different keying waveshapes.

I apologize again for wasting bandwidth and also for my poor English; it is not even my second language, HI.

Vy 73
Chen

Bandwidth versus Keying Speed

by AB0WR on June 2, 2007 Mail this to a friend!

ke3ho:"If you choose a window function that is very broad in the frequency domain, it will intercept multiple teeth of the comb. As you key faster, it will intercept more and more teeth of the comb. You and Chen and I are all in agreement on this.

ke3ho:"So what does that prove? It proves that if you choose a leading and trailing edge wave-shaping function in your CW transmitter that has a very broad FT then you have done nothing more than design the worlds best key-click generator. Chen pointed out that, mathematically, this is what Mickey has done. If you design your leading and trailing edge wave-shaping function so that it is narrow enough in the frequency domain that it only intercepts one tooth of the comb for the fastest keying speed that you are designing for, then your spectrum is the same at all keying speed - you only ever intercept one tooth of the comb. I can't put it any planer than that. "

If all you allow through the system is one frequency how does that somehow turn into a wider bandwidth?

I agree that if you make your filter narrow enough all you will allow through is one frequency. There isn't any doubt about that.

I suspect the problem here is that you are confusing the time domain and the frequency domain. A raised cosine filter in the time domain looks like a damped sine wave. Really, it does. Look it up using Google if you don't believe me. You will find no rise time on the time domain response graph of the function at all.

Yet in the frequency domain the filter can be very narrow. It is the frequency domain response that best shows the bandwidth of a signal. And, yes, the spectrum you see will be the same for all keying speeds. But it won't be wider than the input signal bandwidth for any keying speed. It will be one frequency. (actually in the real world this is impossible because a single frequency which is never turned off or on can carry no intelligence at all).

You seem to be still stuck at trying to confirm that the rise time of an output response, as seen in the time domain, somehow generates harmonics that makes the signal bandwidth wider. It doesn't. The output response will always have a narrower bandwidth than the input driving function in this situation.

<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
Yes, Mickey's analysis is exactly correct. His calculations are without error. The problem is that his analytical model is a model of an outstanding keyclick generator. This is what Chen is saying.

If Mickey had chosen a better window function, one that is narrower in the frequency domain, then the prototype pulse would only ever intercept one tooth of the comb for reasonable keying speeds and the spectrum would be completely independent of keying speed. Mickey chose a window function that was easy to calculate the FT of. Being easy to calculate is not a virtue if it does no represent something that you might actually use in the real world.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

As I said, the filter can't be so narrow as to allow only one impulse through. This would be the same as having a non-varying carrier which, by definition, has zero bandwidth and no intelligence carrying capacity. That is what would make such a narrow filter something you wouldn't use in the real world.

<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
So why does Tom's 751 have a 500Hz signal at all keying speeds? Because that it the width of the sidebands generated by the leading and trailing edge pulse shaping function of the 751. The sidebands are generated by the leading and trailing edge pulse shape of the CW keying function, and are independent of keying speed so long as the FT of the pulse shaping window function is narrower than the spacing of the comb for your highest keying
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

I disagree. As I pointed out in my message explaining output responses from filter functions and square wave driving function, you wind up with a limited bandwidth keying function, i.e. there are only so many odd harmonics that get through. The limited frequency bandwidth of the signal (along with the amplitude relationship between the harmonics) is what determines the shape of the waveform in the time domain. The "shape" doesn't generate anything, it only "describes" what is happening.

It might be instructive to actually graphically convolve a raised cosine response function (a damped sine wave) with a square wave driving function in the time domain. I think it will better demonstrate that it is the convolving of the two functions that determines the shape of the resulting output function and that it isn't the shape of the output function that determines itself, that would violate causual rules.

That keying function, with a limited number of odd harmonics, becomes a driving input function for the next stage in the system.

Modulation in a linear system is done by varying the gain of the system using one input function in order to modulate the other input function. If r(t) is the output and f1(t) is one input and f2(t) is the other input you set the gain of the system to be G(t) = K x f1(t). Then r(t) is:

r(t) = G(t) x f2(t) = Kf1(t)f2(t)

Multiplication in the time domain is convolution in the frequency domain. If w0 is the carrier frequency, i.e. f2(t) then you wind up with a w0+w and a w0-w term for every frequency that exists in the keying waveform, f1(t). (you also have a -w0+w and a -w0-w set of terms but negative frequencies don't concern us in a real transmitter). So what do you get? If your output response from the keying circuity wound up with the fundamental, the 3rd harmonic, and the 5th harmonic you would have sidebands consisting of [w0 + fundamental, w0 + 3rd harmonic, and w0 + 5th harmonic] and [w0 - fundamental, w0 - 3rd harmonic, and w0 - 5th harmonic].

The actual bandwidth becomes twice the bandwidth of the keying waveform because of the upper and lower sidebands that are generated. If you read Mickey's original message I think you will find that he accounted for this in his calculations.

The modulation function still doesn't generate any additional frequencies that aren't already in the driving signal. If your original driving function was a 2hz square wave and you allowed only two odd harmonics through the sidebands would contain frequencies of 2hz, 6hz, and 10hz. The total absolute bandwidth of the output signal would be 20hz.

The "shape" of the keying signal in the time domain did nothing except describe the number of odd harmonics existing in the signal. It didn't generate *anything* in the modulation process beyond what was already there.

I think we agree that an output response square wave with a 5ms rise time indicates a 600hz system bandwidth (approximately). Where I think we disagree is that you say that the rise time generates the bandwidth and just stop there. I say the rise time is the result of an input driving function and a bandwidth-limited system response function, the rise time is not a *cause* but a result. I don't accept that output responses "create" anything, output responses are *created*. That means that the driving function or the system response function is something other than what Mickey and I are looking at.

tim ab0wr

RE: Bandwidth versus Keying Speed

by W8JI on June 2, 2007 Mail this to a friend!

Thank you Chen.

I looked at your page and the diagram of the sidebands within the curve set by the rise and fall shape agree with what my spectrum measurements show if I synchronize my analyzer time base to the dot generator.

I see nothing on your page that disagrees with real world equipment I have measured, and it all fits the practical world.

This has consumed too much time and I think it won't go in a useful direction for anyone, so I've said about all I can say for now.

As you correctly point out the rise and fall is very critical and even a very small glitch can cause a large problem with CW bandwidth. Some radios are too fast, some have poor shapes from ALC, some have poor shapes from poor filtering of the harmonics in the modulating waveform.

As long as we don't pretend sending slower fixes a radio and makes it narrower, I am happy. I agree a 5ms rise and 5ms fall is fast enough. Some radios that allow users to set the rise and fall add both times together, so a 5ms rise and 5ms fall is obtained at a 10ms setting.

73 and thanks
Tom

73 Tom

Bandwidth versus Keying Speed

by K5MC on June 2, 2007 Mail this to a friend!

W8JI: If I do a occupied power measurement of a steady carrier from the same rig the result is an occupied BW of 30 cycles. If I repeat it with a narrower and more selective Selective Level Meter the occupied BW of the carrier is 15Hz.

Tom, I assume you are giving us two different values of occupied/power bandwidth here. (For example, the 99.75% power bandwidth is 30 Hz and the 99.0% power bandwidth is 15 Hz?) I would appreciate knowing the percentages if you have that information handy.

I have little doubt that a 10-Hz sine wave modulating a typical ham AM rig would be doomed to failure in terms of actually seeing the two sidebands distinctly from the carrier on a spectrum analyzer. The spectral purity of the high frequency carrier is simply not good enough. I wonder how high the tone frequency would have to be before we would see on a spectrum analyzer the classic carrier/two sidebands spectral lines that many of us see in our minds when we think of tone modulated AM? 50 Hz? 100 Hz? (I remember from teaching our senior level communications lab several years ago that the tone frequency has to be "pretty" high before students really begin to see the sidebands distinctly from the carrier on the HP 8920A, but I don't believe this particular instrument is the last word on RF spectrum analyzers!)

W8JI: I have a question. My IC-751A's SSB transmitter has an occupied BW of about 2kHz with normal speech. If I talk slower does the transmitter become narrower?

If you do it under what I consider "controlled laboratory conditions" then I would say YES! If you record your audio signal that modulates the SSB transmitter when you send your fixed-length message in real time, then when you send that same message again at the slower rate by dropping the tape recorder speed to 50%, the spectra components will be only 50% along the frequency axis compared to the original message. For a very simple example, let's assume I can whistle a pure tone at 2 kHz. If my original signal is a 2-kHz whistle for 1 second, then when I repeat that signal at half the recorded speed, it will be a 1-kHz whistle that lasts 2 seconds. In sending this "message" (I concede the point that the "information" of this message is very low!) the second time I used half the bandwidth for twice as long.

Now let me ask you a question. Does the bandwidth of an FM signal depend only on the amount of frequency deviation or shift? For example, if I limit the instantaneous frequency of my FM signal to be plus or minus 75 kHz of the center frequency, is my bandwidth confined to be within 150 kHz no matter whether I use a 1-kHz tone or a 10-kHz tone as the modulating signal?

AB0WR: Nothing Chen speaks of will INCREASE the output response bandwidth, it will only reduce it from what Mickey has calculated. You seem to have a disconnect here. Remember, Chen said that Mickeys filter window is "not attenuating the keying sidebands". Yet Mickeys bandwidths are already narrower than what we are seeing the measurements show. Chen's advice will only further narrow the bandwidth and make the discrepancy between the calculations and the measurements even worse!

KE3HO: Mickey - have I unfairly summarized Chen's comments, or have I misunderstood them?

Tim and Jim, I appreciate your comments very much. It's getting really hard for me to keep up with everyone's detailed comments! Jim, as W7AY said himself, I believe you have a good understanding of Chen's comments and I also agree with almost everything Chen has said. The main thing I'm still wondering about is the spectrum plots posted by Tom. As Tim alludes to in his comments above, the 99.1% power bandwidths I calculated for "square-wave" keying at 2.4 wpm and 30 wpm were 42 Hz and 525 Hz, respectively. Tom's measurements are showing that the 99% power bandwidth is about 490 Hz at 24 wpm (10 dits per second) and is adamant that the 99% power bandwidth does not vary with the speed. However, if my model is approximately valid, then as Tim points out, 42 Hz is much smaller than 490 Hz! What's going on here?

As I've already said, I think Tom's spectrum plots are not consistent, although I do concede that his analyzer print outs clearly indicate a "resolution bandwidth" of 10 Hz. If this resolution is referring to the display resolution at 3.5 MHz over a 3 kHz span, then that is very good indeed! If Tom's plots are accurate, then the math model I used is obviously not valid for real world CW rigs, even for the special case of "square-wave keying. (And I'm sure that some actual rigs over the years have been close to that extreme case!)

That's why I was wondering what Tom's analyzer shows for a "good" AM transmitter when tone modulated at low frequencies. Obviously the spectral purity of the high frequency carrier is a limiting factor, but I'm not convinced that Tom's analyzer is not showing the effects of spectral "leakage" due to the finite data record along with the various other pitfalls when making measurements with even the best available spectrum analyzers.

In theory, at least, we should be able to look at the keying envelope of the output CW signal from an actual transmitter on an oscilloscope and model the signal mathematically as a function of time by finding its Fourier series coefficients just as I did with my assumed keying waveforms. I have access to some digital scopes at my school that should be able to do this.

I will save some comments I have regarding fundamental issues of bandwidth versus rate of information (speed) for a later post.

73, K5MC

RE: Bandwidth versus Keying Speed

by KE3HO on June 2, 2007 Mail this to a friend!

Mickey,
<< The main thing I'm still wondering about is the spectrum plots posted by Tom. As Tim alludes to in his comments above, the 99.1% power bandwidths I calculated for "square-wave" keying at 2.4 wpm and 30 wpm were 42 Hz and 525 Hz, respectively. Tom's measurements are showing that the 99% power bandwidth is about 490 Hz at 24 wpm (10 dits per second) and is adamant that the 99% power bandwidth does not vary with the speed. However, if my model is approximately valid, then as Tim points out, 42 Hz is much smaller than 490 Hz! What's going on here? >>

Here is my take on this, in light of what Chen has taught me on this subject in the last couple of days. Changing the keying speed spreads out the teeth of the comb function in the frequency domain. The spectral bandwidth of the output signal is still dominated by the window function. You can spread the comb function out as much as you want, but you will still have your window function overlapping just one tooth of the comb. The bandwidth of the resulting CW signal is dominated by the window function, the shape of the rising and falling edge of the keying waveform, at any speed until you get up to very high speeds where your window function intercepts two or more teeth of the comb. Make your sending speed as slow as you want, the bandwidth of the signal will STILL be set by the rising and falling edges of the keying waveform.

If you look at it another way, as we did early in this thread, during the rise time of the keying function the carrier is modulated by the rising waveform and the sidebands are determined SOLELY by the shape of that rising edge of the keying waveform. Same holds for the falling edge. During the tc period where the keying waveform is constant, the carrier is unmodulated and the bandwidth is determined by several factors such as the frequency stability of the oscillator, phase noise, amplitude stability of the PA, and maybe some other factors too.

The theory and the practical part agree completely.

73 - Jim

RE: Bandwidth versus Keying Speed

by W8XR on June 3, 2007 Mail this to a friend!

Tim,

Well put.

I've had a couple of comments off-list from folks that are a little intimidated by some of the DSP terms in this discussion and I've shared a more intuitive approach in an article that I've been working on that echos your comments.

So for those of you that are looking for a little less technical version of this discussion, (with a tad less shouting), please see: <http://members.toast.net/mark.amos/CW%20Bandwidth%20Analysis.pdf>

Thanks again for all the constructive comments in the thread and off-forum.

Mark
W8XR

RE: Bandwidth versus Keying Speed

by W8XR on June 3, 2007 Mail this to a friend!

Oops again - not enough coffee yet:

JIM,

Well put.

I've had a couple of comments off-list from folks that are a little intimidated by some of the DSP terms in this discussion and I've shared a more intuitive approach in an article that I've been working on that echos your comments.

So for those of you that are looking for a little less technical version of this discussion, (with a tad less shouting), please see: <http://members.toast.net/mark.amos/CW%20Bandwidth%20Analysis.pdf>

Thanks again for all the constructive comments in the thread and off-forum.

Mark
W8XR

RE: Bandwidth versus Keying Speed

by KE3HO on June 3, 2007 Mail this to a friend!

Mickey,

Shortly after posting my last comment, I reread your previous comment and I realized that you were talking about the square wave keying, not the window-shaped keying. I am doing some FT calculations to see what numbers I come up with.

Jim

RE: Bandwidth versus Keying Speed

by KE3HO on June 3, 2007 Mail this to a friend!

Mickey,

I have calculated the FT of a pulse 0.490 sec wide and a pulse 0.030 sec wide and the graphs lay right on top of each other. The envelope is the same, all that is different is the spacing of the lobes. I don't see anything to indicate that one has a bandwidth of 42Hz and the other 525Hz.

73 - Jim

Bandwidth versus Keying Speed

by K5MC on June 3, 2007 Mail this to a friend!

KE3HO: I have calculated the FT of a pulse 0.490 sec wide and a pulse 0.030 sec wide and the graphs lay right on top of each other. The envelope is the same, all that is different is the spacing of the lobes. I don't see anything to indicate that one has a bandwidth of 42Hz and the other 525Hz.

Jim, if FT means Fourier transform, then you have totally lost me. I'm looking on page 81 of Lathi's book right now and he clearly shows that the "essential" bandwidth (such as the 99% energy bandwidth) of a single gate (rectangle) pulse is inversely proportional to the pulse's duration. The Fourier magnitude spectrum plot of a 0.490-second pulse is "stretched out" much further than that of a 0.030-second pulse. (I'm talking about the actual baseband pulses here, which I referred to as the "square-wave" keying waveforms in my article.) If what you are saying is true, then every signal analysis textbook I have will have to be rewritten.

73, K5MC

Bandwidth versus Keying Speed

by K5MC on June 3, 2007 Mail this to a friend!

Here is a very interesting email I just received from SM0AOM.

73, K5MC

SM0AOM: I have been following the discussion on the "keying speed vs bandwidth" subject on eham.net with great interest. As you may have found, I support your and others view that the keying or modulation rate indeed have an influence on the bandwidth of the A1A emission.

It may well be that the generation of "key clicks" is primarily a function of the lack
of proper rise and fall times in the keying envelope function, but I find from a
practical radio engineering and regulatory point of view that the discussion somewhat has gotten out of hand.

The A1A emission bandwidth as used in the ITU Radio Regulations assumes some fundamental properties of the keying shaping function in order to be valid, the most important that the slopes are free of discontinuities.

The examples used by i.a. W8JI are not very well connected to the assumptions used in the ITU-RR, as the keying slopes are not discontinuity-free, and also that the "build-up" or rise time is much faster that needed for a given keying speed or modulation rate. In the ideal world, these times should be a fraction (10 - 20 %) of the time of the shortest signal element used.

For you consideration, I am attaching the latest version of the CCIR/ITU-R Recommendation SM.328 that I was able to find, and also a scan from the Telefunken literature that I referred to earlier. It shows keying spectra of a 40 Baud (about 50 WPM) A1A emission without (left) and with (right) application of the CCIR keying shaping. The "resolution bandwidth" was well below 10 Hz in these spectra. Note that the "sidelobes" that show up in W8JI:s spectrum plots are absent.

It seems that the detalied regulations imposed by the FCC can lead to interesting consequences. If it should be proven that all A1A or CW emissions,regardless of keying rate, have 500 Hz occupied bandwidth the legal framework for band segmentation may very well "fall apart". In Europe, on the other hand, we are mostly not affected by such details any longer.

As a side-effect of telecoms market deregulation in Sweden, all references to the ITU-RR were removed from the domestic amateur radio regulations, with the consequences that suddenly there were no technical requirements any longer on amateur radio emissions. As long an emission with sidebands is contained within the band limits, it can have any spectral contents, which means that "key-clicks" or excessive bandwidth are not illegal in any sense.

Due to "lack of interest" from the regulators, any regular monitoring of the amateur radio bands also has come to an end, as amateur radio in Sweden has become "license-exempt" and therefore has no right to file interference complaints.

Finally, as the interest in A1A emission bandwidth question may not be entirely confined to the American continent only, it may be appropriate to initate a "re-write" of both the relevant parts of the ITU-R Recommendation SM.328 and the the Radio Regulations based on the argumentation put forward. The proper way to do this would be to get the FCC/US Government to file a petition to the ITU Secretariat to initiate an Interim Working Party (IWP) to analyze the question within the framework of the Study Group I.

There may however be practical problems to convene such an IWP, as the interest for the emission characteristics of A1A can be expected to be very small outside the amateur radio community.

It is most unfortunate that Peter, G3RZP, still is in hospital and cannot comment on this matter on eham.net. He has a much longer and more recent affliation with the ITU-R Study Groups than I have.

Sincerely,

Karl-Arne Markstrom
SM0AOM

RE: Bandwidth versus Keying Speed

by W8JI on June 3, 2007 Mail this to a friend!

A few people can post whatever they want based on any analysis they put forth, but that does not change how the systems we all use work.

In the CW systems we all use and have all used, the bandwidth of the signal at a minimum is ALWAYS determined by the shape and duration of the rise and fall. The keyclick at the start and fall has **exactly** the same distributed energy or peak enevlope power at a give bandwidth away from the carrier regardless of keying speed.

This is because that transition point and the sidebands generated to accommodate that transition in level does not change.

Even if a person's logic or mind cannot wrap around that very simple concept, absolutely ANYONE on the face of this earth with a receiver having narrow filters and a transmitter can indeed confirm what I say is true.

It is the nature of CW receivers that they cannot store the energy from a click until the next click come along, except in the AGC system. The AGC being a peak hold system regustes and holds the peak level, but does not add successive clicks to the voltage unless it has slow attack time. But once it is up, it is up and it doesn't matter if one more click per second follows or 40 clicks per second follow. The IF and audio processing right through the CW operator’s brain cannot store the energy of the carrier or the click. A faster or slower repletion of clicks simply means they occur more often or less often, but the level and bandwidth is exactly the same. Only when the speed is so fast or slow the envelope rise and fall changes, or if the clicks are so infrequent most of the desired signal can be copied without harm, are clicks impacted by speed.

So what we are left with is a click of constant amplitude regardless of speed; with the offset or bandwidth of that click tied 100% directly to the envelope transition formation. The sole exception would be another defect like FM’ing, Hum, or composite noise; but there are very few radios where flaws in the nature of the carrier dominate the strong signal produced by the rising and falling edges. Those radios are the rare exception and are caused either by serious design errors (like the IC-775DSP where the VCO seeps during the transition) or defects unique to a particular radio. In such a case the bandwidth of the envelope rise and fall sets a lower bandwidth limit, while the spurious or purity issue extends the bandwidth even further.

Anyone can measure the effects I described above.

Without spending the time to do this all the good things that have been accomplished over the past few years will be turned aside and a few people really trying to understand how this all works will walk away either confused or with a distorted view of what actually happens.

For all those who think the bandwidth changes with speed, I suggest they do a few simple experiments. That will solve the whole issue.

It’s just totally beyond me why anyone would spend so much energy arguing a point endlessly without making some attempt to confirm it through experiment.

It sounds to me like people want reality to change and conform to what they explain, instead of observing the real world effect and explaining it. That’s not good science. It certainly does not advance the state of the art or help anyone. It is harmful, not helpful.

73 Tom

RE: Bandwidth versus Keying Speed

by W9AC on June 3, 2007 Mail this to a friend!

W8JI:

> "It’s just totally beyond me why anyone would spend so much energy arguing a point endlessly without making some attempt to confirm it through experiment..."

To Tom's point, the Scientific Method demands the testing of a theorem or hypothesis. Theories which cannot be tested, because, for instance, they have no observable ramifications, do not qualify as scientific theories. Those who have been part of this discussion and who are engaged in the study and/or teaching of advanced academia have had exposure to the Scientific Method since the time of their first studies in elementary school.

The Scientific Method requires that a hypothesis be ruled out or modified if its predictions are clearly and repeatedly incompatible with experimental tests.

Bandwidth versus Keying Speed

by K5MC on June 3, 2007 Mail this to a friend!

W8JI: In the CW systems we all use and have all used, the bandwidth of the signal at a minimum is ALWAYS determined by the shape and duration of the rise and fall. The keyclick at the start and fall has **exactly** the same distributed energy or peak enevlope power at a give bandwidth away from the carrier regardless of keying speed.

Tom, let's agree to call the bandwidth you describe above as the "keyclick" bandwidth so that we can all talk the same language. I have no problem or disagreement with what you are saying regarding the "keyclick" bandwidth. I've tried to make that point clear from day one. At the end of my article I said that the concept of "power/occupied" bandwidth as defined in Couch's textbook does not say that the strength of the individual key clicks heard decrease as the sending speed is lowered.

I'm certainly willing to learn from you and anyone else that posts comments here. Among a number of hams, SM0AOM has been very helpful to me. Here's a quote from an email that Karl-Arne sent me a few hours ago:

SM0AOM: For you consideration, I am attaching the latest version of the CCIR/ITU-R Recommendation SM.328 that I was able to find, and also a scan from the Telefunken literature that I referred to earlier. It shows keying spectra of a 40 Baud (about 50 WPM) A1A emission without (left) and with (right) application of the CCIR keying shaping. The "resolution bandwidth" was well below 10 Hz in these spectra. Note that the "sidelobes" that show up in W8JI:s spectrum plots are absent.

Unfortunately, eham doesn't allow me to post pictures, but I will be happy to forward the spectrum plots from Karl-Arne/Telefunken to anyone via email. (My email address is k5mc@arrl.org) Just as SM0AOM says, the two oscillograms from an actual transmitter clearly show the distinct keying sidebands (the discrete line spectrum) rather than continuous spectra plots as posted by W8JI.

It's finally becoming clear to me that there are some significant differences in the keying characteristics between various CW rigs. However, there's no doubt in my mind that the assumptions I used in my article will provide the correct value of the "power" bandwidth for equipment having the keying characteristics shown in Karl-Arne's oscillograms. For all of the CW rigs that have continuous spectra rather than discrete line spectra, the Fourier series approach that I used in my article will obviously not work.

I really hope that everyone will try to remember that Tom's "keyclick" bandwidth is not the same thing as the "power" bandwidth as defined by Couch [1]. I will try to stop using the term "occupied" bandwidth as being equivalent to Couch's "power" bandwidth.

[1] Leon W. Couch, Digital and Analog Communication Systems, 7th ed., Pearson Prentice Hall, 2007.

73, K5MC

Bandwidth versus Keying Speed

by K5MC on June 3, 2007 Mail this to a friend!

W8JI: I have a question. My IC-751A's SSB transmitter has an occupied BW of about 2kHz with normal speech. If I talk slower does the transmitter become narrower?

K5MC: If you do it under what I consider "controlled laboratory conditions" then I would say YES! If you record your audio signal that modulates the SSB transmitter when you send your fixed-length message in real time, then when you send that same message again at the slower rate by dropping the tape recorder speed to 50%, the spectra components will be only 50% along the frequency axis compared to the original message. For a very simple example, let's assume I can whistle a pure tone at 2 kHz. If my original signal is a 2-kHz whistle for 1 second, then when I repeat that signal at half the recorded speed, it will be a 1-kHz whistle that lasts 2 seconds. In sending this "message" (I concede the point that the "information" of this message is very low!) the second time I used half the bandwidth for twice as long.

K5MC: Now let me ask you a question. Does the bandwidth of an FM signal depend only on the amount of frequency deviation or shift? For example, if I limit the instantaneous frequency of my FM signal to be plus or minus 75 kHz of the center frequency, is my bandwidth confined to be within 150 kHz no matter whether I use a 1-kHz tone or a 10-kHz tone as the modulating signal?

I'm still looking forward to hearing from W8JI regarding the comments above.

73, K5MC

Bandwidth versus Keying Speed

by AB7E on June 3, 2007 Mail this to a friend!

W8JI:

"It’s just totally beyond me why anyone would spend so much energy arguing a point endlessly without making some attempt to confirm it through experiment."

I'm an electrical engineer myself and totally believe in the absoluteness of mathematics, at least in the context of this discussion, but those who put their faith exclusively in the results of <their> mathematical analysis without even considering whether they have misapplied it seem even less likely to be influenced by real world measurements. If none of the several intuitive explanations put forth here in this thread so far have convinced them they have missed something, why should a measurement that they can so easily attribute to other factors do so?

I'm astounded that supposedly rational people can claim that speeding up the rate of keying transitions, without changing the nature of the individual transitions themselves, can affect the bandwidth that is affected. It's funny how Fourier analysis, which was developed to give us a quantified understanding of observable physical behavior, can be so erroneously applied as to completely contradict that same observable behavior.

Bandwidth versus Keying Speed

by K5MC on June 3, 2007 Mail this to a friend!

KE3HO: I have calculated the FT of a pulse 0.490 sec wide and a pulse 0.030 sec wide and the graphs lay right on top of each other. The envelope is the same, all that is different is the spacing of the lobes. I don't see anything to indicate that one has a bandwidth of 42Hz and the other 525Hz.

K5MC: Jim, if FT means Fourier transform, then you have totally lost me. I'm looking on page 81 of Lathi's book right now and he clearly shows that the "essential" bandwidth (such as the 99% energy bandwidth) of a single gate (rectangle) pulse is inversely proportional to the pulse's duration. The Fourier magnitude spectrum plot of a 0.490-second pulse is "stretched out" much further than that of a 0.030-second pulse. (I'm talking about the actual baseband pulses here, which I referred to as the "square-wave" keying waveforms in my article.) If what you are saying is true, then every signal analysis textbook I have will have to be rewritten.

I meant to say that the magnitude spectrum plot of the 0.030-second pulse is "stretched out" much further than that of a 0.490-second pulse. That is, the "essential" or "energy" bandwidth (as defined in electrical engineering textbooks!) of the 0.030-second pulse is significantly larger than that of the 0.490-second pulse.

Much of the debate concerning my article has obviously been created because of the different terminology used by the various posters. I have about worn down my keyboard typing "power bandwidth" rather than merely "bandwidth" because I wanted everyone to understand that there are many different definitions of bandwidth in the signal analysis/communications world. AB0WR, W1YW, and SM0AOM, in particular, have really understood the purpose of my article because they are electrical engineers by formal training and experience.

73, K5MC

RE: Bandwidth versus Keying Speed

by AB0WR on June 3, 2007 Mail this to a friend!

<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<,
ab7e:"I am an electrical engineer myself and totally believe in the absoluteness of mathematics, at least in the context of this discussion, but those who put their faith exclusively in the results of <their> mathematical analysis without even considering whether they have misapplied it seem even less likely to be influenced by real world measurements. If none of the several intuitive explanations put forth here in this thread so far have convinced them they have missed something, why should a measurement that they can so easily attribute to other factors do so?

I'm astounded that supposedly rational people can claim that speeding up the rate of keying transitions, without changing the nature of the individual transitions themselves, can affect the bandwidth that is affected. It's funny how Fourier analysis, which was developed to give us a quantified understanding of observable physical behavior, can be so erroneously applied as to completely contradict that same observable behavior. "
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

Rather than just denigrate those who ARE trying to understand what inputs and transfer functions are causing the output function why don't you tell us what YOUR model of the input driving functions and the system transfer functions are?

You say you totally believe in the absoluteness of mathematics and then turn around and speak of having faith in "intuitive explanations"?

If you are an electrical engineer you should have some training in the analysis of linear systems. You should remember than in the frquency domain Output(s) = Input(s)Transfer(s).

So far all I have heard is the "intuition" that the output function causes the output function because it just does. I have seen no mathematical modeling from anyone making that "intuitive" claim, however. The only math that I have seen, and it has been confirmed by everyone so far, is that a square wave of fundamental frquency w0 has frequency components made up of w0 and all odd harmonics. And those odd harmonics have amplitudes determined by a 1/n factor.

I have yet to see anyone show any math as to how that all square wave input driving functions, of any fundamental frequency, gets transformed by a transfer function into a bandlimited waveform of about 500hz.

Instead of depending on the "intuitive" explanation that the output causes the output, tell us what your Input(s) and Transfer(s) model is that generates the output function we see on the spectrum analyzer.

Then perhaps we'll see the discussion get furthered rather than just see continued denigrations of how those actually using the math are "irrational".

ab7e"I'm astounded that supposedly rational people can claim that speeding up the rate of keying transitions, without changing the nature of the individual transitions themselves, can affect the bandwidth that is affected."

You are astounded that square waves of varying fundamental frequences (i.e. "speeding up the rate of keying") have different power bandwidths? When and where did you get your electrical engineering degree?

tim ab0wr

RE: Bandwidth versus Keying Speed

by WA0LYK on June 3, 2007 Mail this to a friend!

>>W9AC
>>>>W8JI:
>>>>
>>>>> "It’s just totally beyond me why anyone would
>>>>spend so much energy arguing a point endlessly
>>>>without making some attempt to confirm it through
>>>>experiment..."

>>To Tom's point, the Scientific Method demands the
>>testing of a theorem or hypothesis. Theories which
>>cannot be tested, because, for instance, they have no
>>observable ramifications, do not qualify as
>>scientific theories. Those who have been part of this
>> discussion and who are engaged in the study and/or
>>teaching of advanced academia have had exposure to
>>the Scientific Method since the time of their first
>>studies in elementary school.

>>The Scientific Method requires that a hypothesis be
>>ruled out or modified if its predictions are clearly
>>and repeatedly incompatible with experimental tests.

What you are saying is that every text book written in the last 100 years needs to be tossed out and replaced by the hypothesis that the input rise time of a square wave defines the bandwidth and frequencies included, not the fourier transform of a periodic wave.

I'm sorry, but there will need to be a lot more peer review before this is done. I have not seen one engineer or scientist publish even an article here or post on this thread recommending that W9CF's mathemetics be used to define the bandwidth of a modulated signal in all new textbooks. I wonder why?

I had a long discussion with AB0WR about this. There appear to me to be several things at work here.

One, look on the ARRL web page for reviews of transmitters. You will find that the keying waveform IS NOT duplicated exactly on the output envelope. By definition, this means the transmitter as a system is non-linear. What is the predominate effect of a non-linear sytem? It is intermod products. These have nothing to do with the rise time, only the frequency products contained in an input waveform.

K5MC has already defined the frequency products for low speed keying using fourier analysis and they don't extend out near far enough to generate the kinds of bandwidth W8JI observes, but intermod products would. The only alternative is if you are ready to say that the fourier analysis of a periodic waveform or even a step function is invalid.

Two, if rise times are what causes the minimum bandwidths of 200 - 400 Hz, then how do signals like psk31, psk63 or psk125 achieve such small bandwidths? You can't just say that the math model for determining CW bandwidth by analyzing the rise times applies to CW only. It must apply to any modulating waveform like psk, rtty, etc.

W8JI mentions the FT1000's well known problem with key clicks on his web page and attributes it to rise time problems. This isn't the case. Have a look at Inrad's web page and they explain the problem. The FT1000's ALC doesn't act fast enough and a severe power spike occurs at the leading edge of a CW waveform. The spike is large enough to drive the amps into saturation causing intermod products to be generated.

The Inrad site also mentions the OmniVI+ as having an ALC problem causing distortion of the CW waveform. I suspect this is generally where the problem is originating.

I have dug out my Icom 745, 751 and 761 service manuals. These rigs all use ALC and its time constant to control the output waveform. If you look, every IF and RF amplifier in the transmit chain has a feedback path from ALC. Any time ALC is used in this fashion what you have are non-linear amplifiers, that is, the gain function varies, which will result in intermod products being generated. PSK31 users have known this for a long time. If you see ALC action on a psk31 transmitter, you see intermod products too.

W8JI and W9CF have done a good job analyzing the OUTPUT frequency distribution based upon the rise time of the output but they (and others) then make the logical jump that this also means the output follows the input therefore the rise time of the input is the controlling factor. This logical jump isn't justified without knowing what the transfer function of the transmitter looks like and that it is a linear function. That is, what you put in is what you get out. The ARRL reviews of the CW input/output waveforms conclusively show this is not the case. In math terms:

Input function X Gain transfer function = Output function.

If you don't know the "gain function", you can't know the relationship between the input and output. Therefore, making conclusions about one from the other is not logically correct.

K5MC has shown conclusively that the fourier analysis of the input waveform does show the discreet frequencies in that waveform. Consequently, he has confirmed through the Scientic Method that theory meets results. Yet, there appears to be a wider bandwidth being generated. The logical conclusion is that the transfer function of the transmitter is NOT linear and therefore other intermod products are being generated.

This has the advantage of no one having to say that the analysis (and last 100 years of theory)of the input is wrong or that the analysis of the output is wrong. It simply means no one has arrived at a satisfactory mathemetical description of the transfer function in a typical transmitter.

I will be trying to duplicate K5MC's experiment with function generators. The shaping circuits will be filters, not variable gain amplifiers. I will then run the signal through a linear amplifier to see what comes out. I don't have a spectrum analyzer so I can't use RF darn it.

My guess is that using a simple crystal controlled transmitter with no mixers and only confirmed linear amplifiers will provide a whole different measurement than what Tom has seen with commercial transmitters with multiple variable gain amplifiers and several mixers.

Jim
WA0LYK

Bandwidth versus Keying Speed

by K0RU on June 3, 2007 Mail this to a friend!

You have got to be kidding right? These are engineers? Of what? for what?

Talk about a waste of bandwidth... Duh! read above!

K0RU - Rob
Back to QRQ CW... Where life has a life.

Bandwidth versus Keying Speed

by K5MC on June 3, 2007 Mail this to a friend!

K5MC: AB0WR, W1YW, and SM0AOM, in particular, have really understood the purpose of my article because they are electrical engineers by formal training and experience.

I failed to include WA0LYK in my list above.

WA0LYK: My guess is that using a simple crystal controlled transmitter with no mixers and only confirmed linear amplifiers will provide a whole different measurement than what Tom has seen with commercial transmitters with multiple variable gain amplifiers and several mixers.

Jim, I believe such a rig does have the keying characteristics that I assumed in my simple Fourier series model. I have a variety of rigs myself, including some old Ten-Tecs manufactured 25 to 30 years ago. I'm hoping the HP analyzer I have at school will be adequate to see a discrete line spectrum similar to the Telefunken oscillograms emailed to me by SM0AOM.

BTW, it appears that the arrl.org e-mail domain is down. If anyone would like to see the oscillograms forwarded to me by SM0AOM, you might want to try k5mc@arrl.net rather than k5mc@arrl.org.

73, K5MC

Bandwidth versus Keying Speed

by K5MC on June 3, 2007 Mail this to a friend!

K5MC: I'm hoping the HP analyzer I have at school will be adequate to see a discrete line spectrum similar to the Telefunken oscillograms emailed to me by SM0AOM.

I think the lack of sleep is really starting to catch up with me. I've used the word "oscillograms" several times when what I actually have from SM0AOM are frequency spectrum plots.

73, K5MC

RE: Bandwidth versus Keying Speed

by AB0WR on June 3, 2007 Mail this to a friend!

w9cf:"The Scientific Method requires that a hypothesis be ruled out or modified if its predictions are clearly and repeatedly incompatible with experimental tests. "

The scientific method also requires that a HYPOTHESIS be formulated as the first step.

While I have seen your analysis of the output of a CW transmitter I have yet to see your hypothesis on what the input driving waveform and system transfer function needs to be in order to come up with the spectrum graphs Tom has shown.

Just saying that the output response we see will always be the output response we see because the output response causes the output response just isn't acceptable to me.

With that kind of logic we would not have any knowledge of how things actually work at all.

I suspect that WA0LYK's analysis is correct. It would appear to me that it is confirmed by the fact that many of the CW envelopes seen from CW transmitters actually have an exponential leading and trailing edge. Bandwidth limited square waves do should not have exponential leading and trailing edges.

That would lead me to believe that in many of these transmitters the AM modulation being done in the modulated stage by varying the gain of the system based on the input driving function (i.e. the bandwidth limited square wave) but it is also being varied by an exponential gain transfer function existing in the stage (e.g. an RC low-pass filter being used as a gain control element).

As WA0LYK pointed out this results in a non-linear stage which will generate every conceivable intermod product combination from the frequency elements in the conjoined bandwidth limited square wave thus greatly extending the bandwidth of the transmitted signal.

If this is, in fact, what is causing these CW output responses, which should be much, much narrower than they apparently are, to be extended far beyond theoretical limits there are certainly things that can be done to alleviate this. That is why it is so important to have a firm understanding of both the input driving function as well as the system transfer function. If you just assume the output causes the output you will never be able to make anything any better.

From what I can tell, the 751a keys the an IF oscillator on and off to generate CW. It would be very, very interesting to get an oscilliscope picture of the waveform envelope right after the oscillator and compare it to the transmitter output. I see what I can do to get that. It would help in understanding what is going on.

tim ab0wr

RE: Bandwidth versus Keying Speed

by AB0WR on June 3, 2007 Mail this to a friend!

w8ji:"It’s just totally beyond me why anyone would spend so much energy arguing a point endlessly without making some attempt to confirm it through experiment.

It sounds to me like people want reality to change and conform to what they explain, instead of observing the real world effect and explaining it. That’s not good science. It certainly does not advance the state of the art or help anyone. It is harmful, not helpful. "

Tom,

It is comments like these that make you seem like a total jerk to everyone. It's like a small child complaining that the other kids don't have as many nice toys and saying "why do they want to play with mine?".

Not everyone has $15000 spectrum analyzers sitting in their basements to conduct "experiments" like these. We get by with what we can afford after buying shoes for the kids, paying the car insurance and mortage, and perhaps taking Momma out to supper once in a while.

We depend on others who *DO* have access to the equipment to assist us in learning about this subject we call radio. Whether you like it or not that is just the way the world works.

Whether you remember it or not, Mickey *DID* conduct one of these experiments. Since the results didn't match your worldview you apparently discounted them totally and just blew them out of your mind. And you speak of others wanting reality to change. Heal thyself, physician!

You still seem to be stuck on saying that the output is the output because the output generates the output. You haven't provided a single mathematical model for how the output comes into being. Rise time on an output response is NOT generated by the output response. It is *GENERATED* by the multiplication of a driving function and a transfer response function. When you can offer some insights into what those driving functions and what those transfer response functions might be then I, at least, will be more than happy to look at them and consider them.

Good science attempts to explain the world. It requires *both* hypotheses and experimental results. So far you have only provided the experimental results. W9CF has explained what the output looks like in the frequency domain. Quit complaining about those of us attempting to work out the hypotheses for how this response is generated unless you can contribute something to that piece as well.

If this makes you mad and you want to take your toys and go home, so be it. I found out a long time ago that I'm not indespensible, neither are you. We'll all be sorry to see you go but I doubt anyone will beg you to stay in the conversation.

tim ab0wr

RE: Bandwidth versus Keying Speed

by AB0WR on June 3, 2007 Mail this to a friend!

w8xr:"I've had a couple of comments off-list from folks that are a little intimidated by some of the DSP terms in this discussion and I've shared a more intuitive approach in an article that I've been working on that echos your comments."

Mark,

Some things you may want to consider thinking about so you'll have an answer if someone quizzes you on your writeup.

Your text states that the slope of the frequency determines the bandwidth of the signal (e.g a 50hz sinewave has a steeper slope than a 25hz sinewave).

Yet a cosine wave of 50hz and a cosine wave of 1000000hz neither have any bandwidth at all, their bandwidths are zero.

Because their bandwidths are zero they can't actually have a signaling rate.

A square wave of 50hz and a square wave of 100000hz both have the same slopes with the same absolute bandwidths (their power bandwidths are differ widely) yet their signaling rates are vastly different.

These would seem to be connundrums generated by your explanation.

You might also want to consider something like a raised cosine filter. If you have Filter1 with a bandwidth of T and roll-off of Beta=1 and a Filter2 with a bandwidth of 2T and roll-off of Beta=1 which is the narrower filter and which has the steepest slopes in the time domain?

Another connundrum generated by your explanation.

I think your explanation would help a novice progress in understanding what is going on a lot. But it might also lead that same novice into some bad paradigms if they ever intend to progress on to actually studying the subject at a college level.

Just something to think about.

tim ab0wr

Bandwidth versus Keying Speed

by K5MC on June 3, 2007 Mail this to a friend!

K5MC: In closing, however, I do want to point out that if I have to be subjected to key clicks when operating CW, I would much prefer that the offending transmitter send at a speed of 1 word per 20 minutes rather than 20 words per minute!

The sentence above is the very last one in my article. What was I trying to say here? It was my attempt (apparently, with hindsight, a rather poor one) to vividly illustrate the concepts of AVERAGE power and POWER bandwidth in a simple manner. Let's discuss and compare the two signals above.

In our scenario, the "offending" transmitter is sending at the rate of 20 wpm. For simplicity, let's assume the keying envelope of the CW signal is essentially square wave when we observe it on a decent oscilloscope. Let's assume this transmitter sends a particular message that requires exactly 1 minute of transmission time at 20 wpm.

On the other end, the receiving operator has chosen a filter bandwidth of 250 Hz to copy the 20-wpm message. Unfortunately, the receiving operator misses most of the message because of noise. What can be done to improve this situation?

One approach is to increase the power at the transmitter. But let's assume that that is not an option in this case. Another possible approach is to slow down the rate of transmission! The sending station decides to slow down all the way to 1 word per 20 minutes and, for the sake of discussion, we will assume the receiving operator has plenty of time as well. So the sending operator slows down to 1 word per 20 minutes! (We're talking true proportional spacing here on our code.) Since it took 1 minute to send the message at 20 wpm, it will require 20 minutes to send that same message at 1 word per 20 minutes.

Now what does the receiving operator do before copying this very slow message? He reduces his receiver's bandwidth! He knows that the "essential" or "power" bandwidth of this very slow message is much lower than the "essential" or "power" bandwidth of the faster signal. There's no question that the strength of the individual key clicks generated by the transmitter are just as bad at 1 word per 20 minutes as they were at 20 wpm. But our receiving operator isn't "worried" about the key clicks, his job is to copy the message.

There's no question that W8JI hears the key clicks just as loudly 5 kHz off the transmitter's frequency whether the sending speed is 20 wpm or 1 word per 20 minutes. Yes, indeed, the "keyclick" bandwidth is the same no matter what the speed of transmission is. If W8JI has the patience to hang around for the 20 minutes that it takes to resend the message, then W8JI will hear the same total number of clicks the second time around that he did the first time the message was sent.

The scenario I've just described illustrates a very basic concept used in communication systems, both amateur and commercial. W1YW mentioned EME as one area in which hams do it and I followed up Chip's post by mentioning QRSS.

My scenario above also illustrates essentially the same principle that I used in answering W8JI's question about "talking slower" on phone! I answered W8JI's question (and then asked him a question concerning the bandwidth of an FM signal), but I've yet to see a response from Tom on these particular issues. I think he realizes that the "game" is basically over once he responds to these issues.

73, K5MC

Bandwidth versus Keying Speed

by AB7E on June 3, 2007 Mail this to a friend!

AB0WR: <You say you totally believe in the absoluteness of mathematics and then turn around and speak of having faith in "intuitive explanations"?>

I referred to the intuitive explanations that W8JI, KE3HO, and others have used to describe why the original article by K5MC does not directly relate to observable bandwidth, and their attempts to rationalize where the subsequent differences in viewpoint between you and they are coming from. I don't have "faith" in merely intuitive explanations of any sort, and I never said intuition trumps math ... only the poor or skewed application of it.

AB0WR: <You are astounded that square waves of varying fundamental frequences (i.e. "speeding up the rate of keying") have different power bandwidths?>

I'm astounded that you and K5MC keep pounding on the concept of power bandwidth as if it were relevant. It doesn't directly relate to our collective use of spectrum. A signal with bad rise/fall times is going to mess up everything within a certain bandwidth for any practical keying speed. Yes, if you want to transmit that same clicky signal slow enough, someone might be able to carry on a conversation between the clicks, but that isn't a very useful or practical adjunct of the concept of power bandwidth. If you wanted to stick with a merely mathematical concept, why not just say so? It would have saved a lot of confusion. But then of course the original article wouldn't have been written either ....

AB0WR: <When and where did you get your electrical engineering degree?>

1969, University of Minnesota. But, uh ... it seems to me that you might be carrying the innuendo a bit far here.

Dave AB7E

Bandwidth versus Keying Speed

by K5MC on June 4, 2007 Mail this to a friend!

I've finally figured out what W8JI is showing in his spectrum plots! It is definitely NOT the "occupied" bandwidth defined by the FCC!

W8JI is showing us the spectrum of his Icom rig during the turn-on transient, but that is NOT the definition of occupied bandwidth as defined by the FCC. If he will look at the spectrum over the entire keying period from turn on to turn off over a "string of dits" as I did in my article, he will see a discrete line spectrum similar to that shown in the Telefunken literature forwarded to me by SM0AOM.

The spectrum plots posted by W8JI are continuous because his analyzer is triggered at the same point - the leading edge of the CW signal - over and over. Since his analyzer is effectively just looking at a finite pulse (around 5 ms or so in duration), he sees a continuous spectrum. As long as the rise/fall times and shapes are constant, the "occupied" bandwidth as given by W8JI's analyzer will read essentially the same value regardless of speed. The shapes of the spectrum plots will vary from rig to rig depending upon the waveshaping of the keying pulse, but the plots themselves will follow the "rules" as discussed by W9CF and W7AY.

I'm truly embarrassed that it has taken me this long to finally figure out what W8JI's plots are really about! I've been sidetracked for several days thinking about leakage and various other issues (the spectral purity of the carrier), but it's simply been another case of apples and oranges.

As I've said many times now, the occupied bandwidth as defined by the FCC does vary with speed. If the FCC comes to your house to measure the occupied bandwidth of your transmitter, I can assure you that the FCC engineer will NOT operate his spectrum analyzer the way W8JI did when capturing the turn-on transients of his Icom 751A. What W8JI is demonstrating in his spectrum plots is what I've started calling the "keyclick" bandwidth. I'm not "knocking" the concept of such a bandwidth! The idea of shaping the turn-on and turn-characteristics of your keying waveform is important. But the "keyclick" bandwidth is NOT the power/occupied/essential bandwidth as defined by either the FCC or by any self-respecting electrical engineer!

If you have read my scenario about sending information in the presence of noise (20 wpm versus 1 word per 20 minutes), you should also begin to understand why the concept of power/occupied/essential bandwidth is very important to electrical engineers! It is far from being merely a "mathematical concept" as apparently believed by AB7E. (Perhaps AB7E focused on electric power systems during his college days!)

73, K5MC

Bandwidth versus Keying Speed

by K5MC on June 4, 2007 Mail this to a friend!

K5MC: The idea of shaping the turn-on and turn-characteristics of your keying waveform is important. But the "keyclick" bandwidth is NOT the power/occupied/essential bandwidth as defined by either the FCC or by any self-respecting electrical engineer!

I hope everyone knows that I meant to type "turn-on and turn-off characteristics" in the sentence above.

I want to thank all the hams who have encouraged me during this thread with their posted comments and private emails. Without their support I probably would have given up this effort about a week ago!

73, K5MC

RE: Bandwidth versus Keying Speed

by AB0WR on June 4, 2007 Mail this to a friend!

AB7E:"'m astounded that you and K5MC keep pounding on the concept of power bandwidth as if it were relevant. It doesn't directly relate to our collective use of spectrum. A signal with bad rise/fall times is going to mess up everything within a certain bandwidth for any practical keying speed. Yes, if you want to transmit that same clicky signal slow enough, someone might be able to carry on a conversation between the clicks, but that isn't a very useful or practical adjunct of the concept of power bandwidth. If you wanted to stick with a merely mathematical concept, why not just say so? It would have saved a lot of confusion. But then of course the original article wouldn't have been written either ..."

Let's concentrate on the statement "A signal with bad rise/fall times is going to mess up everything within a certain bandwidth for any practical keying speed."

Question 1: what is a bad rise and fall time? One that is longer or one that is shorter? Tom says one that is longer is worse.

Question 2: How far out in the spectrum is the 31st harmonic (amplitude = 1/30) of a 2hz square wave (5wpm) compared to a 10hz square wave? How far out is the 101st (amplitude = 1/100) harmonic for each?

Question 3: Does the frequency of the 101st harmonic for a 2hz square wave compared to a 10hz square wave tell you anything about how badly each will bother a ham that is 1khz away?

Question 4: What is this "certain bandwidth" of which you speak?

tim ab0wr

RE: Bandwidth versus Keying Speed

by WA0LYK on June 4, 2007 Mail this to a friend!

I still plan to conduct some experiments on the "keyclick" issue. I've just got a sneaking suspicion that most of the rig manufacturers are using ALC to control the pulse edges which result in non-linear amplifier responses during the leading and trailing edges with the corresponding intermod products. Since this non-linearity would only occur during the rising and trailing edge shaping, the corresponding intermod products would only occur at these times also.

It is too easy to take the cheap way out and do this rather than provide actual pulse shaping filters and removing ALC feedback.

I believe this is why psk31 requires one to not see any ALC action. Most folks just assume the intermod generated in this mode arises from overdriving the final amps when ALC is seen but I don't think that is the only isssue. I'm pretty sure the non-linearities introduced by ALC are at least part of the problem also.

That's why I expect a simple rig will end up much cleaner than today's commercial rigs that use an ALC feedback loop to vary amplifier gains.

Jim
WA0LYK

RE: Bandwidth versus Keying Speed

by W8XR on June 4, 2007 Mail this to a friend!

Tim,

Yes that issue of the raised sine "bandwidth" needs some wordsmithing.

In the context of the article, at least when used in a mixer, the signalling rate of a 25hz modulating raised sine wave is 50 elements per second. But, this really is the degenerate case, used to illustrate the concept of mixer output. (Yes, this is contrary to the filter approach and might cause some paradigm issues later, but it's probably more in line with what people learn while studying for the ham exams.)

Another problem that I noticed while reviewing your comments is that the sample waveforms really do need to have labled X and Y axes. I had removed them for simplicity's sake, but the illustrations really could be misleading without them. (For instance, none of the sample wave forms I used have negative amplitude components, as might be misconstrued without labled axes.)

Also, I should have a section that points out discontinuity issues in harder keying waveforms and their effect. (More illustrations in general would be good.)

I think that the "filters" approach is a more advanced albeit interesting one. This will probably be a good place to start a "Beginner's DSP" article. I believe it might just be confusing at this level.

Regarding "lead a novice to some bad paradigms" - you're right. As an educator, I'm sure you're familiar with the tightrope between providing the "whole truth" and confusing the student. I'm just experiencing this with my 10 yo son regarding questions about sex...

Maybe footnoting the tricky parts and providing some links to the larger questions in-line would help.

Thanks for the constructive comments.

Mark

RE: Bandwidth versus Keying Speed

by WR8Y on June 4, 2007 Mail this to a friend!

W8JI:
""""The off and on transitions ALWAYS occupy the same overall bandwidth because they are caused by rise and fall periods, not the spaces between the rise and fall times.

The spaces between the rise and fall times cannot affect the bandwidth occupied by the rises and falls. The rises and falls are so brief they set the ultimate space occupied by the CW signal, not the much slower Morse rate.

I think the difference of opinion would go away if people considered how the system actually works.

You cando this by sending dots and tuning across the signal with a real receiver.

73 Tom""""

With all of the intellectual masterbation going on in this thread, this post is easily missed - but not easily DISmissed!

Mark

Bandwidth versus Keying Speed

by K5MC on June 4, 2007 Mail this to a friend!

K5MC: Since it took 1 minute to send the message at 20 wpm, it will require 20 minutes to send that same message at 1 word per 20 minutes.

Pardon my arithmetic. It would require my two intrepid operators 400 minutes to send the same message the second time. As an old traffic handler, I’m really impressed with their dedication!

73, K5MC

RE: Bandwidth versus Keying Speed

by AB0WR on June 4, 2007 Mail this to a friend!

wr8y:
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
The spaces between the rise and fall times cannot affect the bandwidth occupied by the rises and falls. The rises and falls are so brief they set the ultimate space occupied by the CW signal, not the much slower Morse rate.

I think the difference of opinion would go away if people considered how the system actually works.

You cando this by sending dots and tuning across the signal with a real receiver.

73 Tom""""

With all of the intellectual masterbation going on in this thread, this post is easily missed - but not easily DISmissed!
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

Really, it can't be dismissed, eh?

Do you have a function generator by chance? And either an oscilliscope or a PC with a sound card?

If so, set your function generator to send a square wave with as long of a pulse length as possible, i.e. as low of a frequency as the generator can tune to.

Either hook your oscilliscope up to the function generator or hook in into your sound card and capture a wave file.

Now, I want you to look in the very middle of of one of the positive going pulses, either using the oscilliscope or by using a freeware oscilliscope program.

Extend your sweep time out as far as you can to get the closest look at the square wave you can.

Now tell us if you see only the fundamental frequency being displayed on the oscilliscope when looking at the very middle of the positive going pulse.

Better yet, go to <http://www.tpub.com/content/neets/14181/css/14181_190.htm>
and see just exactly how a square wave is put together by the odd harmonics.

This has a VERY good picture of how a square wave is built.

It also shows you what a shaped, bandwidth limited square wave should look like. That is NOT what the keying pulse shown by Tom for the 751a looks like. Those envelopes look like the result of a non-linear gain function in an amplifier - a.k.a MIXER - generating lots of intermod mixing products at the beginnings and endings of the pulse. As such, the Fourier analysis done by W9CF is not usable since the Fourier analysis is based on a linear system, not on a non-linear system. I believe this is what has led he and Tom to say that a longer slope generates a wider keying bandwidth than a shorter slope.

Rather than telling all of us using the math that we are indulging in intellectual masterbation it would be more beneficial if you could tell us *exactly* how the bandwidth of a square wave appears only at the leading and trailing edges when the frequency components making up the square wave exist throughout the entire period of the square wave and it is those frequency components which make up the bandwidth of the signal.

It would be even better if you could include the mathematical model describing how the bandwidth exists only at the edges of the square wave so we can all make notes in our textbooks showing where they are wrong. I'm sure the Integrated Publishing people would also like to know how they should modify their books to match the theory that you so apparently agree with.

The frequencies at which the fundamental and the odd harmonicss appear in a square wave *IS* based on the "Morse rate". The mixer products in a heavily non-linear mixer may very well NOT be dependent on the keying speed, at least not very dependent.

We did not do a lot of analysis work on non-linear mixing amplifiers during my college days. I'll have to see what I can dig up that shows a mathematical analysis of a non-linear amplifier being fed a square wave and a driving cosine. I suspect it will be heavily Taylor series based math which I will have to refresh myself on.

tim ab0wr

RE: Bandwidth versus Keying Speed

by W6TH on June 4, 2007 Mail this to a friend!

.
Thanks for this:

http://www.tpub.com/content/neets/14181/css/14181_190.htm

Like I told Mickey, his math in the beginning convinced me.

I specialize in analytical geometry, but am going to stay out of this Bandwidth versus Keying Speed as being a ham operator has little in it for me.

73, W6TH.

.:

RE: Bandwidth versus Keying Speed

by W8JI on June 4, 2007 Mail this to a friend!

Tim,

Since at least a dozen different models of radios of all types behave exactly as I say, and since they behave this way using multiple test methods, how to we convince the radios to change the way they behave?

Any suggestions on how to do that?

I think that is the direction where your efforts would be most valuable.

Unless we can convince the CW systems we all use to follow your rules, there will never be a solution.

73 Tom

RE: Bandwidth versus Keying Speed

by W6TH on June 4, 2007 Mail this to a friend!

.
Tom,

Why not get together and look at the design features of the present radios and then take the circuitry and check it out and then do some design work to satisfy ourselves and then recommend the changes to the radio mfgr's.

Don't forget that there are many changes to a great advantage by having the fast breakin system that was never achieved many years ago. Some use relays and some use pins and some use solid state.

In my opinion I believe sincerely that what is being used is within limits and satisfied for the present owners.

I am sure the Icom, Yaesu and Kenwood engineers know what they are doing and of course to keep the cost down and make their profits marginal.

73, W6TH
.:

RE: Bandwidth versus Keying Speed

by W8JI on June 4, 2007 Mail this to a friend!

Vito,

I first became interested in this when the late Bill Fisher, the fellow who started eHam, operated a contest here. Bill found 160 meters was virtually a wall of keyclicks and sked me why that was. That was around 1999.

I had a new 775DSP ICOM that I had to send back for a refund because it didn't pass FCC spurious emissions regulations when it was operated with a linear. It barely met regulations when barefoot, and I would never use a radio like that on the air anyway because if I am 30 over 9 an S5 spurious would be devastating to a weak DX signal under the spur. Beside the minimum amplitude law about spurious emissions there is also an all-encompassing law that says we just cause harmful interference from a spurious regardless of level. So even if a rig passes the -dBc guidelines, the moment it causes a problem through a needless flaw in the emissions it is illegal.

I changed to a FT1000D and no longer had the off-frequency spurious and the clicks were less, but soon W4DR rightfully complained about my signal. When I examined it I had a constant bandwidth regardless of speed of about 2-3 kHz.

The problem in the FT1000D would not have cost a dime to correct, since all Yaesu would have had to do was reroute some traces to send the CW through a CW filter instead of the SSB filter. As a second choice they could have changed the value of existing components to better slope the rise and fall times.

I did the second mod, and reduced the off frequency clicks by 20-30dB. This was done ONLY by reshaping the rising and falling edges with a small active filter in the keying line to the stage that was modulated on CW.

Since then I've looked at hundreds of radios of perhaps a dozen or more brands and models.

I have all the proper test gear and have spent hundreds of hours looking at radios. I can tell you without any doubt at all that the peak power of the sidebands off frequency, so long as the rise and fall shape is not altered by ALC changes, does NOT change with speed.

As such the perceived or real level of clicks off frequency does not change. The clicks may appear more or less frequently, but the peak level and bandwidth over which they appear is not altered.

There are recording on my web page, for example, of an FT1000MP MKV signal from EUROPE on 40 meters that is over 1 kHz wide. Doesn't matter what speed the fellow sends at, except the clicks occur more frequently as he sends faster.

Having looked at so many rigs for hundreds of hours, I don't expect a person who already has decided he knows EVERYTHING in a few minutes to follow the problem....unless that person has the humility to listen and think.

The problem with the flawed analysis here on eHam is a couple people are comparing the power over time of the carrier to the power of the sidebands over time. Say we have a carrier that is on an hour and off an hour. We have a rise time of 5 ms. That 5 ms is very short compared to the hour, so the ratio of energy in that hour to the sideband is very large. The low frequency content of the carrier dominates the energy of the system.

That's all fine, and if we look at things that way indeed the slower the speed the lower the percentage of energy over time is involved in creating that sideband when the carrier rises and falls. The analysis is correct.

The problem is the analysis does not fit how the system works in the real world. It isn't the energy we pour into a bucket compared to the fixed energy in the 5ms rise that matters. There isn't any bucket we fill. What we hear is the level at any instant of time, and once it is gone it is gone for good. That instant of time only has to be long enough to register in the receiver or our brain. We don't care if the dit is 500 ms long or 50 ms long. It sounds the same volume to us; it has the same effect to us.

We also don't care what happened with the signal a few milliseconds later, a second later, or a year later. We can't anticipate the future, we can't store the past. All we know is the PEAK energy in that click during the rising transition and the falling transition is so strong, and the level of that problem depends only on the transition in amplitude. The slope rate sets the bandwidth of that energy.

Even our "S" meters are peak sample and hold indicators that work off the AGC. While some systems have a delayed response and might miss a few clicks, in no time at all a few clicks charge the system and regardless of speed the AGC is hung at the same level.

Every single perception of the operator is tied to the peak level, and that peak level does not change. The PEP power of the carrier is constant, and the PEP level of the click is constant.

That's all that matters.

Now if I view this signal with an instrument approved and accepted by the FCC to measure occupied bandwidth, it also detects the peak powers. It samples the peak powers and stores them. It doesn't care in the least if the carrier peak power is on for 5 days or 5 milliseconds, it is whatever it is. It might be 100 watts in a typical radio. The sideband, the level being determined by the change in amplitude and the frequency being determined by the slope of that change, repeats exactly so long as nothing alters that rise and fall. Every single time the analyzer sweeps by a frequency it reads the peak power at that instant, and it records that peak power. One peak an hour, one peak a millisecond, if it is 10 watts peak power the level indicated on a particular frequency will be constant unless we somehow alter the slope or level change of the rising edge.

This is why a spectrum analyzer agrees with the ear, and why a receiver agrees with the ear and the analyzer.

What Tim and others would like to see happen is all of these responses become the power integrated over time. Unfortunately that isn't how the system works. While their answers are technically correct if we were pouring energy into a bucket and weighing the totals after a long period of time, they are as screwed up as measuring time with a rubber watch when it comes to describing the real time.

Until they get their heads around how the system works, they will keep insisting their answers apply to a real CW system.

The problem isn't their math skills; the problem is they haven't learned how the system works yet.

It's tough to describe something we don't yet understand.

73 Tom

RE: Bandwidth versus Keying Speed

by AB0WR on June 4, 2007 Mail this to a friend!

w8ji:
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
Since at least a dozen different models of radios of all types behave exactly as I say, and since they behave this way using multiple test methods, how to we convince the radios to change the way they behave?

Any suggestions on how to do that?

I think that is the direction where your efforts would be most valuable.

Unless we can convince the CW systems we all use to follow your rules, there will never be a solution.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

It doesn't have anything to do with *my* rules. It has everything to do with what is causing such a wide bandwidth for what should be such a simple process as AM modulation.

How do we convince the radios to change the way they behave?

First, you need to understand *why* they are behaving as they are. In order to do that an understanding of what the input driving functions are and what the system transfer functions are is required.

Once an understanding of *why* things are as they are *then* we can figure out what changes to make in order to cause their behaviour to be what we want.

Saying that the output causes the output because the output causes the output provides exactly *no* understanding of what the root causes are.

I've looked at the 751a CW circuitry. The IF oscillator has RC filters in both the oscillator bias circuits as well as the on-off control circuitry. Not only that but ALC is fed directly into the oscillator to control the level.

That means that the transfer function for the oscillator is quite likely NOT a pure AM modulation scheme but includes some significant non-linear term as well. Thus all kinds of intermod products will be coming out of that oscillator. I've taken some pretty poor pictures of the output of the oscillator while being keyed by a string of dits and they definitely shows the exponential transfer function on both the leading edge as well as the trailing edge of the output response. I'll see if I can find a place to post the pictures for everyone to see but they probably aren't going to show anything more than what most of the other pictures on the internet show. The only really interesting picture is one that seems to show an S-curve shape on the leading edge but it's hard to make out much detail on a small LCD on a digital camera. I'll have to look at it in larger size to make any sense out of it. If it *is* an S-curve, I expect we might be able to match curve to the operating curves of the transistor being used as the oscillator.

In other words, we will be in the domain of large signal analysis with changing operating points as the ALC and keying pulses move the operating point from very low on the operating curves to very high. Definitely a non-linear operation. I'm not sure I have the expertise to analyze such a situation. It might take someone with a circuit emulation program (matlab?) to take a shot at figuring out what is going on.

If we *can* pin this down to non-linear transfer functions in the modulation stage, *then* I might be able to make some suggestions on how to make the bandwidths much narrower by making the stages linear instead of non-linear.

tim ab0wr

RE: Bandwidth versus Keying Speed

by W6TH on June 4, 2007 Mail this to a friend!

.
Tom,

I see and understand your point of view. I had the thought of with our modern day radios that the rise and decay time was carefully calculated and engineered prior to the sales to and for each of use.

I ran some equations with math and have solved the problem, but now realize my calculations may not be the solution. This is normal with any design feature. I also agree with Chen and find it very interesting. The rise time on a square wave did not indicate a higher bandwidth, but did indicate at high speeds there was a change in the decay time compared to a slower rate of speed.

I am kidding here and thought for fun:

This may be due to inter-electrode change of electrolytic capacitance, a fixed capacitor consisting of two electrodes separated by an electrolyte, or two parallel lines the rise and decay.

Vito
.:

RE: Bandwidth versus Keying Speed

by WA0LYK on June 4, 2007 Mail this to a friend!

No one has yet addressed the fact that many data modes have similar rise and fall times as cw. Why do the rise and fall times of psk31 not result in wide, wide bandwidths.

If the assumptions and math that is applied to show that cw rise/fall times is correct, then it must also be correct for other modes that have similar pulses.

Please explain how this can be?

Jim
WA0LYK

Bandwidth versus Keying Speed

by K5MC on June 4, 2007 Mail this to a friend!

W8JI: Now if I view this signal with an instrument approved and accepted by the FCC to measure occupied bandwidth, it also detects the peak powers.

Tom, I believe that you are now agreeing with me that the spectrum plots you posted of your Icom 751A are NOT indicating the "occupied" bandwidth as defined by the FCC. Your plots are showing the so-called "keyclick" bandwidth. If that truly reflects your views, then as far as I'm concerned, you and I have no major disagreements.

It's my opinion that you've been so focused in recent years on the issue of key clicks caused by the poor turn-on and turn-off characteristics (rise/fall times and shapes) of much of the existing ham gear, you lost sight of the very important concept of "power" bandwidth, which is equivalent to the concept of "occupied" bandwidth as used in the FCC's definition. The purpose of my article was to show hams that the "power" bandwidth of a CW transmission clearly depends upon both the sending speed and the types of keying waveforms. If you are willing to acknowledge the accuracy of that fact now, then I am prepared to quietly walk away from this thread.

In closing my comments here, I want to acknowledge again that I think the concept of "keyclick" bandwidth as demonstrated via your 751A spectrum plots is important. Perhaps you might even submit a petition to the FCC regarding the concept of "keyclick" bandwidth that could be incorporated into the Part 97 rules.

73, K5MC

RE: Bandwidth versus Keying Speed

by W6TH on June 4, 2007 Mail this to a friend!

.
Mickey,

As a radio runs with a higher power amplifier, yes, I agree that the higher keying speed does increase the bandwidth. Big difference going with a radio and then adding a 500 watt or more amplifier.

It is like going from a pulse repetition rate of 5 and then increasing to 10 pulses per second, there is a increase in band width as I have noticed in backscatter communications. Power was one megawatt pulsed output.

Is this what the FCC is considering?

.:

RE: Bandwidth versus Keying Speed

by W8JI on June 5, 2007 Mail this to a friend!

Tim wrote:

"It doesn't have anything to do with *my* rules. It has everything to do with what is causing such a wide bandwidth for what should be such a simple process as AM modulation."

That's already been explained. It isn't rocket science. When a carrier is amplitude modulated like in a CW transmitter, it produce an upper and lower sideband. The spacing of the sidebands is determined by the envelope slope, and the amplitude by the envelope level change.

"First, you need to understand *why* they are behaving as they are. In order to do that an understanding of what the input driving functions are and what the system transfer functions are is required."

Oh I understand it quite well Tim. It isn't me that needs the work. The next statement by you shows the real root of the problem. You wrote:

"I've looked at the 751a CW circuitry. The IF oscillator has RC filters in both the oscillator bias circuits as well as the on-off control circuitry. Not only that but ALC is fed directly into the oscillator to control the level. "

That is totally untrue Tim. The radio is not constructed or modulated anywhere near the way you describe. The description you gave shows a very serious error in how you read the schematic and interpreted the system. You clearly do not understand how the radio works, or you have not described how it works in such a terribly wrong fashion.

All of the oscillators in the 751A are on and stable when the rise time starts, and they are running stable while the envelope decays to zero at key open. There is a delay circuit built in that ensures the oscillators are up and stable before the first emission is allowed out at key closure, and ensures they are not released until the enveope reaches zero.

There is a bigger pattern in this.

You ignore the fact every other radio behaves the same way as the 751A. This includes MO-PA radios like a 1950's Globe Scout, FT1000's of all models, and everything else in the world.

I can build and have built PIN diode modulation systems and they behave this way, the Orion generates the CW in a DSP and behaves this way.

You have to understand how the radio works Tim. When you do it will all become clear and you will get on the right track.

I suggest you look at some real radios in operation and maybe build a few simple CW transmitters. Until then you will continue to struggle.

73 Tom

RE: Bandwidth versus Keying Speed

by AD5X on June 5, 2007 Mail this to a friend!

This morning I fired up my old Johnson Ranger and ran a few tests. Keying speeds were 5- and 35-WPM using my Hallicrafters TO Keyer. The Ranger was transmitting into a dummy load on 14.035.00 MHz (it held this frequency surprisingly well after a 15 minute warm-up). I adjusted the level into my Yaesu MKV receiver to be exactly S9 on-frequency (relay short and attenuator on the MKV input, all cables 100% shielded LMR-240). Using the 60Hz DSP filter in my MKV, I measured the following: Offset 0Hz/S9, offset 50Hz/S9, offset 100Hz/S7, offset 150Hz/S5, offset 200Hz/S0 (offsets beyond 200Hz were all S0). I ran these tests numerous times at both keying speeds and could see no difference in level between the keying speeds within my ability to read the bargraph S-meter on the MKV.

Next I went to the 2.4KHz SSB filter, transmitted at 5WPM and tuned the MKV receiver until the key clicks were barely audible. With the S9 on-frequency starting point, I found that the clicks were barely audible 4Khz away (S0 S-meter reading). I re-set the receiver to 0Hz, changed the keying speed to 35WPM, and again tuned the receiver until I could just barely hear the clicks. Again, the “barely perceptible” clicks occurred 4KHz away.

Of course, there is no ALC in the Ranger.

Phil – AD5X

RE: Bandwidth versus Keying Speed

by W8JI on June 5, 2007 Mail this to a friend!

Of course the Ranger you tested works that way Phil. Every radio in the universe except those with rising and falling edge waveshape changes with speed will work that way.

The problem is 1000 people can test the actual system the way the system is actually used and discover the effective bandwidth of the signal remains the same regardless of keying speed, while a few people who can't be bothered learning how the system really works will waste everyone's time arguing nonsense.

Until they learn how the system works they will continue to go down the wrong path. It's a people problem with admitting a mistake or error, not a technical issue.

73 Tom

Bandwidth versus Keying Speed

by K5MC on June 5, 2007 Mail this to a friend!

Tom, I assume by your silence regarding my recent comments that you now agree that my article is 100% correct. As I demonstrated in my article, the "power" bandwidth (which is the same concept as the occupied bandwidth as defined by the FCC) varies with the sending speed. The "power" bandwidth is a fundamental concept in communication systems because it, rather than your so-called "keyclick" bandwidth, is the important parameter when considering communications in the presence of noise. As W1YW and I have pointed out during this thread, EME and QRSS are examples of this fact.

As I've acknowledged several times during this thread, your "keyclick" bandwidth is also important and I now fully understand that the spectrum plots that you've posted for your Icom 751A reflect the "keyclick" bandwidth. Now that I understand how you are triggering your spectrum analyzer, I can verify your results by using Fourier analysis. You are, in effect, using the concept of "short-time" Fourier transforms to measure the "keyclick" bandwidth of your 751A.

There is no conflict between the mathematics and the measurements; the conflict between you and I has been over the meaning of the various types of "bandwidths" used in describing signals. I strongly suggest that you stop using the term "occupied bandwidth" when discussing your "keyclick" bandwidth. The FCC's definition of occupied bandwidth has been established for many years now and it should be understood and respected by everyone.

73, K5MC

RE: Bandwidth versus Keying Speed

by AB0WR on June 5, 2007 Mail this to a friend!

w8ji:
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
That's already been explained. It isn't rocket science. When a carrier is amplitude modulated like in a CW transmitter, it produce an upper and lower sideband. The spacing of the sidebands is determined by the envelope slope, and the amplitude by the envelope level change.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

Tom,

Quite frankly you have a causal problem here that you just seem to keep wanting to ignore.

The envelope shape doesn't create the modulation sidebands. The sidebands created from the modulation process create the envelope shape. Until you can explain how those sidebands are generated from the input driving function and the system response, i.e. the modulation process, you will have no hope of understanding what is going on.

When a carrier is amplitude modulated in a linear manner an upper and lower sideband *is* produced. The spacing of those sidebands is a result of the subtraction and addition of the two input frequencies. That spacing creates the envelope shape. The envelope shape doesn't create the spacing.

With your logic you would have to say that the envelope of a two-tone test creates the two sideband frequencies in the test instead of saying the two sideband frequencies created by the modulation process creates the envelope.

You are still laboring under the viscious circle that the output causes the output because the output causes the output. I just don't know how to put it any plainer than that.

w8ji:
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
That is totally untrue Tim. The radio is not constructed or modulated anywhere near the way you describe. The description you gave shows a very serious error in how you read the schematic and interpreted the system. You clearly do not understand how the radio works, or you have not described how it works in such a terribly wrong fashion.

All of the oscillators in the 751A are on and stable when the rise time starts, and they are running stable while the envelope decays to zero at key open. There is a delay circuit built in that ensures the oscillators are up and stable before the first emission is allowed out at key closure, and ensures they are not released until the enveope reaches zero.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

Oh, really?

Then you are saying that the keying input doesn't go to the delay circuti IC1 which then feeds Q4, a switching transistor in the emitter path of Q3, which is used to then turn on Q3 (the CW IF oscillator)?

When I get home I'll pull the part out of the 751a service manual which describes this circuitry and see what it says about how it works and post it here. Then we'll see if I read it wrong.

I believe you will find that the oscillator keying is delayed in order to allow the application of the T8 voltage to occur and stabilize thus energizing the transmit chain before a signal from the CW oscillator is applied to the rest of the transmitter chain.

I could be wrong but I did follow the keying lead right into IC1, which the service manual describes as a delay IC, and then followed the output of IC1 right into Q4, which is the switching transistor used to turn the oscillator on and off.

There may be, of course, another delay circuit which I didn't find that turns the rest of the transmitter on and off but then the application of a delay IC in the CW oscillator keying circuitry would seem to be nothing more than an unneeded manufacturing cost and an engineering detail that is unneeded.

I am waiting for enlightenment.

w8ji:
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
ou ignore the fact every other radio behaves the same way as the 751A. This includes MO-PA radios like a 1950's Globe Scout, FT1000's of all models, and everything else in the world.

I can build and have built PIN diode modulation systems and they behave this way, the Orion generates the CW in a DSP and behaves this way.

You have to understand how the radio works Tim. When you do it will all become clear and you will get on the right track.

I suggest you look at some real radios in operation and maybe build a few simple CW transmitters. Until then you will continue to struggle.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

I'm not ignoring anything. I am asking for you to provide the mathematical explanation of what the inputs and the system response are that result in this output for all these transmitters.

So far all I have gotten is that the output causes the output because the output causes the output.

This generates the need for such causual impossibilities as saying "The spacing of the sidebands is determined by the envelope slope" instead of saying the envelope slope is determined by the sideband spacing". It's what generates such causual impossibilities as saying the harmonics of a square wave only exist at the leading and trailing edge of the square wave and only the fundamental frequency exists at the middle of the square wave pulse. It's what generates the causual impossibility of a psk31 signal not causing any leading or trailing edge key clicks when it has a zero crossing just like a shaped square wave.

The best explanation I have heard so far is from WA0LYK. The key clicks you hear on a CW signal are exactly analogous to the "buckshot" that can be heard several kilohertz away from a SSB signal whose amplifiers are being driven into an non-linear region. This "buckshot" is caused by intermodulation distortion which causes close-in higher level mixing products to appear on the signal. The key clicks are exactly analogous to a psk31 signal driving the transmitter into its non-linear region thereby creating higher level, close-in modulation products. Since the psk31 signal is constant you get constant intermod instead of like a SSB signal which is transient because the voice is transient.

The envelope shape of the CW pulse indicates me to believe there is a non-linear operating region in play on the leading and rising edge of *something* in the transmitter. This non-linear operating region then causes intermod products to be produced which are heard as key clicks.

The answer then is to find a way to key the transmitter that doesn't result in a non-linear mixing process to be involved on the leading and trailing edge of the keying.

Take a look at <http://www.seed-solutions.com/gregordy/Amateur%20Radio/Experimentation/CWShape.htm> which shows a spectral analysis of the 756pro CW output. This isn't a continuous spectrum which is what your analyzer displays show. This is the classis square-wave pattern. I'm not sure what frequency his dits were at or what shape factor his filter has but this appears to be a classic 100hz square wave. I don't know exactly where everything was set so it is a little difficult to figure it all out. I don't know if the fundamental is at a 600hz offset and the -300hz harmonic (which would be at a 300hz offset) and others are being filtered out or just what.

There appears to be no non-linearity associated with the keying envelope pictures with the 756pro, the slope is a pretty straight line. That's why the frequencies seen are so clean. And they are there for the whole time -- which is what a square wave would generate. The extended rise times only indicate a decreasing bandwidth for the signal, exactly what a bandwidth limited square-wave would indicate, a lowered slope that is a linear line and not an extended exponential charging time which only indicates an increased non-linearity in the modulating element.

I'm glad I found this page. It indicates a method of analyzing signals I hadn't thought of. I'll have to think it through to see if there are any problems with the measurement method but I don't see any immediate ones, at least if the filter bandwidth is considered. I'll have to see if I can find a receiver that has an extended bandwidth I can use to perform such tests. It would be very interested to run the output waveform from the 751a CW IF oscillator through such a process to see what it shows.

This ultimately isn't a matter of how these transmitters behave, it is a matter of understanding why they are behaving this way. So far you have offered nothing to further the understanding of why they behave this way other than to say the output causes the input. You say the output shape generates the output sideband frequencies and the output envelope generates the output sideband amplitudes. If you can't see the causual disconnect in such statements you'll never be able to explain mathematically what is causing the output to happen.

tim ab0wr

RE: Bandwidth versus Keying Speed

by AB0WR on June 5, 2007 Mail this to a friend!

w8ji:
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
The problem is 1000 people can test the actual system the way the system is actually used and discover the effective bandwidth of the signal remains the same regardless of keying speed, while a few people who can't be bothered learning how the system really works will waste everyone's time arguing nonsense.

Until they learn how the system works they will continue to go down the wrong path. It's a people problem with admitting a mistake or error, not a technical issue.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

This is sophistry, pure and plain. You are saying that the output of a system is how something works. It isn't.

Using your logic we would say that the tires on a car is what generates the movement of the car. All cars have tires (or something similar) and the tires on all cars turn when the car is moving so it must be the tires that cause the car to move.

The tires turning is an OUTPUT, not an input. The tires generate nothing on their own. It is the burning of fuel in an engine that is the input and it is the engine and gear train that are the system response that winds up generating the movement of the tires. The tires don't turn the engine which is what your logic leads to.

Similarly, the output of a transmitter generates nothing on its own. It is the result of *SOMETHING*. So far you have not contributed one single, solitary bit of understanding toward what those *SOMETHINGS" must be.

Saying you know how something works because you know the output function is just plain wrong.

You can continue to denigrate everyone else for not believing in your article of faith that the output generates the input but you are only ruining your credibility in doing so.

Again, give us the math that shows a variable input driving function coupled with a fixed system response that results in a fixed output response. The rest of us are trying to come up with this understanding and all you can do is stand back and denigrate those that are doing so.

You keep saying that we don't know how things work but you provide no explanation of how they work either. You just keep falling back on the carnard that the output explains how something works.

You may as well just say that birds fly because birds fly -- that's just how things work.

It would make as much sense as claiming the transmitter output causes the input.

tim ab0wr

RE: Bandwidth versus Keying Speed

by VA3NR on June 5, 2007 Mail this to a friend!

I'm surprised any confusion continues... its a matter of how long of a time period you use to average the power. Imagine this: You invite the FCC to your station, and you transmit a steady carrier at 14.050 Mhz for 99.1 seconds, and then send a carrier at 13.950 Mhz for 0.9 seconds. You try to tell the FCC that was legal because your 99.1% long-time-averaged power bandwidth was entirely inside the 20m band. Do you think they would agree with that method of spectrum measurement?

Averaging over short window, and taking worst case (short-time-average) bandwidth throughout transmission is more appropriate way of looking at bandwidth of finite time transmissions.

73,
Chris VA3NR.

RE: Bandwidth versus Keying Speed

by W8JI on June 5, 2007 Mail this to a friend!

Mickey,

I'm not saying anything I haven't said all along, and I disagree that your analysis means anything to the problem of bandwidth. Your analysis is correct if long term power ratios are the problem, but they are not. They have no effect on adjacent channels.

You've gone out of your way to discredit the established fact that the rise and fall determine the interference bandwidth of the CW, and this has confused people who don't understand how the system works but are impressed by math.

Anyone reading what you wrote would think filtering of transitions is unimportant and speed is everything, but the fact is filtering of transitions is everything and speed means very little except how frequently the sidebands appear.

That doesn't help the problems we have with poor equipment design. We should be working towards solutions to problems, not going backwards.

If you object to a definition that's fine, but let's not make the CW bands useless by telling people the transitions don't mean anything or that a slower speed narrows the bandwidth occupied by a CW station.

73 Tom

Bandwidth versus Keying Speed

by K5MC on June 5, 2007 Mail this to a friend!

VA3NR: You invite the FCC to your station, and you transmit a steady carrier at 14.050 Mhz for 99.1 seconds, and then send a carrier at 13.950 Mhz for 0.9 seconds. You try to tell the FCC that was legal because your 99.1% long-time-averaged power bandwidth was entirely inside the 20m band. Do you think they would agree with that method of spectrum measurement?

No, of course the FCC would not agree with that method of spectrum measurement. Chris, you are misrepresenting what I discussed in my article and you are misunderstanding the 99.1% power bandwidth concept as applied to a CW signal.

Please read my article again. If you will do that, you will see that I clearly said that the CW signal being modeled was a string of DITS! I very carefully described my keying waveforms with such phrases as 50% duty cycle, 2.4 words per minutes, 30 words per minute, etc. At a speed of 2.4 wpm, an electronic keyer will produce 1 dit per second; at 30 wpm it will generate 12.5 dits per second. I never said anything about the bandwidth of a transmitter during a "long" key down (that is, using a hand key). My keying waveforms consisted of a long string of dits as produced by an electronic keyer.

If you will look in a recent ARRL Handbook (such as on page 11.6 in both the 2005 and 2006 Handbooks), you will clearly see the types of keying waveforms I used in my article.

73, K5MC

RE: Bandwidth versus Keying Speed

by VA3NR on June 5, 2007 Mail this to a friend!

Mickey,
I don't see how I misrepresented anything - I didn't even mention your article. I accept that for the keying waveforms presented in the article, the infinite-time average power bandwidth will be exactly as you calculated.

I was hoping my hypothetical example might help illustrate how the choice of time period affects the average power calculation, and how to a regulatory body, the infinite-time average power might be less important than worst case short-time average.

I understand now you wish to keep comments strictly on the signals defined in the article. Those signals don't have any relevance to me so I will have no further comment.

Chris VA3NR

RE: Bandwidth versus Keying Speed

by W8JI on June 5, 2007 Mail this to a friend!

Of course they don't have any meaning to you Chris.
They don't have any meaning to anyone who operates CW.

No matter how fast or slow someone sends, someone else will hear their radio exactly the same distance off frequency with the same strength. The only thing that will happen is the clicks will occur less frequently or more frequently.

The sole exception to this is when the ALC or some other abnormal change modifies the slope or duration of the rise and fall.

The only effect of the speed change is how often we hear the click, and the only way to fix the click is to modify the rise and fall times and/or shape of the transition where the rise and falls occur.

It's just the nature of CW.

73 Tom

Bandwidth versus Keying Speed

by K5MC on June 5, 2007 Mail this to a friend!

W8JI: There seems to be some lingering debate about keying speed affecting occupied bandwidth of a transmitter. I'm fortunate enough to have equipment that directly measures occupied bandwidth. The FCC accepts this currently certified equipment as proof of bandwidth.

W8JI: We see the actual measured occupied BW of a relatively good CW transmitter is essentially the same and does not track CW speed.

The above quotes are copied directly from http://www.w8ji.com/occupied_bw_of_cw.htm Along with these sentences, W8JI shows spectrum plots and a table with the "99% occupied" bandwidth for his Icom 751A at three different speeds.

Tom says the measured "99% occupied" bandwidths for the 751A are 490 Hz and 500 Hz at speeds of 24 words per minute (10 dits per second) and 96 words per minute (40 dits per second), respectively. Now let's imagine the following scenario:

Joe is a new ham anxious to operate CW, but he's just getting his feet wet and can't manage much more than 5 wpm code speed. Joe happens to own an Icom 751A and is wondering how its "occupied" bandwidth compares to its "necessary" bandwidth. Joe understands the following from the FCC rules:

97.307(a) No amateur station transmission shall occupy more bandwidth than necessary for the information rate and emission type being transmitted, in accordance with good amateur practice.

Joe then does some further reading of the FCC Rules (Part 2) at http://www.access.gpo.gov/nara/cfr/waisidx_06/47cfr2_06.html There he reads the following definition:

Occupied bandwidth. The frequency bandwidth such that, below its lower and above its upper frequency limits, the mean powers radiated are each equal to 0.5 percent of the total mean power radiated by a given emission.

Now Joe is a pretty sharp guy, but he realizes that he doesn't really understand the definition of occupied bandwidth. Joe then reads the following definition of "necessary" bandwidth:

Necessary bandwidth. For a given class of emission, the minimum value of the occupied bandwidth sufficient to ensure the transmission of information at the rate and with the quality required for the system employed, under specified conditions.

Joe's not too sure about this definition, either, but he does see the following simple equation provided by the FCC to calculate the necessary bandwidth for CW telegraphy:

Bn = BK

where Bn is the necessary bandwidth
B is the modulation rate (symbol rate) in bauds
K is either equal to 5 (fading circuits) or 3 (no-fading circuits)

Since Joe is a new ham, he's interested in sending at the rate of 6 words per minute. He reads in a recent ARRL Handbook that the commonly accepted ratio for bauds to words per minute is 1.2 B = wpm. Therefore, B = 5 bauds when the code speed is 6 wpm. So Joe then calculates that the necessary bandwidth is (5)(5) = 25 Hz if K = 5 and the necessary bandwidth is (5)(3) = 15 Hz if K = 3. Let's summarize these numbers below:

Necessary bandwidth Bn = 25 Hz for fading circuits at 6 wpm

Necessary bandwidth Bn = 15 Hz for non-fading circuits at 6 wpm

Now Joe is informed by W8JI that the "99% occupied" bandwidth of an Icom 751A is about 500 Hz regardless of sending speed. What is Joe's conclusion? If Joe takes everything that we've just discussed at face value, then he had better decide to NOT operate his 751A at 6 wpm because the necessary bandwidth is, at most, 25 Hz, but the "99% occupied" bandwidth specified by W8JI is about 500 Hz! As a matter of fact, Joe calculates that the minimum speed that he must send to satisfy 97.307(a) is 120 wpm for K = 5 or 200 wpm for K = 3!

Did everybody understand that last sentence? Joe must send at least 120 wpm for fading circuits and at least 200 wpm for non-fading circuits if W8JI is correct.

Joe decides that he will have to practice his code speed a little bit more before he will be ready to send CW on the air and still satisfy 97.307(a).

Of course, I believe it very likely that Joe will question the "99% occupied" bandwidth values specified by W8JI. Joe then decides to read up on the issue of "occupied" bandwidth and sending speed in his 2006 ARRL Handbook. On page 9.7 he reads the following:

2006 ARRL Handbook: The bandwidth occupied by a CW signal depends on the keying rate, with higher speeds requiring a wider filter to pass the sidebands. In addition, occupied bandwidth depends on the rise and fall time and the shape of the keyed RF envelope.
Joe also reads the following sentence on page 9.7 of the 2006 ARRL Handbook:

2006 ARRL Handbook: ARRL has long recommended a 5-ms rise time for CW, up to 60 wpm, which keeps the signal within a 150-Hz bandwidth.

Joe also sees Figure 9.9 on page 9.8 of the 2006 ARRL Handbook showing the keying speed versus rise/fall times versus bandwidth for fading and non-fading communications circuits.

Joe also reads the eham article (Bandwidth versus Keying Speed) recently posted by K5MC that appears to be consistent with the ARRL Handbook. Joe notices that K5MC is very careful in his article concerning the various definitions of "bandwidth" and Joe further notices that K5MC quotes the definition of "occupied bandwidth" directly from the FCC rules along with the definition of the "99% power" bandwidth from what appears to be a reputable book on communication systems, at least according to its title as referenced by K5MC.

After all of this reading, Joe decides that W8JI's values of "99% occupied" bandwidth for an Icom 751A must be misleading, if not downright ridiculous. Ignoring W8JI, Joe fires up his 751A by calling CQ at 5 wpm on 3.573 MHz.

73, K5MC

Bandwidth versus Keying Speed

by K5MC on June 5, 2007 Mail this to a friend!

While Joe is enjoying a QSO at 5 wpm on 3.573 MHz with his Icom 751A, maybe W8JI can figure out how to operate his spectrum analyzer to truly measure the occupied bandwidth (the 99% power bandwidth) just like an FCC engineer would measure it.

Since W8JI seems to be rather clueless, however, let me offer a comment or two regarding the proper operation of a spectrum analyzer when measuring the spectrum of a CW transmitter sending a long string of dits (dots). W8JI needs to remove the cable that is connected between his keyer and the spectrum analyzer. W8JI needs to operate his analyzer in the "free running" mode, not in the "triggered" mode as he usually does when measuring the "keyclick" bandwidth.

If W8JI will operate his analyzer as I just described, he will see a discrete line spectrum on his analyzer when his CW transmitter is sending a long string of dits at a sufficiently high speed. If the sending speed is too low, it will be hard for him to see the keying sidebands distinctly because of the frequency resolution of his analyzer. W8JI will clearly see that the location of the sidebands move further away from the carrier (center) frequency as he increases his sending speed. That is, the bandwidth of the CW signal will increase with the sending speed. W8JI should even be able to provide Joe now with the correct values of occupied bandwidth for an Icom 751A.

73, K5MC

RE: Bandwidth versus Keying Speed

by W8JI on June 5, 2007 Mail this to a friend!

<<
K5MC on June 5, 2007 Since W8JI seems to be rather clueless, however, let me offer a comment or two regarding the proper operation of a spectrum analyzer when measuring the spectrum of a CW transmitter sending a long string of dits (dots). W8JI needs to remove the cable that is connected between his keyer and the spectrum analyzer. W8JI needs to operate his analyzer in the "free running" mode, not in the "triggered" mode as he usually does when measuring the "keyclick" bandwidth.>>

Sorry Mickey. The data on my page is without the spectrum analyzer being synced to the source. It is free running.

As a matter of fact I almost never sync the analyzer to the dots because it is a PITA and it doesn't really change the overall results one bit.

Now that we know that.... let's look at what else you just said:

<<If W8JI will operate his analyzer as I just described, he will see a discrete line spectrum on his analyzer when his CW transmitter is sending a long string of dits at a sufficiently high speed. If the sending speed is too low, it will be hard for him to see the keying sidebands distinctly because of the frequency resolution of his analyzer. W8JI will clearly see that the location of the sidebands move further away from the carrier (center) frequency as he increases his sending speed. That is, the bandwidth of the CW signal will increase with the sending speed. W8JI should even be able to provide Joe now with the correct values of occupied bandwidth for an Icom 751A. >>

Wrong again. The spectrum analyzer was in free-running mode, so all of your predictions are wrong.

I can tell you exactly what does change when the sweep is synced to the dots. What changes is the analyzer draws a trace exactly like W9CF, KF6DX, and Chen (W7?) show on their web pages. It shows ripples within the skirts. The skirt follows the peaks of the ripples and remains exactly the same shape. The skirt is established by the rise and fall times and slope of the rise and fall.

All the speed does when synced is move small sidebands around inside the skirt. Without the sync it is exactly as I show, and in either case the occupied BW is nearly the same (within a few Hz).

I've already explained all this at least once before.

Mickey, perhaps some time away from this forum and on a bench with a receiver and transmitter would be helpful. This should be educational. There isn't any reason for this to be a peeing contest.

All you have to do is the same experiments WR8Y and the other people have done and you will see that if you set a receiver some amount off frequency and change the CW speed the click bandwidth and level does not change. All that really happens is the sidebands appear more or less frequently as the speed is changed.

The few exceptions to that have already been covered over and over again.

A few minutes with a receiver and transmitter would really help a lot Mickey.

73 Tom

RE: Bandwidth versus Keying Speed

by W8JI on June 5, 2007 Mail this to a friend!

Mickey,

If I've made you angry or frustrated you I'm sorry. That really isn't my intention.

My goal is to have people understand how the system really behaves.

Hopefully you will find time to observe a real radio on a receiver, selective level meter, or analyzer. That will do a lot more good than anything else I can say.

Perhaps you didn't read the sweep speed or the resolution bandwidth on the display of the analyzer. If you did, you will note the sweep time is VERY long, 90 seconds for one sweep across the bandwidth of the display. This is necessary when the bandwidth is very narrow. In this case I used 10Hz bandwidth.

What the analyzer draws is almost exactly what a step by spet plot of levels using a very narrow high quality selective voltmeter produces. It is also like a selective communications receiver indicates, althhough the bandwidth and level accuracy of the communications receiver does not match the performance of the better test gear.

When I look at an unmodulated carrier from the 751A it is about 15-30Hz wide, which is logically correct since the bandwidth would equal 2X the selectivity of the measuring device if it occupied zero bandwidth.

While Tim clings to the idea the 751A is somehow uniquely flawed, any radio I put on the system measures about the same way. My Viking Valiant, my Globe Scout, my DX60's, my Yaesu FT1000, my FT1000MOP, my FT1000MP MK V, my Orion, my Drakes, my Kenwood TS930, and the list goes on.

They all behave the same so long as the dots don't get so fast or slow that they alter the rise and fall times or shapes.

73 Tom

RE: Bandwidth versus Keying Speed

by AB0WR on June 5, 2007 Mail this to a friend!

w8ji:
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
While Tim clings to the idea the 751A is somehow uniquely flawed, any radio I put on the system measures about the same way. My Viking Valiant, my Globe Scout, my DX60's, my Yaesu FT1000, my FT1000MOP, my FT1000MP MK V, my Orion, my Drakes, my Kenwood TS930, and the list goes on.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

Now you are just being a jerk again. You are putting words in my mouth. I've *never* said the 751a is uniquely flawed. I *have* said that any rig with an exponential leading and trailing edge is operating with a non-linear gain function at the leading and trailing edge somewhere in the transmitter chain. The 751a fits this description perfectly.

BTW, do you remember this post of yours?

w8ji:
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
That is totally untrue Tim. The radio is not constructed or modulated anywhere near the way you describe. The description you gave shows a very serious error in how you read the schematic and interpreted the system. You clearly do not understand how the radio works, or you have not described how it works in such a terribly wrong fashion.

All of the oscillators in the 751A are on and stable when the rise time starts, and they are running stable while the envelope decays to zero at key open. There is a delay circuit built in that ensures the oscillators are up and stable before the first emission is allowed out at key closure, and ensures they are not released until the enveope reaches zero.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

For those that are interested, Tom will never admit he was wrong in this. Here, however, is what the 751a Service Manual gives for a circuit description:

<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
Section 4.2.5 CW, RTTY OSCILLATOR CIRCUITS
...........The emitter resistor of Q3 is connected to the collector of Q4 to control oscillation. .........

Section 4.2.6 CW KEYING CIRCUIT
A keying signal from the [EXT KEY] JACK is applied to Q4 through a delay circuit which consists of IC1, R31, and C23 (delay time is approximately 6ms).
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

In other words the CW IF Oscillator does NOT run all the time. It *IS* keyed on and off by the keying circuit.

There *is* a delay circuit that keeps the CW oscillator from being keyed for 20ms when the rig changes from receive to transmit. This is to allow the T8 voltage (which is keyed on when the rig changes to transmit) to be applied everywhere in the chain, for the transmitter chain to stablize, and for all relays to operate. When that delay is over, the CW oscillator *can be and is* keyed. It is keyed on and off without any further 20ms delay as long as the rig stays in transmit (e.g. semi-breakin or the xmit/rcv switch in transmit). I can show it to you on the oscilliscope any time you would like to look.

Before telling someone that they don't know how a radio works you might want to insure that YOU know how one works.

And in the emitter of the oscillator and in the base to emitter feedback loops *are* capacitive elements that must be charged and discharged on each leading and trailing edge which causes that oscillator to be a very good mixing circuit as well as oscillator because the gain is being varied in a non-linear, exponential manner during the start and end of the keying pulse. When it is fed the harmonics from a keying square wave significant intermodulation products will be generated during the beginning and end of the keying pulse -- i.e. key clicks.

A true AM modulator would not start off with a circuit element that is in cutoff mode and then have the modulation be such that an exponential charging cycle is needed to move the modulator circuit element to its linear operating point. Yet I can guarantee you that is what is being done in every rig that has an exponential rise time on the leading or trailing edge of the keying pulse.

I think I will try to find a general coverage receiver I can feed the oscillator signal into directly and then use the Spectrograph software to see just what the spectrum is. My guess is that I will *NOT* find a classic square wave pattern by itself, it will be combined with a host of intermod products. We'll see.

If that is true then the next step would be to try and build a linear AM modulator that does NOT have an exponential gain function at the start and end of the keying pulse and see if that fixes the problem.

I will keep eham.net apprised of any progress in this area.

tim ab0wr

Bandwidth versus Keying Speed

by K5MC on June 5, 2007 Mail this to a friend!

W8JI: If I've made you angry or frustrated you I'm sorry. That really isn't my intention.

Tom, I'm not angry. I'm amused that you still apparently consider your "keyclick" bandwidth to be equivalent to the FCC's definition of "occupied" or "power" bandwidth.

Did you read my rather long post earlier about Joe, the new ham? The necessary bandwidth is 25 Hz for a keying speed of 6 wpm for a fading circuit. The "99% occupied" bandwidth according to your spectrum plots is about 500 Hz regardless of speed. Please reconcile this patent absurdity and explain how Joe can operate without violating 97.307(a). For your convenience, here is the text:

97.307(a) No amateur station transmission shall occupy more bandwidth than necessary for the information rate and emission type being transmitted, in accordance with good amateur practice.

73, K5MC

Bandwidth versus Keying Speed

by K5MC on June 5, 2007 Mail this to a friend!

W8JI: I have a question. My IC-751A's SSB transmitter has an occupied BW of about 2kHz with normal speech. If I talk slower does the transmitter become narrower?

K5MC: If you do it under what I consider "controlled laboratory conditions" then I would say YES! If you record your audio signal that modulates the SSB transmitter when you send your fixed-length message in real time, then when you send that same message again at the slower rate by dropping the tape recorder speed to 50%, the spectra components will be only 50% along the frequency axis compared to the original message. For a very simple example, let's assume I can whistle a pure tone at 2 kHz. If my original signal is a 2-kHz whistle for 1 second, then when I repeat that signal at half the recorded speed, it will be a 1-kHz whistle that lasts 2 seconds. In sending this "message" (I concede the point that the "information" of this message is very low!) the second time I used half the bandwidth for twice as long.

K5MC: Now let me ask you a question. Does the bandwidth of an FM signal depend only on the amount of frequency deviation or shift? For example, if I limit the instantaneous frequency of my FM signal to be plus or minus 75 kHz of the center frequency, is my bandwidth confined to be within 150 kHz no matter whether I use a 1-kHz tone or a 10-kHz tone as the modulating signal?

Since W8JI still hasn't responded to this particular post of mine, I assume that he agrees with my answer to his question about "talking slower" on phone and that he apparently does not know the answer to my question about FM.

73, K5MC

RE: Bandwidth versus Keying Speed

by W8JI on June 5, 2007 Mail this to a friend!

Hi Tim,

All of the waveshaping in the IC751A is on the T8 line. The T8 line follows the CW, and it it has multiple RC filters in consecutive stages following the oscillator.

You seem to keep focusing on the IC751A as an abnormal rig becuase the carrier oscillator is switched.

The fact is ALL rigs behave like I describe, not just the 751A.

It will be a welcome relief when you finally test a rig and see the off frequency clicks change neither in level nor width as speed is varied.

I expect when you finally actually measure something you will appear here and set the record straight.

Have a nice night! Looking forward to you actually testing a rig.

73 Tom

RE: Bandwidth versus Keying Speed

by AB0WR on June 6, 2007 Mail this to a friend!

w8ji:
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<

Hi Tim,

All of the waveshaping in the IC751A is on the T8 line. The T8 line follows the CW, and it it has multiple RC filters in consecutive stages following the oscillator.

You seem to keep focusing on the IC751A as an abnormal rig becuase the carrier oscillator is switched.

The fact is ALL rigs behave like I describe, not just the 751A.

It will be a welcome relief when you finally test a rig and see the off frequency clicks change neither in level nor width as speed is varied.

I expect when you finally actually measure something you will appear here and set the record straight.

Have a nice night! Looking forward to you actually testing a rig.

73 Tom
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

I am focusing on the 751a because I now have one. What is so hard to understand about that? You ascribe some kind of fanaticism to the fact as a subtle denigration when it is no more meaningful than it is what I have to work with.

I would suggest that you re-read my post. I do NOT attribute anything to the oscillator being keyed other than it has a non-linear transfer function at the start and end of each pulse. That non-linear transfer function will generate significant intermod products from a square wave rich in harmonics as long as it is the main contributor to the system transfer function, i.e. the start and stop of the pulse.

You are also continuing to put words in my mouth. STOP IT!

I have said that the key clicks *must* come from something other than a linear modulation stage combining a square wave and a sine wave if they occur only at the leading edge and the trailing edge of the pulse.

Your answer has been only to say that it is just the way it is. Birds fly because birds fly.

That is what has led to the faulty conclusion that the harmonics in a square wave exist only at the beginning and end of a pulse. "It just has to be that way because that is what the output is" -- that's no answer at all. If you can't describe what the input driving signal and the system response function is, you simply cannot describe how the output comes about. "It just is" is not an answer, it is an excuse.

And I already *have* tested it. The output of the CW portion of the rig *does* have a non-linear exponential gain function at the beginning and end of each pulse.

As I keep telling you, *THAT* is what causes the key clicks, not the envelope shape or that square wave harmonics only exist at the beginning and end of square wave.

I am not very hopeful that the Spectrograph software will be very useful in capturing such transients by using the recovered audio from a receiver listening to the signal but I'll give it a shot.

And you STILL HAVE NOT figured out how that 751a works.

1. The T8 line does NOT follow the CW pulse
2. The T8 line is applied 20ms before any CW pulse can occur. Check out IC1c and R451. R451 adjusts the delay time after T8 has been applied before any CW pulse can be applied through Q17, IC1b, IC1c, and Q4 to the CW IF oscillator of Q3. (I forget the diode numbers that perform this gating function)
3. The T8 line is turned on and allowed to stabilize for 20ms before any pulsing is done. The T8 line can, therefore, provide NO wave shaping.
4. If you don't believe me, put an oscilliscope on the T8 line, flip the transmit switch to on, and then start your CW keying. You will see NO CHANGE in the voltage level of T8. It can, therefore, do no waveshaping in either the oscillator or in stages subsequent to the oscillator.

(If you *do* see any voltage changes in T8 I would suggest you check your voltage regulators and on board electrolytics. Voltage sags in linear amplifiers can be a contributor to non-linear stage gains and therefore cause additional intermod)

You seem to be flailing at straws here to try and show me as being wrong. Perhaps you should sit down and actually do some circuit analysis before making wild claims about how the 751a works and telling me that I don't know what I am talking about. So far you are 0 for 2.

Oh, and all rigs apparently do NOT act like you say. Did you bother to check out the page I quoted showing the 756pro? The CW waveshape does NOT appear to have an exponential gain function on the leading and trailing edges. It is trapezoidal shaped. And the output shows the classic square wave spectrum of harmonics (taking into account receiver filter characteristics). The key clicks for this signal are close-in harmonics generated by the square wave affecting directly adjacent channels. They are *not* transient splatter 5khz away generated by intermod products from non-linear system response functions. They are therefore amenable to treatment by further limiting of the bandwidth of the system response function.

BTW, the best way to do the Fourier analysis of a trapezoidal wave is to find the second derivative of the input wave (hint: impulse functions) and calculate the Fourier transform. Then apply the integration factor to the resulting transform)

If you are not willing to assist in actually determining the driving input signals and system response functions that result in outputs that cause splatter 5khz away from the base frequency and want to continue indulging in such old wives tails as square waves only having harmonics on the leading and trailing edges -- HAVE AT IT. If you want to continue in the causal fallacy of claiming that the output causes the input (i.e. envelope slope generating frequency spacings and envelope amplitudes determining input amplitudes) -- HAVE AT IT.

I will continue investigating what the root causes are and how to do things better so that something as simple as excessive CW bandwidths don't have to be.

tim ab0wr

RE: Bandwidth versus Keying Speed

by AB0WR on June 6, 2007 Mail this to a friend!

ad5x:
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
This morning I fired up my old Johnson Ranger and ran a few tests. Keying speeds were 5- and 35-WPM using my Hallicrafters TO Keyer. The Ranger was transmitting into a dummy load on 14.035.00 MHz (it held this frequency surprisingly well after a 15 minute warm-up). I adjusted the level into my Yaesu MKV receiver to be exactly S9 on-frequency (relay short and attenuator on the MKV input, all cables 100% shielded LMR-240). Using the 60Hz DSP filter in my MKV, I measured the following: Offset 0Hz/S9, offset 50Hz/S9, offset 100Hz/S7, offset 150Hz/S5, offset 200Hz/S0 (offsets beyond 200Hz were all S0). I ran these tests numerous times at both keying speeds and could see no difference in level between the keying speeds within my ability to read the bargraph S-meter on the MKV.

Next I went to the 2.4KHz SSB filter, transmitted at 5WPM and tuned the MKV receiver until the key clicks were barely audible. With the S9 on-frequency starting point, I found that the clicks were barely audible 4Khz away (S0 S-meter reading). I re-set the receiver to 0Hz, changed the keying speed to 35WPM, and again tuned the receiver until I could just barely hear the clicks. Again, the “barely perceptible” clicks occurred 4KHz away.

Of course, there is no ALC in the Ranger.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

I'm sorry, I missed initially missed your post.

To what do you attribute this phenomena?

1. Square waves only have harmonics at the leading and trailing edges?

2. Output waveforms are frequency generators?

3. That's just the way transmitters work?

4. That intermod products are being formed at the leading and trailing edges?

5. That exponential gain functions in a circuit element somewhere in the Ranger are involved?

I'd be very interested in your view of what the root causes of this phenomena are.

tim ab0wr

RE: Bandwidth versus Keying Speed

by WA0LYK on June 6, 2007 Mail this to a friend!

W8JI:
All of the waveshaping in the IC751A is on the T8 line. The T8 line follows the CW, and it it has multiple RC filters in consecutive stages following the oscillator.
-----------------

The T8 is switched on each time the rig goes into transmit mode. With full breakin, the rig switches back into receive between characters so the T8 line goes low during during this time and back high when characters are being sent. With semi-breakin the T8 line remains high until a sufficient pause in sending occurs (VOX delay) that allows the rig to switch back into receive. If the transmit switch is placed in the transmit position, the T8 line stays high until the switch is placed back into receive.

The T8 line DOES NOT do the waveform shaping. T8 is held on during semi-breakin and when the transmit switch is on, i.e. when the rig is in transmit ready. Therefore, it cannot shape the waveform in these conditions. It is merely the 8 volts used to power components that are active only during transmit. It is activated by the "send" line which is activated by the vox circuit (which is activated by the keying circuit), the PTT on the mic connector, or the transmit/receive switch.

The delay in sending when in full breakin may not allow the T8 line to fully settle in, however you can measure this. If the waveforms you are measuring stay the same in full breakin, semi-breakin, and transmit then the T8 line is not the culprit.

Jim
WA0LYK

RE: Bandwidth versus Keying Speed

by AD5X on June 6, 2007 Mail this to a friend!

Hi Tim – Let’s re-cap a bit and then I’ll answer your question about my Johnson Ranger measurements. Early on in this thread I stated that during my engineering career, I found that when I measured something other than what theory predicted, 99% of the time it was because the theoretical model was incorrect. Your response:

AB0WR – “Please, this is nonsense…. If what you build doesn't do what your math says it should and your math follows established process then it can hardly be the model that is wrong….”

Of course, I’ve never challenged the math. Only the model that the math was applied to. When I disagreed and stated that you must consider that either the model or the measurement (or both) could be at fault, I got the following response from another:

W1YW – “And again, you have those with the experience to disagree with this comment.”

Of course I do have some experience. 35 years in new product development in phased array radar design, S-band satellite transmitter design, and digital microwave and high speed lightwave transmission product design. Now it has been quite awhile since I graduated (BSEE Va. Tech 1972, MSEE SMU 1974) so my technical skills may be a tad outdated. After all, back then the periodic table of the elements consisted of earth, air, fire and water. And if you can believe it, I was even taught that there were nine planets. But I have had my hands in a lot of designs since then, and I know that accurate mathematical models of complex systems can take awhile to develop – and part of this development includes extensive testing in the lab. And as I believe you are now admitting, there is something in the system we don’t understand, since the theoretical model doesn’t appear to match the measurements.

Over and over again I’ve found that the process must be: theory-measurement-theory-measurement-theory-measurement, etc. After awhile everything converges and you really understand your theoretical and physical models (and you start sleeping all night long). The theory helps you build the proper physical model, and the physical model helps you understand where the theoretical model is lacking.

Now, regarding my Ranger measurements:

AB0WR “I'm sorry, I missed initially missed your post. To what do you attribute this phenomena?
1. Square waves only have harmonics at the leading and trailing edges?
2. Output waveforms are frequency generators?
3. That's just the way transmitters work?
4. That intermod products are being formed at the leading and trailing edges?
5. That exponential gain functions in a circuit element somewhere in the Ranger are involved?
I'd be very interested in your view of what the root causes of this phenomena are.”

I ran these same tests on an IC-706MKIIG earlier. But someone (maybe you?) commented that ALC may be the reason for this discrepancy with theory. So I ran the tests on the Johnson Ranger which basically showed the same results. And, of course, the same results that W8JI has measured.

I do not really know for sure why all transmitters seem to have a CW transmitted bandwidth that is independent of keying speed, but I’ll give you my thoughts (since you asked).

Let’s say you are modulating an RF carrier with a square wave to give the string of dots. This is, of course, a mixing process so you get the carrier and sum and difference sidebands. Since the square wave has essentially infinite harmonics, you will get an infinite spectrum assuming no transmit filtering. Of course the speed at which the spectrum drops off theoretically does change as a function of the keying speed.

Now instead of a square wave, let’s modulate the carrier with a pure sine wave. In this case the sum and difference frequencies are very limited, as the pure sine wave doesn’t have harmonics. In this case, you would see sum/difference sidebands that extend outward as a function of keying speed because as the modulation (keying speed) frequency increases, the sideband separation from the carrier increases.

Of course, in the real world we have something in-between a square wave and a sine wave as this modulation source so there are more sidebands. But let’s assume that it is a sine wave anyway. The problem is that modulation is a mixing process, and only perfect mixers give you this pure carrier plus sum/difference sidebands. Due to even minor non-linearities in the transmitter, you will get the carrier mixing with the sidebands and these sidebands mixing with themselves (the lower sideband mixing with the upper sideband) and the carrier, etc etc etc. The old 2A-B intermod problem that many of us have experienced over and over again. This fills in carriers in between and around the original sidebands. On top of this, add in the phase noise of the transmitter which will smear everything further. I believe that the result of this is a spectrum that basically holds the same shape regardless of the modulating frequency – at least at the CW speeds at which we operate.

Of course, as my wife will attest, I am frequently wrong. In any case, I’m hopeful that the result of this extremely interesting thread will be better understanding by all of us about this specific issue.

Phil – AD5X

Bandwidth versus Keying Speed

by AI8H on June 6, 2007 Mail this to a friend!

Mickey,

Great constructive and informative article.

Hopefully, some have retrieved and took to heart the very basic theory that you have cited and reinforced from within the very long and overly-complicated responses.

The example of "Joe" was a stroke of genius and brought your original thoughts back to base.

Jeff ~ ai8h

RE: Bandwidth versus Keying Speed

by W8JI on June 6, 2007 Mail this to a friend!

Jim,

You are correct about the T8 line, I was wrong. I was looking at it in QSK.

Let's move the argument away from the 751A and the claim the 751A is somehow abnormal causing the behavior I measured.

I posted measurements of the FT-1000MP MK V at this URL:

http://www.w8ji.com/occupied_bw_of_cw.htm

We see the following. The IC 751A OBW is:

Dot speed ---OBW 99% power
10 ----------490 Hz
25 ----------430 Hz
40 ----------500 Hz

The FT1000MP MKV measures:

Dot speed ---OBW 99% power
5 dps------- 780 Hz
10---------- 460 Hz
20---------- 550 Hz
40 ----------460 Hz

I've measured Globe Scouts, Yaesus, Kenwood, ICOM, Viking Valiant, Ten Tecs, and other rigs and NONE of them follow the theory that OBW or width of clicks tracks keying speed.

When every radio in the world disagrees with a theory, it might be time to stop and rethink the theory.

I'm waiting for Tim to actually measure a few radios, like others have done. You'll notice all the measurements posted in this thread agree with what I say...and not the misapplied theory.

73 Tom

RE: Bandwidth versus Keying Speed

by W8JI on June 6, 2007 Mail this to a friend!

Phil,

The reason all transmitters seem to have an OBW independent of keying speed is because, by definition, the bandwidth must accomodate the fastest cahnge in the waveform. The fastest change is the rise and fall, not the very slow repetition.

It is actually impossible to have 2.5 ms rise (which would be 1/2 of the on and off cycle) without at least one sideband 200 Hz above and below the carrier.

If you look at the waveform of the IC-751A and FT1000MP MKV I measured on a scope, they each have about a 2-3 ms rise and fall time.

It's not unexpected at all that the bandwidth would be at least 400Hz for both rigs if the rise and fall was reasonably shaped.

So you see if we stay away from the odd notion that a slow CW speed allows BW to be less than that required to send the rising and falling edges, everything makes total sense.

If we somehow assume we can transmit those sharp rising and falling edges magically without producing sidebands that are tied to the duration of the rise and fall, then we are mystified by this simple process and look for faults or excuses.

73 Tom

RE: Bandwidth versus Keying Speed

by AD5X on June 6, 2007 Mail this to a friend!

W8JI: "The reason all transmitters seem to have an OBW independent of keying speed is because, by definition, the bandwidth must accomodate the fastest change in the waveform. The fastest change is the rise and fall, not the very slow repetition. It is actually impossible to have 2.5 ms rise (which would be 1/2 of the on and off cycle) without at least one sideband 200 Hz above and below the carrier."

This is very clear and certainly makes sense. Thanks.

Phil - AD5X

Bandwidth versus Keying Speed

by K5MC on June 6, 2007 Mail this to a friend!

AI8H: The example of "Joe" was a stroke of genius and brought your original thoughts back to base.

Jeff, I really appreciate your comments!

Perhaps before too long W8JI and some others will understand that there are other definitions of bandwidth besides "keyclick" bandwidth that are important, even in the world of amateur radio communications. I keep thinking that the examples of EME and QRSS might help these folks understand the concept of (time averaged) power bandwidth, along with the related concepts of communications in the presence of noise, signal to noise ratios, (average) signal power versus (average) noise power, transmission rate versus "essential/necessary" (power) bandwidth, and so forth. Apparently, however, some hams continue to think that "keyclick" bandwidth is the only type of bandwidth needed in order to understand how communication systems actually work.

73, K5MC

RE: Bandwidth versus Keying Speed

by AB0WR on June 6, 2007 Mail this to a friend!

ad5x:
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
Of course, in the real world we have something in-between a square wave and a sine wave as this modulation source so there are more sidebands. But let’s assume that it is a sine wave anyway. The problem is that modulation is a mixing process, and only perfect mixers give you this pure carrier plus sum/difference sidebands. Due to even minor non-linearities in the transmitter, you will get the carrier mixing with the sidebands and these sidebands mixing with themselves (the lower sideband mixing with the upper sideband) and the carrier, etc etc etc. The old 2A-B intermod problem that many of us have experienced over and over again. This fills in carriers in between and around the original sidebands. On top of this, add in the phase noise of the transmitter which will smear everything further. I believe that the result of this is a spectrum that basically holds the same shape regardless of the modulating frequency – at least at the CW speeds at which we operate.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

So you would expect to see the waveform taper off with the same drop-off as Taylor series describing a non-linear mixing process, right? I haven't analyzed Tom's pictures to see if that might be the case. It would be an interesting exercise. I wish I could remember the amplitude factors for 3rd, 5th, and 7th order intermod products. I'll have to look them up.

The products will get even more interesting considering the harmonics existing in a square wave.

It would seem then, that we should be able to fix this by using modulators (mixers) that are more linear, right?

What would be even more interesting would be to put the output of my square wave generator directly into the mic input of the 751a and see what the output waveform looks like. If it is a non-linear mixing process after the 1st local oscillator, then the same thing should show up. I might try this next week.

Thank you for your thoughts. I may have more questions later.

tim ab0wr

RE: Bandwidth versus Keying Speed

by W8JI on June 7, 2007 Mail this to a friend!

Tim and Phil,

I have designed PIN diode modulators and used them with very clean unkeyed oscillators (pulse transmitters) for LASAR and medical applications and the transmitters do not change signal level vs spacing from carrier as pulse repetition rate is changed.

As a matter of fact when I measure the OBW of a steady carrier with any of the rigs I tested it is in the area of 20-30Hz, so the phase noise (more correctly it should be called composite noise)isn't an issue. It's all modulation products of the rise and fall in any well-designed properly operating transmitter, and except for things that might change rise and fall times it remains essentially constant.

As a matter of fact it is just as effective to shape the pulse rise and fall as it is to run the pulsed output of the modulator through a bandpass filter.

CW transmitters are no different. Running unfiltered very wide CW with a fractional millisecond rise and fall through a narrow filter 500Hz wide produces a ~4 ms rise and fall on the envelope at any keying speed.

If the average carrier power during on times is 100 watts PEP, the sideband power at a given spacing remains the same regardless of speed so long as rise and fall time and shape isn't changed. How many seconds, days, or years the pulse goes on has nothing to do with it.

I tried to bring that out in my question where I said, "if I talk slower does the BW of my SSB transmission decrease?" to which the reply was "yes".
This shows the person responding "yes" doesn't understand how the system behaves in the real world.

Imagine telling a guy up or down the band who is overdriving an amplifier "Hey you're splattering. Please talk slower." Or telling the FCC as the VA3 gave the example, "well I transmitted for ten minutes on 7.002 MHz before transmitting on 6.999 MHz for 10 seconds, so my occupied BW was well within the 40M band."

The fact is how strong you hear somone off frequency doesn't change much with speed if the envelope rise and fall times and shape don't change.

73 Tom

RE: Bandwidth versus Keying Speed

by AD5X on June 7, 2007 Mail this to a friend!

I am really enjoying this thread. Mentally stimulating. Now that I'm retired, I have this thread, my gadget building and honey-do's - and I'm enjoying this the most.

W8JI: "As a matter of fact when I measure the OBW of a steady carrier with any of the rigs I tested it is in the area of 20-30Hz, so the phase noise (more correctly it should be called composite noise) isn't an issue. It's all modulation products of the rise and fall in any well-designed properly operating transmitter, and except for things that might change rise and fall times it remains essentially constant."

Now remember, I agree with you that the bandwidth doesn't change as you change keying speed. However, I'm not sure I agree that it is "all modulation products of the rise and fall". I believe that the system is more complex than any of us are considering. I agree that the rise time of the cw waveform is going to define sidebands offset by 200-300 hz (and their harmonics, which will be band-limited) from the carrier as you suggest. However, the average energy of these clicks has to be extremely low, which means that the rise time BY ITSELF would contribute little to the occupied bandwidth. However, I believe that the peak energy of the clicks is very high. This high peak energy may be a significant contributor to the generation of the IMD products consisting of the mixing of the composite noise, the modulation frequency (dit-rate), and the click sidebands. So the instantaneous transmitter signal path non-linearity due to the high peak energy pulse then causes the resulting fixed spectrum, whose boundaries are defined by the rise/fall times.

73,
Phil - AD5X

RE: Bandwidth versus Keying Speed

by W8JI on June 7, 2007 Mail this to a friend!

Hi Phil,

It's GOOD to see someone wanting to disect the issue with a motivation of defining how the system actually works. After all, that is the ONLY thing important.

You wrote:

<<Now remember, I agree with you that the bandwidth doesn't change as you change keying speed. However, I'm not sure I agree that it is "all modulation products of the rise and fall". I believe that the system is more complex than any of us are considering.>>

I certainly agree with that. If someone wanted to really define the system in terms of interference bandwidth it would have to include information on the signal other channel (the speed, selectivity, and S/N ratio) as well as the repetition rate of the unwanted sidebands.

The fact is that is so subjective and so complex means we have to simplfy it. That's why in the most simple form we can say this:

Unless keying speed somehow changes the waveshape of the rising and falling edges, keying speed only changes the repetition rate of the interference.

<< I agree that the rise time of the cw waveform is going to define sidebands offset by 200-300 hz (and their harmonics, which will be band-limited) from the carrier as you suggest.>>

Careful there. The bandwidth of the sidebands assuming no major defects in the transmitter is set by the rise and fall caracteristics. It isn't always 200-300Hz offset. That would only be for a nearly perfect raised sine modulation with about 2.5 ms rise and fall. Some transmitters are 1 ms or less rise and fall, and most are not a raised sine shape. Some are longer and the Ten Tec Orion is indeed a raised sine.

<< However, the average energy of these clicks has to be extremely low, which means that the rise time BY ITSELF would contribute little to the occupied bandwidth.>>

I disagee. This is 100% modulated AM. It goes from zero carrier to some defined maximum power. That same maximum power is reached no matter how long the on period.

Now the receiver and the operator, by definition of what they are doing, cannot store that energy in a bucket. It is not integrated over a time even close to a dot length or dot space, or the dots would smear. The response always has to be real-time and be able to follow the rise and fall period.

Because of that longer term effects like the slow rate don't really matter. The energy cannot be accumulated, so you read the peak envelope power at any frequency. As a matter of fact the mean power is defined to be tied to the modulation rate by this clause in ATIS standards:

" mean power (of a radio transmitter)
mean power (of a radio transmitter): The average power supplied to the antenna transmission line by a transmitter during an interval of time sufficiently long compared with the lowest frequency encountered in the modulation taken under normal operating conditions. [NTIA] [RR] Note: Normally, a time of 0.1 second, during which the mean power is greatest, will be selected. "

They only want to read the power a time "sufficently long" to read the lowest frequency modulation envelope power, they don't want it accumulated over infinite time as some might suggest.

Peak Envelope Power is a way to do this with what amounts to automatic reading of the slowest rate power. Otherwise we would have to use a radio equivalent of kilowatt hours of energy delived to kilowatt hours of spurious.

The bottom line in ANY measurement is we always want to know the effect of the modulation on adjacent channels, and with CW it is NOT long term power. It is simply if the PEP of sidebands exceed the PEP level of signal on the other channel.

<< However, I believe that the peak energy of the clicks is very high. This high peak energy may be a significant contributor to the generation of the IMD products consisting of the mixing of the composite noise, the modulation frequency (dit-rate), and the click sidebands.>>

Unfortunately not. The composite noise is constant, and mainly in most transmiters I have measured the broadband noise is Johnson noise in low level semiconductors. To a lesser extent the sysnthesizers produce noise, but it is many dB per Hz down from the carrier power. It is down so far it does not affect OBW or interference bandwidth of the clicks.

To put this into a perspective most Hams would follow, with an S meter pinning signal from a local 1500 watt transmitter just hundreds of feet from a receiving antenna composite noise is only a few S units.

I know all this very well because I spent months looking at many different radios so I could duplex on CW during contests.

As I've said, I've designed pulse transmitters for medical and industrial applications and some of these had very quiet local oscillators and good low noise amplifier chains. In one application the FCC set a bandwidth limit for a 27.120 MHz pulse signal while the FDA controlled the average power, pulse rate, and rise and fall times. It was every bit as effective in that system to control the pulse rise and fall as it was to simply generate the pulses and feed them through a filter. Despite the fact the pulses varied from a few pulses per second to hundreds of pulses per second, the peak envelope power of sidebands at a given spacing allowed by FCC requirements remained the same. It was set by the rise and fall of the envelope.

You'll notice the same effect regardless of what radio you test. You can use tubes, semiconductors, or spark.

Now it is true the faster rate repeats more and the faster repetition would mean you copy less and less as speed is increased in the offending transmitter while being constant in the victim's equipment, but that isn't the law we live under for CW. The law we live under is we are not allowed to cause harmful interference on adjacent frequencies from clicks. Since the level and bandwidth of clicks remains the same at a given spacing we have to contyrol the rise and fall.

Transmitting less is not a way to mitigate interference, unless you are willing to just shut it off.

Most manufacturers, thanks to efforts by many people, now understand they will create problems when they sell a rig with 1 ms rise and fall and now are shaping the rise and fall. They now also understand the shape is important. The Handbook is now corrected. This was a major advancement in our hobby and we all reap the rewards.

I'd hate to see it undone by a very small number of people who promote a correct but meaningless position. The math has to fit the system because we can't change how the system actually works.

73 Tom

RE: Bandwidth versus Keying Speed

by AD5X on June 7, 2007 Mail this to a friend!

Hi Tom – My comments:

W8JI: “Unless keying speed somehow changes the wave shape of the rising and falling edges, keying speed only changes the repetition rate of the interference.”

I agree.

W8JI: “The bandwidth … isn't always 200-300Hz offset...”

Yes. I was assuming reasonable rise/fall times as you’ve discussed. I know how bad this can be. My MKV had HORRIBLE key clicks until I did your mod. Thanks for that.

AD5X: “However, the average energy of these clicks has to be extremely low, which means that the rise time BY ITSELF would contribute little to the occupied bandwidth.”
W8JI: “I disagree. This is 100% modulated AM. It goes from zero carrier to some defined maximum power. That same maximum power is reached no matter how long the on period. Now the receiver and the operator, by definition of what they are doing, cannot store that energy in a bucket. It is not integrated over a time even close to a dot length or dot space, or the dots would smear. The response always has to be real-time and be able to follow the rise and fall period. Because of that longer term effects like the slow rate don't really matter. The energy cannot be accumulated, so you read the peak envelope power at any frequency.”

I understand what you are saying. But it doesn’t “feel” right. I.e. when I think of occupied power bandwidth, I think of power integrated over a reasonable (fraction of a second?) period of time creating the spectrum. Now if part of this spectrum display has to do with an extremely short pulse, then I find it difficult to see how this short pulse contributes to the power in the spectrum. I’m certainly not saying that you are wrong and I am right. I just need to go wrap my brain around this a little longer.

AD5X: “However, I believe that the peak energy of the clicks is very high. This high peak energy may be a significant contributor to the generation of the IMD products consisting of the mixing of the composite noise, the modulation frequency (dit-rate), and the click sidebands.”
W8JI: “Unfortunately not. The composite noise is constant, and mainly in most transmitters I have measured the broadband noise is Johnson noise in low level semiconductors. To a lesser extent the synthesizers produce noise, but it is many dB per Hz down from the carrier power. It is down so far it does not affect OBW or interference bandwidth of the clicks.”

So what happens to this phase noise and dit-sidebands when mixed with the click sidebands in a highly non-linear system? Again, the impulse due to the rise time has (I think) a very high peak level. Your transmitter circuits don’t have infinite headroom (well, not infinite but you know what I’m getting at). High order IMD products can be pretty bad under such potentially extreme (non-linear/high level) conditions.

W8JI: “As I've said, I've designed pulse transmitters for medical and industrial applications and some of these had very quiet local oscillators and good low noise amplifier chains.”

Yes, and pulse transmitter designs I’ve been involved with had to have very high overhead (very high saturated output power capability) so they could handle the high peak powers. I’m not sure you can say the same about the typical amateur transmitter.

W8JI: “The law we live under is we are not allowed to cause harmful interference on adjacent frequencies from clicks. Since the level and bandwidth of clicks remains the same at a given spacing we have to control the rise and fall.”

Yes, absolutely. Key clicks can be very much of an interference issue. But I’m not sure that this corresponds to the power bandwidth of the signal due to the short duration of the pulse. Again, I have to think about this some more.

W8JI: “The math has to fit the system because we can't change how the system actually works.”

Absolutely. I’ve said this from the start. Now if we were starting a design from scratch, then we could change how the new system would work.

I’m going to spend the next two days at Hamcom here in Dallas – my poor man’s substitute for Dayton. I couldn’t make Dayton this year as my daughter (AC5NF) is getting married in August (to KD5EVW), and money for that is taking precedence!! So if I don’t respond over the next few days, it is not because I’m ignoring anyone.

73,
Phil – AD5X

RE: Bandwidth versus Keying Speed

by AB0WR on June 7, 2007 Mail this to a friend!

w8ji:"As a matter of fact it is just as effective to shape the pulse rise and fall as it is to run the pulsed output of the modulator through a bandpass filter. "

Exactly what do you think you are doing when you "shape" a pulse rise and fall?

w8ji:"CW transmitters are no different. Running unfiltered very wide CW with a fractional millisecond rise and fall through a narrow filter 500Hz wide produces a ~4 ms rise and fall on the envelope at any keying speed. "

Exactly what do you think the filtering is doing to the wideband signal?

Answer to both: You are filtering the signal. You are going from a non-bandwidth limited signal to a bandwidth limited signal. That is what generates the rise time. The rise time doesn't generate the input, the input plus the system transfer function shapes the output giving it a rise time.

tim ab0wr

Bandwidth versus Keying Speed

by AB0WR on June 7, 2007 Mail this to a friend!

w8ji:
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
The reason all transmitters seem to have an OBW independent of keying speed is because, by definition, the bandwidth must accomodate the fastest cahnge in the waveform. The fastest change is the rise and fall, not the very slow repetition.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

A square wave has to have infinite bandwidth in order to be a square wave. Any circuit with a bandwidth limit will eliminate those high frequency harmonics that make up the sides of the start and end of a square wave pulse.

It is this bandwidth limitation that determines the rise and fall time, not the other way around. Rise time is only an *indicator*, it is not a generator.

tim ab0wr

Bandwidth versus Keying Speed

by AB0WR on June 7, 2007 Mail this to a friend!

w8ji:
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
If the average carrier power during on times is 100 watts PEP, the sideband power at a given spacing remains the same regardless of speed so long as rise and fall time and shape isn't changed. How many seconds, days, or years the pulse goes on has nothing to do with it.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

This is just plainly untrue. It is a disservice to young amateur aspiring to become engineers. It is a disservice to those non-technical amateurs who might be trying to actually learn accepted theory.

See the discussion below.

w8ji:
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<,
he fact is how strong you hear somone off frequency doesn't change much with speed if the envelope rise and fall times and shape don't change.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

w8ji:
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
Unless keying speed somehow changes the waveshape of the rising and falling edges, keying speed only changes the repetition rate of the interference.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

Let's go through this one more time.

1. A square wave is made up of an infinite number of harmonics at odd integer intervals.
2. The fundamental AND the harmonics exist for the entire time the square wave exists. They don't magically "die away" part way through the pulse.
3. The energy in the sidebands of a CW signal is distributed throughout the sideband in direct relationship to the amplitudes of the high frequency components.
4. The fundamental frequency and the harmonics make up the envelope shape, not the other way around. That would be a causal inconsistency.

Fourier Series of a square wave. If Fn is the individual component frequency, Sa(x) indicates the sinx/x function, n is the harmonic, and w = radian frequency, then the form of the Fourier Series is

Fn = (A/2) Sa(n w/2) = (A/2)(2/nw) sin(nw/2) = (A/nw) sin(nw/2)
Pn = |Fn|^2 (Fn squared)

In the frequency domain the power spectrum again looks like a series of individual component frequencies with amplitudes as specified above. The amplitudes of the square wave fall off at 6db/octave (1/n) while the power spectrum falls off at 12db/octave (1/n^2).

These harmonics and their contribution to the power spectrum exist throughout the pulse, not just at the beginning and edge of the pulse.

When you bandwidth limit a square wave, you eliminate high frequency components which results in an increase rise time on the square wave. This relationship is rise-time = pi/bandwidth.

Now, as to rise-time and envelope shape. If I give you a square-wave with a rise-time and an envelope can you tell me what square-wave components makes up that rise-time and envelope?

Answer: NO, emphatically NO!

Consider a system transfer response with a bandwidth limit of 500hz, that is a 250hz upper sideband and 250hz lower sideband.

Case 1: a 2hz square-wave is applied to this system transfer function. At 250hz we have harmonic number 125 (250/2). So we have the fundamental and all odd harmonics up through 125 making up our output envelope. Guess what? You will see a 6.3ms rise time on the envelope. And the envelope will look just like a bandwidth limited square wave of amplitude "A" based on the PEP rating of the transmitter.

Case 2: a 10hz square-wave is applied to this system transfer function. At 250hz we have harmonic number 25 (250/10). So we have the fundamental and all odd harmonics up through 25 making up our output. Guess what? You will see a 6.3ms rise time on the envelope. And the envelope will look just like a bandwidth limited square wave of amplitude "A" based on teh PEP rating of our transmitter.

Let's now consider the power spread betweeen 30hz and 50hz for both cases.

Case 1: harmonics 15, 17, 19, 21, 23 and 25. These have normalized squared components of .0072051, .0056095, .0044907, .0036761, .0030645, and .0025938. Total normalized power from all components = .0266396

Case 2: harmonics 3, and 5. These have normalized squared components of .1801265 and .0648456 for a total normalized power of .2449721. Almost a 10db difference in contribution to the power spectrum from just a 20hz wide section of the sideband.

So we see that the envelope rise time and shape is the *SAME* for two totally different waveforms. How then does the envelope waveform and shape determine anything? There are a multiplicity of inputs which will result in this exact rise time and envelope shape when used with the same bandwidth-limited system transfer response. The power contributions for the same sideband frequency spread is different for the two different waveforms even though the output waveform has exactly the same rise time and envelope shape. So, again, how can the power contribution be the same for any separation from the fundamental? The TOTAL power in the sideband is the same, the distribution *is not*.

Let's talk about how strong someone listening off frequency hears you, say at 250hz. With a 2hz signal, the frequency component at 250hz (harmoic 125) will be .0101859. For a 10hz signal, the frequency component at 250hz (harmonic 25) will be .0509296. That is a ratio of -15db for the 2hz signal over the 10hz signal (5wpm versus 25wpm). That's only between 2 and 3 S-units but that *is* a signficant difference.

The next time someone says this has never been shown and tests on radios need to be made, I *IMPLORE* you go to web site <http://www.seed-solutions.com/gregordy/Amateur%20Radio/Experimentation/CWShape.htm> and take a look at the spectrum plots provided by w8wwv. Listen to the waveforms with a good speaker. What you will hear is the higher pitched harmonics being eliminated as the bandwidth filtering gets narrower and narrower (i.e. the rise time gets extended because the higher harmonics aren't there). This can be seen on the spectrum plots AS WELL AS spectrum distribution of the discrete frequencies making up a square wave. While it is difficult to tell from this plot it appears reasonable that a 6db/octave falloff (i.e. a 1/n decrease) is what the plot is showing, again, exactly what a square wave distribution would show. I hope to have similar plots for my 751a in the next couple of weeks. I fully expect them to show exactly the same thing.

Again, I *IMPLORE* those reading this subject to go to Google and type in "square wave" and "Fourier Series". You will get a wealth of information on exactly how a square wave comes about and what bandwidth limitations do to it. Apply that information using basic modulation theory (i.e. cos(wc-w) and cos(wc+w) frequencys from modulation) and you can easily get the output waveform for a square wave driving signal and a bandwidth-limited system response function.

I have to go to a dance recital now. Perhaps I'll post more later.

tim ab0wr

RE: Bandwidth versus Keying Speed

by AD5X on June 7, 2007 Mail this to a friend!

AB0WR: "I have to go to a dance recital now. Perhaps I'll post more later."

It is nice when you have more than one hobby. Enjoy your dancing :-)

Phil - AD5X

Bandwidth versus Keying Speed

by K5MC on June 7, 2007 Mail this to a friend!

I've posted some pictures at http://www.arrl.org/sections/?sect=LA that I hope will be of interest to those folks still following this thread. The pictures are not the highest quality by a long shot, but I think they are adequate until I can make some higher quality photos and upload them to a more permanent website.

The first figure is two keying spectrum plots emailed to me by Karl-Arne SM0AOM. These plots are from Telefunken literature and both of them clearly show a discrete-line spectrum, unlike the spectrum plots posted by W8JI. The Telefunken plots are what I would expect to see on a high quality RF spectrum analyzer when measuring the spectrum of a typical CW transmitter being keyed by a uniform string of dits at a sufficiently high rate of speed. The distance between the sidebands is determined by the sending speed. The keying sidebands in the Telefunken plots are distinct, just as my spectrum plots are for the two keying waveforms I assumed in my article. (That is, I calculated the Fourier series for each of the periodic keying waveforms that I described in my article.)

Figure 2 shows the audio output signal as measured by an oscilloscope across the loudspeaker of my MFJ-447 electronic keyer when it is sending a string of dits at about 40 wpm. The rise/fall times and shapes of this keyer are actually rather close to the "sinusoidal" waveform I modeled in my article. The time base on the oscilloscope in this figure can clearly be read to be 10 ms per division and the rise/fall times of the signal are both approximately 5 ms by inspection. The fact that the output frequency of this keyer is approximately 1 kHz rather than 3.5 MHz makes NO difference in how one uses Fourier analysis to determine the "power" bandwidth of a CW signal or in comparing the measured results from this particular keyer to CW signals in general.

Figure 3 shows the magnitude spectrum of my keyer around 40 wpm with the HP analyzer span equal to 100 Hz. The keying sidebands are clearly distinct and the spacing between adjacent sidebands is approximately 17 Hz, corresponding to 17 dits per second or about 40 wpm.

Figure 4 shows the same magnitude spectrum as Figure 3 except the frequency span of the analyzer is now set equal to 400 Hz rather than 100 Hz. Figure 5 shows the magnitude spectrum of my keyer at a speed of about 10 wpm with the analyzer span also equal to 400 Hz. Because the keying sidebands are 4 times closer together at 10 wpm as they are at 40 wpm, the keying sidebands are starting to "run together" in Figure 5 and the spectrum appears to be "continuous" rather than discrete.

Although Figure 5 is rather fuzzy in appearance because I'm a lousy camera operator, it is still quite obvious that the "bandwidth" of the signal in Figure 4 is considerably larger than the "bandwidth" of the signal shown in Figure 5. (Remember that Figure 4 and Figure 5 have the same span, 400 Hz.) The bandwidths at 30 dB down are about 115 Hz and 240 Hz at 10 wpm and 40 wpm, respectively. The bandwidths at 40 dB down are about 240 Hz and 320 Hz at 10 wpm and 40 wpm. (BTW, the concept of "dB" bandwidth is not, in general, consistent with the 99% power bandwidth.)

Why is the "bandwidth" of the signal shown in Figure 4 larger than the "bandwidth" of the signal shown in Figure 5? It's because the signal shown in Figure 5 is the keyer output at a speed of about 10 wpm rather than about 40 wpm! What kind of "bandwidth" is the spectrum analyzer really giving us here? It's the (time averaged) power bandwidth of the keyer audio output signal while sending a string of dits at a constant rate of either 10 wpm or 40 wpm. I know that this analyzer is measuring the (time averaged) power bandwidth because it was designed by Hewlett-Packard engineers who studied the theory of Fourier transforms just as I have. The theory came before the spectrum analyzer was built!

This result is completely consistent with Fourier analysis and it is completely consistent with the results I presented in my article. As the ARRL Handbook says, the bandwidth "occupied" by a CW signal is a function of both the sending speed and the rise/fall shapes and times of the keying envelope. In making this statement, the Handbook authors are using the FCC definition of "occupied" bandwidth, which is equivalent to the definition of the 99% (time averaged) power bandwidth that I discussed in my article.

Let me also add the fact that the keying envelope of my Kenwood 940 appears to be free of any weird transients that seem to continually haunt W8JI's rigs. The rise time of my 940 at 3.6 MHz when observed on a 150-MHz scope is approximately 5 ms with a rather smooth transition, although it is definitely not sinusoidal in appearance. The trailing edge of the keying envelope is also distinctly different in shape from the leading edge. The trailing edge is essentially a straight-line drop over a time of approximately 8 ms. Because of my understanding of Fourier analysis and the basic concept of (time averaged) power/occupied bandwidth, I know that there is no way my 940's "occupied" bandwidth as defined by the FCC will remain constant at all speeds as maintained by W8JI.

In closing, I truly hope that my posted figures will convince the hams who have been strong adherents of the W8JI School of Signal Analysis that the concept of "power" bandwidth is very worthy of respect in its own right. As I've said many times now, the concept of "keyclick" bandwidth is also important; the mathematical techniques used by such hams as W9CF and W7AY to minimize the undesirable effects of key clicks is essentially the concept of "short-time" Fourier transforms as I mentioned some time ago. However, nobody genuinely interested in understanding communication systems should lose sight of the important role played by the concept of power bandwidth.

73, K5MC

RE: Bandwidth versus Keying Speed

by W8JI on June 8, 2007 Mail this to a friend!

Mickey,

I really wish you would abandon the straw-man arguments and measure some real rigs.

You keep picking on my test gear, but I have current expensive Agilent equipment that has a resoltion bandwith of only 10 Hz.

Forst you wrongly publically claimed I was syncing the dots to the trace, now you imply my rigs or my test gear has some odd abnormal problem.

The fact is ALL of my rigs are common rigs and all of the "abnormal problems" with them are common to all equipment.

For example ALC systems are notoriously bad about adding transients during the leading edges. Everyone who has anything to do with radios and performance knows this. When you back the dot speed down low enough for the ALC to drop between dots, the following dot will be reshaped by the ALC. The leading edge rise period will ALWAYS be truncated or made more vertical.

Also the tone of this isn't very professional when it's something like "W8JI's rigs blah abnormal blah blah bad test method blah blah my math blah blah". I'm simply explaining how this works, and it isn't personal. It's how every radio from a Johnson Ranger to a FT9000 work in the real world. We might not like it, we might not agree, but it is factual.

This is why every person who has tested what I said agrees with what I say. I am describing how the rigs behave, I have offered links to other people who's analysis agree. Chen agrees, everyone agrees. Even the new ARRL Handbook agrees. Anyone who observes the effects on the air agrees.

Let's quit beating a dead horse. Your math is correct IF the effect on adjacent channels was an accumulated power over time. The problem is the interference is NOT an accumulated power ratio over time because the nature of the system is such that energy isn't stored. There isn't any error correction, it is simply a matter of the clicks peak envelope power level and duration and that does not change unless we change the slope or time of the rise and fall.

Is it really so tough to do the right thing for the hobby? Do we have to belabor meaningless points that only serve to confuse people?

If we want a clean rig that meets FCC bandwidth requirements we have to shape or filter (same thing) the envelope rise and fall. Sending slower will reduce the reoccurance of the disruptive sidebands, but it will not change there absolute level. It also will NOT change the ratio of power in those clicks to the peak envelope power of the carrier.

Please, let's not set the clock backwards. Rigs are now being improved because manufacturers understand how it really works. Let's not undo that.

73 Tom

RE: Bandwidth versus Keying Speed

by AD5X on June 8, 2007 Mail this to a friend!

K5MC: "I've posted some pictures at http://www.arrl.org/sections/?sect=LA that I hope will be of interest to those folks still following this thread."

Mickey - These spectrum photos are not the output spectrum of a real radio. Why can't you measure a real radio? You keep arguing your point, but you won't measure a radio to verify it. Whereas there appears to be measured data that refutes what you say. I think that all this can be reasolved with some real measurements on your part. If your measurements don't agree with Tom's measurements (and others), then we can all try to figure out who is doing what wrong. But unto all parties actually make measurements, I don't see how we can move forward. It will continue to be "This is what the math says" vs "This is what I measure."

Phil - AD5X

RE: Bandwidth versus Keying Speed

by KE3HO on June 8, 2007 Mail this to a friend!

Mickey,

Looking at the figures that you posted on the ARRL LA section page, am I correct in assuming that in Figure 1 everything is equal between the left and right pictures (vertical scale, frequency span, etc.) except for the absence or presence of leading and trailing edge shaping on the keying waveform? If so, then my interpretation of those two plots is that the bandwidth of the signal is DRASTICALLY affected by the rising and falling shape of the keying waveform. How about repeating that same measurement, only this time use the “CCIR keying shaping” for both plots and show us the spectrum at 5 wpm and at 40 wpm. That might show something to support your claim.

73 - Jim

RE: Bandwidth versus Keying Speed

by AB0WR on June 8, 2007 Mail this to a friend!

Ad5x:

Phil,

ROFL. I did my dancing 20-30 years ago. I do some infrequent ballroom dancing now but no recitals -- about 150lbs too heavy!

My 18year old son is a competitive tap and jazz dancer and the studio he is at is giving a performance this weekend. They will bring in well over a thousand people over two shows. I believe they have about 40 dances each night, he is in eight of them.

My hobby is taking pictures at the dress rehersal!!

tim ab0wr

RE: Bandwidth versus Keying Speed

by AB0WR on June 8, 2007 Mail this to a friend!

ad5x:
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
Mickey - These spectrum photos are not the output spectrum of a real radio. Why can't you measure a real radio? You keep arguing your point, but you won't measure a radio to verify it. Whereas there appears to be measured data that refutes what you say. I think that all this can be reasolved with some real measurements on your part. If your measurements don't agree with Tom's measurements (and others), then we can all try to figure out who is doing what wrong. But unto all parties actually make measurements, I don't see how we can move forward. It will continue to be "This is what the math says" vs "This is what I measure."
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

Phil,

Do you have the test equipment to do these measurements with?

Why would you expect the common ham to have them if even a University lab doesn't?

Why would you expect Mickey or I personally to have such equipment?

Spectrum analyzers capable of 10hz resolution at 3.5Mhz don't grow on trees. Even a good used one will buy my two college students *very* nice cars to leave town in this fall.

I've given you a web site twice now that shows measurements by w8wwv that clearly show spectral lines in the CW output of a 756pro.

Mickey has now provided pictures from SM0AOM that clearly show the distinct spectral lines in the RF output of a CW transmitter and how filtering can decrease the number of harmonics (that is what the spectral lines represent) being sent.

Next week I hope to get a setup simalar to w8wwv hooked up to my computer. I may have to run my keying speed as fast as it will go to get resolvable spectral lines but if you get specific spectral lines at high speeds you would expect the same spectral lines at low speeds. It's just a matter of proving the math to be correct.

BTW, modulation is nothing more than the multiplication of two signals in the time domain which is a convolution of the signals in the frequency domain.

If it is shown that one of the signals (i.e. a square wave) is a combination of spectral lines in the frequency domain and that the other is a single frequency (i.e. the carrier) why would you *NOT* expect the output to be a convolution of the two signals in the frequency domain?

Mickey is showing you what one of the modulation signals look like, i.e. the square wave.

If the modulation output didn't represent the convolution of the two modulating signals wouldn't you wonder what is going on?

The pictures from SM0AOM clearly show the spectral lines in the output of the transmitter.

If the modulation does NOT result in a convolution of the signals in the frequency domain what is the cause?

I have yet to see any mathematical explanation for why the RF output of an amateur transmitter should be any different from what is predicted by the math we currently know.

I don't understand why people are still saying that no measurements have been taken to prove what Mickey has tried prove mathematically. Two distinct measurements have been given that shows what Mickey is saying.

Who's going to be the first to step up and label the pictures Mickey has posted as a hoax?

tim ab0wr

RE: Bandwidth versus Keying Speed

by W8JI on June 8, 2007 Mail this to a friend!

Mickey,

Thank you VERY much for posting your measurements of the audio tone of the MFJ keyer.

Your measurements in figure 3 and 4 agree exactly with what I have been saying. You can confirm this if you read bach through my posts.

If you look at the slope of the sideband peaks, you will find that slope stays the same regardless of speed. In other words the amplitude vs. distance from the carrier is the same for all speeds you measured.

This is exactly what Kevin Schmidt W9CF and everyone else (including me) predicts.

Now if I synchronize the time base of my spectrum analyzer to the dots speed, or if I do a single sweep it will show the same thing. However, it is much more accurate to do multiple sweep averages because momentary small anomalies are averaged out.

So you see indeed what you measured at audio agrees exactly with what happens at RF, it doesn't matter if we modulate the tone at 400Hz or a signal at 3.5 MHz.

The slope of sideband attenuation with frequency distance from the carrier remains the same regardless of CW speed. The effect of this is the peak power on adjacent frequencies remains the same regardless of speed.

Everyone, even your measurements, are now in agreement. The signal does NOT get narrower with reduced speed, it simply repeats the sidebands less frequently. As such when we scan across the sideband with a slow moving spectrum analyzer, it appears to have peaks and valleys but the tops have the same slope rate from the carrier regardless of speed.

By the way Mickey, if you remove the R/C lowpass filter I put in that keyer, the bandwidth will greatly increase. That filter rounds the leading and falling edges a small amount.

You should put a parallel L/C hi-Q filter on the audio output. Then it will even more closely resemble a transmitter.

73 Tom

RE: Bandwidth versus Keying Speed

by AB0WR on June 8, 2007 Mail this to a friend!

ke3ho:
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
Looking at the figures that you posted on the ARRL LA section page, am I correct in assuming that in Figure 1 everything is equal between the left and right pictures (vertical scale, frequency span, etc.) except for the absence or presence of leading and trailing edge shaping on the keying waveform? If so, then my interpretation of those two plots is that the bandwidth of the signal is DRASTICALLY affected by the rising and falling shape of the keying waveform. How about repeating that same measurement, only this time use the “CCIR keying shaping” for both plots and show us the spectrum at 5 wpm and at 40 wpm. That might show something to support your claim.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

Jim,

Wait a minute. What makes you believe the rise and fall times of either the 10wpm or the 40wpm signal is different? Mickey only showed the envelope for 40wpm. It would be interesting to see if the same rise time applies for a 10wpm signal. If the MFJ has a fixed bandwidth filter in it (probably does, I doubt if they change bandwidth based on keying speed) then my post above applies.

125 harmonics of a 2hz keying wave (i.e. a 250hz bandwidth) gives exactly the same rise and fall time as 25 harmonics of a 10hz keying wave (i.e. a 250hz bandwidth).

If MFJ limits the bandwidth of the keying waveform to about 625hz total(i.e. pi/rise-time or pi/.005=625), then the rise time for a 16.6hz (40wpm) square wave, a 10hz square wave (25wpm) and a 2hz square wave (5wpm) will all be exactly the same. The only thing that will change is the number of spectral lines seen in that bandwidth.

At 40wpm or 16.6hz with a 312hz filter bandwidth for the square wave (half the total, one for usb and one for lsb), you would expect to see 17 or 18 harmonics (others may be seen base on a non-ideal filter slope). For 10wpm or 4hz with a 312hz bandwidth you would expect to se 312/4 or the 77th or 79th harmonic in that same bandwidth.

So we would go from seeing 17 lines on the display to seeing about 77.

If you show 400hz of a 625hz bandwidth you would expect to see 10 or 11 harmonic lines on each side of the fundamental. That is exactly what we see.

For the 4hz signal we would expect to see about 49 spectral lines in 200hz. Even using my magnifying glass I can't quite count the number of lines in the display. Suffice it to say that it is a LOT more than with the 10hz wave. Is it 4.5 times as many? I don't know. I'll bet it is close.

You can't infer rise time and fall time from the shape of the frequency plot. A 4hz square-wave and a 10hz square wave, viewed over the same partial bandwidths will look totally different in the frequency domain but be exactly the same in the time domain.

I am not an expert on the CCIR stuff but doesn't it suggest a goal of a rise time of about 20% of the initial portion of the element length? If you assume a maximum keying speed of 50wpm or 20hz you would get a rise time of (1/20)*.2 = 10msec or a 300hz bandwidth. If you assume a 25wpm (10hz) typical speed you would want a bandwidth of about 150hz. This is far, far narrower than most filters in amateur transmitters.

A 300hz bandwidth or a 10ms rise time would be seem to be a much better average bandwidth for the typical user although people operating at faster speeds might want the option of a wider bandwidth filter.

tim ab0wr

RE: Bandwidth versus Keying Speed

by KE3HO on June 8, 2007 Mail this to a friend!

Tim,

<<< Wait a minute. What makes you believe the rise and fall times of either the 10wpm or the 40wpm signal is different? >>>

I don't believe that. What makes you think that I believe that? I never said anything like that. I pointed out that in Figure 1 the plots showing VASTLY different bandwidth are at the SAME CW sending speed, just with different rise and fall times (which shows very nicely what Tom, myself, and others have said about the effect of the leading and trailing edge pulse shape vs bandwidth). I asked if he could make the same measurements with fixed rise/fall speed and shape but at two different sending speeds.

I see from another post since my last that Mickey did not make these measurements, so my requests to repeat them under different conditions is a moot point anyway.

73 - Jim

RE: Bandwidth versus Keying Speed

by W8JI on June 8, 2007 Mail this to a friend!

Everything keeps coming back to the same thing anyway.

If you look at the attenuation of sidebands vs. frequency delta from carrier for a constant rise and fall time, the slope of the sidebands with a given frequency delta stays the same. The rise and fall stay the same so long as we keep the speed high enough to stay out of ALC defects, but low enough that we don't truncate the steady-state parts of the waveform.

Most rigs use a simple R/C filter to shape the edges, and that doesn't lead to an optimum waveshape of the rising and falling edges. Now, thankfully, some are using better filtered keying either through keying line shaping or low-pass filtering before a linear modulator followed by linear PA stages, or a smart system that uses a DSP or RF bandpass filters followed by linear stages.

The end-effect is the same, controlled bandwidth at all speeds.

So far as I am aware there aren't any systems that intentionally slow the rise and fall as speed is reduced, probably because people would find the signal unpleasant at slow speeds. It would be "pingy". Some radios actually tend to get wider at slow speeds, because the ALC drops between dots and on the next character it truncates the rise.

I can fix that problem in my Yaesus, if I ever want to send real slow, by backing off the TX gain in the hidden menu. I just set the TX gain so the ALC is just barely active. If I run normal ALC, at about 5-8 dits per second the BW starts to climb as speed is further reduced. This is because the leading edge rise period of the elements are truncated due to ALC action.

This is a very common defect among rigs, but if we stay out of that slow-spped area the BW remains very constant with speed variations.

73 Tom

RE: Bandwidth versus Keying Speed

by W8JI on June 9, 2007 Mail this to a friend!

Also check out this site by SM5BMZ of Linrad fame. All over the SM5BMZ site we find the bandwidth of CW discussed.

http://www.sm5bsz.com/

Especially read Doug Smiths Occupied BW article at:

http://www.sm5bsz.com/others/occbw.htm

Doug Smith states:

Granted, such an envelope can be produced by a simple R-C network. Rise and fall times may be controlled by the time constant of the network. The trouble is that such an envelope produces significant and unnecessary keying sidebands. It does that because it contains amplitude discontinuities; its amplitude does not change smoothly as it begins rising or falling. It has abrupt changes in its slope at those points.

Fig 2 is a spectral analysis of the waveform of Fig 1. Spectral occupancy is chiefly determined by the envelope shape and not by the keying speed. To be sure, keying such a waveform at high speed puts more energy into adjacent frequencies than at low speed; but the instantaneous amplitude of the keying sidebands is constant during the rise and fall times, regardless of keying speed.>>>

Same exact thing I have been saying all along, and it agrees with how radios (and even MFJ Keyers) actually work if we test radios.

SM5BMZ highlights the ALC issue I discussed.

It all makes good reading for those interested in what really happens.

73 Tom

RE: Bandwidth versus Keying Speed

by W8JI on June 9, 2007 Mail this to a friend!

I'm sorry that is SM5BSZ who did Linrad, not BMZ. The link was correct.

Bandwidth versus Keying Speed

by K5MC on June 9, 2007 Mail this to a friend!

KE3HO: Looking at the figures that you posted on the ARRL LA section page, am I correct in assuming that in Figure 1 everything is equal between the left and right pictures (vertical scale, frequency span, etc.) except for the absence or presence of leading and trailing edge shaping on the keying waveform? If so, then my interpretation of those two plots is that the bandwidth of the signal is DRASTICALLY affected by the rising and falling shape of the keying waveform. How about repeating that same measurement, only this time use the “CCIR keying shaping” for both plots and show us the spectrum at 5 wpm and at 40 wpm. That might show something to support your claim.

Jim, you are correct in your assumptions and I also completely agree with you about why the bandwidth of the signal shown in the Telefunken literature is drastically reduced. My own article compares the 99.1% power bandwidth of "square-wave" keying versus 5-ms "sinusoidal" keying at 2.4 wpm and 30 wpm. Table I in my article shows that the 99.1% power bandwidth is 525 Hz for square-wave keying at 30 wpm, but the 99.1% power bandwidth is only 150 Hz for 5-ms "sinusoidal" keying at 30 wpm.

BTW, the speed in the Telefunken plots is nearly 50 wpm. If I had used 48 wpm, for example, rather than 30 wpm for my calculations, the difference between the 99.1% power bandwidths for "square-wave" keying versus 5-ms "sinusoidal" keying would have been even more impressive. The power bandwidth for square-wave keying is directly proportional to the speed; this fact comes directly from Fourier analysis. So the 99.1% power bandwidth for square-wave keying at 48 wpm is 840 Hz simply because 48/30 multiplied by 525 equals 840. Without doing the detailed calculations, my guess is that the 99.1% power bandwidth for my 5-ms "sinusoidal" keying waveform would increase from 150 Hz to around 200 Hz when the sending speed goes from 30 wpm to 48 wpm.

In general, the power bandwidth for any keying waveform having constant rise/fall times and shapes is not directly proportional to the keying speed. My article reported that the 99.1% power bandwidth for the 5-ms "sinusoidal" waveform increased from 32 Hz to 150 Hz when the sending speed increased from 2.4 wpm to 30 wpm. That is, the power bandwidth increased by a ratio of nearly 4.7, but the sending speed increased by 12.5. However, since the rise and fall times for square-wave keying are zero by definition, the increase in power bandwidth is directly proportional to the speed for that special case.

Now let's discuss some details of the "unfiltered" transmitter shown in the Telefunken plots. First off, SM0AOM kindly emailed those to me and I posted them, in part, so that everyone would know that discrete lines are to be expected in the spectrum plots of CW transmitters when keyed by a periodic signal such as a string of dits, although the ability to actually see the discrete lines will depend upon the frequency resolution of one's spectrum analyzer. Just because you don't see discrete lines in the various spectrum plots presented by W8JI, for example, you can be sure that they (the keying sidebands/discrete lines) are there unless the transmitter is operating in an erratic fashion from one dit to the next dit. The spectrum plots shown by the Telefunken literature clearly demonstrate a transmitter operating in a "normal" fashion when observed on a spectrum analyzer with sufficient resolution.

According to SM0AOM, the symbol rate of the transmitter shown in the Telefunken literature is 40 baud. That means the sending speed is actually 48 wpm, rather than the 50 wpm approximation I used in the caption of Figure 1. Since we know the exact sending speed is 48 wpm, we can calculate the frequency locations of the various keying sidebands.

The fundamental frequency of the keying waveform is equal to the number of dits per second being transmitted. At 48 wpm, the number of dits per second is 20. Therefore, the first pair of keying sidebands will be located plus and minus 20 Hz away from the carrier frequency. Continuing in this fashion, we know that the second pair of sidebands are located plus and minus 40 Hz from the carrier, the third pair of sidebands are located plus and minus 60 Hz from the carrier, and so forth.

A close inspection of the spectrum plot on the left side in Figure 1 shows that every other pair of keying sidebands are much lower in amplitude than the others. These "missing" sidebands are the "even" harmonic pairs, starting with the second pair of sidebands at plus and minus 40 Hz from the carrier. The reason the even frequency harmonic sideband pairs are very low in amplitude relative to the others is that the square-wave keying waveform has so-called half-wave symmetry. One of the fundamental results from Fourier analysis of periodic signals is that those signals having half-wave symmetry will contain only odd-frequency harmonic components in their Fourier series.

With all of this information, we can now determine the frequency span in the Telefunken plot for the "unfiltered" transmitter. If you do it carefully, you will see that the total span of the spectrum plot is 2 kHz. We can also readily determine the 99.1% power bandwidth of the CW signal from the "unfiltered" transmitter. From my square-wave keying waveform study, I found that 99.1% of the total average power residing in the square-wave output signal is the sum of the carrier power and the powers of the first 21 harmonics symmetrically located about the carrier. If you examine the amplitudes of the two very distinct 21st harmonic sidebands on either side of the carrier (these specific keying sidebands are located plus and minus 420 Hz from the carrier), you will see that they are each about 27 to 28 dB lower in amplitude than the carrier. The frequency locations of these two specific keying sidebands are plus and minus 420 Hz away from the carrier because 21 (the harmonic "order") multiplied by 20 Hz (the frequency displacement of the first pair of sidebands located on each side of the carrier) is equal to 420.

The relative amplitude of these two specific keying sidebands located 420 Hz from the carrier is found from the Fourier series representing the "raised" square wave that I used in my article. The (time averaged) powers of the DC and 21st harmonic components in the Fourier series on a 1-ohm basis are the squared values of 0.5 volts and (1.414)/(21 pi) volts, respectively. These squared values turn out to be 0.25 watts and approximately 0.0004595 watts. Now let's compare the ratio of these two average powers on a log scale to find how many dB "down" these two specific keying sidebands are from the DC (carrier) term:

10 log (0.0004595/0.25) = -27.4 dB

That is, the two keying sidebands plus and minus 420 Hz from the carrier are 27.4 dB lower in amplitude than the carrier. This is essentially a perfect fit to the same two sidebands shown in the Telefunken literature for the "unfiltered" transmitter. We would also say that the 99.1% power bandwidth of this particular CW signal is 840 Hz because 420 Hz multiplied by 2 equals 840 Hz.

I hope everyone agrees that the frequency locations of the keying sidebands shown by an ideal spectrum analyzer are determined by the sending speed of a "normal" transmitter. This is a fundamental result of the Fourier series that represents the keying (periodic) waveform. If a transmitter is operating erratically from one dit to the next dit because of ALC "pumping" or other such issues, then the keying envelope of the CW signal is not periodic and the Fourier series approach is not valid. If we increase the sending speed of a "well designed" CW transmitter to 96 wpm, for example, the number of dits per second double to 40 and so the spacing between the adjacent keying sidebands will increase from 20 Hz to 40 Hz.

To summarize this post, at a constant sending speed the amplitudes of the carrier and the keying sidebands shown by an ideal spectrum analyzer depend upon the characteristics of the specific keying waveform (for example, sinusoidal keying versus square-wave keying). The frequency locations of these keying sidebands depend only upon the sending speed assuming the transmitter is not operating in an "erratic" fashion. The 99% power bandwidth (and the occupied bandwidth as defined by the FCC) for a "well designed" CW transmitter depends upon both the sending speed and the rise/fall times/shapes of the specific keying waveform just as my article demonstrated. The spectrum plots that I have posted of my MFJ keyer also clearly demonstrate these facts. (I agree with W8JI that the MFJ-447 electronic keyer is a "well designed" CW transmitter!) Hams who disagree with these statements either do not understand Fourier analysis or they do not understand the meaning of average (mean) power.

73, K5MC

RE: Bandwidth versus Keying Speed

by AB0WR on June 9, 2007 Mail this to a friend!

From Doug Smith:
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
Granted, such an envelope can be produced by a simple R-C network. Rise and fall times may be controlled by the time constant of the network. The trouble is that such an envelope produces significant and unnecessary keying sidebands. It does that because it contains amplitude discontinuities; its amplitude does not change smoothly as it begins rising or falling. It has abrupt changes in its slope at those points.

Fig 2 is a spectral analysis of the waveform of Fig 1. Spectral occupancy is chiefly determined by the envelope shape and not by the keying speed. To be sure, keying such a waveform at high speed puts more energy into adjacent frequencies than at low speed; but the instantaneous amplitude of the keying sidebands is constant during the rise and fall times, regardless of keying speed.>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

I don't agree with Mr. Smith's analysis. An RC circuit has NO discontinuities. It is an exponential. while the slope of the response curve *does* change it does so smoothly. Mr. Smith is confusing "linear" with "smoothly". The slope of an RC circuit *is* smooth, it *is not* linear. I could speak of the definition of discontinuity if anyone is interested but I'll leave that to another time. Thus, any extra keying sidebands would be due to INTERMOD produced by a non-linear mixing process and not by "discontinuities".

The statement that the "instantaneous" sideband amplitudes are constant "during" the rise and fall times is very, very confusing. How do you have "instantaneous" values (indicating a specific value of "t") over a period of time such as 5-10ms?

I believe what he is saying is that the harmonics of a square wave exist during the whole keying pulse and any specific harmonic stays at the same amplitude during the entire pulse. That is exactly what Mickey and I have been trying to say. The harmonics don't exist just during the rise and fall times nor do they just gradually "die away" during the rise and fall times. They exist during the whole pulse at the same amplitude.

Mr. Smith is also contradictory in saying that "Spectral occupancy is chiefly determined by the envelope shape and not by the keying speed." when he turns around just a sentence later and says "keying such a waveform at high speed puts more energy into adjacent frequencies than at low speed".

Both can't be right. You can't put more energy into adjacent frequencies for one keying speed over another if the spectral occupancy is not dependent on keying speed.

w8ji:
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
Same exact thing I have been saying all along, and it agrees with how radios (and even MFJ Keyers) actually work if we test radios.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

Well, let's see what you've been saying.

w8ji:
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
If you look at the slope of the sideband peaks, you will find that slope stays the same regardless of speed. In other words the amplitude vs. distance from the carrier is the same for all speeds you measured.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

The amplitude does NOT stay the same regardless of speed, it does NOT mean that amplitude vs distance from the carrier is the same for all speeds.

If you will contact Mickey I think you will find out that such an appearance is an artifact of the photo's. You will find that there is about a 10-13db difference in amplitudes between the two speeds at the same bandwidth.

I think if you will analyze W9CF's plots you will find this to be true there also. Those are energy density plots, not frequency<->amplitude plots.

Before you start whining about me not knowing how transmitters work, please note that energy density is based on A^2 x tau^2 where tau is the period of the waveform. Therefore a waveform with a longer period will have a larger energy density for the same A value. It is the A value of the fundamental that determines the height of the envelope and determines the amplitudes of the harmonics. You simply cannot overlay an energy density pattern for two square waves of different periods and claim that the amplitudes of at the same frequency separation will the same. All you have found in that case is that the energy density falls off at 12db/octave -- a 1/(n^2) rolloff which is exactly what would be predicted. That is all the energy density graphs on W9CF's page can tell you.

You would find exactly the same thing if you plot spectral density which is A x tau. Since tau is different for each square wave you cannot overlay the spectral density graphs and say that the amplitudes of the harmonics are the same either.

If you want to say that the strength of the signal someone will hear is based on the spectral density or the energy density from freq1 to freq2 (e.g. over the bandwidth of a 250hz filter, we may very well be able to agree on that. I haven't actually calculated the total energy of a 2hz and a 10hz square wave from 200-250hz. They may very well be the same.

That is a far cry, however, from saying that the amplitudes of the harmonics for two different square waves will be the same at the same frequency separation. They won't.

(if you want to confirm these are energy density plots, look at the amplitude shown at the fundamental. They are different. If this were an amplitude-only plot they would be the same since the amplitude of the fundamental determines the height of the envelope. Therefore, the fundamental amplitudes have to be the same for any square wave that has the same envelope height)

tim ab0wr

Bandwidth versus Keying Speed

by K5MC on June 9, 2007 Mail this to a friend!

Perhaps some of the misunderstanding between the various posters to this thread might be caused by how one interprets the plots from a spectrum analyzer.

Let's focus on the two plots presented in the Telefunken literature for an "unfiltered" and a "filtered" transmitter posted at http://www.arrl.org/sections/?sect=LA

The two plots shown in Figure 1 have a total span of 2 kHz. The transmitter in each case was sending a string of dits at a speed of 48 wpm. The "27-dB" bandwidth of the unfiltered Telefunken transmitter is approximately 840 Hz. When I call this value of 840 Hz the 27-dB bandwidth, I am saying that the average power of the signal at plus or minus 420 Hz from the carrier frequency is 27 dB lower than the average power of the carrier.

Now let's estimate the 27-dB bandwidth of the filtered Telefunken transmitter. My estimate is 270 Hz, although I can agree that others might estimate it to be closer to 250 Hz or perhaps 300 Hz.

If everyone agrees with what I'm saying above, then everyone should agree that the 30-dB bandwidth of the unfiltered transmitter is greater than 840 Hz, but it is finite. (My estimate of the 30-dB bandwidth here happens to be 1200 Hz from observing the spectrum plot.) Likewise, the 30-dB bandwidth of the filtered CW transmitter is greater than 270 Hz (or 250 Hz or 300 Hz, depending upon your 27-dB estimate before).

If everyone still agrees with me at this point, then I believe the main thing left for me to do is convince everyone of the definition of (time average) power bandwidth. The power bandwidth is not the same concept as the "keyclick" bandwidth that so many folks here keep going back to. Another subtle point is that the 99% power bandwidth for two different signals is not exactly equivalent to a fixed value of dB bandwidth. For example, the 99.1% power bandwidth for square-wave keying at 30 wpm is the 27.4-dB bandwidth, but the 99.1% power bandwidth for my 5-ms sinusoidal keying waveform at 30 wpm is the 16.6-dB bandwidth. In other words, the 27-dB bandwidth of the filtered Telefunken transmitter (estimated to be around 270 Hz) is probably closer to being the 99.75% power bandwidth rather than the 99.1% power bandwidth.

73, K5MC

RE: Bandwidth versus Keying Speed

by W8JI on June 9, 2007 Mail this to a friend!

Tim,

OK. It seems we all now agree the peak power at any frequency is the same regardless of keying speed. The only question is if the choice of accumulated power over long very periods of time compared to the modulation rate is a good definition for defining channel bandwidth.

It seems to me what you and Mickey now say is we should use energy accumulated over very long periods of time compared to the modulation rate, while most others want to use the mean power only at a sufficiently long time to ensure all of the power is accounted for (and no longer than that).

The receivers we use, by definition, cannot store energy over time. The system, by definition, is not bothered or limited to a collision rate problem between undesired interference and the desired signal. It is simply a matter of whether an adjacent channel transmission causes interference, and the answer to that at reasonable transmission rates is tied only to the peak envelope power distribution over a certain frequency bandwidth.

The receiver by definition cannot hold, accumulate power, or store anything for a time even nearly as long as a rise or fall time or the receiver would be modifying the rise and fall times and altering the sound of the desired signal.

As a general rule the mathematical expression, description, or definition of problem has to fit the physical reality we encounter. Otherwise it is of no practical use at all.

This is really why those who test real systems, through whatever method that repeats real life they choose, find agreement with Doug Smith, Kevin Schmidt, Chen, SM5BDZ, I, and countless others who have looked at the actual systems disagree with Mickey and you.

Like everyone else certainly does, I care only if a guy 1 kHz away is bothering me and how strong those clicks are compared to his on-frequency signal. I care less about the ratio of kilowatt hours of his carrier on time to the kilowatt hours of the clicks.

We all now agree the peak envelope power in any slice of spectrum would remain the same regardless of keying speed if the speed change does not affect the rise and fall times that we all agree dominate the spectral distribution or bandwidth of the signal. We may very well have to agree to disagree since the argument now seems to have shifted to what each of us think are proper definitions rather than results or effect we see in the real world.

I’ll continue, like most people, to defining interference bandwidth as a point where I start to hear unnecessary crud from the other guy that affects my ability to hear a station I am working and my S meter, and you are certainly free to use kilowatt hours or even kilowatt years.

73 Tom

Bandwidth versus Keying Speed

by K5MC on June 9, 2007 Mail this to a friend!

W8JI: The only question is if the choice of accumulated power over long very periods of time compared to the modulation rate is a good definition for defining channel bandwidth.

The rise and fall times (that is, the time durations of the leading edges and trailing edges of the keying waveforms) for our CW signals are typically somewhere between 1 millisecond and 10 milliseconds. The "modulation rate" is determined by the keying speed. At the typical code speeds used by most hams (let's say from 5 wpm to 60 wpm) the time period between one dit to the next dit (assuming proportional spacing/50% duty cycle at all speeds as I've said many times now) lies somewhere between 40 milliseconds (at 60 wpm) and 480 milliseconds (at 5 wpm)! These time periods are slightly smaller than "hours" or "even years" as you suggest below.

W8JI: I’ll continue, like most people, to defining interference bandwidth as a point where I start to hear unnecessary crud from the other guy that affects my ability to hear a station I am working and my S meter, and you are certainly free to use kilowatt hours or even kilowatt years.

As I've said many times during this thread, the concept of "interference" or "keyclick" bandwidth is important. I've merely tried in my article and during this thread to restore some sense of balance to the discussion of "bandwidth" among hams in general. Without the concept of "power" bandwidth (and, by extension, the "occupied" bandwidth as defined by the FCC), it is very hard to explain why "slowing down" increases the signal-to-noise ratio in a communication system.

Although most hams may have little or no interest in such modes as EME and QRSS that dramatically illustrate the concept of power bandwidth, I think we should all appreciate one of the most fundamental principles in communication systems. One interesting site to check out is http://www.ussc.com/~turner/qrss1.html

Perhaps now I can walk away from this thread. I want to thank all of the hams who have posted comments. I particularly want to thank the hams who have encouraged me to "stay the course" during the past two weeks.

73, K5MC

RE: Bandwidth versus Keying Speed

by AB0WR on June 9, 2007 Mail this to a friend!

w8ji:
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
OK. It seems we all now agree the peak power at any frequency is the same regardless of keying speed. The only question is if the choice of accumulated power over long very periods of time compared to the modulation rate is a good definition for defining channel bandwidth.

It seems to me what you and Mickey now say is we should use energy accumulated over very long periods of time compared to the modulation rate, while most others want to use the mean power only at a sufficiently long time to ensure all of the power is accounted for (and no longer than that).
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

I don't know where you are getting this from. Neither Mickey or I have ever said this is necessary. It would only be necessary if the harmonics of a square wave did *not* exist during the entire period of the square wave. Since the harmonics *do* exist for the entire period of the square wave why would Mickey and I suggest that you need to collect anything over time?

I've asked you before: Stop putting words in our mouth.

w8ji:
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
The receivers we use, by definition, cannot store energy over time. The system, by definition, is not bothered or limited to a collision rate problem between undesired interference and the desired signal. It is simply a matter of whether an adjacent channel transmission causes interference, and the answer to that at reasonable transmission rates is tied only to the peak envelope power distribution over a certain frequency bandwidth.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

Receivers don't have to store energy over time. The concept that they do is an artifact of your claim that the harmonics of a square wave only exist during the rise and fall time of the square wave. I think Mickey has shown conclusively with his MFJ keyer as well as the spectrum of the CCIR sample CW transmitter that the harmonics of a square wave do NOT die off after the rise time of a square wave and magically reappear at during the fall time of the same pulse, they are there all the time.

Your concept of PEP "distribution" over a frequency bandwidth is also questionable. PEP is defined as the average power of one RF cycle at the peak of the envelope. Since we are comparing envelopes of the same height and with a flat top, all we need to do is measure one RF cycle of the carrier to calculate PEP. Since the height of the envelope determines the PEP value and since the height of the envelope is determined by the voltage peak of the fundamental frequency of a square wave, PEP doesn't address power "distribution" at all, at least as far as I can see. Once the voltage level has been determined for the fundamental, all the harmonics can be calculated using the 1/n rule.

w8ji:
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
The receiver by definition cannot hold, accumulate power, or store anything for a time even nearly as long as a rise or fall time or the receiver would be modifying the rise and fall times and altering the sound of the desired signal.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

Again, since the entire harmonic content of a square wave exists for the entire period of the square wave, why would the receiver *have* to hold, accumulate, or store ANYTHING? Even bandwidth limiting a square wave (i.e. limiting the number of harmonics that are present) doesn't make the harmonic content inside the bandwidth magically appear and disappear during the rise and fall times.

The only thing that appears and disappears seems to be the intermodulation products associated with the exponential non-linearities at the very beginning and end of each pulse.

w8ji:
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
As a general rule the mathematical expression, description, or definition of problem has to fit the physical reality we encounter. Otherwise it is of no practical use at all.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

No kidding? That's what both Mickey and I have been saying. We've shown that the psuedo-math we've seen that says square wave harmonics only exist during the rise and fall times is incorrect. And we've shown that the psuedo-math that says the amplitudes of the harmonic content of a square wave are constant at the same distance from the center frequency regardless of the square wave frequency is incorrect also. We've shown that the claim that the rise time of the output envelope determines the input frequency spacing is incorrect, the actual fact is the other way around. The output envelope is indeterminate of the input. The input, on the other hand *is* determinate of the output.

I would say our math has proven pretty accurate in describing the real world.

We've asked for the ACTUAL math that shows ours to be wrong or that substantiates these claims. The actual math for either has never been forthcoming. I guess the readers can determine for themselves why that is.

w8ji:
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
This is really why those who test real systems, through whatever method that repeats real life they choose, find agreement with Doug Smith, Kevin Schmidt, Chen, SM5BDZ, I, and countless others who have looked at the actual systems disagree with Mickey and you.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

I don't know what you have been reading but Chen said Mickey's calculations ARE CORRECT.

I've given you my critique of Doug Smiths claims in his writings. I have yet to see any refutation, (e.g. proof that an exponential curve is "discontinuous", proof that the inconsistent claims of saying spectral occupancy is not determined by keying speed but that faster keying speeds puts more energy into adjacent frequencies than slower speeds can somehow make sense , etc...). Somehow I don't expect to see any refutations, we haven't seen any for anything else.

The web site you gave for Kevin Schmidt has exactly zero for articles that bear on this subject (at least that I can find) so you are doing nothing more here than name dropping. Freshmen debaters learn quickly to watch out for that debate tactic.

Your claim here seems to be just as wild as your claim that square wave harmonics exist only during the rise and fall times of the square wave.

w8ji:
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
Like everyone else certainly does, I care only if a guy 1 kHz away is bothering me and how strong those clicks are compared to his on-frequency signal. I care less about the ratio of kilowatt hours of his carrier on time to the kilowatt hours of the clicks.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

If you don't care about the kilowatt hours why do you think anyone else would?

w8ji:
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
We all now agree the peak envelope power in any slice of spectrum would remain the same regardless of keying speed if the speed change does not affect the rise and fall times that we all agree dominate the spectral distribution or bandwidth of the signal. We may very well have to agree to disagree since the argument now seems to have shifted to what each of us think are proper definitions rather than results or effect we see in the real world.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

But the peak envelope power staying the same doesn't mean that the interference to adjacent channels will stay the same since different keying speeds will result in harmoics with different amplitudes in adjacent chanels. And, once again, the rise and fall times do not "dominate" anything. You are still living in a causal discontinuity. Input waveforms and system response functions (i.e bandwidth) determines the output rise and fall times not the other way around.

You also still seem to have some inconsistencies with your claims. Your use of the term "spectral distribution" is so vague as to be meaningless. You seem to be confusing amplitude distribution with spectral occupancy distribution with energy density distribution. Spectral occupancy distributions and energy density distributions are typically associated with collecting something over a time period (e.g. collecting energy) which is something you said receivers can't do. The amplitude distribution which can cause something to happen in a receiver *does* vary with keying speed.

I don't think we can agree on anything till you get all your terms and claims straight so they make sense. It would help if you could describe this in terms of system transfer functions and input waveform functions so we can all follow along to what the output function looks like and then use consistent analysis techniques on that output.

w8ji:
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
I’ll continue, like most people, to defining interference bandwidth as a point where I start to hear unnecessary crud from the other guy that affects my ability to hear a station I am working and my S meter, and you are certainly free to use kilowatt hours or even kilowatt years.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

The major problem is that you still haven't defined anything yet. I have yet to see a single speck of any mathematical definitions or calculations from you. I have seen you quote things that are meaningless (an exponential being "discontinuous) or incorrect (energy density distibutions as amplitude distributions).

When you can do something like calculate the amplitude of the harmonic at 250hz for a 2hz keying wave and a 10hz keying wave and then determine what the db difference is in their levels then perhaps we can begin to talk about defining adjacent channel interference levels.

We are all waiting.

tim ab0wr

RE: Bandwidth versus Keying Speed

by AB0WR on June 9, 2007 Mail this to a friend!

<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
Perhaps now I can walk away from this thread. I want to thank all of the hams who have posted comments. I particularly want to thank the hams who have encouraged me to "stay the course" during the past two weeks.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

Mickey,

I certainly appreciate what you've done in debunking the seemingly commonly held beliefs that square wave harmonics only exist during the rise time and fall time and that the harmonics and their levels are determined by the output rise time and not the square wave input frequency and system response function. .

If even one student aspiring to learn about Fourier analysis learned the proper math instead of old wives tails, your time was well spent.

CU on the air,

73,

tim ab0wr

RE: Bandwidth versus Keying Speed

by W8JI on June 11, 2007 Mail this to a friend!

..and in closing it is very important for people to remember that the signal level as you will note on a receiver tuned above or below the interfering station will remain the same regardless of speed when you look at it with a CW receiver, and the only way to narrow bandwidth is to filter the bandwidth which in effect is the same as controlling the rise and fall.

Those clicks, assuming the rig is of good design, do not change with keying speed. They just occur more or less frequently.

So if you don't want a nasty signal, shape the rise and fall by filtering either before or after modulation of the carrier. The speed you send won't make a difference except in how often the problem repeats, or in some meaningless analysis that includes energy over time longer than the time that affects the receiver or what we hear.

73 Tom

RE: Bandwidth versus Keying Speed

by AD5X on June 12, 2007 Mail this to a friend!

Well, probably no one is reading this any longer, but I’ve been away from the computer for several days so I just wanted to respond:

AB0WR: “Phil, Do you have the test equipment to do these measurements with? Why would you expect the common ham to have them if even a University lab doesn't? Why would you expect Mickey or I personally to have such equipment? Spectrum analyzers capable of 10hz resolution at 3.5Mhz don't grow on trees. Even a good used one will buy my two college students *very* nice cars to leave town in this fall.”

Response: Whenever statements and theories are stated, you must have physical measurements to back them up because you can never be absolutely sure until you’ve verified the model as well as the design. I’ve worked for a large company where test equipment costs were no big deal. In my last company, a very small start-up, money was so tight that buying a DMM required tremendous justification. But it seems that you believe I could have saved my company the cost of a spectrum analyzer by saying “We’ve got the best optics team in the industry, and they say this is how the system should work. We’ve got the best circuit designers around, and here’s the design. No point in testing it as obviously everything will work as modeled and designed. So let’s just release it to production.”

AB0WR: “I've given you a web site twice now that shows measurements by w8wwv that clearly show spectral lines in the CW output of a 756pro. Mickey has now provided pictures from SM0AOM that clearly show the distinct spectral lines in the RF output of a CW transmitter and how filtering can decrease the number of harmonics (that is what the spectral lines represent) being sent.”

Response: Yes, I’ve seen those. In both cases the radio output measurements are shown at a constant keying speed. And yes, you can see the spectral lines. But the question here is if you look at the same spectrum at a different keying speed, will the spectrum still be the same – recognizing that the spectral line separation will be different. I.e., will the 99% power bandwidth change? The only spectrum analyzer measurements I've seen of spectrums at two different keying speeds were made by W8JI, and these don't agree with the premise stated (bandwidth changes with keying speed).

AB0WR: “I don't understand why people are still saying that no measurements have been taken to prove what Mickey has tried prove mathematically. Two distinct measurements have been given that shows what Mickey is saying. Who's going to be the first to step up and label the pictures Mickey has posted as a hoax?”

Response: No one has ever stated that the pictures are a hoax. But I would like to see spectrum pictures of two different keying speeds, and see what the bandwidth looks like. I.e., does the energy drop off faster at lower keying speeds? And no, I don’t have a spectrum analyzer to make these measurements – I just used my receiver as a selective level meter which appears to show that the spectrum doesn’t really change. But again, you guys are stating that BW changes with keying speed, while others say that measurements don’t support this. So you need to provide spectrum analyzer data supporting your model.

73,
Phil – AD5X

RE: Bandwidth versus Keying Speed

by W9AC on June 12, 2007 Mail this to a friend!

AB0WR:

> "I certainly appreciate what you've done in debunking the seemingly commonly held beliefs that square wave harmonics only exist during the rise time and fall time and that the harmonics and their levels are determined by the output rise time and not the square wave input frequency and system response function...If even one student aspiring to learn about Fourier analysis learned the proper math instead of old wives tails, your time was well spent."

Tim,

This has not been the forum to learn about Fourier Analysis. The reality is that Fourier only requires a single sine wave after the completion of the rise envelope and just prior to the decay of the fall-time envelope. No further complex transpositions of additional sine waves are required, nor "harmonics," to construct just one sine wave function and just one sine wave is what we have with a steady-state CW transmission after the key is pressed. Nothing has been debunked here...

The discontinuities of non-sinusoidal rise and fall envelopes do in fact require construction from more than one sine wave. But your position that a pure CW carrier requires more than a single sine wave is contrary to Fourier. Think about it -- does Fourier really require more than one sine wave to construct...a single sine wave? Fourier insists that any function, no matter how complex, can be constructed by sine waves of varying phase and amplitude.

I believe this entire discussion can be summed up in differences of opinion between how bandwidth, (including power bandwidth) is actually measured and the relevancy of "occupied bandwidth" at typical CW operating speeds. Measured spectrum analysis has conclusively shown that BW generated by the rise/fall time of the CW carrier trumps any additional BW generated by keying speed at typical CW keying rates.

RE: Bandwidth versus Keying Speed

by W9AC on June 12, 2007 Mail this to a friend!

AD5X:

> "Response: No one has ever stated that the pictures are a hoax. But I would like to see spectrum pictures of two different keying speeds, and see what the bandwidth looks like. I.e., does the energy drop off faster at lower keying speeds?"

Good point, Phil. The biggest problem with using the MFJ keyer at audio frequencies to determine the relationship of BW and keying speed is that in the measured plots are we seeing the effects of harmonics generated from the keyed switching? I can't tell what the span is from those fuzzy pictures.

We need to subtract harmonics out of this particular analysis. The discussion from the beginning has been on bandwidth at the operating frequency versus keying speed.

For example, a CW transmitter keying on 28 MHz produces a first harmonic at least twice the operating frequency. But when we bring the keyed waveform analysis to audio frequencies, and set the span of the audio spectrum analyzer to 2F or more, we're going to see harmonics that are otherwise filtered out of an RF system. It's what is happening in and around Fc that we're concerned with.

I am fully supportive of using a CW keyer to demonstrate the effect of keying speed on BW, but we need an apples-to-apples comparison. The best way to test K5MC's hypothesis is to keep all other factors constant -- and by shifting tests from the RF domain to the audio spectrum, measurement and analysis errors are bound to creep in.

RE: Bandwidth versus Keying Speed

by AB0WR on June 12, 2007 Mail this to a friend!

AB0WR> "I certainly appreciate what you've done in debunking the seemingly commonly held beliefs that square wave harmonics only exist during the rise time and fall time and that the harmonics and their levels are determined by the output rise time and not the square wave input frequency and system response function...If even one student aspiring to learn about Fourier analysis learned the proper math instead of old wives tails, your time was well spent."

W9AC:
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
Tim,

This has not been the forum to learn about Fourier Analysis. The reality is that Fourier only requires a single sine wave after the completion of the rise envelope and just prior to the decay of the fall-time envelope. No further complex transpositions of additional sine waves are required, nor "harmonics," to construct just one sine wave function and just one sine wave is what we have with a steady-state CW transmission after the key is pressed. Nothing has been debunked here...

The discontinuities of non-sinusoidal rise and fall envelopes do in fact require construction from more than one sine wave. But your position that a pure CW carrier requires more than a single sine wave is contrary to Fourier. Think about it -- does Fourier really require more than one sine wave to construct...a single sine wave? Fourier insists that any function, no matter how complex, can be constructed by sine waves of varying phase and amplitude.

I believe this entire discussion can be summed up in differences of opinion between how bandwidth, (including power bandwidth) is actually measured and the relevancy of "occupied bandwidth" at typical CW operating speeds. Measured spectrum analysis has conclusively shown that BW generated by the rise/fall time of the CW carrier trumps any additional BW generated by keying speed at typical CW keying rates.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

Do you see a single time where I have said that a multiple sine waves are needed to construct single sine waves?

A square wave modulating a carrier creates an ENVELOPE on the oscilliscope display, at least it does if the keying speed is high enough to generate a fundamental and harmonics with sufficient amplitude for the oscilliscope to display them. That flat top envelope DOES require higher level harmonics, just as the Fourier series analysis of a square wave shows.

You are still propagating the bunk that the harmonics of a square wave die out after the rise time and magically reappear just before the fall time. Do you honestly beleive that anyone still believes that? After the displays that Mickey has provided that show differently? After the displays provided by SM0AOM that show differently? After the displays provided by w8wwv that show differently? After all the web sites that have been given that show a square wave is made up of harmonics that last throughout the period of the square wave?

Where do you think these harmonics in the modulating square wave get filtered out after the rise time and before the fall time? They certainly exist in the modulation signal. What do you think cancels them out?

The answer is that they don't disappear. They are what causes the modulation envelope.

A carrier left keyed on long enough for the fundamental and harmonics to be so low in frequency and so low in amplitude as to not be displayed only shows a carrier frequency, not an envelope. That doesn't mean the fundamental and harmonics don't exist.

So why don't you quit putting words in my mouth and address the real issue? Show me where Mickey's math is wrong since it matches with what I know from doing Fourier series on square waves?

You still don't even have what Mickey is saying down correctly. He is NOT saying anything about " additional BW generated by keying speed at typical CW keying rates.".

In fact he is saying exactly the opposite. You are putting words in his mouth as well as mine and then building an argument against YOUR words, not his.

You and Tom may very well be right about bandwidth of a square wave when considering energy density or spectral occupancy, I haven't completed my calculations on that and I am having to leave town today to take care of some family business. When I get back I will continue working on that. I will say, however, that I agree with Tom, energy density and spectral occupancy, since they are time dependent (i.e. calculated over a period of time), are probably NOT a good method of measuring interference potential in a receiver. For that, harmonic amplitudes ARE probably the best and those do NOT have equal power at the same frequency separation from the fundamental frequency.

tim ab0wr

RE: Bandwidth versus Keying Speed

by W9AC on June 12, 2007 Mail this to a friend!

AB0WR:

"Do you see a single time where I have said that a multiple sine waves are needed to construct single sine waves?"

What I see is this statement:

"You are still propagating the bunk that the harmonics of a square wave die out after the rise time and magically reappear just before the fall time."

Unless the square wave is coupled to an inductance and ringing of a square wave results, that is exactly what I am saying. I don't disagree that a square wave generates odd harmonics whose amplitude decreases at the rate of 1/3 Fc, 1/5 Fc, etc. But these harmonics are filtered in an RF transmission system. Transmitting a square wave at 7 MHz creates a harmonic of 1/3 the Fc amplitude at 21 MHz in an unfiltered, linear transmission system.

Using the tests with an MFJ keyer/oscillator will show these harmonics if the span is set wide enough. But once again, for the purpose of K5MC's hypothesis, we're interested in what is occurring at and near Fc, not in the area of the harmonics. You're confusing two separate mechanics occurring with switched square waves.

Otherwise, after a key is pressed in CW mode and remains pressed, what else remains other than a sine wave at Fc in a linear transmission system? Key a transmitter at one minute intervals (i.e., 0.0167 Hz) and aside from the bandwidth consumed during the rise/fall period, we are left with one sine wave transmitting at Fc for a one minute period of time.

Tim, after the completion of the rise envelope, and just before the envelope decay when the key is released what do you believe the spectrum consists of for that one minute duration?

Bandwidth versus Keying Speed

by AB0WR on June 12, 2007 Mail this to a friend!

ad5x:
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
Response: Whenever statements and theories are stated, you must have physical measurements to back them up because you can never be absolutely sure until you’ve verified the model as well as the design. I’ve worked for a large company where test equipment costs were no big deal. In my last company, a very small start-up, money was so tight that buying a DMM required tremendous justification. But it seems that you believe I could have saved my company the cost of a spectrum analyzer by saying “We’ve got the best optics team in the industry, and they say this is how the system should work. We’ve got the best circuit designers around, and here’s the design. No point in testing it as obviously everything will work as modeled and designed. So let’s just release it to production.”
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

ROFL!!!!

Phil,

You have to be kidding!

You are trying to justify the need for *ME* to spend $15,000 or more on a spectrum analyzer because a business needs one for its operation?

If you can't see the difference between these apples and oranges you just aren't bothering to look.

AB0WR: “I've given you a web site twice now that shows measurements by w8wwv that clearly show spectral lines in the CW output of a 756pro. Mickey has now provided pictures from SM0AOM that clearly show the distinct spectral lines in the RF output of a CW transmitter and how filtering can decrease the number of harmonics (that is what the spectral lines represent) being sent.”

ad5x:
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
Response: Yes, I’ve seen those. In both cases the radio output measurements are shown at a constant keying speed. And yes, you can see the spectral lines. But the question here is if you look at the same spectrum at a different keying speed, will the spectrum still be the same – recognizing that the spectral line separation will be different. I.e., will the 99% power bandwidth change? The only spectrum analyzer measurements I've seen of spectrums at two different keying speeds were made by W8JI, and these don't agree with the premise stated (bandwidth changes with keying speed).
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

Please, the pictures show the math to be correct for one speed. Take a look at one of Mickey's analyses of the pictures. If the math predictions are right at one speed do you have any reason whatsoever to believe that the math predictions wouldn't be right at a different speed? Especially when Mickey has posted spectrum analyzer displays of his MFJ keyer giving putting out the exact spectrum that the math predicts?

The spectrum analyzer displays of W8JI's don't show the spectral lines at all until you get to the very fastest speeds, and then only one or two show up. Yet the spectrum analyzer display from SM0AOM distinctly show them.

No one has yet shown Mickey's calculations to be wrong. They look correct to me. Mr. Chen said they were correct. The displays from SM0AOM match the math. Mickey's displays match the math. In fact, I am working on devolving W9AC's energy density graphs back to amplitude level graphs and I'll bet they show the exact same thing.

AB0WR: “I don't understand why people are still saying that no measurements have been taken to prove what Mickey has tried prove mathematically. Two distinct measurements have been given that shows what Mickey is saying. Who's going to be the first to step up and label the pictures Mickey has posted as a hoax?”

ad5x:
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
Response: No one has ever stated that the pictures are a hoax. But I would like to see spectrum pictures of two different keying speeds, and see what the bandwidth looks like. I.e., does the energy drop off faster at lower keying speeds? And no, I don’t have a spectrum analyzer to make these measurements – I just used my receiver as a selective level meter which appears to show that the spectrum doesn’t really change. But again, you guys are stating that BW changes with keying speed, while others say that measurements don’t support this. So you need to provide spectrum analyzer data supporting your model.
>>>>>>>>>>>>>>>>>>>>>>>>>>>

Mickey provided signals from his MFJ keyer for two different keying speeds showing two different sets of harmonics. The harmonics of one are down about 10db at the same frequency separation from the carrier just as the math would predict. Did you go look at those yet? Since those waveforms would be the modulating signal applied to a carrier, the exact same relationship should be seen in the convolved spectrum in the frequency domain.

Absolute signal bandwidth (which I like better than "keyclick bandwidth") is determined by the system response function. That function will limit the absolute bandwidth of any signal applied as an input. That is what you will measure if you look for the "absolute" last vestige of signal that you can hear. That is NOT, however, the POWER bandwidth as the FCC and ITU defines it. The amplitude of a square wave drops off as 1/n. A raised cosine filter will lower the amplitudes of the outer harmonics even more. Do the calculations to see where the power bandwidth for a lower frequency square wave with its major contributing harmonics closer to the center frequency comes out.

You ask "does the energy drop off faster at lower keying speeds". Tom says energy isn't a good measurement for this since receivers can't "store" energy. I tend to agree. That leaves only the power bandwidth to be used which is determined solely by the amplitudes of the harmonics and not by a product of their amplitudes and period. The amplitudes *MOST DEFINITELY* drop off faster at lower keying speeds when the metric is separation from the carrier frequency. Again, do the 1/n thing applied to the harmonics. A 2hz wave will have its harmonics down to 1/125 at the 125th harmonic (250hz). A 10hz wave will will have its harmonics down only 1/25 at the 25th harmonic (250hz). The 2hz wave will be 5 times lower in amplitude 250hz away from the center frquency. You should find almost a 15db difference in the power levels at 250hz away from the center frequency -- a good 2 S-units on many receivers, perhaps even three S-units on some.

I have yet to see a spectrum analyzer display that disproves that the harmoics of a square wave don't exist in the modulated signal. I have yet to see a spectrum analyzer display that doesn't show these harmonics dropping off by a 1/n rate as you move away from the center frequency. I have yet to see any mathematical explanation of how anything different could happen when applying a square wave as th modulating signal to a carrier.

Do you have any math to offer that would disprove the power bandwidth calculations Mickey has done? No one else has so far.

tim ab0wr

RE: Bandwidth versus Keying Speed

by AB0WR on June 12, 2007 Mail this to a friend!

W9AC:
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
What I see is this statement:

AB0WR>>>>"You are still propagating the bunk that the harmonics of a square wave die out after the rise time and magically reappear just before the fall time."

Unless the square wave is coupled to an inductance and ringing of a square wave results, that is exactly what I am saying. I don't disagree that a square wave generates odd harmonics whose amplitude decreases at the rate of 1/3 Fc, 1/5 Fc, etc. But these harmonics are filtered in an RF transmission system. Transmitting a square wave at 7 MHz creates a harmonic of 1/3 the Fc amplitude at 21 MHz in an unfiltered, linear transmission system.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

Paul,

I simply don't know how to make it any plainer. Your explanation is just wrong. Go to *any* of the following web sites and they will show graphically how a square wave is made up of harmonics that last the duration of the period of the square wave.

http://mathworld.wolfram.com/FourierSeriesSquareWave.html
http://cnx.org/content/m0041/latest/
http://www.stewartcalculus.com/data/CALCULUS%20Early%20Transcendentals/upfiles/FourierSeries5ET.pdf
http://homepages.gac.edu/~huber/fourier/index.html
http://en.wikipedia.org/wiki/Square_wave
http://mathforum.org/key/nucalc/detail.html
http://ptolemy.eecs.berkeley.edu/eecs20/week8/examples.html
http://ptolemy.eecs.berkeley.edu/java/ptolemy.plot2.0/ptolemy/plot/demo/FourierSeries.html
http://www.facstaff.bucknell.edu/mastascu/eLessonsHTML/Freq/Freq4.html

These harmonics are NOT filtered in an RF transmission system. They are the modulating signal for the carrier. Unless you put a filter *so* narrow in the system response that *only* the fundamental frequency can pass *some* harmonics will appear as modulation products on the modulated signal. I sincerely doubt that very many people can design an implementable filter than can pass a 2hz fundamental while blocking a 6hz (3rd harmonic) signal and higher.

The *carrier* does not have harmonics (hopefully). It is the carrier. It is the cos(wt) signal that is modulated. The modulating signal (i.e. the square wave) is what has the harmonics. So you don't wind up with a 7Mhz, 21Mhz, 35Mhz signal, etc. You wind up with a 7.000.002Mhz signal, a 7.000.006Mhz signal, a 7.000.010Mhz signal, a 7.000.014Mhz signal, etc......

No filter I have ever seen at RF is narrow enough to filter out all of these harmonics.

W9AC:
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
Using the tests with an MFJ keyer/oscillator will show these harmonics if the span is set wide enough. But once again, for the purpose of K5MC's hypothesis, we're interested in what is occurring at and near Fc, not in the area of the harmonics. You're confusing two separate mechanics occurring with switched square waves.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

At or near Fc would be at 7.000.002Mhz, 7.000.006Mhz, 7.000.010Mhz, 7.000.014Mhz, etc.

I am not confusing anything. I know that two signals multiplied in the time domain, i.e. a carrier of cos(wt) at 7.000.000Mhz and a modulating square wave signal at 2hz made up of all the odd harmonics of 2hz, wind up as a convolution in the frequency domain. If the square wave is bandwidth limited to less than an infinite number of harmonics you *STILL* get the harmonics that aren't filtered out.

If you look at Mickey's pictures of his MFJ keyer you *will* see all these harmonics just as the math predicts. When you convolve these in the frequency domain you essentially wind up with the spectrum of the square wave both above and below the carrier frequency (i.e. an upper and lower sideband). That is exactly what the pictures SM0AOM provided show for a CW signal with the modulating signal bandwidth limited to CCIR specifications. Not all harmonics were removed, only some.

You are asking us to believe either that a square wave doesn't have harmonics lasting the entire period of the square wave or that the modulation theorem of

f1(t)f2(t) <==> F1(w) * F2(w)

is incorrect.

Please show me the math that disproves these long held theorems. I would love to see it.

W9AC:
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
Otherwise, after a key is pressed in CW mode and remains pressed, what else remains other than a sine wave at Fc in a linear transmission system? Key a transmitter at one minute intervals (i.e., 0.0167 Hz) and aside from the bandwidth consumed during the rise/fall period, we are left with one sine wave transmitting at Fc for a one minute period of time.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

I gave you this answer earlier. Apparently it didn't mean anything to you. You are assuming you can see the modulation envelope from a 0.0167Hz fundamental and its odd harmonics on your oscilloscope or on your spectrum analyzer.

Need I point out just what kind of an assumption this is?

Not being able to see something doesn't mean it doesn't exist. I can't see the backside of the moon either. That is no indication it doesn't exist.

What remains is the modulated signal. That signal is modulated by a square wave with a fundamental of .0167hz and all its odd harmonics. That means that with as small as a 10hz resolution you will have 599 harmonics. At the 10hz point the 599th harmonic is down to 1/599 of the fundamental.

Did you REALLY expect to be able to see that?

Since you CANNOT see it are you really expecting us to believe that it doesn't exist? And therefore the harmonics of a 2hz wave doesn't exist either?

W9AC:
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
Tim, after the completion of the rise envelope, and just before the envelope decay when the key is released what do you believe the spectrum consists of for that one minute duration?
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

I believe it consists of a modulated signal that has a carrier frequency of 7.000.000Mhz with upper and lower sidebands consisting of all odd harmonics of .0167hz.

Where do YOU think the harmonics come from JUST BEFORE you release the key? Do you really expect us to beleive that the universe somehow knows when you are going to release that key and magically, quantum physics perhaps?, starts up the odd harmonics again?

If that is true then you should really sit down with the religious experts of this world and tell them that their views about free will are wrong or that physics somehow has a prescience factor that no one yet knows about.

As I've tried to point out here continually, rise time and fall time of an output wave do *not* create anything. That is a causal discontinuity. Rise times and fall times are *results* of an input and a system response. If the input is a square wave then the system response works on that input to form the output response.

Again, go look at the web sites above. They will *show* you with pictures how the rise and fall times of a square wave depend on the higher level harmonics and if you bandwidth limit the number of harmonics you can change the amount of rise and fall time.

Your claim that the harmonics of a square wave disappear after the rise time and reappear during the fall time violates everything printed in the textbooks about square waves. It violates the theory explained in the above 9 web sites. Your claim that the odd harmonics of the square wave somehow don't wind up in the modulated signal violates every textbook I have that discusses modulation theory. How does your "filter" know to knock out the odd harmonics during the "flat top" of the modulation envelope but not during the rise time and fall time? It violates the Convolution theorem totally.

Do you have *any* math to show that all this theory is wrong?

tim ab0wr

RE: Bandwidth versus Keying Speed

by W9AC on June 12, 2007 Mail this to a friend!

> Tim, after the completion of the rise envelope, and just before the envelope decay when the key is released what do you believe the spectrum consists of for that one minute duration?
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
AB0WR:

> "I believe it consists of a modulated signal that has a carrier frequency of 7.000.000Mhz with upper and lower sidebands consisting of all odd harmonics of .0167hz."

Wow.

You're suggesting that if we key a 40M CW transmitter at one minute intervals (one minute on, one minute off), that sidebands are created and sustained every 0.167 Hz from an Fc of 7.0 MHz for the entire one minute duration that the transmitter is keyed?

Bandwidth versus Keying Speed

by K5MC on June 12, 2007 Mail this to a friend!

Doug Smith: ". . . the instantaneous amplitude of the keying sidebands is constant during the rise and fall times, regardless of keying speed."

A key point to be made, however, is that spectrum analyzers do NOT measure the "instantaneous" amplitudes of the keying sidebands during the rise and fall times (typically 1 to 10 milliseconds) of a CW signal. For periodic signals such as the ones I assumed in my article (a string of dits with 50% duty cycle), an ideal analyzer will measure the amplitudes of the keying sidebands over one period of the signal. (And these amplitudes are constant as long as the keying envelope is repeated from one dit to the next dit.)

For example, 5 dits per second (12 wpm) means the fundamental frequency of the keying waveform is 5 Hz. Therefore, the first pair of keying sidebands would be located plus and minus 5 Hz from the carrier. Since the time period of a 5-Hz sine wave is 200 milliseconds, the time period in which the power bandwidth is calculated is 200 milliseconds for a sending speed of 12 wpm. If the speed is increased to 48 wpm (20 dits per second), the time period in which the power bandwidth is calculated is reduced to 50 milliseconds.

When we calculate the average (mean) power dissipated by a 1-ohm load supplied by a 120-V (rms) 60-Hz sine wave voltage, most of us don't confuse that type of power with the "instantaneous" power. In addition, you don't have to integrate the instantaneous power over "hours" or "years" as implied by W8JI. You merely integrate the instantaneous power over one time period of the "signal," which in this example is 16.67 milliseconds because that is the time period of a 60-Hz sine wave. (Actually, most electrical engineers will take advantage of the rms concept rather than crank out integrals in the time domain!)

Now suppose the voltage source is distorted because it has a third harmonic component at 180 Hz with an rms value of 40 V in addition to the 120-V (rms) component at 60 Hz. Then the 1-ohm (average) power of this distorted "signal" can be calculated as follows:

(120)^2 + (40)^2 = 16,000 W

Although the superposition principle (from electric circuit theory) is not generally valid for power, it is valid when the voltage components making up the "signal" are at different frequencies. The mathematical approach I used in solving the (time averaged) power bandwidths in my article are essentially just as I've described above. After calculating the Fourier series coefficients for the 5-ms "sinusoidal" and "square-wave" keying waveforms, I was able to find the 99.1% power bandwidth along the same lines as described above for the distorted 60-Hz signal.

W8JI: " . . . it agrees with how radios (and even MFJ Keyers) actually work if we test radios."

I'm glad to see that W8JI agrees that the fundamental principles of signal analysis are consistent whether the carrier frequency is 1 kHz or 3.5 MHz. Anyone who looks carefully at Figures 4 and 5 posted at http://www.arrl.org/sections/?sect=LA should agree that the "bandwidth" of the signal shown in Figure 4 is larger than the "bandwidth" of the signal shown in Figure 5. In addition to the dB bandwidth estimates I listed in my post several days ago, I want to list the following approximate dB bandwidths as shown in Figures 4 and 5:

25 dB BW is approximately 100 Hz at 10 wpm and approximately 200 Hz at 40 wpm
35 dB BW is approximately 200 Hz at 10 wpm and approximately 300 Hz at 40 wpm
45 dB BW is approximately 300 Hz at 10 wpm and approximately 400 Hz at 40 wpm

There is no question that the dB bandwidths measured by my very good low-frequency spectrum analyzer (an HP 3561A) clearly demonstrate the variation of bandwidth with keying speed! (I also verified that the rise/fall shapes and times of this keyer did not change with speed.) As I said before, the bandwidths displayed by a spectrum analyzer are based upon time averaged values; they are not a measure of the "instantaneous" values during the rise and fall times of the keying envelope.

Some hams may want to argue that my MFJ keyer does not accurately model the behavior of CW transmitters. I have observed the keying envelopes of my Kenwood 940 and Ten Tec Corsair on an oscilloscope at speeds between 10 and 40 wpm, for example, and I see no evidence at these speeds that the Fourier series approach I used in my article is not valid.

For those hams who still disagree with the results presented in my article, do they think that the 99% power bandwidth (which is equivalent to the FCC's definition of occupied bandwidth) is the same identical concept as the "keyclick" or "interference" bandwidth constantly on the mind of W8JI? If they do think that these bandwidth definitions are equivalent, how do they reconcile the rather sad plight faced by Joe, the new ham, who wants to operate his Icom 751A at 6 wpm and still be within the letter of the law as given in Part 97.307(a)? (My story of Joe's bandwidth dilemma was posted on June 5.)

For those hams who do understand the distinction between the 99% power bandwidth (which is equivalent to the FCC's definition of occupied bandwidth) and the "keyclick" bandwidth, do they simply believe the concept of power bandwidth is merely an "academic" exercise and has no practical value? If that explains their position, then I suggest they think about such modes as EME and QRSS that dramatically illustrate the importance of power bandwidth.

73, K5MC

RE: Bandwidth versus Keying Speed

by W8JI on June 12, 2007 Mail this to a friend!

Hi Mickey,

Either I misread wht you wrote, or you seem to have some confusion about what the spectrum analyzer does.

The spectrum analyzer is nothing more than a selective level indicator that scans across a predetermined bandwidth and records the signal level on a display as it hppens to cross that point.

It makes a "level" or amplitude plot of the signal and STORES that information on the screen. It does not mean the level is there constantly during the seeep, just that it happened to be there as it passed any particular point.

My analyzer is one of those very expensive analyzers that measures many things directly, and can do so in 10Hz bandwidth resolution. It can average multiple sweeps to weed out momentary glitches or things it might miss on a single sweep.

It calcultes occupied bandwidth according to FCC requirements, and so what you see on the display is really what it is.

Now it just happens that what is reads agrees very closely with Kevin W9AC and many other people, and disagrees with you and Tim.

KE3HO sent me his analysis and I posted it as a web page at:

http://www.w8ji.com/cw%20bandwidth%20analysis.htm

So we have virtually every analysis, as well as common sense and measurements by multiple people, disagreeing with Tim and your conclusions.

We also have people here who have taken the time to listen on a receiver while they adjusted speed of a transmitter and they have found the system behaves as Kevin W9AC, Dough Smith, KE3HO, and others predict.

Now we have Tim claiming an unmodulated steady carrier sustains sidebands while at a steady state.

I'm really not sure how to resolve this Mickey.

If the system doesn't behave as someone describes in his analysis or model, we can't make the system change. Something else has to give.

I think the problem is you are considering long term accumulated power, but there is no energy storage in the system. The sidebands ALWAYS have the same energy level, frequency spread, and duration regardless of keying speed. If it is a 5 ms rise the sideband has a 5 ms duration. If we don't alter the level change or shape we don't alter the duration or frequency spread, and we can't alter the power. The transmitter carrier power is 100 watts PEP in a 100 watt PEP rig, no matter how fast we key. it is 100W PEP if we hold the carrier on an hour (assuming nothing blows up or overheats and changes the power through a defect) or send one dit.

The sidebands have the same peak envelope power energy level and same bandwidth and duration, they simply repeat more or less often with keying speed.

Now other defects can certainly change things. The ALC in the FT1000MP MKV for example can increase bandwidth when the dot speed is so low the ALC collapses between dots, but in a perfect CW rig bandwidth does not change with keying speed.

73 Tom

RE: Bandwidth versus Keying Speed

by W8JI on June 12, 2007 Mail this to a friend!

Mickey,

Please read this and tell us what you think.

http://www.w8ji.com/cw%20bandwidth%20analysis.htm

73 Tom

RE: Bandwidth versus Keying Speed

by W9AC on June 12, 2007 Mail this to a friend!

K5MC:

> "A key point to be made, however, is that spectrum analyzers do NOT measure the "instantaneous" amplitudes of the keying sidebands during the rise and fall times (typically 1 to 10 milliseconds) of a CW signal."

Mickey,

Although I don't believe it's even necessary at 5ms switching speeds, we can capture "instantaneous" amplitude with a S/A if we sample the analyzer in a storage peak-hold mode and observe the resulting bandwidth. For example, if we sample a string of dits at a 40 WPM transmission rate with a reasonable sweep rate for one minute, surely the analyzer will capture any instantaneous amplitude maxima in and around Fc at some time during that one minute event.

In the alternative, we can manually sweep the analyzer and fix placement of the cursor X Hz from Fc. My experience has been that a S/A is ample fast to capture any bandwidth generated by 1-10 ms switching slopes. The equivalent F of a 5 ms transition time is only 200 Hz. The S/A is capable of resolving this accurately.

P.S. - Several replies by others during this discussion have confused my callsign with that of Kevin, W9CF. My call is W9AC and I have no affilition with Kevin. Thanks.

RE: Bandwidth versus Keying Speed

by W8JI on June 12, 2007 Mail this to a friend!

Woops. Old age or too much Internet I guess.

I'm starting to forget callsigns.

:-)

RE: Bandwidth versus Keying Speed

by W8JI on June 12, 2007 Mail this to a friend!

by W9AC on June 12, 2007

Although I don't believe it's even necessary at 5ms switching speeds, we can capture "instantaneous" amplitude with a S/A if we sample the analyzer in a storage peak-hold mode and observe the resulting bandwidth. For example, if we sample a string of dits at a 40 WPM transmission rate with a reasonable sweep rate for one minute, surely the analyzer will capture any instantaneous amplitude maxima in and around Fc at some time during that one minute event. >>

Right you are Paul!

I know it would be nice to have an "out" and be able to say the analyzer isn't reading the right thing, but the reason the analyzer sweeps so slow at very narrow resolutions is so the very narrow window has enough time to fully sample signals as it moves across the frequency.

My analyzer for example takes 90 seconds to sweep 3 kHz, or about 30 milliseconds per Hz when at 10Hz resolution bandwidth. It has all the time in the world to catch sidebands that are generated every 1/10 of a second (5dps) or faster. To be extra sure I caught everything, I did a 5 sweep average. The results actually don’t change very much.

It automatically goes into “storage” for the full sweep time when doing measurements, unlike older analyzers.

http://www.w8ji.com/occupied_bw_of_cw.htm

By the way Paul, the FT1000MP MKV shows the same ALC problems that plagues many rigs at slow dot speeds (7dps or slower). This extends BW at very slow speeds when the ALC falls out between dots, especially if the power control is turned down.

Fortunately at higher more common speeds it stabilizes. Of course I can fix that problem by turning the TX IF gain down until ALC disappears, but it isn't a problem at normal speeds (unlike the Omni 6).

A receiver shows exactly the same results, so the analyzer clearly describes and agrees with the real world system.

73 Tom

RE: Bandwidth versus Keying Speed

by AB0WR on June 12, 2007 Mail this to a friend!

> Tim, after the completion of the rise envelope, and just before the envelope decay when the key is released what do you believe the spectrum consists of for that one minute duration?
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
AB0WR:

> "I believe it consists of a modulated signal that has a carrier frequency of 7.000.000Mhz with upper and lower sidebands consisting of all odd harmonics of .0167hz."

W9AC:
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
Wow.

You're suggesting that if we key a 40M CW transmitter at one minute intervals (one minute on, one minute off), that sidebands are created and sustained every 0.167 Hz from an Fc of 7.0 MHz for the entire one minute duration that the transmitter is keyed?
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

No, that is not what I am suggesting.

I am suggesting that the keying will generate a square wave ofa fundamental frequency of 0.0167hz along with all of its odd harmonics, e.g. 0.0167 x 3 = .0501Hz, 0.0167hz x 5 = .0835hz, 0.0167hz x 7 = 0.1169hz, etc... out to the bandwidth of the system. The harmonic at .0501hz will be 1/3 the value of the fundamental, the harmonic at 0.0835hz will be 1/5 the value of the fundamental, the harmonic at 0.1169hz will be 1/7 of the value of the fundamental.

When the carrier Fc is modulated by this square wave you will wind up with sideband frequencies around 7.000.000Mhz of 7.000.000.0167hz, 7.000.000.0501hz, 7.000.000.0835hz, 7.000.000.1169hz, etc.....

Are you still suggesting that this is NOT what happens?

Did you go look at *any* of the sites I listed in my message? Can you explain to us mathematically just how they are *ALL* wrong? Can you explain how the math behind the Convolution theorem must be wrong and give an alternative mathematical explanation?

I've already shown Tom how the rise and fall times are NOT determinate for the harmonic frequencies that cause the rise and fall times. Different frequencies of square waves can give exactly the same rise and fall time. The square wave input function and the system transfer function *ARE* determinstic for the harmonics involved. The math shows that those harmonics exist for the entire period of the square wave and all of the spectrum displays I've given you show these harmonics existing.

I've answered your questions, you have yet to answer any of mine.

Inquiring minds would probably like to know whay that is.

What mathematical model leads to the harmonics during the rise time to damp out and disappear? It can't be filtering, no filter is narrow enough to do this. What mathematical model leads to the damping of the harmonics to suddenly disappear and allow them to reappear during the fall time of a square wave?

Surely you have some mathematical model to explain this, right?

tim ab0wr

RE: Bandwidth versus Keying Speed

by WA0LYK on June 12, 2007 Mail this to a friend!

Here is the flaw in the logic that the modulation harmonics only exist during the rise and fall times.

For those who subscribe to the theory that the rise/fall times are what creates the modulation harmonics you need to explain why we should not be searching for the shortest possible rise/fall times. This would minimize their duration to the absolute shortest possible time. A rise/fall time of 1 us or even 1 ns would be desirable.
The modulation harmonics would only exist for a period of time that could not be heard and afterward only the carrier or nothing. This would certainly reduce the interference to others on adjacent channnels. A click only lasting 1 us wouldn't cause much damage.

Jim
WA0LYK

RE: Bandwidth versus Keying Speed

by AB0WR on June 12, 2007 Mail this to a friend!

W8JI:
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<

KE3HO sent me his analysis and I posted it as a web page at:

http://www.w8ji.com/cw%20bandwidth%20analysis.htm

So we have virtually every analysis, as well as common sense and measurements by multiple people, disagreeing with Tim and your conclusions.

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

Tom,

You know, I really sorry about this but all this proves is that a bandwidth filtered square wave has a rise time and fall time dependent on the filtering and that the magnitudes of the harmonics outside the passband of the filter are affected by the filter.

The rise time and the fall time don't DETERMINE squat. They are DETERMINED by the input and the system transfer response, in this case a bandwidth filter.

You and Jim are still stuck in a causal discontinuity.

Jim goes through a big explanation about filtering the the keying wave and then conveniently forgets that and says that the rise and fall times determine the bandwidth.

It is exactly the opposite. The bandwidth determines the rise and fall times.

He states in his write up that the magnitudes of the different harmonics ARE different but then conveniently forgets that the magnitudes and their relationships are what determines power bandwidths.

Your, and Phil's, and Jim's explanations all have holes in them big enough to drive trucks through. You basically want to say that almost 200 years of Fourier analysis is wrong and that your observations of the real world are right.

ROFL.

Let's see, in order for yous, Jim's, and Phil's views to work you have to claim:

1. Outputs cause inputs, i.e. rise times and fall times generate bandwidth limits, not bandwidth limits generate rise times and fall times.
2. Square wave harmonics only appear during the rise and fall times and disappear all other times.
3. That square wave harmonics all have the same magnitude at the same spacing from the carrier.
4. That square wave rise time and fall times are deterministic for the frequency spacing of the harmonics in a square wave.
5. That the Convolution theorem is wrong but you can't quite explain how mathematically.

Have I missed any?

I would also caution Jim to check his calculations carefully. His Figure 3 is for a 0.5ms rise time. Using the formula of rise-time x bandwidth = pi, this should give a bandwidth of about 2khz for the system response.

Square waves of 16.67hz (0.03sec period) and 1.667hz (0.3sec period) should have significantly different harmonics involved. Figure 3 does not show this. This is a straight analysis of a low frequency bandwidth limited square wave and if the very first plot shown does not distinguish between the two then something is not right.

At 83.5hz the 16.67 hz 5th harmonic should be at 1/5 the fundamental value while for the 1.667hz signal at 83.5hz you should be seeing the 50th harmonic which should be down 1/50 or an order of magnitude less in strength.

Since the signal strength at 100hz should be at least an order of magnitude less than the bandwidth of the system, there should be no impact on these harmonics.

The fact that this 1/n relationship doesn't show in the plot indicates a problem somewhere. I would, therefore, be very cautious in using these plots to verify *anything*.

I don't have the newest Excel with the Fourier Analysis package. I'll see if I can come up with one in the next few days and see if I can duplicate the graphs. It might be useful to see the plots zoomed in to 100hz and see if Excel is actually calculating the correct magnitudes.

tim ab0wr

RE: Bandwidth versus Keying Speed

by AB0WR on June 12, 2007 Mail this to a friend!

w8ji:
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
Now we have Tim claiming an unmodulated steady carrier sustains sidebands while at a steady state.

I'm really not sure how to resolve this Mickey.

If the system doesn't behave as someone describes in his analysis or model, we can't make the system change. Something else has to give.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

Tom,

It's really sad that you do not understand the math and what it implies.

If you think you have equipment that can capture modulating frequencies down into the hundredths of a hertz I would like to know both the manufacturer and the model number.

My guess is that you can't.

Since you can't your only defense is to say the math is wrong.

It isn't.

Just because you can't measure sidebands at 0.01667 hz doesn't mean they don't exist.

In your world most of our electronics wouldn't exist. Electrons of energy Y should not be able to get past an energy barrier of 2Y --- but they do. Just because YOU can't see it doesn't mean it doesn't exist.

In your world Calculus wouldn't exist because the concept of a vanishingly small delta-x could not exist. Taylor series couldn't exist because the concept of a series converging at infinity could not exist.

There has never been a steady unmodulated carrier that started at negative infinity and which will end at positive infinity. Therefore the math says that harmonics *do* make up the square wave that steady carrier actually is. They exist. Whether you like it or not, they exist. Just as integration and differentiation exist.

Fourier series exist whether you like it or not.

Apparently you have never bothered to go and look at any of the nine web sites I provided. Each and every one of those will show that square waves consist of harmonics. Those harmonics last the entire period of the square wave. Mickey even showed you pictures of the harmonics. Those harmonics get convolved into upper and lower sidebands when used to modulate a carrier.

Do you really have the gall to claim that the Fourier theorem and the Convolution theories are wrong?

I am still waiting for YOUR mathematical model of a square wave and for the modulation theory that the Convolution theorem prdicts.

When will we get it? I would settle for a mathematical model that shows the harmonics of a square wave die out after the rise time and reappear just before the fall time. When will we get YOUR mathematical model for this?

tim ab0wr

RE: Bandwidth versus Keying Speed

by AB0WR on June 12, 2007 Mail this to a friend!

w8ji:
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
I think the problem is you are considering long term accumulated power, but there is no energy storage in the system. The sidebands ALWAYS have the same energy level, frequency spread, and duration regardless of keying speed. If it is a 5 ms rise the sideband has a 5 ms duration. If we don't alter the level change or shape we don't alter the duration or frequency spread, and we can't alter the power. The transmitter carrier power is 100 watts PEP in a 100 watt PEP rig, no matter how fast we key. it is 100W PEP if we hold the carrier on an hour (assuming nothing blows up or overheats and changes the power through a defect) or send one dit.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

*THIS* is what I would like to see the math for.

Just what generates these sidebands only during the rise time and fall times?

Does the universe just know to do it?

As I've already pointed out the rise times and fall times are not deterministic for what harmonics should appear. So there must be some "magic" involved somewhere.

What mathematical wizardry do you have to show us as to how the universe can magically decide what harmonics to create during those rise and fall times?

Is it the "Hand of God" maybe?

Please, Tom. Enlighten us. I'm sure that there are tens of thousands of engineers who would like to learn the math that apparently only you know as to how this happens.

tim ab0wr

Bandwidth versus Keying Speed

by AB0WR on June 12, 2007 Mail this to a friend!

Oh, my. I just tumbled to this.

Does anyone here actually know what a raised cosine filter shape looks like in the time domain?

Does anyone actually know what that does to the square wave in the time domain when the two are multiplied in the frequency domain, i.e. convolved in the time domain?

What Jim, KE3HO has done is applied the shape of a raised cosine filter in the frequency domain to a square wave in the time domain. That is not going to work right no matter how accurate his calculations are.

Has *anyone* actually gone to look at what a bandwidth limited square wave (bandwidth limiting is a FREQUENCY DOMAIN operation people) actually looks like in the time domain? (I have, btw)

It does NOT look like what Jim is analyzing. I suspect *THAT* has as much to do with the outcome of the analysis as anything.

I think once the overshoot and ripple in the square wave that results from frequency domain bandwidth limiting is actually considered, significantly different results will be seen in the analyses.

Does *anyone* actually want to know how to Fourier analyze a bandwidth limited square wave mathematically? I had this in a Word document and deleted it but I can recreate it if anyone cares.

tim ab0wr

Bandwidth versus Keying Speed

by K5MC on June 13, 2007 Mail this to a friend!

W8JI: Please read this and tell us what you think.

http://www.w8ji.com/cw%20bandwidth%20analysis.htm

Tom, I've glanced over the spectrum plots generated by KE3HO at the above website. In his first figure, Jim is showing three different keying waveforms. The most extreme waveform in terms of generating keyclicks has rise/fall times of 0.5 ms. The other two keying waveforms will be much better in terms of "keyclick" bandwidth; I certainly would expect the raised sine wave to be the best one of the three shown in terms of minimizing the adjacent channel keyclicks. A small argument I would have with Jim concerning his Figure 1 is that the time durations of his pulses are not exactly 30 ms; the 0.5 ms rise/fall "trapezoidal" waveform is closer to 31 ms in duration and the other two waveforms are 35 ms in duration. However, as Jim notes in his comments, he was referring to the time duration in which the pulses are 100% amplitude and so I can accept his definition of pulse width as being 30 ms in all three cases.

Where Jim starts missing the concept of (time averaged) power bandwidth is shown in Figure 3. He superimposes two keying pulses that differ in time duration by a factor of 10 on the same spectrum graph, but even more than that, he extends his frequency axis entirely too far to really see what's going on as far as the "essential" or "necessary" bandwidth is concerned. BTW, since Jim is looking at the Fourier transforms of pulses with time durations of 30 ms and 300 ms, rather than periodic keying pulses as I assumed in my article (my string of dits with 50% duty cycle), we need to use the term "energy" bandwidth rather than "power" bandwidth because a single pulse is an energy signal, not a power signal.

The essential energy bandwidth (for example, the 99% energy bandwidth) of the 300-ms pulse in Figure 3 is probably around 15 Hz; the corresponding 99% energy bandwidth of the 30-ms pulse will be 10 times that of the 300-ms pulse, or probably around 150 Hz. If you will recall, I mentioned this very concept early in this thread by my description of s1(t) and s2(t) back on May 27 as follows:

K5MC: For example, let's consider two sinusoids of equal amplitude, say 1 volt. Assume that s1 is a 1-kHz sine wave that lasts for exactly 1 second and s2 is a 1-kHz sine wave that lasts for exactly 2 seconds. Therefore, s1 will consist of 1000 successive sine waves, with each wave having an amplitude and period of 1 volt and 1 millisecond, respectively. Similarly, s2 will consist of 2000 successive sine waves, with each wave also having an amplitude and period of 1 volt and 1 millisecond, respectively. The 99% energy bandwidth (just to be specific on my definition of bandwidth here) of s1 will be exactly twice as much as that of s2. By my calculations, the 99% energy bandwidth of s1 is 20.6 Hz and the 99% energy bandwidth of s2 is 10.3 Hz.

Expanding on my May 27 comments above, let's assume we have a third signal consisting of a finite-duration sinusoid similar to s1 and s2, but let's assume s3 is a 1-kHz sine wave that last exactly 100 ms. Therefore, the 99% energy bandwidth of s3 would be exactly ten times as large as that of s1, or 206 Hz.

Until Jim can demonstrate results that are consistent with the 99% energy bandwidths that I've mentioned above, we will not make much headway in our discussion. I really believe if Jim and you would forget about Fourier transforms and think instead about Fourier series, you would begin to understand how and why the 99% power bandwidth does vary with both the sending speed and the rise/fall times and shapes of the keying envelope.

Everything I reported in my article is consistent with recent editions of the ARRL Handbook, with the FCC Part 2 rules concerning the relationships between "occupied" bandwidth and "necessary" bandwidth (which are themselves essentially copied straight from the ITU-R SM.328 document concerning the spectra and bandwidth of emissions), and with the fundamental theory of Fourier analysis. Jim and you and a few others continue to be at odds with the rest of the world regarding the concept of power/occupied bandwidth.

You continue to either misunderstand the definition of power bandwidth or you think that the concept of power bandwidth is unimportant. Some of your comments during this thread have clearly indicated to me that you don't understand the definition (and you certainly have some ideas about signals that are definitely at odds with Fourier analysis). On the other hand, your other comments make me think that you do understand to some degree the definition of power/occupied bandwidth, but you believe that the only definition of bandwidth important in amateur radio is the "keyclick" bandwidth.

73, K5MC

RE: Bandwidth versus Keying Speed

by AB0WR on June 13, 2007 Mail this to a friend!

To KE3HO:

Jim,

The time domain function you should be analyzing should be of the form:

(2A)(1/tau)(1/w2)[cos(aw) - cos(bw)]cos(wc)

where tau is the rise time, a is the beginning of the rise time, b is the end of the rise time, w is radian frequency, and wc is the carrier frequency.

I'm not sure that is the waveform you are analyzing.

tim ab0wr

RE: Bandwidth versus Keying Speed

by W8JI on June 13, 2007 Mail this to a friend!

You continue to either misunderstand the definition of power bandwidth or you think that the concept of power bandwidth is unimportant.>

It is unimportant Mickey.

It is unimportant to the people using CW, it is unimportant to the FCC. It is unimportant, as you use it, to everyone except those who like to argue about unimportant things.

Some of your comments during this thread have clearly indicated to me that you don't understand the definition (and you certainly have some ideas about signals that are definitely at odds with Fourier analysis).>.

Oh I understand the Fourier analysis. I also understand that the use of any tool, and the Fourier analysis is a tool, must fit the system we are trying to describe.

There's nothing wrong with your analysis, it just doesn't apply to the real-world operation of system you are analyzing.

I tried to get you to understand that by pointing out with a given voice if we talk slower (fewer words into a SSB system, your application would indicate the occupied BW of a SSB signal would be less.

You agreed the bandwidth would be less, which really just shows how far from real-world importance you have focused on.

<< On the other hand, your other comments make me think that you do understand to some degree the definition of power/occupied bandwidth, but you believe that the only definition of bandwidth important in amateur radio is the "keyclick" bandwidth. >>

Keyclick or keying sideband bandwidth the only one the FCC regulates, and it's the only thing that means anything to the guy using his radio.

When a person sits with his radio tuned to the side of a CW transmitter, assuming it has enough selectivity to not hear the tone and the receiver isn't overloading, he hears clicks. The receiver will register these clicks or we can measure their power level or amplitude.

For any frequency we put the receiver on that level stays absolutely constant with speed so long as the waveform of the rise and fall do not change.

All the slower speed stuff does is move close spaced sidebands around in that window, but there is no net effect on the operator or receiver at all except the clicks occur less frequently.

Now some rigs do have defects that cause bandwidth to change with speed, like the FT1000MP MKV where the ALC falls out at real slow speeds increasing bandwidth, but if we have a well-designed rig we will observe the sidebands at the same distance and level.

This is why instruments like my Agilent Analyzer measure occupied BW like they do. The FCC and everyone else are interested in the effect on other communications systems, not some very long term change that doesn't affect other users.

This is the entire area where you are at odds with everyone else.

The only bad thing about this is some won't fully understand the differences between what you are saying (which is technically correct) and what I am saying, which is also technically correct.

I am saying the only thing important and the only thing we should consider is what is important to operation of the system.

Although you are correct, in theory we can narrow the *very long term power bandwidth* by transmitting half a day instead of all day, it just doesn't mean a thing to other users. It won't make the signal narrower. This extends to dash time even. The dot and dash times are significantly longer than any "memory" the system has. Certainly there is very low frequency energy in those transitions, but it does not affect the occupied bandwidth we observe. The Morse speed doesn't affect the receiver or the apparent level of sidebands at any spacing that we can observe; it simply makes the sidebands we observe appear more or less frequently.

You'll notice everyone who checks the effect on a real receiver with a real transmitter agrees with me.

Now Mickey I can indeed measure what you describe, but I have to use a power averaging instrument rather than one that measures envelope power. I have to use an instrument that integrates the sidebands on a given frequency over a very long time period, so slow that there are no recognizable dots or dashes.

The problem is such an instrument (for good reasons) is not accepted by the FCC because it falsely indicates level of sidebands decreases with less frequent occurrence of those sidebands. In other words it doesn't behave like the system we are trying to define.

I really don't know how to make you see this, or even if you want to see it.

I understand well what you are saying, but as I've said all along it doesn't apply to how the system really works and what we are really trying to determine. You might as well toss in what happens each year in the transmitter, and throw that into the analysis. Then we can make our power bandwidth decrease just by taking a year off the radio.

You can pick at me and say I don’t understand your analysis, and I’ll continue to pick back and say you don’t understand the transmitter and receiver or the human operator and how they work. The real problem is I’m describing the effect on the working system, and you are describing something that doesn’t mean anything to the people using the system. It will never end.

73 Tom

RE: Bandwidth versus Keying Speed

by W8JI on June 13, 2007 Mail this to a friend!

Mickey,

Let me try one last time to explain why you and many others including myself disagree.

We all know, or should know, as we keep on throwing in slower and slower changes in level each of those changes can be represented in a Fourier analyses as a sine wave.

As we add slower and slower (or lower frequency) sine waves, we now look at all of the energy over an increasing time period. The very long period variations in level we add in effect reduce the contribution of higher frequency signals. So from this standpoint you are correct.

We could even add to the analysis the fact that the signal wasn't there a minute ago and it there now, and we could further extend that to the fact the signal wasn't there before we were licensed and won't be there after we are silent keys. This adds an even slower sine wave.

The problem is all in how the system behaves, and what is important to users.

The receiver cannot register or store the energy from the high frequency signals over the period of very slow variations. It just doesn't matter that they occur because the sample rate of the human is by definition much faster than the slowest rates involved. The receiver for example has to respond much faster than the rise and fall times, or it will extend the rise and fall times and make the CW "soft". This tends to blur the difference between rough periodic noise pulses and the actual signal. Everything including a very fast transient comes out as a rising and falling "dot".

The operator also only hears the peak level of things and how they repeat over a slow period. He can't hear below 20-40Hz, it isn't even registered as a sound.

Furthermore, when all of the sine waves subtract there is no sound or carrier. During that time period for all purposes the signal is zero, it is off. It might as well be off for 200 years as off for 200 milliseconds.

The same thing happens on the on time. When the signal is out of the level transition periods at the rising and falling edges and on the peak, so far as the radio, a spectrum analyzer, the operator, or anything else is concerned it is a constant level without bandwidth. Again this goes back to how the system behaves. We can't listen to a carrier and say "oh, that carrier is certainly changing at a slow rate" while all of our sense and the S meter tells us it is steady. We don't know when it will disappear, and we can't hear how it got there as a low frequency signal.

Obviously from the way the human and the receiver behave we have to set a lower limit. The AGC is a peak detector with storage. It filters any tailing edges out. It has to do that or the receiver would be very unpleasant, almost useless, on CW or SSB. So it sees the rising edges and the point where the envelope crest is reached and then holds that level for some period of time longer than a dot. That is the SLOWEST responding part of the entire system.

The human hears the signal only as an off and on, and the nature of the receiver is such that all of the small sidebands we might see when we look at the signal over a very long time with energy storage or memory time are merged.

The result of all this is when we tune across a signal we see the same slope in level with frequency change at 40 dots per second as we do at 5 dots per second, so long as the rig isn't changing rise and fall shapes or times. The only thing we notice, and the only thing the S meter records, is the peak level in the sidebands and that level stays the same regardless of speed (within the limitations outlined earlier).

This is because the receiver and the human cannot accumulate energy over the time periods necessary to include the very slow waveforms that make up things that happen over dozens of milliseconds, seconds, days, months, or years.

This is why when we tune across a signal we observe the bandwidth remains the same regardless of speed (within limits of the rig NOT modifying rise and fall times), and why the FCC and everyone else doesn't allow every slow periodic variations into the measurement of occupied bandwidth.

What really matters is the EFFECT of all this on the receiver and the operator, and with CW (and SSB) how fast the information is transferred just doesn't matter. It's all about the bandwidth limits set by transmitter filters and transmitter modulation products, not the very slow long term averaging we create when we toss in things that are meaningless.

I've tried several way to get you to follow why Chen (I think that was his name, W7AY?) agreed with your analysis but disagreed with your results. Your math is flawless, but it includes things that are meaningless to the real application. As a result it is garbage in and garbage out. We can’t stretch the time of the analysis out so long that we are looking at things that change very fast over many dozens of slowly changing cycles when the fast things are exclusively cause the problems we are concerned with.

73 Tom

RE: Bandwidth versus Keying Speed

by KE3HO on June 13, 2007 Mail this to a friend!

<<< What Jim, KE3HO has done is applied the shape of a raised cosine filter in the frequency domain to a square wave in the time domain. That is not going to work right no matter how accurate his calculations are. >>>

Not at all. I have applied the raised SIN to the CW signal in the time domain, then calculated the frequency components of that signal. I did the same thing with the trapezoidal rising and falling edges.

Tom - thanks for posting the paper on your web page.

73 - Jim

RE: Bandwidth versus Keying Speed

by KE3HO on June 13, 2007 Mail this to a friend!

Tim,

After reading your post with the equations, I see why you made the comment about the raised cosine filter. NOBODY here has advocated applying a raised cosine filter. NOBODY. In my analysis I made no attempt to use a raised cosine filter. Early on in this discussion, Chen and others discussed the mathematical advantage to using a raised sin waveform as the leading and trailing edge of the keying function (in the time domain) because it is a continuous function and its derivative is continuous. There was NEVER any discussion of applying a raised cosine filter in any way.

73 - Jim

Bandwidth versus Keying Speed

by AB7E on June 13, 2007 Mail this to a friend!

<WA0LYK: For those who subscribe to the theory that the rise/fall times are what creates the modulation harmonics you need to explain why we should not be searching for the shortest possible rise/fall times. This would minimize their duration to the absolute shortest possible time. A rise/fall time of 1 us or even 1 ns would be desirable.
The modulation harmonics would only exist for a period of time that could not be heard and afterward only the carrier or nothing. This would certainly reduce the interference to others on adjacent channels. A click only lasting 1 us wouldn't cause much damage.>

I don't think even the math guys are going to agree with such an erroneous conclusion.

1. Those faster rise/fall times would increase the peak energy in the clicks and accordingly be more objectionable.

2. Key clicks trigger the AGC on any receiver and partially blank reception for a period much longer than the duration of the clicks.

3. Those faster rise/fall times would generate objectionable clicks further away from the carrier frequency, thereby affecting more adjacent QSOs.

4. If everyone used such faster rise/fall times the band would be saturated with overlapping clicks because of #3. Everyone becomes a Russian Woodpecker.

Dave AB7E

RE: Bandwidth versus Keying Speed

by KE3HO on June 13, 2007 Mail this to a friend!

Mickey,

Your assertion that Tom and I don’t understand power bandwidth and Fourier analysis is absurd.

Our disagreement is in the usefulness of "power bandwidth". If you would like numbers from my analysis, I can give you the following, which I have calculated directly from the data used to create the graphs in my paper posted on Tom’s web site:

99.1% Power Bandwidth (full width centered at nominal carrier frequency)

30 mS wide 0.5 mS trapezoidal keying 479 Hz

300 mS wide 0.5 mS trapezoidal keying 44 Hz

30 mS wide 5 mS trapezoidal keying 156 Hz

300 mS wide 5 mS trapezoidal keying 29 Hz

30 mS wide raised SIN 5 mS keying 171 Hz

300 mS wide raised SIN 5 mS keying 29 Hz

We don’t disagree on the analysis. I said early on that your analysis was correct.
Where we disagree is on the significance of “power bandwidth”. Power bandwidth is virtually meaningless for anything but certain FCC compliance tests. When you key at slower speeds you increase the power in the very low frequency components (within 5 to 10 Hz of the carrier nominal frequency) while taking an INSIGNIFICANT amount of power from each of the higher frequency components. So what is the effect of this shift in power? No measurable change in the bandwidth of the signal. Yes, there is a difference in “power bandwidth”, but that difference has nothing to do with the actual bandwidth (by any reasonable definition). If you had a spectrum analyzer that could plot your transmitter signal with a resolution of 1 Hz, you would see a change in the spectrum versus keying speed within 10 Hz of your center frequency. You would also see no noticeable change in the overall shape of the spectral curve beyond 20 Hz or so.

Power bandwidth changes with keying speed. No argument there. However, power bandwidth is a nearly meaningless measure when it comes to determining how wide the spectrum of a transmitter is.

Here is an absurd, totally unrelated example. I have a vacuum cleaner at home that says “4.2 Horsepower” on the top cover. 4.2 HP = 3133.2 watts. At 120Vac that implies a current draw of more than 26 amps. This vacuum only draws about 8 amps when running. However, if you were to load down the blower motor and all of the electrical attachments to the vacuum until everything is just about ready to stall, it might draw 26 amps briefly (just before everything burned up). Is 4.2 HP any sort of meaningful measurement? Of course not. Can it be measured in a lab? Sure. Power bandwidth is no indication of the bandwidth of a transmitter by any reasonable definition of bandwidth. Can it be measured in a lab? Sure.

73 - Jim

Bandwidth versus Keying Speed

by N1EA on June 13, 2007 Mail this to a friend!

The K factors point out that when conditions are poor, it is beneficial to have harder keying. This is especially true when having co-channel interference. This is why some experience operators find they can copy through QRM with the use of wider (2 or 3 kHz) bandwidth selectivity.

73

David J. Ring, Jr., N1EA
=30=

Bandwidth versus Keying Speed

by K5MC on June 13, 2007 Mail this to a friend!

KE3HO: Your assertion that Tom and I don’t understand power bandwidth and Fourier analysis is absurd.

Jim, based upon some comments that both W8JI and you have made over the past several weeks, there's no question that the two of you don't understand some of the finer points of Fourier analysis. However, rather than re-plowing old ground at this time, let's move on to your data below.

KE3HO: If you would like numbers from my analysis, I can give you the following, which I have calculated directly from the data used to create the graphs in my paper posted on Tom’s web site:

99.1% Power Bandwidth (full width centered at nominal carrier frequency)

30 mS wide 0.5 mS trapezoidal keying 479 Hz

300 mS wide 0.5 mS trapezoidal keying 44 Hz

30 mS wide 5 mS trapezoidal keying 156 Hz

300 mS wide 5 mS trapezoidal keying 29 Hz

30 mS wide raised SIN 5 mS keying 171 Hz

300 mS wide raised SIN 5 mS keying 29 Hz

What were the sending speeds for these various 99.1% power bandwidth values? (I'm assuming you were sending dits at a uniform speed with 50% duty cycle just as I described in my article.)

BTW, it must be a wonderful feeling for folks like W8JI and yourself who can confidently proclaim to all the rest of us that the power bandwidth of a signal is "virtually meaningless for anything but certain FCC compliance tests." In truth, however, your statement tells me that you have read virtually no signal analysis/communication textbooks such as those used everyday in electrical engineering programs around the world. More significantly, however, such a statement tells me that you have a rather parochial view of how communication systems work.

73, K5MC

RE: Bandwidth versus Keying Speed

by AB0WR on June 14, 2007 Mail this to a friend!

ke3ho:
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
<<< What Jim, KE3HO has done is applied the shape of a raised cosine filter in the frequency domain to a square wave in the time domain. That is not going to work right no matter how accurate his calculations are. >>>

Not at all. I have applied the raised SIN to the CW signal in the time domain, then calculated the frequency components of that signal. I did the same thing with the trapezoidal rising and falling edges.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

Jim,

If you believe that to be the representation of a bandwidth limited square wave then you have NOT bothered to go look at any of the web sites I have quoted which will show you what the shape of a bandwidth limited square wave will look like.

Has ANYONE on here bothered to take a look at what a bandwidth limited square wave will look like? Can anyone besides me describe what a square wave lacking its high frequency components will look like?

If you can't even draw a proper waveform then how do you wxpect an FFT to do a proper analysis?

tim ab0wr

RE: Bandwidth versus Keying Speed

by AB0WR on June 14, 2007 Mail this to a friend!

ke3ho:
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
After reading your post with the equations, I see why you made the comment about the raised cosine filter. NOBODY here has advocated applying a raised cosine filter. NOBODY. In my analysis I made no attempt to use a raised cosine filter. Early on in this discussion, Chen and others discussed the mathematical advantage to using a raised sin waveform as the leading and trailing edge of the keying function (in the time domain) because it is a continuous function and its derivative is continuous. There was NEVER any discussion of applying a raised cosine filter in any way.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

Just exactly how do you propose getting that "raised sine" shape *on* a CW keying waveform?

Exactly what system response function will you use to provide that shape? Be specific. Show me the math.

tim ab0wr

RE: Bandwidth versus Keying Speed

by KE3HO on June 14, 2007 Mail this to a friend!

Tim,

The raised SIN function was suggested by Chen as one that has mathematical advantages for the purpose of fourier analysis. As such, I included it in my set of examples. Exactly how would I put that waveform onto the keying waveform of a real CW transmitter? I wouldn't. However, as Chen pointed out, people who design data communications equipment using DSP do exactly that. They calculate optimum waveshapes for a given application and generate them in DSP.

None of my examples were intended to necessarily represent real keying waveforms from real transmitters, but were presented as examples of different shapes that have varying effects on bandwidth.

73 - Jim

RE: Bandwidth versus Keying Speed

by KE3HO on June 14, 2007 Mail this to a friend!

Mickey,

If you were designing a data communications system and were given a channel of specified bandwidth, you would certainly want to calculate the effect of data rate on your power bandwidth so that you could determine your maximum data rate for a given signal to noise ratio and expected data error rate. In THAT context, power bandwidth is extremely useful. However, the context of THIS forum is Amateur radio, and specifically the context of this article is the bandwidth of an Amateur CW transmitter. In THIS context, power bandwidth is virtually meaningless. Here is the effect that you are describing:

Two college professors go to the beach, each with a pail and a teaspoon. One starts at 40th street walking North, the other starts at 80th street walking South. At every third step they each scoop up a teaspoonful of sand and put it into their pail. When they meet at 60th street they dump the sand from their pails into a pile and declare, “We have resculpted the beach!”. One very observant and highly anal FCC employee (who just happens to be vacationing at the beach at 60th street at the time) looks at their pile of sand and agrees with them. Meanwhile, the hundreds of other beach-goers between 40th street and 80th street are NOT MISSING the teaspoonfuls of sand that they have carried away. This is how the change in power bandwidth with keying speed affects the occupied bandwidth of an Amateur CW transmitter.

You have succeeded in showing a mathematical connection between keying speed (a tangible parameter) and “power bandwidth” (an intangible and meaningless parameter in this context). Is there any harm in that? A college professor would say no. Guys like me say yes, because people who may not appreciate the INSIGNIFICANCE of “power bandwidth” in THIS context might assume that “power bandwidth” has some connection with occupied bandwidth and come to the incorrect conclusion that keying speed affects the occupied bandwidth of a CW transmitter.

My conclusions:

1. The power bandwidth of a CW transmitter is affected by keying speed.
2. The power bandwidth of a CW transmitter is affected by the shape of the rising and falling edges of the keying waveform.
3. Power bandwidth, in the context of bandwidth of an Amateur CW transmitter, is virtually meaningless.
4. The occupied bandwidth of an Amateur CW transmitter is unaffected by keying speed.
5. The occupied bandwidth of an Amateur CW transmitter is determined almost exclusively (assuming no other serious design flaws) by the shape of the rising and falling edges of the keying waveform.

You are free to draw your own conclusions. As far as I am concerned, this is concluded. Flame on.

73 to all, and to all a good day.
Jim

RE: Bandwidth versus Keying Speed

by KC8HZM on June 14, 2007 Mail this to a friend!

The theory and the practical part are in complete agreement.

There is a problem of perspective and definition.

This discussion sort of reminds me of the three blind Indians and the elephant. Three blind men encounter an elephant, one grabs a hold of the tusk, another grabs the tail, and the third the trunk. Each one is grabbing the same elephant, but one states that it is smooth, another describes it as hairy, and the third insists that it is thick and wrinkly. I don't mean to imply that anyone here is blind!

The issue of perspective is that fourier analysis is in the frequency domain, and we humans have a hard time thinking like that. We like our time domain, 3 dimensional, linear thinking patterns. In the frequency domain, all signals are there for all time! That means that no matter how long a carrier is sent, all of the spectral components are there for all time. In the time domain, all of those spectral components add up, peaks and nodes, in such ways that reinforce and cancel each other, to yield the resulting wave form in the time domain. This includes both the rising and falling edges, as well as the flat parts between them. This is the same way that the square wave is built up with the addition of appropriate harmonics. The length of the flat Tc between rising and falling edges does indeed contribute inversely to bandwidth!

That is also why it is not necessary for the receiver to “store” energy to time average the power over time. The receiver doesn’t have to “store” or “remember” anything, all spectral components are present all the time! It is not just the rising and falling edges that contribute to bandwidth. The mathematics are completely sound, and correctly applied, it is a matter of reconciling perspective and definition at this point, which more math won’t help us do.

Many times in the real world experiment and measurement don't back theory. In most cases it is because the real world has other variables that complicate the situation, but that doesn't invalidate sound theory. Ask any physicist; getting good experiments and measurements is no small feat!

Imagine trying to describe that the world is spherical and not flat. One person holds up a horizontal ruler and says, "See? The world is flat! The horizon matches my straight ruler. Anyone anywhere in the world can go out and measure this for themselves. The world can't be spherical because I just proved that it isn't by my measurement!" "Intuitive" explanations can be incredibly misleading. Intuitively it seems like the sun revolves around the earth. But once again, a true explanation requires a very clear big picture of math, theory, and all variables. Please, I don't mean to be insulting by comparing the "bandwidth is independent of keying speed" perspective to believing the world is flat or the sun revolves around the earth. I'm trying to make a point about "intuitive" reasoning and experiments or measurements that defy well founded theory.

In my communications course, we used the Couch text and measured the bandwidth of such signals in our labs. In fact I still have the lab write-ups burned to a CD some where; I really should try and find them. It is quite straightforward, easier then showing that the world is not flat.

I think that there are a few key points that help illuminate the confusion here. One, the analysis used exact wave shapes, clearly defined. Real world transmitters don't have precise wave shapes that can be as easily mathematically defined. Plus this is all complicated by the transmitter being non-linear. But even dis-regarding the unknown wave shapes, the effect of keying speed on bandwidth is still very real and can be measured and demonstrated.

Here are some things I believe everyone agrees on:

"Keyclick bandwidth" (which hasn’t been precisely defined yet) is not primarily dependent on keying speed. (Note the use of the word “chiefly” elsewhere) That is what W8JI is most concerned with, as that is the primary consideration in real world operating. It can be significantly larger then the occupied bandwidth that a proper CW signal would occupy. Plus, the key click bandwidth is so much easier to experience, by audio and by visual means. Ears hear keyclick bandwidth, spectrum analyzer sees this keyclick bandwidth. At human operator speeds, occupied bandwidth of a proper signal should never be too wide, but the keyclick bandwidth of a poor signal at *any* speed is objectionable!

If I understand K5MC, he agrees that changing keying speeds doesn't reduce keyclick bandwidth to acceptable levels. I believe everyone will agree to this.

K5MC is correct that changing keying speeds does affect occupied bandwidth. This is true for all signals, from square signals to properly shaped CW signals.

If all the underlying assumptions are understood and applied, there is no tension between these two statements above.

In the real world of CW operating, key-click bandwidth is more important, simply because it is so disruptive. At human operator speeds, a proper CW signal without key-clicks should never be too wide to be disruptive. W8JI should be applauded for his work on reducing this annoying key-click bandwidth.

But from a communications standpoint, a good understanding of occupied bandwidth is important because of the underlying theory, from Fourier Analysis, to Shannon's equations, and beyond. It applies to all signals, not just CW.

It has been a very fascinating discussion, I just can't help but throw my thoughts in the mix also. Thanks to all who contributed!

Marten
KC8HZM

RE: Bandwidth versus Keying Speed

by N1EA on June 14, 2007 Mail this to a friend!

Martin,

You write very beautifully and clearly.

Is there any software program that can take a certain waveform with (a certain contstant value = n) ms rise and decay time on each end, and vary the central portion from zero (making the pulse equal to 2n), to, let's say, 20 seconds, and display the frequency width?

A constant carrier has very little bandwidth unless it has a small bit of hum, but as modulation (changes in the carrier) is applied - such as is done by insertation of audio modulation be various schemes - the earliest to be done with continuous waves was the "chopper" which was a very fast switching on and off by contacts on a motor which switched at an audio rate - usually between 400 and 800 "chops" per second.

This pulse made the CW signal wider and impressed it with modulation so that it could be detected by crystal (diode) detection. Magnetic and coherers could detect the presence of CW but were sluggish and as improvements in magnetic detection came about, the glass envelope incandescent filament and plate diode (valve or tube) was coming into being.

The ITU/CCITT k factor points out that with fading circuits a wider (or stronger) signal is needed. A very gradual rise and decayed bell-sounding CW transmitter - while a joy to copy when signals are quite strong and not fading, is uncopyable at low signal strengths and expecially with fading and phase distortion, while a transmitter at the same location with identical power, antenna (and direction) will result in the same S meter reading, but will be copyable.

I know I am talking about several properties - but I wanted to mention them both in one email. The first mention of the "chopper" shows that when the pulse rate per second is increased the bandwidth is increased as actual modulation is heard on the signal which would not be produced if the carrier was identical to keyed (non pulsed or "chopped") CW.

Also if you start to send with a bell shaped CW transmitter, you can't copy it above about 33 wpm, but you can copy a more square waved transmitter up past twice that amount. The reason: The bandwidth is restricted by the shape of the pulse. The data is flowing too fast for the data. These things were known in use of submarine cable also where because of capacitance on the long underwater cables, there was an upper limit to make and break and current reversal modulation schemes. Underwater cables had very limited bandwidth! This improved with vacuum tube repeaters which cut down on the extremely long rise and decay times by shortening the run the signals had to travel. These repeaters basically improved the high frequency response of the underwater transmission line - which could send from DC to only a few wpm of morse unaided. Just prior to the installation of the French Telegraph Company (FTC) Cable in Duxbury, MA (about a mile from me) in 1870 (first NA to EU cable) the maximum speed was 2 wpm. This was improved on the FTC cable by "siphon receivers" and later time division multiplex (TDM) transmission of Emile Baudot with his five level code.

Nyquist Interval:

"If the essential frequency range is limited to B cycles per second, 2B was given by Nyquist as the maximum number of code elements per second that could be unambiguously resolved, assuming the peak interference is less half a quantum step. This rate is generally referred to as signaling at the Nyquist rate and 1/(2B) has been termed a Nyquist interval."

As the number of pulses in a time period goes up, the bandwidth goes up. As the sharpness of the pulse goes up, the bandwidth goes up. There exists a relation between the two such that the bandwidth can be restricted by factors and a code speed of a certain maximum can not be exceeded. In the 1970s, the U.S. Navy's Cutter Radio (Maine) station NAA was unable to send faster than about 16 wpm due to bandwidth problems with the antenna (it was a LF 1.5 Megawatt transmitter around 20 kHz - the bandwidth rose with keying speed - the wave shape being identical - but when 1 wpm was increased the SWR would shut down the transmitters as the bandwidth of the antenna was exceeded.

Thanks for the nice responses to read.

73

David Ring
N1EA

=30=

Bandwidth versus Keying Speed

by W1YW on June 14, 2007 Mail this to a friend!

Mickey,

Thanks for not giving up on us. I found it refreshing to actually read something interesting here on qrz, rather than the usual indication of how poorly the ham population is informed.

Fortunately, on this thread, we've had some superb engineers make some excellent comments. My general sense is that they relate to issues that do not address the main thesis of your article, but are interesting in themselves. The hang-up on wording rather than concept is regrettable, however.

Can we have MORE (interesting stuff) like this on qrz, please?

I like being made to think and learn. That's why I got into ham radio.

73 to all,
Chip W1YW

RE: Bandwidth versus Keying Speed

by W8JI on June 14, 2007 Mail this to a friend!

Marten,

I agree with most of what you say except occupied bandwidth.

Keyclick bandwidth and occupied bandwidth are essentially the same, except occupied BW is the point where 99% of the power (normally) is contained. Certainly there is a point beyond that frequency bandwidth where clicks can be heard.

Now what the FCC actually says, and it is very clear, is a CW transmitter cannot cause harmful interference to signals on another frequency through keyclicks. This is the technical limit, not occupied bandwidth (99% power) or "power bandwidth".

Power bandwidth (average power over very long time) is really very different and has no useful application in the system we use. I have been trying to drive that point home.

Occupied BW is normally measured by taking the peak envelope power contained in a certain channel width and finding the points where that power, when measured over a significantly long time to capture all modulation product power peaks, drops to 99% of the power inside upper and lower frequency limits.

This is exactly what my Agilent Analyzer does, and the results are accepted by the FCC.

I can look at ANY transmitter or source, even a continuous oscillator driving a linear modulator, and the rise and fall times almost exclusively control the occupied bandwidth.

Let's not confuse power bandwidth, which really has no use in this type of communications system, with the occupied bandwidth.

You can see occupied bandwidth measurements of two transmitters at:

http://www.w8ji.com/occupied_bw_of_cw.htm

73 Tom

RE: Bandwidth versus Keying Speed

by W8JI on June 14, 2007 Mail this to a friend!

By the way, The ARRL has re-written and corrected some earlier incorrect statements in the section on CW and bandwidth of CW.

People keep referring to earlier erroneous text to support their position, but the newer Handbooks have the correct information.

73 Tom

Bandwidth versus Keying Speed

by K5MC on June 14, 2007 Mail this to a friend!

KC8HZM: The theory and the practical part are in complete agreement. There is a problem of perspective and definition.

Marten, I really appreciate your comments at this time. I can't help but say, however, that I wish you had jumped into this thread about two weeks ago! (BTW, we're using Lathi's textbook at LA Tech for our senior-level communications course, but I like Couch's book very much.)

In my article's summary I tried to point out to everyone that the concept of occupied bandwidth (that is, the FCC's definition of occupied bandwidth, which is equivalent to the 99% power bandwidth) doesn't say that the keyclicks are reduced in strength when the sending speed is decreased. Perhaps I should have been more direct in how I worded that relationship in my article. There's no question that one must properly shape the turn-on and turn-off characteristics of the keying envelope to avoid excessive keyclicks.

W1YW: The hang-up on wording rather than concept is regrettable, however.

Like Chip, I truly regret the "hang-up" by the various posters on the wording rather than the concept. To the degree that I've added confusion by my posted comments, I am sorry. I also apologize for the occasional sarcasm in my posted comments. (I do admit to some frustration at times during this thread in trying to convey some of the concepts!)

73, K5MC

RE: Bandwidth versus Keying Speed

by KE3HO on June 14, 2007 Mail this to a friend!

Mickey,

I want to apologize for the tone of my last post. Rereading it, I find that it was rude with more than a little arrogance thrown in. Please accept my apology.

73 - Jim

Bandwidth versus Keying Speed

by K5MC on June 14, 2007 Mail this to a friend!

N1EA: In the 1970s, the U.S. Navy's Cutter Radio (Maine) station NAA was unable to send faster than about 16 wpm due to bandwidth problems with the antenna (it was a LF 1.5 Megawatt transmitter around 20 kHz - the bandwidth rose with keying speed - the wave shape being identical - but when 1 wpm was increased the SWR would shut down the transmitters as the bandwidth of the antenna was exceeded.

David, thanks very much for all of your comments. Your story about NAA is particularly interesting to me.

KE3HO: I want to apologize for the tone of my last post. Rereading it, I find that it was rude with more than a little arrogance thrown in. Please accept my apology.

Thanks very much, Jim. I know some of my comments appeared arrogant at times.

This thread will soon disappear from the eham homepage. In what should be my last posted comments, I want to again thank everyone who submitted comments to my article. It's been a very interesting experience for me!

73, K5MC

RE: Bandwidth versus Keying Speed

by W8JI on June 15, 2007 Mail this to a friend!

As I understand from a good friend who helped design VLF transmitters at RCA, NAA and other VLF transmitters use a slow FSK rather than off-on keying.

Years ago he told me on off keying (like we call CW) was a real problem for the antennas and transmitters because of the bandwidth required to have reasonable rise and fall times. Because of that everything was FSK.

This seems to be verified in multiple places like:

http://coldwar-c4i.net/VLF/design.html

and

http://en.wikipedia.org/wiki/Very_low_frequency

73 Tom

RE: Bandwidth versus Keying Speed

by AB0WR on June 15, 2007 Mail this to a friend!

KE3HO:
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
The raised SIN function was suggested by Chen as one that has mathematical advantages for the purpose of fourier analysis. As such, I included it in my set of examples. Exactly how would I put that waveform onto the keying waveform of a real CW transmitter? I wouldn't. However, as Chen pointed out, people who design data communications equipment using DSP do exactly that. They calculate optimum waveshapes for a given application and generate them in DSP.

None of my examples were intended to necessarily represent real keying waveforms from real transmitters, but were presented as examples of different shapes that have varying effects on bandwidth.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

Jim,

Go look at these pages for a description of a raised cosine and raised root cosine filter.

http://www.filter-solutions.com/raised.html
http://www.filter-solutions.com/data.html
http://www.iowegian.com/fir/tutor/rcfilt.htm
http://www.dspguru.com/info/faqs/rcform.htm

I think that what you will find is that you are doing an FFT on a shape that is a *Frequency Domain* filter shape, not necessarily a time domain filter shape or even the time domain result of a filter response multiplied by an input waveform.

We need to be very careful what we are talking about here. Saying the modulation envelope should look like a raised cosine is a very different thing than saying a raised cosine filter should be applied to the CW keying waveform. A bandwidth limited CW keying waveform will take on the appearance of a square wave with a limited number of harmonics. Any of the web sites I listed earlier will show you what a square wave with limited harmonics will look like. They won't be exactly the same since no filter is perfect and the upper harmonics will actually be there in the bandwidth limited square wave only limited in magnitude further than the 1/n factor would give.

The only way I can see to get an actual raised cosine shape on the keying waveform (and/or modulation waveform) is to do it with an input/output amplitude relationship that changes over time (i.e. the gain of an amplifier stage) somewhere in the black box known as the transmitter. Whenever you start doing this, however, the result will probably be a non-linear stage resulting in all kind of intermod-products.

For instance, take a look at the example transistor characteristic curves shown at http://www.st-andrews.ac.uk/~jcgl/Scots_Guide/info/comp/active/BiPolar/bpcur.html.
With a completely open emitter on the transistor you have an operating point at the origin, zero base current and zero collector current. When you then ground the emitter lead and a capacitor is involved in the bias circuits for the emitter and base you do NOT get an initial linear transistion up and down a load line, for a period of time you follow the characteristic up the non-linear portion at the very left of the curve until a constant load point is reached after the Vce, Ib, and Ic have stabilized.

Again, let's be very careful with our terms. Transitory key clicks, which is what most people term as actual key clicks, are almost certainly generated by this kind of phenomena. Non-linearities in the system transfer function can cause mixing of ALL the harmonics in the square wave thus generating keyclicks at frequencies FAR separated from the actual operating frequency. One way to minimize this is to limit the number of harmonics in the square wave in order to limit the number of mixing products. The other way is to minimize the non-linearities in the system transfer function.

Much more attention has been paid to the former than to the latter.

This is *totally* separate from close-in "key clicks" that aren't really key clicks at all but actual interference from the harmonics of the square wave that exist throughout the keying pulse.

Take a look at my oscilloscope displaying the output from my 751a at www.photobucket.com. Type in ab0wr as your search term and then when asked if you want to see the ab0wr album, click on the place indicated.

You will see an output waveform that has an initial shape of a gain function that is controlled by a *decaying* RC time constant, i.e. a capacitor holding the stage gain down to cutoff and then decaying quickly to allow the gain to build quickly and then slowly tapering off to the final operating point.

This could also be explained by being the shape of a semiconductor junction at low voltages where the characteristic is described as i= ae + be^2, where i is the current through the junction and e is the terminal voltage. This is what would be expected at the start up of an oscillator as the base-emitter voltage builds up from initially from zero.

Both of these characteristics would explain a short burst of transitory key clicks at both the beginning and end of a CW pulse.

I truly believe that you are going to find the actual answer here to be much more complicated than the old wives tail that the harmonics of a square wave only exist during the rise and fall time of the square wave.

Remember, for a linear modulation scheme, you can use a stage where the gain is as follows:
Gain= K x fin(t).

If you then put fin2(t) = f(wt) = cos(wt) as one input and fin(t) as the other you get
fout(t) = Gcos(wt) = Kfin(t)cos(wt)

If K is a time dependent function itself, especially a non-linear one, you will not only get intermod products but a modulation envelope that is modulated by the Gain function as well as by the input CW keying function. If,during the very beginning of the pulse, the base current i=(ae+be^2) you would get get an output voltage that would follow the same shape scaled by some factor "L".
fout(t) = L(ae+be^2)fin(t)cos(wt)

Not an easy situation to analyze, certainly. And the "rise time" on the output modulation envelope wouldn't even be totally due to a bandwidth limited square wave. The time dependent gain function would be part of the shape as well. With an e^2 term multiplying both the fin(t) and the cos(wt) functions you will get significant transient intermod products.

This seems to me to be a much better explanation of why you get transient key clicks than saying square wave harmonics only exist during the rise and fall times.

tim ab0wr

RE: Bandwidth versus Keying Speed

by KC8HZM on June 15, 2007 Mail this to a friend!

N1EA:
<quote>
Martin,

You write very beautifully and clearly.

Is there any software program that can take a certain waveform with (a certain contstant value = n) ms rise and decay time on each end, and vary the central portion from zero (making the pulse equal to 2n), to, let's say, 20 seconds, and display the frequency width?
</quote>

Thank you David! There are some programs out there like Iowegian's Scope DSP ( http://www.iowegian.com/scopedsp.htm ) that are fun to play with and could do something like that. It would be possible to write an excel script that could generate wave forms of either straight lines or some other shape, and change the dit length. (basically doing numerically what Mickey has done mathematically) I was hoping to find the lab write-ups from my communications course because those were measurements made with a spectrum analyzer on some real equipment, but it appears most of my college material is now buried in my attic!

Interesting historical reading about the choppers, underwater cables, and NAA. Fascinating.

I echo Chip's comments, thank you Mickey and everyone! This has been very refreshing indeed, a quality article and an engaging discussion with lively and respectful contributions. Lets have more!

W1YW:
<quote>
I like being made to think and learn. That's why I got into ham radio.
</quote>

Same here!

W8JI:
<quote>
Now what the FCC actually says, and it is very clear, is a CW transmitter cannot cause harmful interference to signals on another frequency through keyclicks. This is the technical limit, not occupied bandwidth (99% power) or "power bandwidth".

Power bandwidth (average power over very long time) is really very different and has no useful application in the system we use. I have been trying to drive that point home.
</quote>

Tom, I'll agree that there are different ways to define bandwidth. In a hobby like amateur radio where we have operators with widely varying levels of experience, it is important to have understandings and definitions that support "good amateur radio practice", technical communication skills, and understanding of the theory behind it all. Certainly key-clicks are not good amateur radio practice! In your extensive experience, you have focused a lot of effort and helped many hams to become better operators by reducing the key-clicks of their transmitters. Thank you, our airwaves are in better shape for it. Now, we can work on creating clearer definitions.

Mickey, I just happened to stumble across this article, I actually rarely read eham.net, but if this is a sample of what might come, I'll have to come back more often!

Have a good weekend everyone,

Marten

Email Subscription
You are not subscribed to discussions on this article.

Subscribe!
My Subscriptions
Subscriptions Help

Other Recent Articles

Student Sends MIT Letter to Space:

Amateur Radio Club Talks to Hams Worldwide on Centennial:

New Communication Exhibit Helps Kids Get the Message:

Transmission of Images - No Internet, Satellite, Cable, or Cells Needed!

Deltona Youth Loves to Ham It Up on the Radio: