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Where Does 468 Come From?

from Ward Silver - N0AX on May 4, 2010
View comments about this article!

“Where Does 468 Come From?”

We’ve all seen this number over and over again – the “magic number” that gives us the length of a half-wavelength dipole in feet from the dipole’s resonant frequency: L = 468/f. In free-space the wavelength in feet is 492/f, but a practical half-wavelength antenna is shorter so the constant is smaller. The number 468 is on the license exams and in the literature. It’s been there ever since I started reading about ham radio in the mid-1960s. It’s a pillar of amateur antenna theory. Every ham is expected to memorize it. And it’s wrong.

It would be more accurate to say that it’s rarely correct. There are certain instances where it’s close, but using it often leads to wasted wire. The usual instructions to a new ham are, “Calculate how much wire you need using 468/f and then add a couple of feet.” What that really means is the value 468 is too small and we compensate for the error by “adding a couple of feet”. If 468 isn’t right, why do we use it? Answering that question requires a trip along the paths of history.

Recently, I had the opportunity to spend a few days at ARRL Headquarters to plan upcoming writing and editing projects. The ARRL has a great Technical Library with every edition of ARRL publications and technical publications going back decades. (If you ever get close to Connecticut, it’s well worth dropping in on the ARRL for a tour!) I had some time one afternoon and decided to find out when and how the number 468 first appeared in the ham literature.

My first stop was the ARRL Antenna Book’s initial edition in 1939. Sure enough, on page 13 in the chapter on “Antenna Properties”, the familiar formula 468/f appears. The Antenna Book states that the “end effect” due to the attachment of insulators at the ends of the antenna results in the approximately 5% reduction in length from the free-space 492/f to 468/f. The text goes on to state that the percentage “varies slightly with different installations”, but doesn’t say how, nor is a citation provided to identify how the value of 468 was obtained.

Since it is unlikely that the value of 468 appeared in the Antenna Book without any “prior art”, I next turned to the ARRL Handbook’s first edition in 1926. That turned out to be a dry hole – no formula for antenna length and nothing in 1927 or 1928 either. Then, in the 1929 edition’s “Antennas” chapter on page 128, I hit pay dirt! The text defines natural wavelength as the highest wavelength (the lowest frequency) at which the Hertz antenna (a half-wavelength dipole) will resonate. It is stated that “The natural wavelength of the wire…will be its length in meters multiplied by 2.1” Hmmm…2.1 is 5% longer than would be the free-space value of 2. (Remember, the text is discussing wavelength, not frequency.) Farther down the page I saw, “Speaking in terms of feet, the natural wavelength of the antenna will be its length in feet divided by 1.56.” That equation translates to L = (300 x 1.56)/f and 300 x 1.56 is 468! Here were the headwaters of the mighty River 468!

Still, no background for the correction was given. Where does the use of a correction factor originate? Back to the stacks! Did I really want to go through all of the QST magazines until I found my answer? Well, not really, but inspiration struck in the form of the online QST archives. I logged into the ARRL Web site, brought up the QST archive search page, and…hit another roadblock. I couldn’t very well search for “468” because it was unlikely to be a keyword. “Dipole” would return hundreds of hits. Then I realized that in the early days, a half-wavelength dipole would have been referred to as a “Hertz antenna” or “Hertzian antenna”. I entered the former and scrolled down to the very earliest entries.

Heinrich HertzThe oldest article on Hertz antennas was in the July 1925 issue by 9BXQ and titled “The Hertz Antenna at 20 and 40 Meters” but it didn’t discuss a formula for length. The next oldest article, October 1926’s “The Length of the Hertz Antenna” by G. William Lang, turned out to be what I was looking for. In the article, Lang (who was apparently not a ham, but worked in the Dept of Radio Operations for Radio Station WBZ in Boston) set up some Hertz antennas at amateur station 1KA and also measured antennas at station 1CK and 1KF. He used an oscillator and a wavemeter to determine the frequency at which the antenna resonated then measured the entire antenna - tip-to-tip, including the counterpoise. A table of correction values was derived, with the free-space wavelength in meters multiplied by an average value of 1.46 to get the antenna’s resonant wavelength in feet. This corresponds to an equation of L = 438/f. This is the first suggestion that the actual resonant length of a practical amateur antenna can be predicted by using a correction factor to a free-space wavelength.

The early experiments of 1925 and 1926 took place on or near 40 meters. In those days, CW operation on what we now call the “low bands” of 80 and 40 meters was the norm. At these wavelengths, a half-wavelength dipole was of a reasonable length. It could be made of ordinary copper wire, probably #8 to #14 AWG, and installed in the back yard at heights of 20 to 40 feet. For these antennas, 1/8th to 1/4th wavelengths above ground, a value of 468 is about right, resulting in the equation printed in the ARRL Handbook in 1929.

In truth, many variables affect the resonant frequency of a half-wavelength dipole, the two primary factors being the length-to-diameter ratio of the antenna conductor and most strongly, the antenna’s height above ground. These can combine to change the actual correction factor quite a bit! (Insulation can also affect an antenna’s electrical length.) In my November 2009 QST column, “Hands-On Radio: Antenna Height”, I modeled a typical 20 meter dipole made of #12 AWG un-insulated wire at heights from 1/8th to 2 wavelengths over realistic ground and calculated the correction factor at each height. It varied from 466 to 481 over that range! Clearly, using 468/f would lead to an antenna being too short most of the time.

If 468 is too small and rarely correct, what should you do? Realistically, you should expect to trim your dipole to get the resonant frequency you want. Instead of being frustrated that the calculations aren’t exact, learn to adjust the antenna’s length efficiently by using an instrument such as an antenna analyzer. Start with an estimated value based on a more realistic formula such as 490/f that results in a small amount of extra wire for attaching insulators. During tuning, twist the wire connections together or use clamps, then raise the antenna into position and measure. When it’s right, only then solder and weatherproof the connections. Recognize that every antenna’s circumstances are slightly different – height, ground conductivity, thickness of wire, nearby conductors, and so forth.

Another lesson to learn from this exploration is to realize that “magic numbers” in formulas have often been determined through experimentation under specific circumstances. As such, they likely depend on a variety of factors that you may not be able to replicate. They will only approximate what you actually encounter. If the assumptions behind the value are given – you can use that information by comparing it to your situation. If the assumptions are not known – you should allow for variations or try to find a more accurate model representative of your own circumstances.

I hope you’ve enjoyed reading about this journey as much as I enjoyed taking it, opening the covers of books nearly 80 years old and mapping the stream of knowledge back to its sources - finding there the footprints of wireless pioneers that set ham radio on the course we travel today.



Member Comments:
This article has expired. No more comments may be added.
 
Where Does 468 Come From?  
by K6SI on May 4, 2010 Mail this to a friend!
Nice 468-CSI investigation.
 
Where Does 468 Come From?  
by K9ZF on May 4, 2010 Mail this to a friend!
Fascinating piece of history Ward! Thanks for sharing.


73
Dan
--
Amateur Radio Emergency Service, Clark County Indiana. EM78el
K9ZF /R no budget Rover ***QRP-l #1269 Check out the Rover Resource Page at:
<http://www.qsl.net/n9rla> List Administrator for: InHam+grid-loc+ham-books
Ask me how to join the Indiana Ham Mailing list!

 
RE: Where Does 468 Come From?  
by K5DVW on May 4, 2010 Mail this to a friend!
Heck, I use 300/f as the full freespace wavelength in meters since we call all our bands by their wavelength in meters!
 
RE: Where Does 468 Come From?  
by AA4PB on May 4, 2010 Mail this to a friend!
Here's a procedure that I use for "trimming" a dipole that only requires one cut:

1) Using L = 468 / F, cut the wire a bit long but then measure its actual length ACCURATELY.

2) Raise the dipole into place and measure its resonant frequency with an antenna analyzer or by finding minimum SWR.

3) Using the formula C = L * F, calculate the value of C, a new constant in lieu of 468. L is your accurate measured length and F is the measured resonant frequency.

4) Using the formula L = C / F, calculate the real length for the desired frequency. Use your real value for C (which should be in the vicinity of 468) and the desired resonant frequency for F.

5) Drop the antenna and accurately cut it to the new length. Raise it back into the same position and you should find resonance very close to your desired frequency.

By the way, this process works even if you accidentally make the antenna a little short to start with. You then have to lengthen the antenna instead of shortening it, which of course is a bit more difficult.

I find this much quicker than the traditional method of lowering the antenna, trimming a little from each end, raising the antenna, finding the new resonant frequency, lowering the antenna, trimming off a bit more, raising the antenna..... etc, etc, etc.
 
Where Does 468 Come From?  
by KZ1X on May 4, 2010 Mail this to a friend!
I have often been thankful that we have the 17 and 15 meter bands.

These bands have been very useful to me over the years, most frequently after I built antennas for 20 meters.

;-)

 
RE: Where Does 468 Come From?  
by AA4PB on May 4, 2010 Mail this to a friend!
Measure twice, cut once :-)
 
Where Does 468 Come From?  
by KL7AJ on May 4, 2010 Mail this to a friend!
There's a profound lesson in human nature here, far beyond the scope of this investigation...a very good one, by the way, Ward...our willingness to accept ANY information that comes from an "authority". It is for this very reason that I wrote "SWR Meters make you Stupid"!

I might add, however that the correction factor actually comes out almost exactly right for most A.M. broadcast antennas, which are typically a lot fatter than wire antennas. NEC modeling will readily show the foreshortening of any antenna as it becomes fatter. This is all hashed together as "end effect" but actually is a "capacitance everywhere" effect.

Does anyone here know why American gauge railroad uses a 4'6" spacing? Another very similar story. :)

Eric
 
RE: Where Does 468 Come From?  
by KB2VUQ on May 4, 2010 Mail this to a friend!
But I cut it twice and it's still too short!
 
Where Does 468 Come From?  
by W5SO on May 4, 2010 Mail this to a friend!
Good job Ward!
 
RE: Where Does 468 Come From?  
by K8QV on May 4, 2010 Mail this to a friend!
Measure once, curse twice.
 
RE: Where Does 468 Come From?  
by KG6MZS on May 4, 2010 Mail this to a friend!
AA4PB Bob Wrote:

>>>Here's a procedure that I use for "trimming" a dipole that only requires one cut: <<<

Great! I always knew that this could be done but didn't know how to mathematically articulate the idea. Between this and the author's suggestion I am set.

Thank you guys for a great contribution!

73 de Eric, KG6MZS
 
RE: Where Does 468 Come From?  
by KG6MZS on May 4, 2010 Mail this to a friend!
KL7AJ Eric wrote:

>>>I might add, however that the correction factor actually comes out almost exactly right for most A.M. broadcast antennas, which are typically a lot fatter than wire antennas.<<<

Boy, did I ever learn this lesson in a hurry just yesterday. I built a 10m rotatable dipole using 1/2" copper pipe. As you might guess I cut it way too short.

73 de Eric, KG6MZS
 
RE: Where Does 468 Come From?  
by WS4E on May 4, 2010 Mail this to a friend!
>Here's a procedure that I use for "trimming" a dipole that only requires one cut:


Thanks for great, easy to understand lesson in technique. I am going to save this one to try on the carolina windom I am building right now.
 
RE: Where Does 468 Come From?  
by K7PEH on May 4, 2010 Mail this to a friend!
NOAX -- Great Article -- reading it was a nice morning break from work.

But, that photo -- did you realize that it looks a little like you.
 
RE: Where Does 468 Come From?  
by N1DVJ on May 4, 2010 Mail this to a friend!
At least with copper pipe you can easily sweat solder on a bit more...
 
RE: Where Does 468 Come From?  
by N8AUC on May 4, 2010 Mail this to a friend!
<Does anyone here know why American gauge railroad uses a 4'6" spacing? Another very similar story.>


The standard railway gauge in the United States is actually 4' 8 1/2". But yes, it's called the Stephenson gauge. Named after an Englishman named George Stephenson, who was one of the first to put a steam engine on a mining cart.

Prior to the Civil War, there were many different gauges used in the US, ranging from 3' to 6', but the old Stephenson gauge was the most common. During the Civil War, thousands of miles of new track was laid in order to move military supplies. Every time the track gauge changed, the trains had to be unloaded and reloaded. This was expensive, and time consuming.

For this reason, the US Congress decided that all transcontinental railways would be built to the 4' 8 1/2" standard.

Interesting story at:
http://www.truthorfiction.com/rumors/r/railwidth.htm

 
RE: Where Does 468 Come From?  
by WI7B on May 4, 2010 Mail this to a friend!

Ward N0AX,

Thanks for the historically insightful article!

73,

--* Ken
 
Where Does 468 Come From?  
by WD8OQX on May 4, 2010 Mail this to a friend!
And here I thought there were "Pee-on Monkey's" in the back of taco bell making up all these formulas!

Good research!!!

73 - Tim
 
RE: Where Does 468 Come From?  
by K7DAA on May 4, 2010 Mail this to a friend!
Ward:

Thanks very much for the well-written and -researched article. Very informative, historically fun, and made me smile. I'll think of this every time I go out and cut a new dipole or loop, hoping that, just once in my life, I'll get it right on the first cut. Don't know if I'll live that long, though!

73,

Dave - K7DAA
 
RE: Where Does 468 Come From?  
by KB5ZXM on May 5, 2010 Mail this to a friend!
all this time? I had thought it was based on the Roman road and cart paths for war chariots, and a comfortable distance for men marching double file ?
 
RE: Where Does 468 Come From?  
by KI4GSV on May 5, 2010 Mail this to a friend!
Mr. Ward,

Thank you for writing such a superb piece and your willingness to share it.

73, Fair Winds

Bill
 
RE: Where Does 468 Come From?  
by N4KC on May 5, 2010 Mail this to a friend!
Ward, your healthy curiosity and willingness to write about its results has once again paid off! That's one reason I enjoy your writing and the contest newsletter so much. Like others, I have often wondered about the magical "468," but just not enough (energy wanes with old age!) to do the research. Thank you for saving us lazy guys the trouble.

One point this article shows us again: we should never talk about "antennas." We should talk about "antenna systems." Unless we happen to live and operate in a vacuum with no other structures or heavenly bodies within a great distance, there is always much more to an "antenna" than a couple of pieces of wire, some insulators, and a transmission line.

And on commercial radio stations...I have never seen an AM station, no matter how carefully the tower/antenna was designed to frequency...long, short, fat...that did not have some sort of matching network between transmitter and antenna. Resonant? Yes, but only after some reactance was cranked in!

Sure it is easy to trim a few inches from that dipole, but move a few kilohertz either way from that resonant frequency...

Don Keith N4KC
www.n4kc.com
www.donkeith.com
www.n4kc.blogspot.com
 
RE: Where Does 468 Come From?  
by AA4PB on May 5, 2010 Mail this to a friend!
To expand on the excellent article a bit further:

The number 468 is actually based on the speed of light and other electromagnetic radiation in a vacuum which is 300,000,000 meters per second. The length of a wavelength is the speed divided by the frequency (in Hz) so:

L(m) = 300,000,000 / F(hz)

1 MHz = 1,000,000 Hz so L(m) = 300 / F(mhz)

Since we are looking for a half wavelength divide by 2 and the formula becomes L(m) = 150 / F(mhz)

Since 1 meter = 3.2808399 feet multiply 150 by that to arrive at L(f) = 492.125985 / F(mhz)

The speed of RF in a wire is about 5% slower than in a vacuum so multiply 492.125985 x 0.95 to arrive at 467.5196858. Rounding to a whole number, the value becomes 468 so:

L(f) = 468 / F(mhz)
 
Where Does 468 Come From?  
by G0GQK on May 5, 2010 Mail this to a friend!
Hello Ward,

Many years ago, when I could afford to buy QST magazine, I live in the UK, and postal costs are expensive these days, I used to buy QST. Anyway, in one of the issues sometime during the 90's there was an article about the subject you are discussing. One would have thought that the QST editors or whoever is involved with these technical matters would have amended their formula after reading the article.

Like Kurt N.Sturba wrote in one of his books regarding amateur radio fallacies, authors just copy the "standard" facts and formulae from one book to another and have been doing this for years, without ever checking that the "facts" are correct. People read books and quote what they've read,and one of these "facts" was that a wire antenna doesn't radiate as well if the antenna is brought into resonance by using an ATU.

Anyway, write these into your book of facts

For a dipole over very good earth 470.8/ F. Mhz

For a dipole over average earth 472.7/ F. Mhz

For a dipole over poor earth 473.9/ F. Mhz

Try it, and then tell the ARRL its in their archives

Mel G0GQK
 
RE: Where Does 468 Come From?  
by AA4PB on May 5, 2010 Mail this to a friend!
Like I said, the formula is based on the speed of light. It is not wrong, it just doesn't account for all the possible variables in a real world antenna installation. You will never find a formula that will account for all the possible variables and put you exactly on frequency every time. You will always wind up "tuning" the antenna in place. Its just like many critical circuits in our transceivers. You always find a variable capacitor or a slug in the coil - something you can use to "tune" it precisely because you can't come up with a formula to account for all the variables that can change from one radio to the next. Tuning is a fact of life :-)


 
RE: Where Does 468 Come From?  
by W1XZ on May 5, 2010 Mail this to a friend!
AA4PB is 100% correct. Good job.
 
Where Does 468 Come From?  
by N0AX on May 5, 2010 Mail this to a friend!
Thanks for the many kind words. I'm glad the article was found useful - it's the kind of subject that comes up now and then, "Where does ... come from?" Now we all know that the constant...isn't.

As to whether I look like der Herr Professor...I suppose that's not too bad :-)

73, Ward N0AX
 
RE: Where Does 468 Come From?  
by WI7B on May 5, 2010 Mail this to a friend!

N0AX is correct. Don't compliment him on an excellent article and then say he's wrong..that 468 is a significant number based on the speed of radio energy in a copper wire.

468 is not signficant. It's unduly approximate. Either radio energy travels at c in free-space, or it travels at something less than c in constrained-space.

A bare 22-gauge copper wire lying on the ground is one form of constraint. A bare 16-gauge copper wire dangling vertically is a completely different form of constraint. An insulated 24-gauge copper wire hanging above the ground is even a more radical constraint. Each on of these constraints varies the speed with which radio energy travels and depend on their environment and the frequency of radio energy.

In the real world, 468 is the crudest form of approximation. I think that's the point of the article. It's a number based on a simple-minded approach, not on rigor.

73,

---* Ken

 
Where Does 468 Come From?  
by K0IC on May 5, 2010 Mail this to a friend!
As a former broadcast engineer I found out it does not take much variation to mess up matching with broadcast antennas. My solution is to use a tuner because ice on the system can make chaos too.
 
Where Does 468 Come From?  
by HAMILTON_EX_W8GX on May 5, 2010 Mail this to a friend!
Great article Ward!!
 
RE: Where Does 468 Come From?  
by AA4PB on May 6, 2010 Mail this to a friend!
If you didn't have 468, what would you use to make the initial cut on a dipole? How would you know whether to make a 20M dipole 33 feet or 60 feet long? What if I want a dipole for 18.925 MHz? There is no magic number that works exactly in all cases, BUT any number that works will be withing a few percent of 468.

I say 468 is a very useful number, one that every ham should know. What the article correctly points out is that it is only an approximation and the dipole is quite likely to require adjusting the length when installed in its environment. Like many other things in electronics, 468 is a tool. It's a hammer, not a micrometer :-)

 
RE: Where Does 468 Come From?  
by W5ESE on May 6, 2010 Mail this to a friend!
Excellent article, Ward.

I enjoy mucking about in the QST archives, too!

Really appreciate the ARRL making the files available
online.

73
Scott W5ESE
 
RE: Where Does 468 Come From?  
by N1LO on May 6, 2010 Mail this to a friend!
Unbelievable!

468 is *not* wrong! It's a good, practical number as a *starting point*.

C'mon Ward! Just as AA4PB keeps pointing out, the wire length is shorter simply because the velocity factor of *average* bare wire is around 0.95.

RF travels more slowly through various conductors than it does through air.

That's all.

There's no mystery here
...<imitating Bill Nye> "It's SCIENCE!"

Have you ever noticed that when you build an antenna from insulated wire, that it has to be even shorter?
Objects on and around the conductor slow down the RF even more (an arguably simplistic explanation).

The 'electrical length' of a conductor, in feet, for one full wavelength, would be:

1/2 wavelength = (984/f)*Vf

Where f is in MHz and Vf is the velocity factor.
Some typical velocity factors are:
1 air/free space
0.95 bare copper wire
0.93 insulated copper wire
0.91 window line
0.88 coax with foam dielectric
0.66 coax with solid dielectric.

To roll it all into one convenient number for a half wave in *average* bare copper wire, you can combine part of the equation:

(984/2)*0.95 = 468 (well.. 467.4 actually)

.. leaving us with one handy dandy equation:
half wavelength in *average* bare copper = 468/f

Of course, your explanation is a whole lot more entertaining!

The number I like to remember is 11811 (roughly 984 x 12), which returns a length in inches. It's a palindrome: the same forwards as it is backwards, and is sometimes handier when making calculations for higher frequency antennas.

"Science Rules" .. even if it isn't so glamorous sometimes.

Respectfully,

--...MARK_N1LO...--
 
RE: Where Does 468 Come From?  
by N1LO on May 6, 2010 Mail this to a friend!
whoops! correction:

The 'electrical length' of a conductor, in feet, for one full wavelength, would be:

1 wavelength = (984/f)*Vf

--...MARK_N1LO...--

 
RE: Where Does 468 Come From?  
by K4JSR on May 6, 2010 Mail this to a friend!
Ward,
I have enjoyed your books any many articles in QST.
However, I do regret having to inform you that this
article may cause some to want a "NOAX NO TELL" rule
to be imposed! Sigh! Just a sign of our politically
correct times! ;-)

Just keep 'em coming!
73, Cal K4JSR
 
RE: Where Does 468 Come From?  
by WI7B on May 6, 2010 Mail this to a friend!

Now I understand what some folk's confusion with this 468 number and copper wire.

They believe the radio energy actually travels IN the copper wire instead of in the space around it!

No folks, radio energy occupies the space and environment AROUND the copper wire, not IN the copper wire. That's why environment plays the large role it does.

73,

---* Ken

 
Where Does 468 Come From?  
by KJ6FLH on May 6, 2010 Mail this to a friend!
I'm getting ready to put together a 40 meter dipole. I think you may have saved me a lot of work. FB!

- 73 -
Joe
 
RE: Where Does 468 Come From?  
by N3OX on May 6, 2010 Mail this to a friend!
"468 is not signficant. It's unduly approximate. Either radio energy travels at c in free-space, or it travels at something less than c in constrained-space.
"

Wave speeds in the area around a conductor can get really low when you coil it.
 
Where Does 468 Come From?  
by N0AX on May 6, 2010 Mail this to a friend!
A bit of clarification...

Yes, the speed of light is slower in a medium other than free space, including through the surface layer of a conductor. The slower velocity means the constant 492 in the free space formula for a half-wavelength, L=492/F, will need to be reduced when calculating the necessary physical length of wire that results in an electrical half-wavelength. We're all agreed there. That's not quite the point, though.

The point is that the traditional value of 468 in the formula L=468/F is usually quite a bit too small to use as a starting point for a wire dipole other than for 40 or 80 meters, 1/8 to 1/4-wavelength above the ground. For most dipoles for the HF bands, the constant is somewhere between 470 and 485 and the actual value for a particular antenna will depend on a variety of factors the simple formula L=constant/F can't account for.

So...my suggestion is to forget about the "magic value" of 468 that really only applied to a limited set of circumstances. Use the formula L=490/F to get an approximate length that is slightly too long in nearly all circumstances and be prepared to trim. The procedure for measuring the resonant frequency of the initial length and then calculating how much wire to remove will get you close enough. This is far more practical advice.
 
RE: Where Does 468 Come From?  
by WA7PRC on May 6, 2010 Mail this to a friend!
The origin is the speed of light (C)*, which is the same as the speed of radio waves:

C = 299,792,500 m/s
= 983,571,100 ft/s

And, the wavelength is inverse to frequency:

L = 983,571,100 / F(Hz) or 983.571100 / F(Mhz)
Therefore, a half wavelength is 491.78555 / F(Mhz).

This is the speed & wavelength in free space. In a conductor, it travels slower (think of a feedline as also being a delay line). And, think of an antenna element as a single conductor feedline. Typically, the velocity factor of a single conductor is around 0.95 or so.

Thus, a half wavelength antenna in free space is around 491.78555 x 0.95 / F(MHz)... or 467.1962725 / F(MHz). Close proximity to other conductive objects (Earth, parasitic elements, etc) will modify this formula, to some degree.

73,
Bryan WA7PRC

* I used the free units converter to find C: http://joshmadison.com/software/convert-for-windows/
 
RE: Where Does 468 Come From?  
by W4JLE on May 7, 2010 Mail this to a friend!
To the gentleman that stated that minimum SWR was the resonant frequency, not so Sir! The resonant frequency is the point that X=0. The two may or may not coincide.
 
RE: Where Does 468 Come From?  
by KE7HLR on May 7, 2010 Mail this to a friend!
> WI7B said:
>
> Now I understand what some folk's confusion with
> this 468 number and copper wire.
>
> They believe the radio energy actually travels IN
> the copper wire instead of in the space around it!
>
> No folks, radio energy occupies the space and
> environment AROUND the copper wire, not IN the
> copper wire.

Oh come on! I've heard of "skin effect," but "aura effect"?

Next, you'll be telling us that you can insulate a two-wire transmission line with 1/4-wave sections of solid wire....And then you'll be telling us that you can line-up an infinite number of these 1/4-wave sections to form a hollow rectangular tube that acts as a transmission line.

Oh, wait...I've seen these somewhere...
 
RE: Where Does 468 Come From?  
by K9COX on May 7, 2010 Mail this to a friend!
But where does 420 come from?
 
RE: Where Does 468 Come From?  
by K6SGH on May 8, 2010 Mail this to a friend!
Everyone knows the best way to reduce a standing wave is to tell it to sit down.

Oh...that hertz!

--k6sgh
 
RE: Where Does 468 Come From?  
by AE6RO on May 8, 2010 Mail this to a friend!
N0AX: The last time I constructed a resonant dipole was when I was a 14 year old Novice. I used stranded Radio Shack "antenna wire" because no-one told me it might stretch.

I measured it as closely as I could based on the formula l=468/f, with f = 7.175 MHz, then center of the pre-1972 Novice band. I found out my coax was too short, so I bought extra and spliced it, using an old spring from a microphone connector. Again, no-one told me you shouldn't splice that way.

Using a Heathkit HW-16, the silly old thing had an acceptable SWR of 1.5 to 1. The formula had worked well enough. From Socal I regularly worked into Washington state evenings, sometimes Canada, and the vilified of late--Arizona state in the daytime. 35 watts of CW. On 15 meters it had something like 1.8 to 1 but I could still work into the Midwest, like Michigan.

Also built a number of resonant 1/4 wave verticals. When I used the formula, the SWR was always 1.5 to one or better. Later on, I found another formula that took into account the K factor of conductor size. Guess what? Those verticals had worse SWRs, so I had to match them. What a pain.

This was around 1971 and '72, the declining side of Solar Cycle 20. Which brings me to my question: Why is the ARRL so silent on the ongoing Solar minimum? Most of the time QST has nothing on the subject. They had one "It seems to us..." which was cautiously optomistic. Or are we supposed to pretend that nothing is going on? Or is it because of the potential for climate change that might contradict the party line? 73, John
 
Where Does 468 Come From?  
by KB2HSH on May 10, 2010 Mail this to a friend!
N0AX:

Agreed! I've always used 492/F for my dipoles. It's easier to subtract wire than to ADD it!

KB2HSH
 
RE: Where Does 468 Come From?  
by N1DVJ on May 10, 2010 Mail this to a friend!
"Agreed! I've always used 492/F for my dipoles. It's easier to subtract wire than to ADD it!"

So True! People just don't think it out before-hand.

While you CAN add wire, and it's not that tough, it usually has a 'mechanical' weakness. Especially at solder joints. And if the solder is exposed to the elements?

One trick I was taught was to always cut a few feet longer. Then strip the end, pass it through your egg (or whatever you use for strain releif, then wrap it around the original wire. You should have enough friction for it to hold, at least while you do initial testing. Need to shorten or lengthen? Just unwrap, change the length, and wrap it back up. Once you get it right, THEN you cut and make it permanant.

 
RE: Where Does 468 Come From?  
by WI7B on May 10, 2010 Mail this to a friend!


"Oh come on! I've heard of "skin effect," but "aura effect"?" - KE7HLR

Apparently you've heard of skin effect, but you don't know what it is.

Skin effect is a property of high frequency alternating current in a conductor. It is not a property of radio energy.

Skin effect can be induced by radio energy when it couples with the conductor, such as a radio transmission with a copper wire antenna. The induced electrical current produce magnetic fields which induce their own eddy currents. These eddy currents constructively enhance the alternating current flow near the surface and oppose destructively the alternating current flow within the conductor.

Radio energy can be constrained and interact not only with conductors, but also insulators. That is the reason insulated copper wire acts differently than bare copper wire when used in antennas.

Also, go back to the basic electricity lesson you had to gain your license. Why are capacitors used to shunt radio energy out of a circuit to ground? Their is no direct electrical connection between the electrodes in a capacitor. In fact, their is an insulator between the electrodes.

Yet radio energy is transferred thought the conductor. Because that radio energy exists in the fields around the electrodes and dielectric not IN them.

If you like to think of electromagnetic fields as "auras", I see no harm in that.

73,

---* Ken

 
RE: Where Does 468 Come From?  
by WA2JJH on May 12, 2010 Mail this to a friend!
468 certainly is far from perfect. PI is rounded off down to 2 decimal places. For HF work, it is not that much of a factor.

At UHF 300-3000mhz the equation becomes very requency dependent. PI is an irrational number.
It has no exact value. 3.14 is what is normally used.
3.141592654 is what most calculators give.

Also, there was talk of the US going all metric in the 1970's. 40 Years later, we are still stuck using feet and inches. The 468 formula does use a metric to english built in math trick for an easy to remember
formula.

Sure is a simple formula, however 468 is no type of natural constant in metric or english.
Other posters have pointed out that for certain types of antennae, it is off enough to give a high SWR.

One can say it would be good enough when designing an RX only not so random length wire antenna for SWL apps 30KCS-30mhz.
 
Where Does 468 Come From?  
by VY1PG on May 14, 2010 Mail this to a friend!
Wow, I'm sort of glad I'm from Canada and didn't have to memorize the 468 number. We use metric, and can fairly easily calculate the length of wire antennas directly. Thank you for the history lesson though. It just goes to prove that you should always ask questions instead of blindly following what everyone else is doing.

:)

Keep up the good work and find some more gems for us to ponder.

Paul
 
RE: Where Does 468 Come From?  
by KT8K on May 17, 2010 Mail this to a friend!
I, too, usually use something approaching the 490/f mHz formula for the initial measurement of my half wave dipoles, but I do have my wire stretcher nearby, stored in the box next to my hole shrinker ... just in case.
73 de kt8k - Tim
 
Where Does 468 Come From?  
by KH6DC on May 21, 2010 Mail this to a friend!
Thanks for the awesome information and bit of history. I've been using 300 to get the wavelength in meters then converting the answer into feet. But sometimes I use quick and dirty 468. No wonder some of my dipoles turned out to be wire dummy loads.
 
RE: Where Does 468 Come From?  
by K8JD on May 28, 2010 Mail this to a friend!
"comes out exactly for broadcast towers"?
Verticals and dipoles a lot different, where is the height above ground effect that is a big factor in a dipole ?
BTW;
I was quite surprized when I finally figured out that AMBC antennas are rarely exactly a quarter, a half or five eights wavelength tall !
The FCC database shows the antenna heights in electrical degrees (halfwave = 180 degrees)and they are all over the place in height.
73...K8JD
 
RE: Where Does 468 Come From?  
by K8JD on May 28, 2010 Mail this to a friend!
AA4PB is furthering the myth about the speed of light, it is actually closer to 299.8 megameters per second in free space.
 
RE: Where Does 468 Come From?  
by K4KYV on May 28, 2010 Mail this to a friend!
I have never worried too much about it. If you use open wire tuned feeders, the exact length isn't important. Use the formula for frequencies at the low end of the band if possible, since more wire in the air results in a better antenna. The tuner should easily be able to compensate for any error or variation in the velocity factor calculation. I just remember that a half wavelength for 80m is about 135'. Double it to 270' for 160m and halve it to 67.5' for 40m, etc.

Better to make the wire slightly too long as a safety factor. It's easier to trim a foot or two off than to splice an additional foot or two on.

Don k4kyv
 
RE: Where Does 468 Come From?  
by N4KC on May 29, 2010 Mail this to a friend!
The point about AM broadcast towers rarely being a true quarter wavelength for their operating frequency has been made often here. Anytime someone argues that antennas MUST be resonant or are inefficient, or that "antenna tuners" are there to "fool the transmitter," we have to point this out.

By FCC dictate, broadcast stations have to serve their licensed community with a signal that meets the criteria of the license grant. That means the antenna must be efficient. And I have never seen an AM broadcast station with the feedline running directly from the transmitter to the tower base. It always goes through what amounts to an "antenna tuner." Granted, that tuner is not easily adjusted in most cases, because the transmitter is going to sit there and work into virtually that same load on a single frequency from now on, once properly adjusted. But it is a means of varying inductance and capacitance to achieve a "match" to the antenna. A match that may vary over time with changes to the ground system, far-field, feedline and more.

73,

Don Keith N4KC
www.n4kc.com
www.donkeith.com
www.n4kc.blogspot.com
www.facebook.com/donkeith
 
Where Does 468 Come From?  
by AA4HA on May 29, 2010 Mail this to a friend!
Since much of this is based off of the speed of light (in a vacuum) the more accurate number would be 491.04 for feet calculation /or/ 299.792458 for meters calculation.

Since the speed of light is typically expressed in a vacuum we need to apply the refractive index n=c/v depending upon the material(s). Air, wire, insulation, etc.. all contribute to this refractive index (velocity factor) and lead to a difference from the 491.04 number.
 
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