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Author Topic: Loading coil calculation for a short dipole  (Read 7267 times)
KI6NUJ
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« on: June 18, 2008, 05:18:40 PM »

Hi,

I am trying to determine the right dimensions for constructing a loading coil for a short dipole.

The dipole is meant for my balcony where I can put up an inverted V dipole of about 20 feet length. The loading coil will be built with #14 magnet or insulated wire, both of which I have plenty.

To calculate the antenna's dimensions, I put the numbers in this calculator online for 7.1Mhz:
http://www.k7mem.150m.com/Electronic_Notebook/antennas/shortant.html

Center Frequency: 7.1Mhz
Dimension "A": 20 feet
Wire: #14

The result is that configuration "5" seems optimal with the coil at the center of each arm of the dipole. The suggested coil inductance is 35.3 uH.

For now I ignore the coil's self-resonance that the calculator suggest since someone earlier on this forum said that does not appear to be correct.

Next, I use the coil calculator here:
http://www.k7mem.150m.com/Electronic_Notebook/inductors/coildsgn.html#Initial_Design

Required Inductance: 35.3
Wire Size: 14
Turns per inch: 5

Now, my first question is about TPI. What is the TPI rule of thumb? I could wind 10 turns of #14 insulated stranded copper wire in an inch but as I understand the winding should be at least one diameter apart so is 5 TPI a good value for #14 wire?

With 5 TPI and form diameter of 4 inches and 24 turns, I get the dimensions for a coil with 35.3 uH inductance and length of just over 4 inches. It also gives me L/D ratio of 1.2:1 which seems good.

Next, I use another calculator to check the self-resonance frequency of the coil at:
http://hamwaves.com/antennas/inductance.html

D = 101.6 mm
N = 24
l = 124mm
d = 1.63mm
f = 7.1Mhz

This calculator confirms the coil's inductance at 34.8 uH but the self-resonance shows up as 13.8Mhz as against the 9.8Mhz the antenna calculator shows.

So self-resonance at 13.8Mhz is good since it is close to the ideal self-resonance frequency of 14.2 Mhz, right?

I checked with another calculator here:
http://www.smeter.net/feeding/selfres3.php
(scroll to the bottom for the exe file)

This calculator takes a few more parameters but shows similar numbers for inductance at 34.4 uH. The self-resonance frequency is calculated to be 15.98 Mhz.

The numbers I entered in this last calculator, other than the ones used in the earlier calculator are:
E. Leads length,mm = 6mm

G. Line length, waves = 0.038
This is the ratio of the half length of one arm of the dipole to the full wavelength, right? 5 feet / 131 feet for 40m.

H. Termination, ohms = 50 (since it is fed by a coax and a 1:1 current balun, right? )

Gives me a Q of 281 at the design frequency which seems to be good.

I would appreciate if someone can please verify the assumptions and calculations above.

73,

- Siddhartha WV6U
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KI6NUJ
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« Reply #1 on: June 18, 2008, 05:24:11 PM »

Please allow me to add that the maximum power this antenna and coil will see is 100 watts.

Thanks,

- Siddhartha
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W5FYI
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« Reply #2 on: June 18, 2008, 08:01:03 PM »

The first site you listed clearly says that the antenna should be no shorter than about 27'. It also does not indicate what the radiation resistance is, nor what impedance to expect at the feed point. A 1:1 balun there does not automatically make the feed point Z=50 ohms.

In general, the farther apart you can get the loading coils, the higher the radiation resistance will be. However, I realize you have cramped space and no room for a larger dipole, so you will have to live with whatever you can work out. I'd give the antenna a try and see what it does.

The coil-winding formula I use is I(µH)=(n²×r²)/(9r+10L), where I is inductance, n is number of turns, r is form radius in inches, and L is coil length in inches. AWG14 enameled magnet wire gives approximately 15 turns per inch single-spaced, 7½ t.p.i. double-spaced, and about 5 t.p.i. triple-spaced (wind three wires side-by-side, then unwind two to get 5 t.p.i., if that's what you want). For starters, I'd wind the coils on a light-weight plastic form and use a couple of ribs of hot glue to hold them in place. When (if) you get the antenna where you like it, you can go back and make the coils and the rest of the antenna more permanent.

Just my 2¢ worth. Stew
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WB6BYU
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« Reply #3 on: June 18, 2008, 08:53:59 PM »

>  So self-resonance at 13.8Mhz is good since it is close to the ideal self-resonance frequency of 14.2 Mhz, right?


Where did this "ideal self-resonance frequency" come from?

That might apply if you wanted to use the inductor both
as a loading coil for 40m and a trap for 20m (in which
case the length of the wire between the feedpoint and
the coil would have to be about a quarter wavelength on
20m) but otherwise the self resonant frequency of a coil
is not a critical parameter in this use.  (As long as it
is high enough above the operating frequency.)

I suspect you will find that none of the calculators are
accurate enough to get your antenna resonant on 40m.  Not
due to any inherent fault of the calculators (though I'd
tend to trust the ON4AA calculator on hamwaves more than
the others) but simply because any stray capacitance
from the antenna to the surrounding environment on your
deck will shift the resonant frequency of the antenna.
(As will minor variations in wire length due to connections
to insulators, knots in the wire, the dielectric
properties of any insulation on the wire, etc.)  You just
can't make the calculations that accurate in the real
world.

But that shouldn't keep you from building the antenna.  
Just add a few extra turns to the coil then unwind them one
at a time while checking the SWR with the antenna
installed in its final position.  When you get the
SWR curve centered where you want it, you're done.
(Except perhaps weatherproofing the coil, but that will
shift the antenna resonance a bit, too.)

If that is too inconvenient you can change the effective
wire length instead.  Wind the coil as calculated.  Allow
a foot or two of wire to hang down on each end at the
insulator, measure the SWR curve and trim off an inch
or two at a time from the hanging ends to get minmum SWR
at your desired operating frequency.

You can also fold the end of the wire back onto the
standing part instead of trimming it:  given the narrow
bandwidth of such an antenna it may be a good idea to
plan to be able to tune it for different parts of the
band.  If you allow two or three feet of wire on each
end to drop down from the end insulator then go back up
and tie to the standing part of the antenna, you can
adjust the antenna by sliding the knot up and down the
standing wire (up to the point where the whole end wire
is running back up parallel to the wire, which will give
the highest resonant frequency.)  You can also use a
second wire tied to the end of the loading coil and
adjust the angle between the movable and stationary
wires.  I've used both of these methods to tune
shortened dipoles for 160m, as well as full-length
dipoles for 80m where the SWR bandwidth is too narrow
to cover the whole band.

Also, expect the SWR to be somewhat high on a shortened
dipole like this (unless the coils are very lossy.)
You can add a small coil across the feedpoint as a beta
match:  put the antenna up and measure the SWR at
resonance, then calculate the required inductance (from
charts in the ARRL Antenna Book, online calculators,
EZNEC, or wherever) based on the measured SWR.  You may
have to readjust the antenna tuning slightly but you
should be able to get a good low SWR this way.

I'm in the middle of building a proportionally shorter
antenna (for 160m in the length of a 80m dipole) so have
been dealing with some of these issues myself.


Good luck!

- Dale WB6BYU
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W8JI
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« Reply #4 on: June 19, 2008, 02:52:37 AM »

Hi Siddhartha,

<<For now I ignore the coil's self-resonance that the calculator suggest since someone earlier on this forum said that does not appear to be correct.>>

You are dealing with one of the most difficult things to model accurately when you start dealing with coils operated anywhere near self-resonance. Always remember that.

<<Now, my first question is about TPI. What is the TPI rule of thumb?>>

Pretty much for any form factor, the ideal spacing of turns comes out at one conductor diameter. Obviously that means for any inductor the TPI varies with wire gauge.

<<I could wind 10 turns of #14 insulated stranded copper wire in an inch but as I understand the winding should be at least one diameter apart so is 5 TPI a good value for #14 wire?>>

The optimum spacing of the conductors in the coil does not count the insulation. The ideal spacing between conductors will always center pretty close to one conductor diameter.  

<<With 5 TPI and form diameter of 4 inches and 24 turns, I get the dimensions for a coil with 35.3 uH inductance and length of just over 4 inches. It also gives me L/D ratio of 1.2:1 which seems good.>>

Why does that seem good? If the inductor is used on a frequency where the reactance is very high, perhaps 500 ohms or more, then we want to start stretching the coil out longer and using smaller diameter. The less inductance we need the more compact the inductor can become, so the form factor can be 1:1 or less without harm.

 <<This calculator confirms the coil's inductance at 34.8 uH but the self-resonance shows up as 13.8Mhz as against the 9.8Mhz the antenna calculator shows. >>

This is one of the most difficult things for people to write a model for.

<<So self-resonance at 13.8Mhz is good since it is close to the ideal self-resonance frequency of 14.2 Mhz, right? >>

Wrong. I don't know what you are reading but there is no "optimum" self resonant frequency except as far above the resonant frequency as possible without hurting the ESR of the inductor at the desired frequency. I can't imagine why anyone would focus on an "optimum" SRF!!

<<This calculator takes a few more parameters but shows similar numbers for inductance at 34.4 uH. The self-resonance frequency is calculated to be 15.98 Mhz. >>

I would expect this because SRF is one of the most unreliable things to model.

<<Gives me a Q of 281 at the design frequency which seems to be good.>>

Another difficult thing to predict, that is more often very wrong than close, is inductor Q.

Siddhartha, if you are that interested in the details of inductor design get a copy of John Kuecken's book Antennas and Transmission lines. It has a section on inductors and loading antennas. The book is based on a series of lectures back around the 60's. MFJ has reprinted that book.

That book has the most detailed and accurate section on loading inductors for short antennas of any book I have ever seen.

You may be overthinking the inductor for your application, but you are certainly learning useful things for later. I strongly urge you to stop with the web pages for a while until you read the chapter's about loading inductors and short antennas. Much of what I find with programs is very wrong, but some things get close in some applications.

The most difficult thing to model accurately is a very short loaded antenna and a high reactance inductor used to load a short antenna. The best approach is almost always direct measurement and cut-and-try. That's why it is fun for everyone, including people trying to understand it.

73 Tom
   
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KI6NUJ
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« Reply #5 on: June 19, 2008, 03:27:59 AM »

Thanks All - Stew, Dale and Tom for very informative comments.

I think I am done researching and should get down to some experimentation now and see how it works out.

The 14.2Mhz self-resonance frequency for a coil to be used in a 40m antenna comes from this statement on K7MEM's antenna calculator page:
"For optimum efficiency, self-resonance should be near 14.2 MHz". I guess a coil's Q is highest around double the operating frequency of the antenna?

On the subject of short dipoles, the hamstick dipole I erected on the balcony now shows 1:1 SWR on 7.07Mhz (for PSK) after some tweaking with the whips. This is without engaging the built-in tuner. Of course, I have no idea if the efficiency is any good at all. I could not test it today because the band had closed by the time I was done with the tweaking.

The miniVNA that I have been using all this while as the antenna analyzer turns out to be highly unreliable. While the radio's SWR meter and an inline SWR meter show 1:1 SWR for the dipole at 7.07Mhz, the miniVNA shows random numbers that keep varying. This is after calibrating the miniVNA and verifying that it shows 1:1 SWR when loaded with a 50 ohm resistor.

Again, thanks for the inputs and I will post some results as soon as I am done building a workable solution.

73,

- Siddhartha WV6U
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WA3SKN
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« Reply #6 on: June 19, 2008, 05:03:11 AM »

Siddhartha...
You are going about this all wrong!
Using a 2-4 inch form, make a space-wound coil.  Take about 50-60 feet of wire and fold over, then close-wnd it on form, then remove one leg of it to convert it to space-wound.  Connect one end of coil to ground and use the other leg of wire to connect to the coil and an insulator.  Make a "shorting bar" using an alligator clip and adjust (short) coils til you get resonance.  Take a coax feed and find tap coil for 50 ohm match.
Operate!
To change frequency, retune taps on coil!
73s.

-Mike.
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K4SAV
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« Reply #7 on: June 19, 2008, 11:08:50 AM »

This is one of those antennas where modeling usually fails.  The reason is that the coil has to be very high inductance because of the very short antenna.  That invariably causes the coil self resonance to be a lot lower than desired.  When this happens, NEC will not give a very inaccurate answer unless a physical model of the coil is used.  Often this is not possible because NEC can't handle the closely spaced wires.  So usually you have to start with a best guess and do some experimenting from there.

I have a coil program that does a reasonable job of calculating the self resonant point.  I used your data, #14 bare wire, 5 TPI, 24 turns, 4 inch diameter form, freq = 7 MHz.  You didn't give the form material which is a critical parameter, so I am assuming PVC.  The coil self resonant point calculates to be 8.3 MHz, much too low!  The coil wound on a PVC form will not be usable, because at 7 MHz, its apparent inductance goes to something like 145 uH, even though at low frequencies its inductance is about 40.5 uH. If the coil had been wound on an air core the resonant frequency would have been about 11.5 MHz, still much too low to allow an accurate calculated answer by NEC (but maybe allowing an experimental answer).  The 7 MHz apparent inductance of this air coil is 64 uH and the low frequency inductance is 40.5 uH.  If all of this is confusing, welcome to the club.  Inductors are not easy to understand, and all of the calculators I have seen on the web do a very poor job of calculating inductors for use at high frequencies.

However you do need to put forth a good effort to keep the coil self resonance as high as possible, because in this case it is very easy to make a coil whose self resonance is below the operating frequency, and that will cause you lots of confusion when experimenting, because you will never be able to find resonance. (Resonance will probably end up over 28 MHz.)  When trying to shorten an antenna this much, most experiments end in "I could never make it work".  Others will build an antenna out of a lot of wire wound on a long stick and they will be able to make it resonant at a desired frequency, but that always has very poor performance because of the huge wire loss.

I started to give you my best estimate for a coil design, but then I remembered that bandwidth and feedpoint impedance are two other major items to overcome.  With a good coil, and an antenna this short, the bandwidth is going to be very narrow, probably less than 20 KHz.  The feedpoint impedance is also going to be very low, so you will also need a matching network at the feedpoint.  Another problem experimenters see with an antenna like this is that they try to feed it directly with coax.  After playing with it for a while they finally get it to resonate somewhere close to what they want.  What usually happens is that because of the very low feedpoint impedance and feeding it with unbalanced coax, common mode currents become huge, and the feedline becomes the major radiator.  That has very unpredictable performance because it is totally dependent on the feedline.  Note: There are several commercial antennas on the market that operate like this.

So far I have done nothing but rain on your parade, sorry.  I hope I don't discourage your experimentation.  I wanted to help add a little understanding to the problems you may encounter when doing these experiments.  Shrinking an antenna this much is a very difficult design for anyone.

Jerry, K4SAV
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W9OY
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« Reply #8 on: June 19, 2008, 01:36:07 PM »

Why don't you construct a link coupled balanced tuner on a little sheet of aluminum and place it in the center of the balcony and run the wire from each side of the coil to the ends of the balcony.  You could also try an inverted half square giving you the greatest length of wire connected to the tuner.  You would need a cap to resonate the center coil and a cap to resonate the link and a link coil wound over the center coil, a few stand off insulators and a SO239.  here is a pic of the kind of thing I am talking about

http://mndx.blogspot.com/2008/05/my-home-made-link-coupled-tuner.html

You will probably have to tap down the center coil for a short antenna to get it to resonate, but once you get it tapped you can solder it up.  

A custom made link coupled tuner like this can be made quite efficient and you can tune it and move around the band.  You will have to go out on the balcony to tune the thing and beware of RF but you should be able to make a pretty efficient system, and the link will get most of the common mode off the coax.  I have wound coils for this kind of thing using #14 but I like something like #10 or larger because it self supports better.  I usually have one of those 10 buck SWR bridges screwed to the aluminum plate so you can resonate the thing easily.  You have the advantage of being one of the few hams who actually could get the coupler at the center of the antenna and you will be nicely matched to 50 ohms

73  W9OY
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K4SAV
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« Reply #9 on: June 19, 2008, 05:57:43 PM »

That is a good suggestion W9OY made.  That antenna should work with reasonable efficiency.  I'll add a few items.  I don't think you will need the cap across the big coil, just a cap in series with the link.  Adjust it like this:  Set the cap for maximum. Then adjust the taps on the big coil until you get resonance on the low end of 40 meters.  Then adjust the number of turns used on the link until the SWR drops close to 1.0.  After that you should be able to adjust the cap for the operating frequency you want.  The cap will be fairly small, probably less than 100 pf (depending on the dipole length), but it will need wide plate spacing.

A word of caution.  Don't operate this where anyone can touch the components.  At 100 watts there will be several thousand volts on the cap and a lot more across the coil (depending on dipole length).  If the dipole length is 20 feet then the coil may have as much as 9 to 10KV across it.  (That's another reason you don't want a cap across the big coil.)

Lee that is beautiful work you did on building that coil.  I'm not sure how you did that, but it looks really good. Siddhartha if you want a good example of how to build a high Q coil, take a close look at how that coil is constructed.

Jerry, K4SAV
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W8JI
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« Reply #10 on: June 20, 2008, 04:45:40 AM »

<<<The 14.2Mhz self-resonance frequency for a coil to be used in a 40m antenna comes from this statement on K7MEM's antenna calculator page:
"For optimum efficiency, self-resonance should be near 14.2 MHz". I guess a coil's Q is highest around double the operating frequency of the antenna? >>>

That statement as given is incorrect as a general statement, although it could be correct only in very specific cases.

Knowing the root of the mistake will probably help you. Consider a given inductor and how it behaves.

At very low frequencies there is almost no inductive reactance. Nearly all of the cross section of the conductor is reducing resistance, but the inductive reactance is low. It is the ratio of inductive reactance to resistance that sets the Q. If we blindly look at Q, then we see inductor Q gets higher with frequency because conductor resistance increases slower than reactance with increased frequency.

The problem is when we get anywhere near the SRF of the inductor funny things happen. The distributed capacitance greatly increases inductive reactance, but it does so with a severe penalty most people ignore. The stray parallel capacitance across the inductor and between turns increases circulating currents inside the inductor. Since loss is the square of current this additional current that does NOT appear outside the inductor terminals greatly increases losses.

Now here is what it odd to most people, and what most people overlook. The inductor behaves as if Q was higher, even thouse losses are much higher. If we did a bandwidth test to look at system Q, it would be narrower! That's because we now have a parallel capacitance instead of a pure loading inductor, so the slope of reactance with frequency change is much greater. If we don't add the circulating currents into our model and look only at skin depth resistance and reactance to determine Q, it looks like the Q went way up as we approach self-resonance.

It is a very difficult and complex balance to get circulating currents caused by internal capacitance into the equation.

People who totally leave them out will have programs that calculate Q's in the thousands near the SRF. When they are included the Q will peak well below SRF. If people measure using bandwidth they will get a very incorrect result, they would have to measure the equivalent series resistance and the net reactance of the inductor and not bandwidth in a resonant circuit or not calculate using skin depth resistance effects and overall reactance.

The overall rule is we want the SRF as far away from the operating frequency as we can get, so long as that does not increase the conductor resistance too much.

The real answer is the lowest acceptable SRF would depend on the reactance needed and the form factor of the inductor. There is no "optimum" SRF because everything the capacitance does that causes the coil to have a SRF is a NEGATIVE effect.

I could wind a very good coil with high SRF, place a capacitor across it, reduce the SRF and the effect of that would be to increase the series resistance of the coil. Does this help you see why there is no universal optimum SRF? We just want it as high as possible with the minimum acceptable set by the impedances in the entire system and in the coil itself.

73 Tom



 
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KI6NUJ
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« Reply #11 on: June 20, 2008, 02:56:19 PM »

Thanks Tom. That was a very insightful post. I will sure be reading it over and over and will need to refer some books to fully understand everything you said in there Smiley

But yes, I do understand the gist of it.

Thanks again,

- Siddhartha
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KI6NUJ
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« Reply #12 on: June 20, 2008, 03:12:45 PM »

Hi Tom,

I sent this email to your qrz/eham email address at contesting.com but the mail bounced so I am posting it here:

-----------xxxxxxxxxxxx---------------
I have been reading all the highly informative articles on your site and the helpful posts that you write in response to questions people have on the eham site. It is very obvious to me that you have a wealth of knowledge.

I was wondering if you have already written a book on ham radio or considering writing one? A lot of your comments/articles/posts go against some "conventional" wisdom in ham radio but all the same they are firmly based in science and logic so magazine articles aside I think you should definitely consider putting together the knowledge you've gathered in a book. I would definitely buy a copy right away Smiley
-----------xxxxxxxxxxxx---------------

73,

- Siddhartha WV6U
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W8JI
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« Reply #13 on: June 20, 2008, 03:48:16 PM »

Gosh, thanks. That was nice. I'd like to do that but the time it takes is far more than I have. Maybe after I win the lottery or if there is a good partner....
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K1BXI
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« Reply #14 on: June 20, 2008, 06:37:13 PM »

There is nothing I can help with answering Siddhartha's post, but I would also like to add my thanks to Tom for his advice given on e-Ham to us, and his website. I too would buy any book you would publish Tom.

John.....K1BXI
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