Loading coil calculation for a short dipole

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Siddhartha Jain:
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

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

Thanks,

- Siddhartha

Claude Stewart:
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

Dale Hunt:
>  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

Tom Rauch:
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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