How do you make a short dipole? The answer is, put two loading coils at a distance B from the dipole feed point at its center. You can probably get loading coils from MFJ but it is really more fun to make them yourself. You need to know the position B and the overall length A of the dipole, the wire thickness D and the resonance frequency f.

In the rest of this blog you find all essential ingredients to design a short tuned dipole. The first part is the function loadingcoil, it is written for MATLAB and it estimates the inductance that you need. The second part is a MATLAB program to demonstrate the functionality of function loadingcoil, the third part shows NEC validation with a Smith chart of a 4.3 m dipole tuned for 10.1 MHz, this is the 30m radio amateur band that I currently use for WSPR.

### MATLAB function loadingcoil

function [H] = loadingcoil( f,A,B,D,metric )

%

% What loading coils are required for a short dipole? This problem is

% described by Jerry Hall K1PLP in QST Sep 1974, 28-34. The relevant

% equation and a script can be obtained from

%

% https://m0ukd.com/calculators/loaded-quarter-wave-antenna-inductance-calculator/

%

% To compute the loading coil inductance for a dipole of length A where

% two loading coils are placed at distance B from the center of the dipole,

% you need the wire thickness D, and the frequency f. The variable are:

%

% A is the overall length of a dipole in meter

% B is the place where you put the coil in meter

% D is the thickness (diameter of the wire) in meter

% f is the frequency in MHz

% H is the returned loading coil that you need

% metric=1 when in Europe (all values are in meter), otherwise metric=0 for US/UK

% (feet for A and B and inches for D)

%

% To verify this function you can use the script on the website of m0ukd

% listed before, but bear in mind that he speaks about the height of a

% quarter wave antenna and not the length of a dipole, so there is a factor

% two difference.

%

if (metric == 1),

inch = 0.0254;

foot = inch*12;

A = A/foot;

B = B/foot;

D = D/inch;

end

T00 = (234/f)-B;

T01 = log(24*T00/D)-1;

T02 = (1-f*B/234)^2 – 1;

T03 = (A/2)-B;

T04 = ((f*A/2-f*B)/234)^2 – 1;

T05 = log(24*T03/D)-1;

T06 = 1e6/(68*pi*pi*f*f);

H = T06 * ((T01*T02)/T00-(T04*T05)/T03);

%

% Last update: 1-jan-2017;

### MATLAB example for loadingcoil function

% Jerry Hall K1PLP equation

%

% Checking this design:

% https://www.nonstopsystems.com/radio/antenna_80m_vertical-cntr-loaded.htm

% loadingcoil(3.58,20,5,0.0015,1) should result in 42.555 microHenry

%

clear

f = 3.58;

A = 20;

B = 5;

D = 0.0015;

metric = 1;

H = loadingcoil( f,A,B,D,metric );

fprintf(‘F=%8f MHz A=%7.3f B=%7.3f D=%7.5f metric=%1d H=%7.3f microHenry\n’,f,A,B,D,metric,H);

This program should produce:

F=3.580000 MHz A= 20.000 B= 5.000 D=0.00150 metric=1 H= 42.555 microHenry

### Verification of a short dipole at 10.14 MHz for WSPR

To validate the results of part 1 and 2 I use the NEC software which is in the public domain. The design criterium is that a short horizontal dipole has to fit between two chimneys under the roof of our house. The solution is: A=4.315m B=0.1m, D=0.8 mm wire and H=13.7 microHenry. It is always a wise idea to independently verify whether the computed values make sense, so this is where the NEC code assumes that there is a 13.7 uH coil at 10cm from the center of the dipole, the value of A was tuned numerically until a minimum SWR relative to 50 Ohm was obtained.

model ( “short tuned 30m dipole” )

{

real length, height, radius, N, X, R, L, d, e;

element driven, left, right, leftmost, rightmost;

frequencySweep( 10.1, 10.15, 10 );

d = 0.05;

e = 0.10;

length =4.315;

radius = 0.0008;

height = 10;

N = 20;

d = 0.05;

e = 0.10;

driven = wire( 0, -d, height, 0, d, height, radius, N);

left = wire( 0, -d, height, 0, -(d+e), height, radius, N );

leftmost = wire( 0, -(d+e), height, 0, -length/2, height, radius, N);

right = wire( 0, d, height, 0, d+e, height, radius, N );

rightmost = wire( 0, (d+e), height, 0, length/2, height, radius, N);

L = 13.7;

X = 2*pi*10.1*L;

R = 0;

impedanceLoad( left, R, X );

impedanceLoad( right, R, X );

voltageFeed( driven, 1.0, 0.0 );

}

This result in the following Smith chart rom which you learn that the SWR relative to 50 Ohm is 8.48.

The conclusion is that the impedance is 5.9Ohm which means that you need an impedance transformer to connect it to a 50 Ohm coax cable, any 1:9 current balun would be fine, I used something I purchased at a radio market, but they are relatively easy to make them yourself. The other option is to use a twin line and an impedance transformer near the beacon. The center section of the dipole consists of 40cm of PVC tube with a diameter of 40mm, at 10 cm from the center there are 17 turns and this results in the required inductance.

Next I measured with my antenna analyzer the resonance frequency of the antenna. With the analyzer at the feed point I cut the length of both arms of the dipole to the desired length so that the resonance dip occurs at 10.1 MHz. The measurement should be done at the antenna feed point, and not at the end of the coax connector that goes to the WSPR transmitter because cable impedances shouldn’t interfere with the measurement. Another verification is, listen with the SDR to the antenna, there are always plenty of signals, and inspect where the signal envelope is largest. I found it to be at the 30m band.

Last update: 6-jan-2017