Calculate the lengths that should be avoided when making "random wire" antennas
The length of a "random wire" antenna has a direct impact on the impedance present at its end for a given frequency.
The tuners commonly available are not very good at tuning high impedances, unless they are specifically designed for this purpose. Therefore, avoiding the lengths that are half-waves or multiples of half-waves on the bands of interest increases the odds that the tuner will be able to do its work properly.
This Scilab program calculates the length of the half-waves and their multiples for the selected amateur bands. The result is the graph below. The dark zones are likely to cause a very high impedance on certain frequencies within the selected bands, and should therefore be avoided.
A rule of thumb is to use a wire length that is at least 1/4-wavelength long on the lowest band of interest, and does not fall in or close to the dark areas on the graph below.
The horizontal axis is in centimeters.
Related information:
//
// Not So Random Wire antenna
//
// Calculates the length of wire that will not be a multiple of a half-wave
// on several bands
//
// Copyright (C) 2011-2025 Christophe DAVID ( ON6ZQ | AC6ZQ )
// http://www.on6zq.be/Scilab/NotSoRandomWire
//
// This program is free software; you can redistribute it and/or modify it
// under the terms of the GNU General Public License version 2 as published
// by the Free Software Foundation (http://www.gnu.org/licenses/gpl.html).
//
//////////////////////////////////////////////////////////////////////////////
//
// This program was last tested with Scilab 2025.0
// http://www.scilab.org
//
//////////////////////////////////////////////////////////////////////////////
// A semicolon at the end of an instruction causes the result not to be displayed.
errclear; // clear all errors
clear; // kill variables
clearglobal // kill global variables
clc; // clear command window
tohome; // move the cursor to the upper left corner of the Command Window
clf; // clear or reset the current graphic figure (window) to default values
//////////////////////////////////////////////////////////////////////////////
HamBands = [ // kHz
// 1810, 2000
3500, 3800;
5351, 5367;
7000, 7200;
10100,10150;
14000,14350;
18068,18168;
21000,21450;
24890,24990;
28000,29700;
// 50000, 52000
];
MaximumWireLength =5000; // centimeters
NumberOfHarmonics = 10;
VelocityFactor = 1;
//////////////////////////////////////////////////////////////////////////////
// create a matrix to contain the results
// one element for each cm from 1 to MaximumWireLength
// initialized with 0's
M =zeros(1:MaximumWireLength);
// printf("The matrix M has %d row(s) and %d column(s)", size(M, 'r'), size(M, 'c'))
// for each band, calculate the lengths that are half-waves or multples of
// half-waves
[_rows, _columns] =size(HamBands);
for i =1: _rows
printf("\nBand %d %d", HamBands(i,1), HamBands(i,2));
for harmonic =1: NumberOfHarmonics
HalfWaveLengthLowEnd =round((15000000/(HamBands(i,1)* harmonic))* VelocityFactor);
HalfWaveLengthHighEnd =round((15000000/(HamBands(i,2)* harmonic))* VelocityFactor);
printf("\n %d -> %d", HalfWaveLengthHighEnd, HalfWaveLengthLowEnd);
if HalfWaveLengthLowEnd < MaximumWireLength then
if HalfWaveLengthHighEnd > MaximumWireLength then
HalfWaveLengthHighEnd = MaximumWireLength;
end
for j = HalfWaveLengthHighEnd : HalfWaveLengthLowEnd
M(1, j)=1;
end
end
end
end
// The black areas show the lengths that will cause very high impedance on one or several bands
// and might be difficult to tune with common tuners
plot2d3(M);
//////////////////////////////////////////////////////////////////////////////