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 GNU Octave 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.

Click to enlarge

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 )
#
##############################################################################

clear;
clc;
close all;

##############################################################################
# Define amateur radio bands in kHz
HamBands = [
    3500, 3800;
    5351, 5367;
    7000, 7200;
    10100, 10150;
    14000, 14350;
    18068, 18168;
    21000, 21450;
    24890, 24990;
    28000, 29700
    # 50000, 52000  # 6m, optional
];

MaximumWireLength = 5000;      # in centimeters
NumberOfHarmonics = 10;
VelocityFactor = 1;

##############################################################################
# Initialize results array
M = zeros(1, MaximumWireLength);

# Loop over bands and harmonics
[bandCount, ~] = size(HamBands);

for i = 1:bandCount
    printf("\nBand %dā€“%d kHz", 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  Harmonic %d: %d cm ā†’ %d cm", harmonic, HalfWaveLengthHighEnd, HalfWaveLengthLowEnd);

        if HalfWaveLengthLowEnd < MaximumWireLength
            if HalfWaveLengthHighEnd > MaximumWireLength
                HalfWaveLengthHighEnd = MaximumWireLength;
            end
            for j = HalfWaveLengthHighEnd : HalfWaveLengthLowEnd
                M(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

figure;
imagesc(M); colormap(flipud(gray));
title("Wire lengths that are half-wave multiples on one or more bands");
xlabel("Wire Length (cm)");
ylabel("High Impedance = 1");
set(gca, "ytick", []);

##############################################################################