# Behaviour of Earth Electrodes at Radio Frequencies

Author: R.J.Edwards G4FGQ © 15th February 1998Notes on Behaviour of Earth Electrodes at Radio Frequencies Basic soil characteristics, Resistivity Rp and Permittivity K, change very little versus frequency. But as frequency increases the magnitude of the soil impedance Z decreases due to the shunt capacitance. The capacitance in shunt with Rp is K times 8.85 picofarads and therefore Z has a negative angle.

Since the main concern is with RF power lost in the ground when aerial current flows into an earth connection, the equivalent series resistive component of Z Rs, will be of greatest interest. Taking typical values of Rp = 100 ohm-metres and K = 14, at a frequency of about 13 MHz the angle of Z is 45 degrees and Rs has fallen to 71 ohms. The series reactive component Xs is also 71 ohms but is not of great consequence because reactance in an earth connection, +ve or -ve, is tuned out when the aerial itself is resonated.

The relationship between RF input resistance of an earth electrode and its DC value (which is usually the only known parameter) versus frequency is complex. The form of electrode and its longest dimension, expressed as a fraction of a wavelength, are the key features. A further complication is due to propagation velocity on a buried electrode being much smaller than the free-space velocity and also varying with frequency. Electrodes may be classed as plates or wires and considered separately. A rod is a very short wire of large diameter. A long thin strip may be considered as a wire with diameter half of the width.

A Square or Rectangular Earth Plate

Up to frequencies at which the length of the longest side is less
than 1/20th of the wavelength in free-space, Rin, the series resistive
component of Zin, may be assumed equal to its DC value, Rdc. When the
angle A of soil impedance is not small, multiply Rdc by Cosine(A). At
higher frequencies, depending on soil characteristics, the series resistance
may increase above the DC value.

Uniformly Spread Radial Wires

Each wire must be considered as a lossy transmission line. Resonance
effects are almost entirely absent because attenuation may be 10 dB
or more per 1/4 wave-length of line. Propagation velocity is frequency
dependent between 1/8 and 1/3 of free-space value. Radials can be very
long in terms of wavelengths.

The RF input resistance of a wire less than 1/40 free-space waves long may be assumed equal to its DC resistance to ground. For a set of radials the DC resistance of the set must be used. For longer lengths input impedance converges on Zo, which, due to wire inductance has a +ve angle. Input resistance is then the resistive component of Zo.

There is no benefit in using radials longer than 1/3-wave. It will always be better to use twice as many radials of half the length.

To study the DC and RF characteristics of a single buried radial use the radioeth.exe program .

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