# Measurement of the ground conductivity and relative permittivitywith high frequency using an open wire line (OWL)

## Motivation

At the simulation of (vertically) aerials there are two determining factors: The conductivity and relative permittivity of the ground with high frequency (short soil conductivity). However, exactly these values are up to now only raw estimates or taken out of the easiest maps for long-wave transmitter and medium-wave radio stations. Information for the short wave band is not to be found at all. Besides, the ground qualities are dependent very much on the frequency. Hence, I would like to observe these values for a longer period together with the amount of precipitation and temperature myself.

The ground qualities can be measured with the shown procedure easily at several places for all desired frequency. The measurement refers of course only on the uppermost layer in that the two-wire line is introduced. With a rock ground with 40 cm of humus in the flowerbed measured this measurement does not show the average of the surroundings! However, with care at the estimations very useful results are absolutely to be achieved.

At last these values serve for the comparison of two groundplane aerials with raised resonant radials or buried radials in the simulation with NEC4.2 as well as with a detailed measurement.

## Theory

A two-wire line is introduced in the ground and the impedance is measured vectorial at the upper end. The two-wire line in the ground is open at the lower end. The two-wire line transforms this impedance as a function of her geometrical qualities and the qualities of the medium (surface of the earth). The general two-wire line equation is used to determine the relative permittivity εr and the specific conductivity σ.

Transformation of the impedance ZL into impedance Zin by a two-wire line with the (complex) impedance Z0 of the length l.

Is worth with

Because the two-wire line is open at the end we choose for ZL a very high still to be determined value which considers the fringing effect of the two-wire line.

Here you can read about a approximation of the fringing effect of a two-wire line.

Furthermore .

C' = ε0 * εr * π / acosh(s/d)

L' = µ0 * µr / π * acosh(s/d)    ; [1]

G' = σ * π / acosh(s/d)

R' = 1,66 * 10-7 * K1 * √f / d    ;with simplification after [2]

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[1] µr at high frequency (~1.0 in the whole HF area, also with magnetic mild steel)

[2] Janzen, Gerd: Kurze Antennen : Entwurf u. Berechnung verkürzter Sende- und Empfangsantennen, 1986, ISBN 3-440-05469-1

 metal K1 aluminum alloyed 1,3 - 2,0 copper 1,0 brass 1,9 - 2,3 zinc 1,9 steel 2,8 - 3,6 stainless steel 7,2

In memory the definition:

## Construction

With the new vector network analyzer of DG8SAQ an exact analysis is possible for every amateur.

All parts required to the measurement.
The mechanical dimensions of my two-wire line are d = 8.0 mm   s = 48.0 mm   l = 400 mm

Measurement with laptop, vector network analyzer of DG8SAQ and two-wire line in the ground.

End of the two-wire line in the ground with adapter and coaxial cable.

The two-wire line to be introduced in the ground exists here of two iron rods with 8 mm of diameter and 40-cm length. Both poles have a thread at the upper end and the lower end is sharpened to make easier to press it into the earth.

One of both steel-plates with two holes is laid on the ground and serves for stabilization of the distance of the poles. The other record is screwed together at the upper end on nuts. Then the poles are fastened together like shown in the picture. After that the rod assembly is to be pressed into the earth. If the two-wire line is completely in the ground both steel-plates are removed and the adapter piece (here with N plug) is screwed on and the measurement is carried out. For the adapter piece two conformist calibrating standards are built to allow a SOL calibration. By using the steel-plate the poles can be also pulled out of the ground one after the other very easily.

## Evaluation

The conversion of the measured impedance into the specific permittivity εr and the specific conductivity σ of the ground is done with a numerical solution by means of Matlab.

The solution of the equation can result in very nice pictures. In the picture the divergence of all possible solutions is shown. The X and Y axes stretch the level of all possible qualities εr and σ. The measurement occurred with DF0DOX and shows the extremely good ground conductivity there.

Tobias (DG9TB) has provided a translation into the free SCILAB. Scripts for both programs can be requested with me. However, you should be familiar in dealing with the respective mathematics program.

## Values from the literature

As described in the appropriate literature the qualities of a more or less thin layer are to be considered. The measured values can be compared to the "classical" results.

 Conductivity Dielectric constant Current penetration depth

## Measuring values in figures

I have shown the measured values at two places here. The first measurement occurred in Immenstaad (near Lake of Constance) at DF0DOX, the second in the flowerbed because the very stony ground on the "Schwäbischen Alb".

Impedance at the end of the two-wire line and the calculated ground qualities.

Calculated ground qualities of both locations in one diagram

The measured values are plausible (see literature on top). The extremely good ground qualities at DF0DOX in Immenstaad (at Lake of Constance) strike and are also to be noted at the radio company clearly by extremely good signal strengths. The area is very similar to a rice field. Besides, the water stood only approx. 50 cm below the grass scar.

## Applicability

The plausibility of the conversion into the earth properties was checked quite several times successfully. With a high conductivity the measurement also occurs in the right depth, because the current penetration depth becomes already very small. If necessary the means from several measurements must be taken in the sphere of the aerial up to several λ distance.