Transient excitation of thin-wire antennas.

Jean-Paul Van Gestel Department of Mining and Petroleum Engineering, Delft University of Technology, Delft, The Netherlands.

To obtain a better insight in the working of the Ground Penetrating Radar we are trying to model this instrument by a theoretical method. Thereby we interpret the two antennas as two thin-wire segments, the transmitter and the receiver. As source of the electric current we take a voltage gap in the middle of the transmitting antenna. If we are able to model this set-up and determine the electric current which flows through the antennas, we get a better insight in the ground coupling of the Ground Penetrating Radar. Our model is independent of the medium parameters like the conductivity, permittivity, permeability and center frequency of the antenna, so these values can be chosen freely.

Starting with the Maxwell's equations, the reciprocity relation is derived. We use this relation to compare the thin-wire antenna state with an auxiliary state. So we arrive at Pocklington's equation, in which the electric current in the antenna is the only unknown factor. The weak form of this one-dimensional integral equation is discretized and solved with the use of numerical methods. Therefore we use a discretized-space and moving-on-in-frequency method. For every frequency we arrive at a matrix-vector equation, which can be solved using the Conjugate Gradient Fast Fourier Transformation method. This numerical method is speeded by using an initial guess, based on results obtained with previously determined frequency values.

When the antenna is perfectly conducting the current in the antenna is reflected in the end-points of the wire and it takes a long time before the wave is attenuated. We can prevent these unwanted reverberations to occur in the antenna with a resistance loading which is put over the antenna. This improves the clearness of the final picture considerably. After the calculation of a single antenna in a homogeneous medium, we extend this configuration to the two antenna case. We can look at the difference between the electric current computed when the receiving antenna is neglected and when the receiving antenna is taken into account. In the last situation the electric current is computed with the use of symmetrical properties and the superposition method.

So in conclusion the electric current is determined in two antennas independent of any medium parameter. The next step in our research is to change from a homogeneous medium to one which exists of two half-spaces and to look at the effects of a buried object. When we succeed in modeling this configuration we can compare the results with practical measurements.

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