Application of Prony´s method to time-domain reflectometer data and equivalent circuit synthesis

The singularity expansion of time-domain reflectometer data has been computed and used to calculate lumped-element equivalent circuits for the impedance of some typical antennas. Prony´s algorithm was used to obtain the poles of the antennas´ terminal voltage waveform due to a step-like excitation. The residues, however, were calculated subject to the uniform-error norm instead of the least-squared-error norm. Although it requires much longer to calculate, the uniform-error norm approximation is often orders of magnitude better than the least-squared-error approximation. The physical realizability of impedance functions obtained from experimental data has been investigated. Also, the procedures necessary to synthesize the lumped-element network have been evaluated. A simple partial-fraction expansion of a realizable impedance function representing an antenna was found to yield nonrealizable element values. A general network synthesis procedure, such as Brune´s method, is required.