Antenna characterization in the time domain

Abstract

A theory for a complete far-field transmit-receive system characterization of short-pulse antennas is derived in the time domain. The transmit-receive antenna system is characterized by a set of cascaded operators, which transform the source waveform and power into similar quantities at the receiving antenna terminals. Two such sets are defined. The first one is phrased in terms of the wave-type "time-dependent effective-height" operator, while the second one is defined in terms of the energy-type "gain operator". Both definitions fit within a complete transmit-receive system description, the latter being equivalent to the frequency-domain Friis equation. However, these operators are derived entirely in the context of the time-domain field equation. The starting point in the time-domain analysis of the effective height is the slant stack transform (SST) of the time-dependent current distribution in a manner equivalent to the spatial Fourier transform used in the frequency domain. The vector autocorrelation of the transmitting effective height is then used to define the time-dependent gain operator under impulsive source excitation. Time-domain reciprocity leads to the definitions of antenna parameters under receiving conditions and the corresponding equivalent circuit. The parameters defined in this way fit within a consistent transmit-receive convolution operator, operating on the autocorrelation of the input signal. This independent time-domain representation is thus similar to the frequency-domain representation. However, unlike the conventional frequency-domain circuit parameters, which relate voltage and current amplitudes, the time-domain circuit representation is based on incident and reflected wave-type constituents. In addition, the use of appropriate norms facilitates the transformation of our operators to stand-alone figures of merits. The general concepts developed are demonstrated for a short dipole antenna.