Semi-analytical formulation for a Unified Time and Frequency Antenna Characterization

Abstract

The definition of parameters that characterize the radiation of electric and magnetic fields for antennas in the time and frequency domain on an unified representation is proposed. The formulation uses a straightforward semi-analytical formulation that can be subsequently applied on the analysis of excited antennas for an arbitrary source with temporal behavior. The effective height is a parameter for antenna analysis defined for quantities in far field region and can be used as a transfer function of the antenna. This transfer function can be described through the antenna singularities which can be obtained by singularity expansion. The Singularity Expansion Method (SEM) is capable to model an electromagnetic quantity with the singularities extracted by the current densities of an arbitrary object. This work proposes that the singularities are extracted by the Matrix Pencil method applied on the current densities. The current densities are obtained numerically through the method of the Finite Differences in the Time Domain (FDTD) for wired log-periodic antenna and, after the singularities are obtained, the formulation of the semi-analytical effective height equation is written. To validate the presented method, a formulation of the time-domain radiation pattern is presented and a corresponding frequency-domain radiation pattern is also presented using Parseval's theorem.