Chapter 4 - Introduction to Numerical Modeling of Wire Antennas

Abstract

Each voltage and current in a circuit problem is a function of a single variable, either time or frequency. In antennas, the essential problem is to find the current at each point on the structure. Current is a function of position as well as either time or frequency. The methods to determine current presented in this chapter are in the frequency domain. For a fixed frequency, the problem reduces for finding a continuous complex-valued function of position. A related problem is the spectral analysis of a periodic signal, where a function of time over a particular interval is known and the amplitudes of the component frequencies are to be determined. The periodic function is approximated by a series of harmonic sine and cosine functions, and the Fourier series formulas is used to find the coefficients (amplitudes) of these sinusoids. The current on an antenna can be represented by a finite series of known functions with unknown amplitudes. Instead of adding up to a known function, the antenna current has to satisfy a boundary condition. The current on a simple structure like a dipole can be represented as a Fourier series. Each function in the series is defined over the entire length of the dipole, so it is called an entire-domain basis function. More complex structures are modeled using current functions defined over only short parts of the structure; these are called sub-domain basis functions.