Source waveforms and time to frequency domain transformation

Abstract

Sources are necessary components of a finite-difference time-domain (FDTD) simulation and their types vary depending on the type of problem under consideration. Usually sources are of two types: (1) near, such as the voltage and current sources described in Chapter 4; and (2) far, such as the incident fields appearing in scattering problems. In any case, a source excites electric and magnetic fields with a waveform as a function of time. The type of waveform can be selected specific to the problem under consideration. However, some limitations of the FDTD method should be kept in mind while constructing the source waveforms to obtain a valid and accurate simulation result. One of the considerations for the source waveform construction is the spectrum of the frequency components of the waveform. A temporal waveform is the sum of time-harmonic waveforms with a spectrum of frequencies that can be obtained using the Fourier transform. The temporal waveform is said to be in time domain, and its Fourier transformed form is said to be in frequency domain. The Fourier transform of the source waveforms and other output parameters can be used to obtain some useful results in the frequency domain. In this chapter, we discuss selected types of waveforms and then introduce the numerical algorithms for calculating the Fourier transform of temporal functions in discrete time.