We specify the excitation of an antenna in the time domain since FDTD operates in the time domain. If all we need is a single-frequency solution, a ramped sinusoidal waveform can be applied. The waveform is tapered from zero in about three cycles and the FDTD solution steps continue until a steady state is reached. It is more efficient to use a waveform that gives a wide-frequency-range response after performing a discrete Fourier transform on the radiating boundary to compute equivalent currents used at a given frequency. The computer storage and run times are the same for the wideband response as the single-frequency response.
A suitable wide-bandwidth excitation is the differentiated Gaussian pulse shown in Figure 1:
 (1)
We calculate the frequency response of the differentiated Gaussian pulse from the Fourier transform of Eq. (1):
 (2)The spectrum of Eq. (2) peaks for  . Figure 2 gives the normalized frequency response and shows that the −20-dB-level normalized frequency extends from 0.06 to 2.75. For example, if we wanted to center the frequency response at 10 GHz, the normalizing pulse time is easily found:
A check of Figure 2 shows that the antenna frequency response could be found from 2 to 22 GHz with only a 10-dB loss in dynamic range compared to the response at 10 GHz. A single time response computation yields a wide-frequency-range response.
FIGURE 1 Differentiated Gaussian pulse time response used in FDTD analysis.
FIGURE 2 Differentiated Gaussian pulse normalized frequency response.
A sinusoidal modulated Gaussian pulse produces a narrow-bandwidth excitation useful in visualization because the bandwidth of the pulse can be controlled:
 (3)
The unmodulated Gaussian pulse shown in Figure 1 has a low-pass frequency response:
 (4)Figure 2 gives the low-pass frequency response of the Gaussian pulse with a −4.37- dB response at . The sinusoidal modulation centers the frequency response of the Gaussian pulse around , and the convolution of the two frequency responses produces a two-sided response of the Gaussian pulse. |
