Since a Gaussian pulse waveform has considerable DC content, it must be used to model lowpass structures. In that case, the center frequency and bandwidth of the project must be set such that Δf = 2f<sub>0</sub> and hence, f<sub>min</sub> = f<sub>0</sub> - Δf/2 = 0, and f<sub>max</sub> = f<sub>0</sub> + Δf/2 = 2f<sub>0</sub>. The width t of the temporal Gaussian pulse is then determined such that at f<sub>max</sub> the spectral Gaussian pulse drops to the d-level from its maximum value of 1. With a bandwidth of Δf, the pulse width must satisfy the following equation:
:<math> \exp[-(\pi f_{\delta} \tau)^2] = \exp[-(\pi \Delta f \tau)^2] = \delta \quad \Rightarrow \quad \tau = \frac{\sqrt{-\ln\delta}}{\pi f_{max}} </math>
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When you set δ = 0.1 (the default value), it means that the Fourier transform of your excitation waveform drops to 10% of its peak at the upper edge of your specified frequency range. For a Modulated Gaussian pulse waveform with a bandwidth of Δf, the pulse width must satisfy the following equation:
:<math> \exp[ -[\pi(f_{\delta} - f_0)\tau] ^2 ] = \exp \left[ -\left(\pi \frac{\Delta f}{2} \tau\right)^2 \right] = \delta\quad \Rightarrow \quad \tau = \frac{2\sqrt{-\ln \delta}}{\pi \Delta f} </math>
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