5.4.1 Pre-defined signal library

QuickWave offers the user a library of pre-defined excitation waveforms. After choosing one of them in port settings dialogue its time domain shape and frequency domain spectrum are displayed schematically (the picture is only qualitative). The following waveforms are available:

delta – this waveform will excite a wave with infinite frequency spectrum and (theoretically) frequency-independent available power. With source amplitude set to unity the time-maximum available power is 1W.
sinusoidal – this waveform will excite a sinusoidal signal of a given frequency. The user can easily define the phase shift (interesting in some applications) by setting an appropriate value of Delay expressed in [ns]. The sinusoidal excitation is typically used when we need a better insight into wave propagation effects at a particular frequency. Note that since the sinusoidal excitation could provide the S-parameters only at one frequency, and since the simulation with such an excitation is not faster than with the pulse, it is never used for S-parameter analysis.

With source amplitude set to A, the time-averaged power available from a template source of sinusoidal waveform is 0.5*A².

pulse of spectrum f<f₂ – this waveform will excite a wave with a frequency spectrum limited from –f₂ GHz to +f₂ GHz. For this waveform type it is required to set a pulse Duration, which is expressed as the number of periods of the signal of the frequency f₂. Setting a very long pulse duration makes the pulse spectrum close to a rectangular shape, with energy being injected only in the frequency range between –f₂ and +f₂. For duration of the order 10..20, the spectrum shape is approximately trapezoidal, with signal value equal to Amplitude around 0, dropping to 0.5*Amplitude at –f₂ and +f_2.. In other words, power available from the source drops by a factor of 4 at –f₂ and +f₂ , with respect to power available at around 0. Longer duration cuts unwanted frequencies outside of the considered frequency band more effectively, but it also prolongs the computing time. The default duration of 3 is usually a wise compromise between those conflicting requirements.

In the case of quasi-TEM lines we can often predict that there will be no resonance within the frequency band quite above the band of interest. In such special cases, it may be better to set f₂ higher than the upper frequency of interest since this will reduce the absolute duration of the pulse, and speed-up the convergence.

pulse of spectrum f₁<f<f₂ – this waveform will excite a wave with a frequency spectrum limited from f₁ GHz to f₂ GHz. For this waveform type it is required to set a pulse Duration, which is expressed as the number of periods of the signal of the frequency f₂. Setting a very long pulse duration makes the pulse spectrum close to a rectangular shape, with energy being injected only in the frequency range between -f₁ and f₂. For duration of the order 10..20, the spectrum shape is approximately trapezoidal, with signal value equal to Amplitude around 0.5(f₁ + f₂), dropping to 0.5*Amplitude at f₁ and f_2.. In other words, power available from the source drops by a factor of 4 at f₁ and f₂ , with respect to power available at around 0.5(f₁ + f₂). Longer duration cuts unwanted frequencies outside of the considered frequency band more effectively, but it also prolongs the computing time. The default duration of 3 is usually a wise compromise between those conflicting requirements.

Gauss of spectrum f=f₁/(-/+f₂) – it is a Gaussian spectrum excitation. For Gaussian pulses the value of Amplitude applies at the centre frequency. Ideally, for an infinitely long Gaussian pulse, its spectrum is also Gaussian. For pulses of duration 3 or more, the spectrum is Gaussian with a very good accuracy, having a maximum signal value equal to Amplitude at the central frequency f₁. The signal value drops to sqrt(0.5)*Amplitude at f₁ + f₂.and at f₁ - f_2. (here it becomes higher when f₁ - f₂ becomes closer to 0 than to f₁). In other words, power available from the source drops by a factor of 2 at f₁ ± f_2., with respect to power available at f₁.
step pulse – this is an abrupt step pulse waveform. This step waveform may be in fact considered as the one with rise time equal to one FDTD iteration, thus to a FDTD time step dt. The value of dt parameter can be read in QW-Simulator in Simulation Info.
step with finite rise time t_r=1/f₂ – this is a step pulse with a finite rise time waveform. By defining a rise time the user avoids exciting the circuit at the frequencies significantly higher than f₂. The difference between this type of waveform and a step pulse is considered in User Guide 3D: A basic time domain reflectometry (TDR) example.

For typical S-parameters calculations we advise the waveforms of limited spectrum f < f₂ or f₁ < f < f₂, with the limits f₁ and f₂ close to the limits of the frequency band of interest. A pulse with a wider spectrum may excite unwanted resonances outside the band of interest, which prolong the transient effects in the modelled circuit and thus the computing time. In the case of cylindrical waveguide ports, resonances can be expected around cut-off frequencies of the consecutive modes.

It should be noted that for all waveform types the Amplitude and Delay of the signal can be set. Those parameters are irrelevant for calculations of S-parameters or radiation patterns (in scaling other than Fields at 1m on the Gain References list). They may be important for visualisation of the effects of concurrent multi-port excitations, for simulation of nonlinear (e.g. temperature dependent) effects, or in cases when one wishes to directly monitor absolute values of fields or power.

Note that in case of template excitation, there is a direct correspondence between waveform Amplitude and power available from the source. For Amplitude set to unity, time-maximum power available from a sinusoidal source is 1W (at the source frequency) while time-maximum power available from a delta source - 1W wide-band. For other waveforms, available power varies with frequency, and equals unity at the centre of the band. The Power Available post-processing shows the time-maximum available power versus frequency. Increasing amplitude by a factor of A means increasing the available power by A². For more information about the normalisation needed to read the absolute values of fields and power please refer to Electromagnetic fields and Determination of input power.

The delay is expressed in [ns]. Note that in the case of sinusoidal excitation, it is directly related to the phase shift, which is interesting in some applications.

It is worth noting at this point that according to the fundamentals of the periodic FDTD algorithm described in [17] and implemented in QW-3D, real and imaginary grids of electromagnetic components are defined for periodic structures (3DP) and thus there are two additional parameters for the imaginary grid which should be also set: Amplitude and Delay.