关于CST产生S参数有波纹变化的官网说明

CST is mainly calculated through the finite time domain integral method. If the frequency band concerned is narrow, the actual simulation frequency band is set wider. In principle, CST can calculate a wider band. This is mainly because: in the time domain solver, the S parameter is realized by transforming the time domain solution to the frequency domain, and there are inevitably errors in this transformation process, and the wider the frequency band, the greater the error.
What are the errors in the transformation from the time domain to the frequency domain? Anyone who has studied signals will understand: time-domain truncation. The default signal form in CST is “quasi-Gaussian” signal, which is called quasi-Gaussian signal because the real Gaussian signal is infinite in the time domain, and the processed Gaussian signal is indeed within a certain time range, which requires time-domain truncation of the ideal Gaussian signal. In other words, the real Gaussian signal that we use is the product of the ideal Gaussian signal in the infinite time domain and the truncation function in the time domain. The independent variable of the time-domain truncation function is in the range of [0,1]. Through product action, it retains the part of the ideal gaussian signal within the interval of [0,1], so that any part outside the interval is zero.
The ideal Gaussian signal itself has Fourier transform symmetry, that is to say, the Fourier transform of the ideal Gaussian is also gaussian. So, the real Gaussian signal corresponds to the frequency domain signal. According to the Fourier transform properties of time-domain product corresponding to frequency convolution, and the characteristics of time-domain truncation signal corresponding to Singer function (sampling function, sin(x)/x), it can be known that the spectrum corresponding to the real Gaussian signal is with “ripple”. Observing the simulated signal, we can see that the duration of input signal and output signal is not the same, and their ripple in the frequency domain is certainly not the same.
Ripple generation is the inevitable result of signal transformation from time domain to frequency domain. Moreover, the amplitude of fluctuation is directly related to the duration of truncation signal in time domain. The longer the truncation signal is, the closer the corresponding frequency domain signal is to the Dirac sampling function, the better the screening property is, and the smaller the ripple is. Conversely, the ripple is larger.
It can be seen that if we want to obtain the frequency domain result without ripple or small ripple interference, we need to adopt truncation signal with long duration. If we have a frequency point or frequency range of concern, when setting the frequency range of solution in the time domain simulator, it is best to use the narrowest possible frequency band, because the narrower the frequency domain signal is, the longer the corresponding time domain signal lasts, and the smaller the error will be generated in the later time and frequency domain transformation. However, the simulation frequency band should not be too small, because if the same frequency band is concerned, the two frequency points concerned will appear at both ends of the Gaussian function in the frequency domain, and the amplitude is very small. The smaller the amplitude is, the more sensitive it is to the error and the less reliable the result is. The range of S parameter is very small, and it also has the problem of small and large interference. Therefore, when S parameter is too small, the calculation is inevitably inaccurate.
Due to the limitations of the algorithm itself, a compromise solution is provided in the software. An AR-filter is provided in the post-processing template of the data. By filtering the S results, the fluctuation can be slowed down to a certain extent. The signal source can also be adjusted by AR-filter to a certain extent, which can automatically reduce the fluctuation in the simulation process, and the post-processing results can greatly reduce the fluctuation.