原创 什么是良好的S参数

良好的S参数包括以下几个特点（hyperlynx手册）：

"Sufficiently Wide Frequency Range"

"Proper Asymptotic Behavior at Zero and Infinite Frequency"

"Sufficient Resolution"

"Proper Even and Odd Behavior"

"Causal Trajectory Plot"

"Passive Behavior"

1.第一点有两种取样模式，对于resonance frequency点附近需要采用adaptive signaling，以获得较好的谐振点深度幅值；

2.DC和infinite频率终点具有良好的渐近线，每个端口的传输函数可以表示为，每个端口多是独立的，在接近DC和infinite frequency处连续点处，传输函数的虚部基本基本为0，所以imaginary part tend to zero；

3.足够的精度可以保证在谐振处的取样充分，良好的还原谐振幅值；

4.In a good model, the real part of a dependency is an even function of frequency [f(x) = f(-x)], and the imaginary part is an odd function [f(x) = -f(-x)].表示real part在零点必须slope为0，而imaginary part必须幅值为0。

Technical Background on System Realness

Although you normally do not build the dependence for negative frequencies, you can. The model time response, including impulse response, is a real function and the impulse response and frequency-domain response are mutual Fourier transforms. If the inverse Fourier transform of a complex frequency response is always a real function indicating system realness, then this complex frequency response must obey the following special property:

The real part of the dependence must be an even function of frequency and The imaginary part must be an odd function If this condition is satisfied, then the imaginary part of the inverse Fourier integral from minus infinity to plus infinity becomes identically zero. Since these functions must also be continuous, it immediately follows that all the following are true:Odd number (first, third, and so on) derivatives of the real part are zero;Even number (zero, second,…) derivatives of the imaginary part are also zero

5.因果轨迹线为顺时针方向的轨迹线，根据第二条条件可以知道轨迹线从imaginary 为0的开始，到imaginary也为0的定终止。

In the trajectory plot of a model dependency, each high-Q resonance creates an almost ideal circle. By contrast, the overlap of several moderate resonances creates a more complicated picture. For example, both of the following examples have clockwise trajectories:

An isolated pair of complex conjugate poles creates a complete circle An isolated real pole creates a half-circle.Thus, the sum of causal dependencies is a causal dependence. Less known is that the product of causal dependencies is also causal. This is related to a property of convolution where you may cascade several causal models and the signal propagating through all of them is properly delayed. In the time domain, cascading means convolving impulse responses of the models, and in the frequency domain it corresponds to finding their product, which must also remain causal. The inverse is also true. If you multiply causal and non-causal frequency dependencies, the product may well be non-causal. 

6.passivity plot的值在全频段多必须在0以上；下图是违反无源性检查的图例。

just for learning exchange, tks!