S-Parameter Sampling in the Frequency Domain and its Time-Domain Response

Abstract

S-parameter characterization of high-speed interconnect components is prone to numerical, modeling, and/or measurement error due, in part, to the sampled nature of the data. This is a problem in modern package design where extensive signal integrity simulations are required to validate a system's performance. This article presents a new method of treating sampled S-parameter data where a criterion is developed to clearly state the minimum number of S-parameter frequency points required to adequately represent an analog physical system in the frequency domain. This criterion is akin to the Nyquist principle when sampling in the time domain. Based on this principle, the proper time-domain representation of S-parameters can be obtained using the inverse fast Fourier transform (IFFT). However, in order to use the IFFT, the bilinear transformation is applied to the vector fit S-parameters to place them in the z-domain. From the z-domain, the proper discrete impulse response is obtained. A lower bound, based on the discrete Heisenberg principle, is also offered to deal with frequency-time resolution of the S-parameters. The proposed method is successfully tested in the measured and simulated S-parameter data. The usefulness of this method is to accurately represent the time-domain behavior of the physical system S-parameter data, i.e., time delay causality, and, therefore, facilitates the applications of well-developed digital signal processing (DSP) techniques in S-parameter sampled data.