Analysis of Analog Sampled S-Parameters Data Using DSP Techniques

$S$ -parameter data of analog high-speed channels or interconnects are based on Laplace transform techniques, i.e., in the continuous frequency domain. However, $S$ -parameter data are typically presented in tabular form. This fact does not mean that the data are coming from digital systems. The channels or interconnects are analog. Yet there is a proliferation of methods using the fast Fourier transform (FFT), which is inherently used for digital systems, applied to sampled analog $S$ -parameter data. In a previous article, we used vector fitting (VF) and bilinear transformation (BT) to place the analog $S$ -parameter data into the z-domain while developing a sampling theorem in the frequency domain (the dual of sampling in the time domain). In this article, we analyze whether using the BT, with its known frequency warping effect, has any impact on the channel impulse response when taking the inverse FFT (IFFT). In addition, the discrete Hilbert transform (DHT) is used to check for causality on the z-domain. It will be shown that by using the DHT, the $S$ -parameters can be classified as causal or not, without needing $S$ -parameter data at infinite, or data extrapolation providing that the $S$ -parameters complies with the sampling criterion. Examples to validate the discussed methods will be shown.