Scattering parameters (better known as s-parameters) are intrinsically a frequency-domain concept. For wireless applications, which deal with a modulated carrier wave, the frequency domain is entirely satisfactory. However, in recent years s-parameters have gained favor in characterizing linear components in broadband (DC to gigahertz) applications like signal integrity engineering. For these multigigabit/s applications we need to derive a time-domain representation from s-parameter measurements, for example to create an eye diagram, or to include it in a system that also contains components transient (SPICE-like) models. Like most things, it turns out that there's a right way and many wrong ways to do this.
This article explains s-parameter theory and shows how to create accurate, delay-causal, and passive time-domain models by combining band-limited s-parameter data with knowledge about the physical characteristics of our component, namely that all physical components of finite size are delay-causal and components with no external energy input are passive. This method saves you the tears of frustration that would be caused by non-causal and non-passive models.
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(Note: there is a linked list of other s-parameter articles available at this site and related sites immediately below the authors' biographies.)
About the authors
Colin Warwick is signal integrity product manager at Agilent EEsof EDA, where he is focused on multigigabit per second signal integrity analysis tools. Prior to joining Agilent, Colin was with Royal Signals and Radar Establishment in Malvern, England, Bell Labs in Holmdel, NJ, and The MathWorks in Natick, MA. He completed his bachelor, masters, and doctorate degrees at the University of Oxford, England. He has published over 50 technical articles and holds thirteen patents.
Fangyi Rao received his Ph.D. degree in physics from Northwestern University in 1997, for research in quantum theory of magnetism and transport. He joined Agilent EEsof in 2006 as a Senior Development Engineer. From 2003 to 2006 he was with Cadence Design Systems, where he made key contributions to the company's Flexible Balance technology and perturbation analysis of nonlinear circuits. Prior to 2003 he worked in the areas of EM simulation, nonlinear device modeling, and optimization.
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