Delay extraction from frequency domain data for causal macro-modeling of passive networks

Causality, which deals with the precise timing of signal propagation through passive structures like interconnects, is an important problem in the time domain simulation of distributed passive networks. If unaccounted for, it can lead to significant error in the signal integrity analysis of high-speed digital systems. Distributed passive systems are characterized by multiple causality conditions in their time-domain response. The port-to-port delay, which is the time taken by the electrical signal to reach from one port to the other, forms the basis for these causality conditions. This paper describes a technique to extract the port-to-port delay in passive networks directly from their frequency domain parameters. The technique can be applied to either S, Y or Z parameters of passive systems. It can also be extended to multi-port networks. The delay thus determined has been used to enforce causality on the S parameters of a passive system.