Time domain analysis of lossy multi-conductor transmission lines using the Hilbert transform

A novel approach of using the Hilbert transform to enforce the causality requirements on the electromagnetic fields in the analysis of high-speed digital circuits is presented. The technique is particularly useful in the absence of extremely accurate broadband data for the complex permittivity of lossy dielectric materials. In order to validate the accuracy and usefulness of this approach, several numerical examples have been solved and compared to lossless and traditional noncausal models. Specifically, the authors consider the example of a two-conductor microstrip transmission line and compute the response of the line using a lossless, a conventional lossy, and the Hilbert transform lossy model.<>