| Signal integrity engineering involves the use of electrical models and time-domain simulation to predict signal waveform degradation as the signal propagates across interconnects. It is employed most prevalently in the design of large digital systems, such as computers. Typically, the analysis and design techniques are concentrated in the continuous time domain, with the evaluation of time-domain waveform signal attributes being the primary tool for quantification of the degradation effects. Consistent with this continuous time-domain approach, the system models are often identified and expressed in the analog frequency domain, since this is the most natural domain for model identification, either by electromagnetic field simulation or empirical measurement. This research investigation focuses on the use of digital signal processing techniques in the discrete time domain and associated discrete frequency domains to augment typical signal integrity engineering techniques. Specifically, it explores in detail the use of Laplace-domain (s-domain) to z-domain transform methods to convert system interconnect models identified in the analog frequency domains to models in the discrete frequency domains. The models are first converted from the analog frequency domain, using known vector fitting algorithms, to form a rational function approximation for the system in the s-domain. They are then converted from the s-domain to the z-domain using methods generally applied in the fields of control theory and digital filter design, but which are less familiar in the field of signal integrity engineering. Two new s- to z- domain transformation techniques are developed that are particularly well-suited for signal integrity applications. The z-domain models are then assessed thoroughly in the z-plane using a variety of pole-zero analysis techniques to gain further insight into the nature of the system, and a new enhanced graphical method is introduced for the efficient assessment of such models in the z-plane. The overall results of this project are targeted toward enhancing signal integrity design methodologies in an industrial setting. |
