An Investigation on Multiple Reflections and Group Delay Behavior in High-Speed System Designs

In this study, the analytical solution for the group delay of a high-speed system with large impedance mismatch is derived. The accuracy and applicability of the solution are validated by comparing the calculated results between the analytical formulation and commercial tool results. Causal frequency-dependent stripline model is used in the formulation, and the derivation of analytical formulation is based on the transmissions and reflections of wave components in the high-speed channel. Therefore, the causality of the system can be ensured, and the number of transmissions and reflections considered in the calculation can be specified in the formulation. The derived analytical results indicate that multiple reflections in a system with impedance mismatch will contribute to oscillations in the group delay curve, but the minimum group delay at the valleys of the oscillations does not appear to be the minimum propagation delay of the system. The benefits of having analytical results play a critical role in identifying channel impairments in high-speed designs.