Delay-Based Macromodeling of Long Interconnects From Frequency-Domain Terminal Responses

We present a robust and efficient scheme for the generation of delay-based macromodels from frequency-domain tabulated responses. These responses can come from both simulation or direct measurement. The main algorithm is based on an iterative weighted least-squares process for the identification of delayed rational approximations. In case that pole relocation is performed during the iterations, the scheme can be interpreted as a generalization of the well-known vector fitting algorithm to delayed systems. Therefore, we denote this algorithm as delayed vector fitting (DVF). In case no pole relocation is performed, the scheme generalizes the so-called Sanathanan–Koerner iteration, calling for the denomination of delayed Sanathanan–Koerner algorithm. These techniques produce compact macromodels that are readily synthesized in SPICE-compatible equivalent circuits including delayed sources or ideal transmission line elements. These macromodels outperform classical rational macromodels in terms of simulation time. Several examples illustrate the advantages of proposed methodology.