An automatic algorithm for equivalent circuit extraction from noisy frequency responses

This paper presents a fully automatic algorithm for the extraction of equivalent circuits from noisy frequency responses. The application area involves the generation of SPICE-ready macromodels for critical interconnects for signal integrity characterizations. Direct measurements are often employed to obtain a characterization of a given interconnect structure, leading to its frequency-dependent scattering responses. The proposed technique processes these responses and outputs an equivalent circuit. The algorithm is based on a modification of the well-known vector fitting scheme, which has now become a standard tool in EMC and SI studies. The presented improvements focus on robustness to noise, which is always present in measured data, and on automatic order estimation. These issues are addressed via an automatic detection of any spurious poles due to the noise, which are hard relocated in order to maximize the model accuracy. Several application examples are presented to illustrate the excellent capabilities of the new fitting scheme.