Circuit extraction via time-domain vector fitting

This paper introduces a new algorithm for the automatic synthesis of SPICE-ready equivalent circuits of complex multiport lumped interconnect structures. The method is named time-domain vector fitting (TD-VF) due to its analogy to the well-known vector fitting algorithm, which operates in the frequency domain. The TD-VF computes a rational approximation of the transfer matrix for the structure under modeling using as raw data its transient port responses to suitable excitations. These include, e.g., the case of transient port scattering responses as typically obtained by full-wave electromagnetic solvers based on the finite-differences time-domain (FDTD) or finite integration (FIT) methods. The TD-VF algorithm works entirely in the time domain, without requiring any knowledge of the frequency-domain responses. This allows direct processing of possibly truncated transient responses, therefore allowing for short full-wave simulations. This paper shows that the accuracy level achievable by TD-VF is excellent. Hence, passivity can be enforced a posteriori using the spectral properties of associated Hamiltonian matrices. Several examples of package, connectors, and discontinuities are provided as illustration.