Causality Enforcement in Transient Co-Simulation of Signal and Power Delivery Networks

Delay extraction based macromodeling techniques for tabulated/measured data

“…For the case of networks characterized by tabulated S, Y, Z, or H frequency-domain data, [23]- [26] present Hilbert transform based delay estimation. The work in [27], [28] incorporates delay estimation into the vector fitting algorithm using op timization.…”

“…Second, a macromodel representing a passive and causal structure, needs to be both passive and causal [23]- [26], [38]- [40], [53]. Third, for long delay lines, the or der of rational approximations can become very high, leading to large macromodels and subsequently, prohibitively CPU expensive transient simulations.…”

“…Causality is an im portant concept to consider since macromodels constructed from causal devices should also be causal [23]- [26]. In the case of linear systems, it was shown th at if the system is passive, then it is also causal [54].…”

“…There have been a handful of papers discussing this (2.79) topic [23]- [25], [27]- [29], and these methods are reviewed in this section. First, Hilbert transform based delay estimation is reviewed [23]- [26]. Second, optimization based delay estimation vector fitting algorithms are discussed [27], [28].…”

“…In order to extract a delay from the transfer function, it is im portant to obtain an accurate method to estimate this delay. It has been shown th at using the properties of minimum phase for passive structures, the port-to-port delay can be estimated using the Hilbert transform [23]- [26]. A function, H(s), is a minimum phase function if all its poles and zeros lie in the LHP.…”