Modeling and simulation of embedded passives using rational functions in multi-layered substrates

The objective of this research is to develop modeling and simulation techniques for embedded passive components using rational functions. We propose an acceleration algorithm that uses a limited set of sampled data to interpolate the response of the embedded passives and represent it as a ratio of two polynomials, providing significant savings in electromagnetic (EM) simulation time. The rational functions obtained in frequency domain by the interpolation technique are then converted into macromodels in SPICE for transient simulation. This enables the capturing of parasitic effects of embedded passive components in a transient simulation. We also propose a structured approach to synthesize equivalent circuits from the rational functions. It is shown that the elements of the equivalent circuits correlate well with the physical layout of the structure, giving insights about the parasitics and other EM effects associated with the structure. The results of the transient simulation have been compared to TDR/TDT measurements to show the accuracy. A new algorithm is proposed for enforcing the stability condition for the rational functions. Finally, both macromodeling and synthesis methods will be applied to circuits that consist of multiple embedded passive components, and the simulation results of the two techniques will be investigated.