In this chapter, we present some general compact model optimization and passivity enforcement algorithms. Model optimization can be viewed as a fitting-based model generation process, where we fit a parameterized model against the simulated or measured data of original circuits. Model optimization methods can be applied to more general modeling applications like modeling RF and microwave circuits where it is difficult to obtain the models directly from the structures of the circuits. Instead, engineers typically model those circuits by fitting full-wave simulation or measured data. One critical issue in such applications is the preservation of some important circuit properties like passivity and reciprocity.

In this chapter, we introduce some efficient model optimization and passivity enforcement methods, as well as some reciprocity-preserving modeling methods developed in recent years.

Passivity enforcement

In this section, we present the state-space based passivity enforcement method, which is based on the method used in [21], but we will show how this method can be used in the hierarchical model order reduction framework to enforce passivity of the model order reduced admittance matrix Ỹ(s).

Passivity is an important property of many physical systems. Brune [12] has proved that the admittance and impedance matrices of an electrical circuit consisting of an interconnection of a finite number of positive R, positive C, positive L, and transformers are passive if and only if its rational function are positive real (PR).