An approach to the analysis of nonlinearly terminated black-box circuits based on polynomial congruence techniques

An approach to the problem of deriving the overall dynamical model of an electrical circuit containing a linear lumped time-invariant black-box network terminated by nonlinear elements (with or without memory) and driven by independent signal sources, is presented. Extensive use is made of polynomial congruence techniques of number theory to determine a nonredundant set of differential equations in the nonlinear port variables and then the set of algebraic dynamical transfer relationships expressing output variables as functions of the integration ones, source signals, and their derivatives. The two-step procedure devised rests on extensive use of polynomial congruence techniques, which allows one to derive the polynomial operators appearing in the system differential equations by simple algebraic manipulations of the linear sub-network matrices. This feature makes the method particularly attractive for computer-assisted design applications, especially in the case of high-frequency circuits, for which a modular black-box approach based on measurement data is often desirable or even required