Simulation of Nonlinear Circuits in the Frequency Domain

TLDR

Frequency‑domain simulation avoids the severe problems of time‑domain tools like SPICE for steady‑state analysis of analog and microwave circuits by replacing nonlinear differential equations with a complex algebraic representation that eliminates issues from distributed components and high‑Q circuits. This paper reviews harmonic balance as a general method for converting differential equations into a nonlinear algebraic system to obtain periodic steady‑state solutions, and introduces new techniques that exploit the formulation’s structure and circuit characteristics. The authors solve the resulting algebraic system using optimization, relaxation, and Newton’s method, and detail an implementation that combines Newton’s method with harmonic balance. These techniques dramatically reduce simulation time and enable harmonic balance to be applied to much larger circuits, making it suitable for monolithic microwave integrated circuits.

Abstract

Simulation in the frequency domain avoids many of the severe problems experienced when trying to use traditional time-domain simulators such as SPICE to find the steady-state behavior of analog and microwave circuits. In particular, frequency-domain simulation eliminates problems from distributed components and high-Q circuits by foregoing a nonlinear differential equation representation of the circuit in favor of a complex algebraic representation. This paper reviews the method of harmonic balance as a general approach to converting a set of differential equations into a nonlinear algebraic system of equations that can be solved for the periodic steady-state solution of the original differential equations. Three different techniques are applied to solve the algebraic system of equations: optimization, relaxation, and Newton's method. The implementation of the algorithm resulting from the combination of Newton's method with harmonic balance is described. Several new ways of exploiting both the structure of the formulation and the characteristics of the circuits that would typically be seen by this type of simulator are presented. These techniques dramatically reduce the time required for a simulation, and allow harmonic balance to be applied to much larger circuits than were previously attempted, making it suitable for use on monolithic microwave integrated circuits (MMIC's).