Simulation of Nonlinear Circuits in the Frequency Domain

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).