NONLINEAR CIRCUIT SIMULATION IN THE FREQUENCY-DOMAIN.pdf

NONLINEAR CIRCUIT SIMULATION IN THE FREQUENCY-DOMAIN? Kenneth S. Kundert Alberto Sangiovanni-Vincentelli University of California, Berkeley, CA. 94720 Abstract Simulation in the frequency-domain avoids many of the severe problems experienced when trying to use traditional time-domain simulators such as Spice [1] to find the steady-state behavior of analog, RF, and mi- crowave circuits. In particular, frequency-domain simulation eliminates problems from distributed components and high-Q circuits by forgoing a nonlinear differential equation representation of the circuit in favor of a complex algebraic representation. This paper describes the spectral Newton technique for performing simulation of nonlinear circuits in the frequency-domain, and its im- plementation in Harmonica. Also described are the techniques used by Harmonica to exploit both the structure of the spectral Newton for- mulation and the characteristics of the circuits that would be typically seen by this type of simulator. These techniques allow Harmonica to be used on much larger circuits than were normally attempted by previous nonlinear frequency-domain simulators, making it suitable for use on Monolithic Microwave Integrated Circuits (MMICs). 1. Introduction It is common for circuits designed to operate at RF and microwave frequencies to be pseudo-linear in nature. By this it is meant that in- put signals are sinusoidal and small enough so that few harmonics are produced. This does not imply that the nonlinearities in the circuit can be neglected. Indeed, mixers and oscillators fit this description and yet they fundamentally depend on nonlinear effects to operate. It is also common for these circuits to have a large number of distributed components such as transmission lines, whose models often include loss, dispersion, and coupling effects. These distributed components are very difficult and often impractical to simulate in the time-domain because the partial differential equations that describe t