Using genetic algorithms for harmonic-balance analysis of nonlinear microwave circuits

Abstract

ABSTRACT: A genetic algorithm has been applied to the harmonic-balance analysis of nonlinear microwa ¤ e circuits. The algorithm does notrequire a Jacobian matrix, and therefore dispenses with the need forderi ¤ ati e information and a good initial guess. Results are presented fora circuit containing a square-law nonlinear resistor. Q 2000 John Wiley& Sons, Inc. Microwave Opt Technol Lett 26: 296]298, 2000. Key words: genetic algorithms; harmonic balance; nonlinear microwa ¤ ecircuit analysis INTRODUCTION Harmonic balance has established itself as one of the mostpopular techniques for finding the steady-state response ofnonlinear microwave circuits, especially those containing dis-tributed elements 1wx]2 . The vast majority of harmonic-balance algorithms employ the Newton]Raphson method tosolve the system of nonlinear algebraic equations that deter-mine the harmonic-balance error. However, the use of New-ton-type techniques brings with it the requirement for Jaco-bian matrix evaluation, which subsequently becomes the mostcomputationally expensive part of the analysis. The convolu-tion-based sample-balance technique 3 , which handles er-wxrors in the time domain rather than the frequency domain, ismore efficient, but it still requires a Jacobian. In order toachieve high levels of accuracy, analytical expressions fordevice nonlinearities are required when calculating the par-tial derivatives of the Jacobian.In a recent letter 4 , it was shown that genetic algorithmswxwx5 can be applied to the sample-balance analysis of nonlinearcircuits. Genetic algorithms 5 are optimization techniqueswxwhich are well suited to solving complex sets of nonlinearalgebraic equations such as those found in both harmonicand sample balance. Results for a circuit containing an idealdiode showed this to be a viable approach which does notsuffer from the limitations of other techniques for solvingsample-balance equations. In particular, the algorithm doesnot require a good initial estimate, nor does it need auxiliaryinformation such as a Jacobian formulation of the circuitequations. In this paper, we extend the work in 4 by apply-wxing a genetic algorithm to the solution of the harmonic-balance equations for a nonlinear one-port circuit. Althoughboth the harmonic- and sample-balance methods operate onthe same state variables, the former is more widely used fornonlinear microwave circuit analysis. This is because har-monic balance applies standard ac analysis techniques suchas those used in linear circuit simulators rather than convo-.lution to the linear subcircuits.HARMONIC-BALANCE GENETIC ALGORITHM HBGA