Harmonic Balance Methods Used in Computational Electromagnetics

The harmonic balance method is a powerful numerical technique for the analysis of high-frequency nonlinear circuits, and has been used to solve nonlinear microwave circuit problems. It is well-suited for simulating analog RF and microwave circuits, since these are most naturally handled in the frequency domain. The method is commonly used to simulate circuits which include nonlinear elements. The harmonic balance technique was first introduced to analyze low-frequency electromagnetics (EM) field problems. Harmonic balance techniques were combined with finite element method (FEM) to accurately solve the problems arising from time-periodic steady-state nonlinear magnetic fields. The harmonic balance FEM (HB-FEM) uses a linear combination of sinusoids to build the solution, and represents waveforms using the sinusoid; coefficients are combined with the finite element method. Harmonic balance can also be applied to EM field analysis, as the fields that contain the harmonics also satisfy Maxwell's equations.