Harmonic balance is a method used to calculate the steady-state response of non-linear differential equations, and is mostly applied to electrical circuits . It is a frequency domain method for calculating the steady state, as opposed to the various time-domain steady state methods. The name "harmonic balance" is descriptive of the method, which starts with Kirchoff's Current Law written in the frequency domain and a chosen number of harmonics. Effectively the method assumes the solution can be represented by a linear combination of sinusoids, then balances current and voltage sinusoids to satisfy Kirchoff's law. The method is commonly used to simulate circuits which include nonlinear elements.
Microwave circuits were the original application for harmonic balance methods in electrical engineering. Microwave circuits were well-suited because, historically, microwave circuits consist of many linear components which can be directly represented in the frequency domain, plus a few nonlinear components. System sizes were typically small. For more general circuits, the method was considered impractical for all but these very small circuits until the mid-1990s, when Krylov subspace methods were applied to the problem. The application of preconditioned Krylov subspace methods allowed much larger systems to be solved, both in size of circuit and in numbers of harmonics. This made practical the present-day use of harmonic balance methods to analyze radio-frequency integrated circuits (RFICs).
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