What is harmonic balance simulation?

From RF Design Wiki · By the RF Design Wiki editorial team · Published October 21, 2026 · Last reviewed October 21, 2026 · How we research

Harmonic balance (HB) solves for the periodic steady state of a nonlinear circuit by representing node voltages as truncated Fourier series. Linear elements are evaluated in the frequency domain, nonlinear devices in the time domain via FFT, and Newton iteration adjusts the harmonic amplitudes until currents balance at every node. It handles distributed elements and high-Q circuits far more efficiently than transient simulation.^[1]

What can harmonic balance compute?

Gain compression, P1dB, saturated power and efficiency.
Two-tone IM3/IP3 and IP2 (multi-tone HB).
Mixer conversion gain, isolation and spurs.
Oscillator frequency, output power and, with noise extensions, phase noise.
Large-signal S-parameters and simulated load-pull.

What determines accuracy and speed?

The number of harmonics and intermodulation products retained (order), the nonlinear model quality, and convergence aids such as source stepping. Strongly nonlinear or switching circuits need many harmonics; transient or shooting methods may then be better.

What is circuit envelope?

An extension that lets the harmonic amplitudes vary slowly in time, enabling simulation of modulated signals (ACLR, EVM) on carrier-frequency circuits without simulating every RF cycle.^[1]

Frequently asked questions

Why not just use transient?

Transient must simulate many RF cycles until steady state, which is slow for high-Q or distributed circuits.

Can HB simulate oscillators?

Yes, with an oscillator analysis that solves for the unknown frequency.

What is the order of an HB analysis?

The maximum harmonic and mixing product index retained.

References

Online sources accessed October 21, 2026; printed works cited by edition. See all sources.

“Microwave Circuit Design Using Linear and Nonlinear Techniques, 2nd ed.”. G. D. Vendelin, A. M. Pavio, U. L. Rohde, Wiley. 2005.

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