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Harmonic balance is a powerful steady-state technique that can be used to analyze linear and non-linear circuits.
In contrast to small signal S-parameter analysis (so-called linear analysis), harmonic balance considers multiple tones, making the assumption that the response can be determined if all of the chosen harmonics satisfy Kirchoff's law. Like electro-magnetic analysis, HB ends up being an approximation that meets an error function that you specify.
With harmonic balance it is possible to model multi-frequency response of receivers and exciters. It can also be employed to look at the non-linear response of a limiter.
HB can predict the performance of power amplifiers, provided you have an accurate large signal model of the transistor. That is a big caveat, ask the best power amplifier designers and you might find they hedge their bets using the Cripps method.
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