Signal space - an implementation of the harmonic balance approach for microwave nonlinear network analysis

Harmonic balance is today the most useful approach for nonlinear microwave network analysis. Usually FFT is used to convert the nonlinear elements time waveforms into the frequency domain as part of the harmonic balance process. This approach is straight forward for a single frequency. excitation, but is quite complicated and time consuming for the multi-frequency excitation case. Steer [1] proposed the Generalized Power Series, which enables for a given nonlinearity a direct calculation of the currents spectrum given the voltages spectrum. In this paper we propose a mathematical model termed Signal Space, which is similar to Steer's approach but better suited to implementation for harmonic balance. In [2] we extracted the signal space and made an approximation between the harmonic currents subspaces to enable a treatment of high nonlinearity of elements. Under describing function criteria we use the Signal Space approach to get expressions for oscillator parameters such as oscillation frequency, stability condition, injection locking bandwidth etc. Our results are compatible with Kurakawa's expressions.