Signal space and its implementation for microwave nonlinear-network analysis

Today, harmonic balance is the most useful approach for microwave nonlinear-network analysis. Fast Fourier transform (FFT) is usually used to convert the nonlinear-elements' time waveforms into the frequency domain as part of the harmonic-balance process. This approach is straightforward for a single-frequency excitation, but is quite complicated and time consuming for the multifrequency-excitation case. In this paper, we propose a mathematical model termed 'signal space,' which enables (for a given nonlinearity) a direct calculation of the currents spectrum (given the voltages spectrum) and is suited for implementation for harmonic balance. Under describing-function criteria, we use the signal-space approach to get expressions for oscillator parameters such as oscillation frequency, stability condition, and injection-locking bandwidth. There is a good agreement between our results and Kurakawa's expressions.