Adaptive harmonic balance analysis of oscillators using multiple time scales

A harmonic balance (HB) method to analyze the steady-state response of free-running oscillators is proposed. It does not require a good initial guess of the oscillation frequency and exploits the frequency-domain latency of circuits by using a different number of harmonics in each variable. For the first time the warped multi-time partial differential equation approach is used to simultaneously bring the circuit state to the region of convergence of the HB analysis and determine the optimum number of harmonics required at each node in the circuit. The analysis of a LC-tuned bipolar oscillator is used to demonstrate the proposed method.