Probe Based Shooting Method to Find Stable and Unstable Limit Cycles of Strongly Nonlinear High-q Oscillators

Probe insertion technique is considered as an exclusively frequency domain approach. It has been developed to increase robustness of the harmonic balance method, when simulating autonomous circuits to avoid the dc degenerate solution. This technique evidences several good properties, for instance when simulating oscillators either employing high quality factor resonators or ac coupled ones. In this paper the probe insertion technique is extended to the time domain. This allows the application of the shooting method to a wider class of circuits including for example crystal oscillators. The inherent superiority of the shooting method to simulate strongly nonlinear circuits and its recent reliable extension to mixed analog/digital ones outperforms the potentiality of the harmonic balance method. Furthermore, this time domain probe insertion technique is exploited to find possible multiple steady state solutions and efficiently check stability properties, thus avoiding to compute the eigenvalues of the monodromy matrix.