Time domain probe insertion to find steady state of strongly nonlinear high-Q oscillators

Probe insertion is traditionally used in the frequency domain to increase robustness of the harmonic balance method and avoid the DC degenerate solution. This technique evidences several good properties, for instance when simulating oscillators that are based on high quality factor resonators or AC coupled ones. In this paper the probe insertion technique is extended to the time domain, allowing the application of the shooting method to a wider class of circuits including for example crystal oscillators. Time domain methods, such as shooting, are superior in the simulation of strongly nonlinear, and, thanks to a recent extention, mixed analog/digital circuits. Moreover, time domain probe insertion can be used to find multiple steady state solutions and check their stability properties, without the need to compute the eigenvalues of the monodromy matrix.