Multi-probe harmonic balance method to simulate coupled oscillators

In this paper the harmonic balance method is considered in conjunction with the probe insertion technique. In general, the nonlinear equations modeling the circuit in the frequency domain are solved with the Newton iterative method. Conventional probe insertion technique has become popular and implemented in commercial analog simulators, since in many cases it shows better convergence behaviour of the Newton method and, therefore, of the harmonic balance one applied to autonomous circuits. The conventional probe technique, which is based on the insertion of a single probe, is here considered in detail, improved and extended through the insertion of two distinct probes working at two different frequencies with non necessarily an integer ratio. This improved version is exploited to compute the steady state working condition of coupled oscillators that operate in a pulling condition and that can switch to a locking one according to variations of circuit parameters.