Initial conditions and robust Newton-Raphson for harmonic balance analysis of free-running oscillators

Poor initial conditions for Harmonic Balance (HB) analysis of freerunning oscillators may lead to divergence of the direct Newton-Raphson method or may prevent to find the solution within an optimization approach. We exploit time integration to obtain estimates for the oscillation frequency and for the oscillator solution. It also provides an initialization of the probe voltage. Next we describe new techniques from borderedmatrices and eigenvaluemethods to improve Newton methods for Finite Difference techniques in the time domain as well as for Harmonic Balance. The method gauges the phase shift automatically. No assumption about the range of values of the Periodic Steady State solution is needed.