Proper Initial Solution to Start Periodic Steady-State-Based Methods

We present a numerical technique that automatically identifies a suitable initial solution to start periodic steady-state methods for simulating non-autonomous circuits at transistor-level. The method avoids the guessing of the initial solution, which may result in divergence of the steady-state method used. For high-Q oscillating circuits, acceleration methods are used to compute the periodic solution. For strongly nonlinear circuits, such as delay-locked loops and switching-mode power supplies, time-domain methods are preferred, e.g., Shooting-Newton. Usually, a number of pre-integration periods is guessed to provide an initial solution for the acceleration method. However, the method may diverge, then the guessing has to be repeated with no clue on the next one. Instead, the technique described here identifies a proper initial solution that makes the method converges, works in the time-domain and makes use of information stored during the integration process, thus is non-invasive for commercial circuit simulators and can be implemented with little effort. Besides, it works in parallel with the integration process, thus computations are cheap to perform. We show experimental results from applying our technique and then start shooting-Newton on five circuits, among which three are industrial and two are strongly nonlinear, that confirm the validity of our mathematical analyses.