Application of Envelope-Following Techniques to the Shooting Method

We consider circuits driven by two or more signals with very different periods and propose a method to determine their steady state solution in the time domain. We present a new version of the shooting method based on the envelope following technique. We show how to use the envelope following method as the new engine to efficiently determine the trajectory of the circuit starting from the new guess of the initial conditions. It substitutes the less efficient time domain analysis used in the conventional implementation of the shooting method. We show that it is well suited to circuits where the ratio between the periods of the slow and fast behaviour is particularly high and characterised by strong non-linearities. The numerical properties at the basis of the proposed method are presented. Its features are shown by simulating different types of slow-fast circuits.