Algorithms for computing almost periodic steady-state response of nonlinear systems to multiple input frequencies

Two efficient algorithms are presented for obtaining steadystate solutions of nonlinear circuits and systems driven by two or more distinct frequency input signals. These algorithms are particularly useful in cases where the steady-state response is either not periodic, or is periodic but its period is too large for existing methods. The first algorithm is applicable to any circuit or system driven by any number of input frequencies. The second algorithm is restricted only to 2 input frequencies and is therefore significantly more efficient than the first algorithm. Both algorithms are formulated for systems described by an implicit system of nonlinear algebraic-differential equations, thereby obviating the need to write state equations. Numerous examples have been solved successfully using these two algorithms. A selection of some of these examples is given for illustrative purposes.