Widely separated time scales arise in many important circuit applications, e.g., switched-capacitor filters, mixers, switching power converters, etc. Detailed analysis of such circuits is often difficult or impossible with available methods, especially when strong nonlinearities are present. In this talk, a novel formulation and numerical methods are presented for analyzing nonlinear circuits with widely separated time scales. The key to the new techniques is the use of multivariate functions (functions of several variables) to represent signals with widely separated time scales efficiently. Using multivariate functions leads to a partial differential form for the circuit or system equations, which we call the Multirate Partial Differential Equation or MPDE. Previous methods for quasi-periodic or envelope analysis of multi-rate systems correspond to specific choices for solving the MPDE numerically.
We present new methods for solving the MPDE in the time domain, enabling strong nonlinearities to be handled effectively. Computation and memory are independent of the separation between time scales, leading to considerable savings when the disparity is large. For large circuits, iterative linear techniques are used to circumvent costly matrix factorizations. Representative circuit examples are analyzed with the new methods.