Time-domain response and sensitivity of periodically switched nonlinear circuits

This paper presents a new sampled-data simulation method for analysis of the response and sensitivity of periodically switched circuits with mildly nonlinear elements at time points of an equal interval. Using the Volterra functional series and interpolating the Fourier series, the method extends the sampled-data simulation algorithm of linear circuits to periodically switched nonlinear circuits. In addition, it extends the two-step algorithm for periodically switched linear circuits to periodically switched nonlinear circuits to handle inconsistent initial conditions encountered at switching instants. The method is a general computer-oriented formulation method. It does not require costly Newton-Raphson iterations. Instead, it performs preprocessing computation of a set of constant matrices and vectors that are used in subsequent simulation steps. The response and sensitivity at time points of an equal space are obtained using elementary matrix algebra. The method is most effective if the nonlinear characteristics of circuits is mild and computationally efficient if the response and sensitivity over a long period of time are needed. The method has been implemented in a computer program. Simulation results on example circuits are compared with those from PSPICE, brute-force (BF), charge conservation, and linear multistep predictor-corrector methods to show the speed and accuracy of the method. The normalized difference between the response and sensitivity of example circuits obtained from the proposed method and those from PSPICE and BF at nonswitching time points is below 0.5%. The accuracy of the method at switching time points is verified using charge conservation.