Analysis of periodically switched nonlinear circuits and nonlinear oversampled sigma-delta modulators

This thesis proposes a new method for time domain response and sensitivity analysis of periodically switched nohnlinear circuits and nonlinear oversampled sigma-delta modulators. Using Volterra functional series and interpolating Fourier series, it extends the sampled datasimulation and two-step algorithm of linear circuits to periodically switched nonlinear circuits. The method can handle the inconsistent initial conditions encountered at switching instants. It is applied to the analysis of nonlinear oversampled sigma-delta modulators. The efficiency and accuracy of the proposed method are assessed using SPICE, brute-force, and the law of charge conservation on periodically switched nonlinear circuits, and nonlinear oversampled sigma-delta modulators. The method does not require the costly Newton-Raphson iterations. It is most efficient for analysis of circuits with mildly nonlinear characteristics and simulation over a long period of time.