Distortion analysis of periodically switched nonlinear circuits using time-varying Volterra series

This paper presents a new frequency-domain method for distortion analysis of general periodically switched nonlinear circuits. It generalizes Zadeh's time-varying network functions and bifrequency transfer functions from linear time-varying systems to nonlinear time-varying systems. The periodicity of time-varying network functions of linear and nonlinear periodically time-varying systems is investigated using time-varying Volterra series. We show that a periodically switched nonlinear circuit can be characterized by a set of coupled periodically switched linear circuits. Distortion of the periodically switched nonlinear circuit is obtained by solving these linear circuits. This result is a generalization of the multi-linear theory known for nonlinear time-invariant circuits. We also show that the aliasing effect encountered in noise analysis of switched analog circuits exists in distortion analysis of periodically switched nonlinear circuits. Computation associated with the folding effect can be minimized by using the adjoint network of periodically switched linear circuits, in particular, the frequency reversal theorem. The method presented in this paper has been implemented in a computer program. Distortion of practical switched circuits is analyzed and the results are compared with SPICE simulation.