Modeling a buck-based switching amplifier for sinusoid wide band tracking by using a nonlinear time varying map

In this paper we derive a discrete time model to characterize the nonlinear dynamic behavior of a buck-based switching amplifier controlled by fixed frequency and PWM with a proportional-integral (PI) corrector. Numerical simulations show that the system can present period doubling bifurcation at the fast scale (switching frequency). As the switching frequency and the modulating frequency become closer, quasi-static approximation is not valid and the results based on it lead to erroneous conclusions about the stability of the system. We derive an exact solution discrete-time model able to predict accurately the nonlinear dynamical behavior of the system. The model is obtained without making quasi-static approximation and it can be used to obtain the useful region in the design parameter space from time domain simulations in a very fast and accurate manner.