Investigation of Nonlinearities Introduced by Multi-sampled Pulsewidth Modulators

Multi-sampled pulsewidth modulator (MS-PWM) digital control is important for reduction of control and modulator delays as well as for noise suppression. To reduce aliasing and modulator nonlinearities, the MS-PWM is often implemented with switching ripple filtering, which limits the obtained dynamic improvements. This article analyzes the multi-sampled modulator nonlinearities in order to provide means for the optimal implementation of MS-PWM without ripple filtering. Depending on the types of intersections between the modulating waveform and the carrier, the nonlinearities are manifested as reduced-gain, zero-gain, and infinite-gain zones in the modulator transcharacteristic. For dc-type converters, the modulator nonlinearities can impair the transient response and give rise to limit cycle oscillations. For ac-type converters, it is shown that the modulator nonlinearities result in a stronger harmonic distortion compared to the aliasing effect. The nonlinear behavior is caused by the modulating waveform steps, whose pattern depends on switching ripple, controller gains, multi-sampling factor, and time delay of the control system. Particularly, the time delay is found to be a crucial factor that determines which nonlinearity is exhibited and to what extent. Discontinuity and nonlinearity graphs are proposed and exploited to adjust the time delay, so as to avoid specific nonlinearity zones and to, partially or completely, linearize the system behavior. The theory is experimentally verified on a dc-dc buck converter and a dc-ac single-phase inverter. This article is accompanied by videos of experimental validations.