Quantization noise analysis of a closed-loop PWM controller that includes Sigma-Delta modulation

Sigma-Delta modulation is a popular noise shaping technique which is used to move the quantization noise out of the frequency band of interest. Recently, a number of authors have applied this technique to a pulse width modulation (PWM) controller for switching power converters. However, previous analysis has not incorporated the effects of analog-to-digital converter (ADC) resolution or feedback control on the Sigma-Delta modulator. In this work, quantization due to ADC resolution and PWM resolution are analyzed, considering the effects of noise-shaping and feedback. A number of simulations have been performed to explore the impact of various design choices on output noise. The study variables included the order of the Sigma-Delta modulator, resolution of ADC, resolution of DPWM, the plant and the compensator. The theoretical model developed is used to generate the expected system Power Spectral Density (PSD) curves for each design choice and simulations techniques are used to validate the analysis. Experimental analysis has been performed on a digital voltage-mode control (VMC) synchronous buck converter and the output voltage PSD curves are generated using the welch method and compared with the theoretical and the simulation results. The experimental PSD curves for the 1st - order modulator match the simulation and theoretical PSD curves. This suggests that the theoretical model is a useful approximation and similar methods can be used to analyze the contribution of the quantizers to the output noise of a closed-loop controller system.