Theoretical bounds on time-domain resolution of multilevel carrier-based digital PWM signals used in all-digital transmitters

Pulse-width modulation (PWM) has been extensively used in switched converter systems, and recently in RF applications, due to an increased interest in all-digital transmitters. These architectures employ high efficiency switched-mode power amplifiers (SMPA), where PWM is commonly used to generate the PA driving signal. However, digitally implemented PWM introduces large amount of in-band distortion, which is traditionally explained by spectral aliasing. In this paper we derive a novel closed-form time-domain expression for the output signal of a multilevel carrier-based digital PWM, driven by an arbitrary bounded input signal. We show that the spectral aliasing effects are equivalent to amplitude quantization of the PWM input signal, and give theoretical bounds on the output signal resolution for a given PWM scheme. Parameters of this quantization process are determined, and their dependence on PWM design specifications is shown. Numerical simulations in MATLAB were used to verify derived analytical expressions.