Compact Analytical Description of Digital Radio-Frequency Pulse-Width Modulated Signals

Radio frequency pulse-width modulation (RF-PWM) has been used as a power coding method in all-digital transmitters, which employ highly efficient switched-mode power amplifiers (SMPA). The main drawback of RF-PWM is the high level of in-band harmonic distortion when digitally implemented. In order to reduce spectral aliasing effects and produce acceptable levels of harmonic noise, ultra-fast clock speeds are required, making it commercially infeasible. In this paper, we derive a novel compact analytical model of a multilevel digital RF-PWM, driven by an arbitrary bounded baseband signal. We show that the spectral aliasing effects are equivalent to a particular amplitude quantization of the input baseband signal. This result implies that highly linear digital RF-PWM can be realized with modest clock speeds if and only if the input baseband signal is pre-quantized according to the inherent quantization process. We provide full description of this quantization process and describe its dependence on RF-PWM design parameters. Presented results enable a complete understanding of the nonlinear behavior of digitally implemented RF-PWM, and therefore can aid in optimal transceiver design. Numerical simulations in MATLAB were used to verify the derived analytical expressions.