The frequency spectrum of polar modulated PWM signals and the image problem

Pulse-width modulators (PWMs) are implemented in wireless transmitters to utilize highly efficient switched-mode power amplifiers (SMPAs) such as Class-D,E,F,J amplifiers. This paper gives the analytical expressions for the natural-sampling trailing-edge PWM (TE-NPWM) signals with input signals bounded by [0, 1]. Such PWM modulators can be incorporated in a polar architecture. Important relations of polar modulated PWM signals are analyzed in detail by exploiting the results of the analysis. The image problem is illustrated when a baseband PWM signal is modulated to the passband with the phase-modulated carrier. A properly designed lowpass filter can be used to reduce the image distortions, but increases the total design costs. It further introduces extra delay and has the possible drawback of reducing the overall efficiency. Based on the spectral analysis, two alternative approaches are proposed to show how the image distortions can be reduced without a lowpass filter. The performance of the presented approaches for the image reduction is demonstrated through numerical simulations.