Precise Mathematical Model of PSCM Class-D Amplifiers

A mathematical analysis of four-level (three-phase) phase-shifted carrier modulation class-D amplifiers with analog feedback is proposed. The nonlinear difference equations are extracted and solved using the perturbation theorem. In this way, a closed-form function describes the low-frequency part of the output for an arbitrary input signal. The results are generalized for an arbitrary number of levels by analogy, well matched with the previous model of two-, three-, and the proposed four-level ones. The analytical results confirm that, apart from switching frequency, the multilevel class-D amplifiers converge to linear amplifiers as the number of output levels increases. An analytical equation expresses the harmonic distortion of practically interesting five-level amplifiers with bridge-tied load. The model is verified by system-level simulations and circuit-level implementation. In this way, a prototype fully differential five-level circuit is implemented on the printed circuit board to confirm the model.