Comparison of Bandpass $\Sigma \Delta$ Modulator Coding Efficiency With a Periodic Signal Model

Maximizing coding efficiency is important in applications where bandpass SigmaDelta modulation is used as a source encoder to synthesize a two-level pulse train in RF class-D amplifiers. A periodic pulse-train model is developed to MIMIC the encoding of a bandpass SigmaDelta modulator for sinusoidal source signals, and it is shown that the coding efficiency of both the model and the modulator vary similarly with changes in carrier oversample ratio. The relationship between coding efficiency and carrier oversample ratio is not monotonic and has significant dips at certain ratios. The predictions of the model are compared with simulation results for a fourth-order bandpass modulator. The results show that coding efficiency is low in a modulator design where the input frequency is one-fourth the sample rate (f_s) and can be increased by as much as 15% by selecting a slightly lower oversample ratio such as (3/10)f_s.