Spectra of delta-sigma modulated inverters: an analytical treatment

Analytic expressions for the output voltage spectrum of an asynchronous delta (or delta-sigma) modulated inverter are reported and supported by experimental data. The analysis yields three functions that give the frequency, phase, and amplitude of each component of the spectrum. These functions are in terms of the sinusoidal reference waveform and the properties of the modulator. The method provides greater accuracy and computational efficiency than the numerical methods reported to date. The spectral components form pairs of sidebands around multiples of the average switching frequency. The functions detail the relationship between the number of significant sideband components and the depth of modulation and illustrate the spread-spectrum nature of delta modulation. Extensions to nonsinusoidal reference waveforms and to hysteresis current controllers are considered