| Sigma-delta modulators are among the key data conversion components in digital audio and multimedia systems. Power electronic converters transform power from one form to another by means of power semiconductor devices. For instance, an electric vehicle is propelled by an ac motor which derives its power from a dc battery. The dc-to-ac conversion is afforded by a power electronic converter. In this dissertation, we demonstrate the strong commonality between sigma-delta modulators and power electronic converters, and exploit this to invent, analyze, and build a new “quieter” and more efficient power electronic converter. Applications of this technology include electric submarines and vehicles, solar distribution systems, and wind turbines.; A novel application and generalization of sigma-delta modulation has emerged in the area of high frequency power electronics. A conventional sigma-delta modulator with scalar signals and binary quantizer is generalized to the hexagonal sigma-delta modulator which comprises vector signals and a hexagonal quantizer. Indeed, power electronic switching states may be thought of as determining the quantizer outputs. The output spectrum is a key performance measure for both communications and power electronics. This dissertation analytically derives the interesting output spectrum of the hexagonal sigma-delta modulator with a constant input using ergodic theory and Fourier series on the hexagon. The switching rate of the modulator is important for power electronic design. Formulas for the average switching rate are derived for constant and slowly varying sinusoidal inputs. Design techniques from communications such as white noise spectral analysis are generalized and applied to analyze the sigma-delta designs so that the noise can be shaped to design requirements and a range of interpolative sigma-delta modulator designs from communications can be drawn upon. Hardware and simulation results demonstrate significantly improved spectral characteristics over prior work. The hexagonal sigma-delta modulator is patented and has been implemented in spectrally demanding commercial power electronic products. |
