Hexagonal sigma-delta modulation

A novel application and generalization of sigma-delta ((sigma)(delta)) modulation has emerged in three-phase powerelectronic converters. A conventional (sigma)(delta) modulator with scalar signals and binary quantizer is generalized to a (sigma)(delta) modulator with 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 paper analytically derives the 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 and formulas for the average switching rate are derived for constant and slowly varying sinusoidal inputs.