Hexagonal Sigma–Delta Modulation

A novel application and generalization of sigma–delta ( ) modulation has emerged in three-phase power-electronic converters. A conventional modulator with scalar signals and binary quantizer is generalized to a 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 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.