"Maximizing the Control Range of Matrix Converters by the Complex Synthesis PWM"

"The complex synthesis PWM is proposed as a versatile modulation method for matrix converters. It draws on the idea of complex representation of converter voltages. That representation, proposed earlier without mathematical justification, is reintroduced here with a rigorous proof of its validity and properties. The method permits the use of barycentric coordinates in the calculation of duty cycles, just like in the case of dc\/ac inverters, thus avoiding the need for using cumbersome trigonometric functions. Based on that idea, this paper discusses two important modulation variants and demonstrates how they can be combined to a hybrid modulation which enjoys maximum control range of input displacement angle, while not sacrificing the voltage transfer ratio and exposing the opportunities to reduce the switching frequency."