Analytical characterization of the spectral performance of matrix converters

This paper proposes an analytical method to obtain accurate spectrum of the switching functions of matrix converter. The challenges associated with the spectral analysis of matrix converter waveforms are two fold. On one hand, the modulation signal contains both the input and output frequencies. Unlike the injected harmonics in the modulation functions, the input frequency and the output frequency may not be related to each other by an integer ratio. On the other hand, it is very common that the switching frequency or the carrier frequency is not rational multiple of either the input frequency or the output frequency. These aforementioned challenges make it an almost impossible task to obtain accurate spectra of matrix converter waveforms through commonly resorted numerical methods such as fast Fourier transform (FFT). The proposed solution is an extension of the double Fourier series expansion for the pulse width modulated waveforms.