Frequency Coupling Matrices

This chapter shows how the frequency coupling matrix (FCM) of a power converter can be obtained by means of frequency‐domain and time domain methods. To convert the differential equation into an equivalent algebraic equation in the harmonic domain, one needs to first understand the concept of matrices of differentiation and Toeplitz. To formulate the FCM directly in the time domain, we need a bridge connecting between time and frequency domains. This can be done by converting the Fourier transform integral to its differential form. This chapter compares the FCMs constructed in the frequency domain and the time domain. To aid comparison with the frequency domain FCM, the time domain FCM in this chapter is derived based on complex Fourier series. An equivalent FCM may be derived based on the trigonometric Fourier series.