Frequency domain techniques for modeling discrete switching events: EMT analysis

This paper reviews and compares three frequency domain techniques for the modeling of discrete switching events. The first one is based on the superposition principle where the open/closed states of the switch are represented by equivalent voltage/current sources. The underlying idea of the second technique is to partition the linear transformation matrix, given by the discrete Fourier transform, based on the switching-on and switching-off times. The third method uses the concept of a time-varying impedance/admittance function representing the switching operations. The impedance/admittance is expressed in the frequency domain as a Toeplitz-type matrix for performing the corresponding convolution with the switch voltage/current variable. Some examples are presented for the numerical comparison of the aforementioned methods.