An Actively Controlled Two-Terminal Network Implementing a Given Linear Nonconvolution-Type Immittance Operator

This paper is a study on the synthesis of digital filters used to control active or self-excited systems. The active two-terminal branch implements a nonconvolution-type immittance operator, which generates a current waveform depending on the given impedance or admittance operator. In this article, for the first time, the method of how to construct immittance operators for linear time-variant (nonconvolution-type) two-terminal circuits, over discrete time, is presented. These operators are useful when calculating periodic steady-state signals of a parametric circuit. The formula for the duty cycle is derived based on the current generated by this branch, assuming a known branch voltage or vice versa. This formula allows us to make a direct calculation of the duty-cycle in an analytical manner and does not refer to any auxiliary signals, e.g., sawtooth signals, or to any control systems, e.g., PI controller. The determined duty-cycles allow us to select the appropriate switching frequency and voltage value for the switched voltage source. With this method, it is also possible to assess the parameters of the current signal that would be generated in the actual active filter branch due to the calculated PWM voltage. The presented method can be an alternative to commonly used PI controllers in feedback for controlling active power filters/inverters.