Transient analysis of circuits including frequency-dependent components using transgyrator and convolution

A method for the transient analysis is presented, in which a circuit containing frequency-dependent components is divided into two parts, linear and nonlinear. The linear part, containing components deened in the frequency domain, is treated as an n-port, for which the complex short-circuit admittance parameters (y-parameters) are calculated. The nonlinear part may contain any components that have a time-domain representation. The equivalent time-domain impulse response functions are obtained from the complex y-parameters using the Fast Fourier Transform. A novel transgyrator transformation is used to make it possible to obtain all impulse responses accurately. The port currents of the n-port can then be calculated in the time domain by numerically evaluating the convolution integrals of the impulse response functions and the port voltages. This method reduces the frequency-dependent components into static voltage-controlled current sources, independent current sources and constant conductances in the time domain, taking frequency-domain characteristics such as dispersion and frequency-dependent losses into account. By minimizing the number of the mathematical operations required, the method becomes useful and eecient.