The Digital Transient Model for Frequency-dependent Parameter Transmission Lines

The algorithm for obtaining the discrete response of popagation function for frequency dependent parameter line is presented. Consider a minimum sampling period Tsm, that is, the highest frequency fu=1/(2Tsm) in the signal is taken into account. The impedance z(omega) and the admittance y(omega) are obtained in the frequency range of [0,fH] by employing the Carson's formula. The propagation function at each frequency point is subsequently obtained, the impulse response in discrete time domain is then obtained using Poision Sum Formula. In order to avoid the long length of impulse reponse under the higher sampling frequency, the poles and zeros of z transform of discrete propagation function are evaluated by the Prony's method. Subsequently, the coefficients of the discrete infinite impulse response of propagation function are obtained. Using these coefficients the wave transfer sources can be easily computed by discrete convolution operation. The simulation tests show that the results using the proposed method is accurate, the error is not more than 1% in contrast of the results generated by EMTP.