Transmission Lines Impedance Fitting Using Analytical Impedance Equation and Frequency Response Analysis

Rational function approximation is commonly used to fit the transmission line impedance over a wide frequency range. Nevertheless, it is computationally costly and challenging to implement in practical applications due to the high number of approximations required to fit the impedance curve for the high-frequency range. Therefore, a novel fitting method of multiconductor transmission line (MTL) based on the analytical impedance equation of a transmission line using the impedance frequency response measurement is presented in this paper. The proposed fitting method is a function of the transmission line length since it is based on the analytical impedance equation of a finite transmission line. Furthermore, the proposed model uses a constant set of equations and calculated parameters to fit the impedance frequency response for a wide range of frequencies. Moreover, the proposed model parameters are calculated using derived resonance equations and the impedance frequency response measurement. In addition, an algorithm is developed to further fit the proposed model to the impedance frequency response measurement of the transmission line. MTL impedance frequency response is measured using a real-time digital simulator (RTDS). To ensure the accuracy of the proposed model, a comparison between the proposed model and vector fitting (VF) is presented.