Wideband model based on constant transformation matrix and rational Krylov fitting

This paper analyzes the use of fitting techniques based on partial fraction expansions in the fitting of modal transmission line functions and the assumption of constant and real transformation matrix (constant T) in the transformation of modal functions into phase domain. The focus is on the fitting of the propagation function due to its complexity compared to the characteristic admittance function. It is demonstrated for the first time that using a constant T can intrinsically violate the passivity of the transmission line system depending on the choice of frequency point for assigning the constant T. Consequently, the final rational model violates passivity at certain frequency intervals. Second contribution is the evaluation of the fitting performance with a new solution strategy based on the recently introduced rational Krylov fitting (RKF). The case studies suggest that RKF results in accurate and less order models compared to the vector fitting (VF) algorithm which is the de facto method in electromagnetic transient-type models. Finally, the fitting accuracy of the legacy constant T model based on Bode fitting is presented in the phase frame giving a clear picture of its poor fitting performance compared to modern methods and explaining its inaccuracies in the time domain.