Calculation of the transient response of lossless transmission lines

2023/05/20 by T. Koyano, Koyano, Takamitsu, J. S. Bobowski +1
Physics and Astronomy · #FOS: Electrical engineering #Lightning and Electromagnetic Phenomena #Signal Processing (eess.SP) #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.2306.09916

openalex publication_date 2023/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present an analytical calculation of the transient response of ideal (i.e. lossless) transmission lines. The calculation presented considers a length of transmission line connected to a signal generator with output impedance Z_g and terminated with a load impedance Z_L. The approach taken is to analyze a circuit model of the system in the complex-frequency or s-domain and then apply an inverse Laplace transform to recover the time-domain response. We consider both rectangular pulses and voltage steps (i.e. the Heaviside function) applied to the input of the transmission line. Initially, we assume that Z_g and Z_L are purely real/resistive. At the end of the paper, we demonstrate how the calculations can be generalized to consider reactive impedances.

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