Calculation of the transient response of lossless transmission lines Koyano, Takamitsu; Bobowski, Jake S.
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 Zg and terminated with a load impedance ZL. 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 Zg and ZL 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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