Lumped-Circuits Model of Lossless Transmission Lines and Its Numerical Characteristics

Abstract

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Aiming at the lumped-circuits model of the lossless transmission line in the digital simulation, the article discusses and analyzes the unit step response generation of the lumped-circuits model by comparing the numerical simulation results of the implicit trapezoidal method, the implicit Euler method, and a multi-step formula. The root cause of numerical oscillations pointed out that using the L-stable numerical algorithm to indirectly simulate the dynamic response of the lumped-circuits model is a numerical method that does not truly reflect the original model, but it can directly reflect the true dynamic response of the lossless transmission line. In this study, a method for determining the chained number in the digital simulation of a lumped-circuits model is given. The simulation results prove the effectiveness of the method.

Keywords

• lumped-circuits
• digital simulation
• lossless transmission line
• numerical method
• chained number