10,11,23,27,24,28,25,29,26,30,32,33,130,129,36,128,124,473,132,483,465,123 Transmission Line Simulation via Numerical Inversion of Laplace Transforms Introduction This application numerically inverts the Laplace transforms that describe the voltage and current in a transmission line, using the numeric option for inttrans:-invlaplace Consider a lumped parameter model of the transmission line: 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Applying Kirchoff's voltage and current laws to this system results in a pair of coupled partial differential equations, commonly called the Telegrapher's Equations: 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When v(x, 0) = i(x, 0) = 0, the partial differential equations are transformed into Laplace-domain equations, given below (Branc\314\214i\314\201k, 2011). where Zc and \316\263(s) are a characteristic impedance and propagation constant, and \317\2011(s) and \317\2012(s) are reflection coefficients: The system is perturbed by a voltage source Vi(s): LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2JVEiTEYnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYuUSomY29sb25lcTtGJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGSS8lKWVxdWFsaXR5R0YxLUkjbW5HRiQ2JFEkMS4wRidGMi8lJ2ZhbWlseUdRJkFyaWFsRicvJSVzaXplR1EjMTJGJy8lK2V4ZWN1dGFibGVHRjFGMg== Parameters 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Numeric Inversion 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Toutain, J., Battaglia, J., Pradere, C., Pailhes, J., Kusiak, A., Aregba, W., and Batsale, J. (January 13, 2011). "Numerical Inversion of Laplace Transform for Time Resolved Thermal Characterization Experiment." ASME. J. Heat Transfer. April 2011; 133(4): 044504. https://doi.org/10.1115/1.4002777 Lubomi\314\201r Branc\314\214i\314\201k (October 13th 2011). "Numerical Inverse Laplace Transforms for Electrical Engineering Simulation", MATLAB for Engineers - Applications in Control, Electrical Engineering, IT and Robotics, Karel Perutka, IntechOpen, DOI: 10.5772/19824. Available from: https://www.intechopen.com/books/matlab-for-engineers-applications-in-control-electrical-engineering-it-and-robotics/numerical-inverse-laplace-transforms-for-electrical-engineering-simulation References 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