Rearch On Lossy And Uniform Transmission Line Unmerical Solution

Transient in transmission lines is vital to analyze the operation of many high-speed integrated circuits such as pulse communication systems and digital electronic circuit. With the increasing signal frequency and decreasing feature size of modern high speed integrated circuits, interconnect transmission line is playing an increasingly important role. Transmission line effects, such as reflection, dispersion and crosstalk, may cause the failure of circuit design. On the other hand, in traditional electricity industry, how to make accurate and efficient fault location is also a popular research area related to transmission line .So a study in transmission line is very significant and valuable.In this thesis, two time domain numerical solution approaches have been deduced by the aid of computational mathematics and circuit theory. Transmission line with loss and dispersion are traditionally modeled and analyzed in the frequency domain, while nonlinear devices or time-varied components must be characterized in the time domain. The prevailing approaches depend on costly time domain convolution, using the frequency domain network parameters such as S-parameter, Y-parameter or ABCD parameters to find analytic solution, and finding the time domain approximations by FFT or even numerical inversion of laplace transform (NITL) if there are a large number of nonlinear devices in the network. However these two methods deduced in this dissertation can get time domain response directly once using numerical solution to large-scale linear equations. Telegraph equations, can be looked as cascade connection of two-port network of lumped circuit of transmission line, is a hyperbolic partial differential equations. This paper implements differential formation of quasilinear differential equations, furthermore Lumped equivalent circuit mode at boundary and constraints between voltage and current have been incorporated to find boundary conditions. Because Partial Differential Equations can transform into Ordinary Differential Equations, It transforms Telegraph Equations into Ordinary Differential Equations. After that, the transient response of transmission line can be analyzed by the method of numerical solution for ODE. 4'th Rounge Kutta and Implicit Euler are implemented to find numerical solution. By comparison, Implicit Euler is better method as a kernel of transmission line simulation Computing and programming to Transmission line transient with different conditions of boundary and two line coupling or even more complicated internal switching or loadingare carried out, simulation waveforms are gotten. All results are accord with practical waveforms, which can be proven by other theory.