Study On Wave Process And Algorithms Of Distortionless Transmission Line

In the past ten years with the rapid development of VLSI (very large scale integration) circuits and continual spread of electric power system scale, transient response of transmission lines has been regarded as an important research field. There are large numbers of literatures about the research on analysis and synthesis of transmission lines in internal and overseas periodicals. The transient analysis is essential for analysis and synthesis of transmission lines, so to solve transmission line equations becomes one important field of studying transmission lines. Because transmission line equations are partial differential equations, it is quite difficult to solve transmission line equations in time-domain or in complex frequency-domain in the condition of the existing mathematical tools and computer technology and it is not easy to obtain general results. In addition, in some special cases analytical solutions can be found, most scholars have used numerical calculation methods for analysis of the transient response of transmission linesIn this thesis, on the basis of the results of distortionless transmission lines, by using complex frequency-domain method and theorem of Laplace transform theory wave process and algorithms of distortionless transmission lines with arbitrary linear load were several aspects of the study as follows:(1) Mathematical models were established, the methods of sovling transmission line equations were discussed and the shortages of time-domain method were put forward.(2) The wave process of distortionless transmission lines with resistance load was analyzed on the basis of analytical solutions and travelling wave's propagation and reflection rules were obtained.(3) Recursive method for calculating voltage and current responses of distortionless transmission lines with inductance or capacitance load were put forward by using Laplace transform theory's time-domain convolution theorem on the basis of travelling wave's propagation and reflection rules.(4) When distortionless transmission lines were connected with arbitrary linear load and internal resistance, or inductance or capacitance's initial values were not zeros, recursive method for calculating voltage and current responses were put forward by using Laplace transform theory's time-domain convolution theorem and other theorems. (5) Zero-state responses of distortionless transmission lines with inductance, capacitance or arbitrary load, zero-input responses and complete responses with inductance or capacitance load were respectively calculated by examples and Matlab programs, and waveforms of each response is sketched. The results and waveforms demonstrated that the proposed method is valid.