Transmission line synthesis by the method of characteristics

In this paper nonuniform transmission lines are synthesized by the method of characteristics in the time-domain. Given m sample values of the near end response at m time points, the impedance profile of a lossless nonuniform line represented by m uniform sections can be obtained. With 2m response samples at 2m time points the impedance and resistance profiles of a lossy nonuniform line are obtained. The propagation velocity of a signal is not necessarily constant, in fact it is not, along the transmission line. The m uniform sections may be different in length, but have a delay time equal to the relevant sample time interval. Two synthesis examples are given, showing good accuracy of the impedance and resistance profiles. The transient responses obtained with these profiles match the given responses satisfactorily over the sample time points.