Estimation of the Impedance of a Distributed Model of a Transmission Line Under a Frequency Sweep

In this paper, an attempt has been made to explore the driving point impedance function (DPIF) of the transmission line. This can be done by constructing the DPIF of a transmission line from sweep frequency response analysis (SFRA) data and comparing its frequency response with the measured frequency response. The DPIF has an extra edge when compared to other transfer functions since only one terminal end is required to be operated. The measured data must be represented as a polynomial in the form of “s,” to construct a rational function. This rational function has to satisfy some properties so that the proposed ladder network can be synthesized. The conditions that must be satisfied are the numerically simulated data corresponds to DPIFs; the rational function generated should be real and positive. Of these, the first one can be checked by performing simulation. Carefully planned experiments are performed for this purpose. To check physical reliability, every function must conform to a Hurwitz polynomial. A generalized analytical equation for the driving point impedance function which is a function of polytopic numbers is also used for comparisons of the obtained impedance graph and derived equation. The results indicate excellent matching of frequency responses of impedance functions constructed from simulated SFRA and analytical function, thus establishing the feasibility of the application of the technique for transmission lines.