Equivalent circuits of binomial‐form nonuniform transmission lines and their application

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Abstract
Among various nonuniform distributed‐parameter transmission lines, the exponential line and binomial line can be analyzed by obtaining the rigorous solutions of the telegraph equation. The exponential line in which the line parameters change exponentially has been studied in the past, but the binomial line has not yet been studied systematically because the rigorous solutions for the voltage and current distributions differ depending on the characteristic impedance. In this paper, the rigorous solution of the telegraph equation for 2nth‐order binomial lines is derived and its equivalent circuit is constructed by a cascade connection of uniform distributed‐parameter lines, lumped reactance elements and ideal transformers. Further, the binomial line is made equivalent to the exponential line by equating the characteristic impedances of both lines at the input and output terminals and by letting the order n of the binomial line be infinite. Finally, as an application example, the high‐pass filter consisting of the series lumped capacitance and uniform distributed‐parameter line is constructed by the quadratic binomial lines and series lumped capacitances.

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