Resonant Impedance of Transmission Lines

The maximum absolute impedance for a tuned circuit which consists of a low-loss radio-frequency transmission line, either short-circuited or open-circuited at its distant end, and shunted at its sending end by a capacitor of negligible resistance is shown theoretically to occur when the line length is practically an integral number of quarter wavelengths and the capacitance is zero. This conclusion disagrees with previous theoretical results, which indicated shorter optimum lengths. It is pointed out that the earlier results are incorrect because of the neglect of the quadrature component of the characteristic impedance. An experimental verification of the theoretical results is provided.