Analytic solutions for the response and natural frequencies of a delay line

摘要

The closed‐form analytic solution for the response of a lossless delay line is presented. The effects of all signal reflections to infinite order from both ends of the line are explicitly taken into account. In contrast with the conventional analyses, in which the natural frequencies of the circuit are given as the roots either of the transcendental equation or of a polynomial of degree equal to the number of LC sections, a simple analytic expression for the frequencies has been obtained. Thus, the present result enables one to avoid having to find approximate numerical solutions for the frequencies. The validity of this expression is demonstrated by comparison with a numerical calculation using the conventional method and with an experiment on a ten‐section line of high‐Q elements.