Broad-band impedance matching of the RLC generator and load

Abstract

This paper presents a simple theory for the design of a broad-band impedance matching network which, when operating between a given RLC generator z 1(s) and an RLC load z 2(s), yields a Chebyshev low-pass or band-pass response. Using realizability conditions of double frequency-dependent terminations, we present a new theorem which states that if there exists a second-order all-pass function such that the resulting reflection coefficients are bounded-real and satisfy Youla's conditions at each zero of transmission of z 1(s) and z 2(s), a ladder equalizer exists. A method to realize such a ladder is described. After choosing the order n of the transfer function not smaller than the total number of the energy storage elements of z 1(s) and z 2(s), the result can easily be extended to any all-pole low-pass response for any non-Foster positive-real impedances z 1(s) and z 2(s) except for the case where z 1(s) and z 2(s) have a common finite zero on the jω-axis.