Broad-band matching with maximally flat group delay characteristics

Abstract

The paper presents a new approach to the design of a broad-band matching network which, when operating between two given terminating impedances, yields a maximally flat group delay characteristic. First, we use the indeterminate coefficients to construct a scattering matrix, and then present a theorem which states that if there exists a set of real numbers such that the scattering matrix satisfies the realizability conditions and the system transmission function possesses the maximally flat group delay characteristic, the problem is solvable. If the equalizer is an all-pole low-pass network, the set of real numbers can be expressed in terms of a normalizing frequency coefficient <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\xi</tex> . The solution is then simplified to that of finding <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\xi</tex> under realizability conditions. The method is simpler and more accurate than that given by Zysman and Carlin using integral restriction and the Appell function.