On optimum broad-band matching

Chebyshev gain functions have been widely employed for tly, matching a complex load to a resistive generator. Such transfer functions do result in optimum response when the terminations are purely resistive. However, assuming the overall transducer gain characteristic has monotone decreasing stopband behavior, the equal ripple transfer function is shown to be not optimum for a complex load. Furthermore, equalizers simpler in structure and superior in frequency response to equal ripple designs can readily be synthesized. Indeed it appears that nonoptimality will generally result whenever analytic gain-bandwidth theory is used to determine the constants of a transfer function belonging to an a priori specified class. Examples are presented for the matching of LCR and CR loads.