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If an equalizer amplitude-response curve is specified, it will be shown that the minimum flat loss obtainable with physical networks is determined. This flat loss, or scale factor on the response curve, is a function of the equalizer output-terminating impedance, which is arbitrary but prescribed, and the specified tolerance on input mismatch. If the output impedance is purely reactive, the limitations on maximum voltage transfer are obtained from a consideration of the open circuit impedance parameters of the system. If power or voltage transfer to a load with finite real part is to be optimized, the scattering parameters of the system are used to determine the limits of performance. Examples will be given comparing the performance of matched and lossless equalizers. In many practical cases the latter do not have substantially higher gain than the matched equalizer.