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The gain bandwidth restrictions are considered for a distributed parameter load consisting of a resistor shunted by an open-circuited stub of delay length . An aperiodic solution for the optimum flat gain response in the frequency domain is obtained by using a computer, solution, which solves the infinite set of simultaneous constraint equations associated with the infinite number of periodically spaced load transmission zeros. It is shown that this solution converges to the largest gain bandwidth product when only the fundamental frequency band is permitted and all higher order periodicities of the frequency response are properly suppressed by progressively shifting the center frequency of the higher order passbands, as their gains are attenuated. Furthermore, a new result for optimum flat gain periodic response is obtained. In this case, the equalizer is a cascade of commensurate lines each of length . This gives twice the gain of the best periodic equalizer employing lines equal to the stub length . Finally, synthesis techniques for realizing the optimum periodic equalizer are discussed.