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Traveling-wave amplification of elastic waves in piezoelectric material can be used to produce net electrical power gain over a wide range of frequencies. It is of interest to estimate how the gains, bandwidths, and noise figures potentially obtainable with this kind of amplifier compare with those for amplification by more traditional methods. Attention is limited to the frequency range such that the wavelength of the sound is large compared with the mean free path of the carriers. Design criteria are suggested and are used to make estimates of performance that should be attainable in the very near future.