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This paper describes a method for adding thermal and amplifier noise to a KLM model for a transducer element. The model is used to compare the magnitudes of various noise sources in a 5 MHz array element typical of those used for linear array imaging with and without an amplifier. Fundamental signal-to-noise ratio (SNR) issues of importance to array and amplifier designers are explored, including the effect on SNR of effective dielectric constant of the piezoelectric material, individual element size, changing the number of elements, and adding an amplifier to an element before and after a cable. SNR is considered both for the case in which the acoustic output is limited by the maximum rarefactive pressure which is considered safe for a particular application (Mechanical Index limitation) and the case in which acoustic output is limited by the maximum transmit voltage than can he delivered by the imaging system or tolerated by the transducer. It is shown that the SNR performance depends on many controllable parameters and that significant improvements in SNR can be achieved through proper design. The implications for 1.5-D and 2-D array elements are discussed.