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Capacitive micromachined ultrasonic transducers (cMUT) have large bandwidths, but they typically have low conversion efficiencies. This paper defines a performance measure in the form of a gain-bandwidth product and investigates the conditions in which this performance measure is maximized. A Mason model corrected with finite-element simulations is used for the purpose of optimizing parameters. There are different performance measures for transducers operating in transmit, receive, or pulse-echo modes. Basic parameters of the transducer are optimized for those operating modes. Optimized values for a cMUT with silicon nitride membrane and immersed in water are given. The effect of including an electrical matching network is considered. In particular, the effect of a shunt inductor in the gain-bandwidth product is investigated. Design tools are introduced, which are used to determine optimal dimensions of cMUTs with the specified frequency or gain response.