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Design of a discretized hyperbolic paraboloid geometry beamforming array of capacitive micromachined ultrasonic transducers (CMUT) has been presented. The array can intrinsically provide a broadband constant beamwidth beamforming capability without any microelectronic signal processing. A mathematical model has been developed and verified to characterize the array response. A design methodology has been presented that enables determination of the array's physical dimensions and CMUT modeling in a straightforward manner. Developed methodology has been used to design two discretized hyperbolic paraboloid geometry beamforming CMUT arrays: one in the 2.3 MHz to 5.2 MHz frequency range and another in the 113 kHz to 167 kHz frequency range. CMUTs have been designed using a cross-verification method that involves lumped element modeling, 3D electromechanical finite element analysis (FEA), and microfabrication simulation. The developed array has the potential to be used in real-time automotive collision-avoidance applications, medical diagnostic imaging and therapeutic applications, and industrial sensing.