This paper presents an analytical design of an ultrasonic power transfer system based on piezoelectric micro-machined ultrasonic transducer (PMUT) for fully wireless brain implants in mice. The key steps like the material selection of each layer and the top electrode radius to maximize the coupling factor are well-detailed. This approach results in the design of a single cell with a high effective coupling coefficient. Furthermore, compact models are used to make the design process less time-consuming for designers. These models are based on the equivalent circuit theory for the PMUT. A cell of 107 um in radius, 5 um in thickness of Lead Zirconate Titanium (PZT), and 10 um in thickness of silicon (Si) is found to have a 4% of effective coupling coefficient among the highest values for a clamped edge boundary conditions. Simulation results show a frequency of 2.84 MHz as resonance. In case of an array, mutual impedance and numerical modeling are used to estimate the distance between the adjacent cells. In addition, the area of the proposed transducer and the number of cells are computed with the Rayleigh distance and neglecting the cross-talk among cells, respectively. The designed transducer consists of 7x7 cells in an area of 3.24 mm2. The transducer is able to deliver an acoustic intensity of 7.185 mW/mm2 for a voltage of 19.5 V for powering brain implants seated in the motor cortex and striatum of the mices brain. The maximum acoustic intensity occurs at a distance of 2.5 mm in the near field which was estimated with the Rayleigh length equation.
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