  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 mice's 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.
