  Ultrasonic backscatter communication has gained popularity in recent years
with the advent of deep-tissue sub-mm scale biosensing implants in which
piezoceramic (piezo) resonators are used as acoustic antennas. Miniaturization
is a key design goal for such implants to reduce tissue displacement and enable
minimally invasive implantation techniques. Here, we provide a systematic
design approach for the implant piezo geometry and operation frequency to
minimize the overall volume of the implant. Moreover, a critical design aspect
of an ultrasonic backscatter communication link is the response of the piezo
acoustic reflection coefficient $\Gamma$ with respect to the variable shunt
impedance, $Z_E$, of the implant uplink modulator. Due to the complexity of the
piezo governing equations and multi-domain, electro-acoustical nature of the
piezo, $\Gamma(Z_E)$ has often been characterized numerically and the implant
uplink modulator has been designed empirically resulting in sub-optimal
performance in terms of data rate and linearity. Here, we present a SPICE
friendly end-to-end equivalent circuit model of the channel as a piezo-IC
co-simulation tool that incorporates inherent path losses present in a typical
ultrasonic backscatter channel. The circuit model is then used to simulate the
channel transient response in a common CAD tool. To provide further insight
into the channel response, we present experimentally validated closed form
expressions for $\Gamma(Z_E)$ under various boundary conditions. These
expressions couple $\Gamma$ to the commonly used Thevenin equivalent circuit
model of the piezo, facilitating systematic design and synthesis of ultrasonic
backscatter uplink modulators
