# A 28 nm Bulk CMOS Fully Digital BPSK Demodulator for US-Powered IMDs Downlink Communications
## 3 Characterization of the US Data Link  
Since the features of links for power and data transfer determine part of the specifications for the all the implemented devices and, in particular, for PMIC and the demodulator, this section focuses on its characterization. It consists of two piezoelectric devices. The first one is the power transmitting piezo, TX PIEZO, which is placed outside the body and used to transfer power and transmit data to the implanted device (down-link); the other one is the RX PIEZO which, as indicated in Figure 1, is implanted together with the entire IC. It harvests the transferred power, receives data, and is also used to send data to the outside device (up-link). US-piezo receivers were selected among the ones present on the market, trying to carry out the best trade-off between dimensions, operating frequency, and the maximum transferable power. As per the results of previously conducted studies, the operating frequency under an electrical resonance condition was selected to be equal to \(f_{0}\sim 2\) MHz, for both piezoelectric devices, with a thickness, \(t\), of about 0.4-0.5 mm for the receiving piezo. This choice was due to a trade-off between the miniaturization  
Figure 2: BER vs. SNR (\(E_{b}/N_{o}\)) for binary modulation schemes: comparison by applying theoretical equations shown in the Ref. [32]. The graph was obtained by using the Matlab code reported in [33], supposing a AWGN channel and a unitary energy-per-bit, while the bit signal length is \(10^{5}\). requirement and the harvested power. In order to emulate the acoustic impedance of body tissues, ballistic gel was used. This solution was already adopted in various medical fields, such as the anthropomorphic cardiac phantom for ultrasound imaging, and thanks to its acoustic properties, and compatibility with conventional plastics molding techniques, it has been designated as among the best materials for tissue-mimicking [34]. Considering that both piezoelectric transducers should be separated by a physical sandwich composed by the skin, vessels, and cerebral cortex, the distance between them should be in the order of \(d=0.5\)-\(1.5\,\mathrm{cm}\); in this way, both the devices are encapsulated in ballistic gel, keeping such a distance fixed. As for the materials selection, they are the same as that used in the Ref. [14]. The TX-PIEZO is the PRY+0111 provided by PI Ceramics. It is made up by a disk of PIC255 with a diameter equal to \(10\,\mathrm{mm}\), with a radial resonant frequency equal to \(250\,\mathrm{kHz}\) and a transverse resonance frequency equal to \(2\,\mathrm{MHz}\). As for the RX-PIEZO, it is the 000065944 provided by the same manufacturer. It is a thin layer of PIC255, with a square form whose area is equal to \(9\,\mathrm{mm}^{2}\) and a thickness of \(t=0.5\,\mathrm{mm}\); its radial resonance frequency is placed at \(500\,\mathrm{kHz}\), while its transverse resonant frequency is about \(2\,\mathrm{ MHz}\). Figures 3 and 4 show the US-data link for testing and the RX-PZT. In detail, Figure 3 shows the encapsulation in ballistic gel with a fixed distance, \(d=1.0\,\mathrm{cm}\) between the RX-PZT and the TX-PZT to mimic the acoustic impedance of tissues, while Figure 4 presents the block diagram of the experimental measurement setup used for the characterization of the US-power link. A signal generator was used to drive the RX-PZT with a 20-\(V_{pp}\) sinusoidal signal, while an oscilloscope measured the received electrical signal over the TX-PZT. Let us now consider the definition of wavelength; \(\lambda=v/f\), when \(f=f_{0}=2\,\mathrm{MHz}\) and \(v\sim 1540\,\mathrm{m/s}\), it follows that \(\lambda=0.77\,\mathrm{mm}\). It means that the distance \(d=1\)-\(1.5\,\mathrm{cm}\) is quite large compared to the US-wavelength in tissues, so the waves propagate in a far-field region. This is further demonstrated by considering (2).