# Acoustic Backscatter Communication and Power Transfer for Batterless Wireless Sensors
## 3 Materials and Methods
### Carrier Generation and Signal Reception  
The reader hardware fulfills two functionalities. It generates a carrier with a customizable frequency and receives and demodulates the reflected signal from the tag. A schematic overview is given in Figure 6. We use a dedicated waveform generator IC for signal generation, the AD9833 from Analog, which allows fine-tuning of the carrier frequency with up to 20 mHz resolution. The generated sine wave is amplified to a 30 V peak-to-peak amplitude to drive the piezo transducer.  
The same transducer is used for continuous signal generation and reception. We measure the current through the transducer to receive the reflected signal. A small 10 \(\Omega\) shunt resistor is placed in series with the transducer so that the voltage drop over the transducer is proportional to the current. After filtering, an analog demodulator removes the high-frequency carrier at \(f_{\text{c}}\), leaving only the backscattered signal at the intermediate frequency \(f_{\text{i}}\). The demodulation of the intermediate frequency is performed in software and is described in Section 3.4.  
Commercially available demodulator ICs are designed to work with RF signals and are unsuitable for frequencies as low as several hundred kHz. Therefore, we construct a demodulator from operational amplifiers and a switch. With the local oscillator as a control input, the switch changes between the received signal and the inversion of the received signal, effectively mixing the received signal with a square wave. After removing the high-frequency contributions of the result with a low-pass filter, the self-interference at  
Figure 5: At the tag, the incoming sine carrier wave is modulated with a PSK-modulated square wave at an intermediate frequency from the MCU. While the square wave has infinite bandwidth, the reflected signal also has infinite bandwidth.  
is shifted to a DC component, and the reflected signal is isolated with a bandpass filter. We provide a detailed mathematical description of the demodulation process in Appendix A.  
After filtering and amplification, the MCU samples the resulting signal with the internal analog-to-digital converter (ADC). The amplifier gain can be dynamically set by MCU, thus allowing the reception of a wide range of signal strengths.  
After introducing the modulation and demodulation scheme and the prototype hardware, we want to clarify the source of the SFE in Figure 7. In a conventional radio, Carrier Frequency Offset (CFO) and SFE are two separate effects, as the carrier is usually generated from a dedicated RF clock, while the baseband signal is generated from a digital device with a dedicated clock source. In our backscatter prototype, the reader generates the carrier frequency and uses the same clock for demodulation. Therefore, no CFO arises at this stage. However, the tag uses its oscillator for the generation of the intermediate frequency \(f_{\mathrm{i}}\) and for symbol timing, and this clock deviates from the sampling clock at the reader. This offset produces a symbol timing error and a phase rotation in the sampled signal. Although the phase rotation is introduced by a mismatch of the intermediate frequency, its effect is the same as from carrier frequency mismatch. Therefore, we will still refer to it as CFO for the remainder of this work.