# Acoustic Backscatter Communication and Power Transfer for Batterless Wireless Sensors
## 4 Evaluation
### Wireless Energy Transfer
#### 4.1.2 Harvester Performance  
In the previous section, we only investigated the maximum extractable AC power at the transducer. However, the harvester has to convert AC into DC power to supply microcontrollers and sensors. In this section, we inspect the efficiency of the harvester only. When considering the harvester's performance, multiple factors may degrade its efficiency: First, the MPPT tracker of the PMU may mismatch the input impedance of the harvester, therefore, not extracting the maximum available power from the source. Furthermore,  
Figure 9: The maximum power point is achieved at half the open circuit voltage. Wirelessly transmitted power is highly frequency dependent, and the distance between transmitter and receiver is important. harvester self-consumption reduces the energy available to the application. This includes power consumed to boost the input voltage in the PMU and leakage currents from the storage and input capacitors. We define the efficiency of the harvester as the amount of power flowing into the storage capacitor divided by the amount of power that is theoretically available at the source. We evaluate the input power by applying a sine generator with variable series resistance \(R_{\text{s}}\) on the inputs of the harvester (see Figure 10a). With knowledge of the current \(I_{\text{H}}\) through and voltage drop \(V_{\text{H}}\) over the harvester, the power uptake is determined. Furthermore, the maximum available power to the harvester \(P_{\text{max}}\) is, according to the maximum power transfer theorem,  
\[P_{\text{max}}=\frac{V_{\text{in,eff}}^{2}}{4\cdot R_{\text{s}}}=\frac{V_{ \text{in}}^{2}}{8\cdot R_{\text{s}}}, \tag{15}\]  
where the sinusoidal source provides the effective (RMS) voltage \(V_{\text{in,eff}}\). Finally, we measure the harvested power \(P_{\text{h}}\) from the storage capacitor voltage  
\[P_{\text{h}}=\frac{\Delta E}{\Delta t}=\frac{C_{\text{ST}}\left(V_{\text{ST}}^{ 2}(t+\Delta t)-V_{\text{ST}}^{2}(t)\right)}{2\cdot\Delta t}, \tag{16}\]  
where \(\Delta E\) is the change in energy stored in the storage capacitor over a short time period \(\Delta t\). During this evaluation, no MCU was connected to the harvester, so all the measured power consumption is self-consumption from the harvester itself. Figure 10b shows the voltage on the storage capacitor over time for different source resistances and input voltages. The time required to fill the storage capacitor up to the maximum voltage varies with available power from the source, and if the source does not provide sufficient power, the storage voltage never reaches its terminal voltage but plateaus at a level where the harvested power and self-consumption are in equilibrium. Figure 10c  
Figure 10: The measurement setup is shown in **(a)**, and charge curves **(b)** show the voltage at the storage capacitor over time. The power consumed by the harvester is suboptimal **(c)**, and the PMU consumes part of the power itself. The self-consumption is dependent on the voltage at the storage capacitor **(d)**. provides a more detailed analysis of the harvested power. In the beginning, when the harvester is in cold start, it takes up about 239 uW, 87% of the maximum available power from the source. That indicates that the impedance match between the source and harvester is not optimal, i.e., the MPPT is not matching the source's resistance perfectly. Furthermore, considerably less power, i.e., 115 uW, ends up in the storage capacitor. The PMU consumes the remaining power itself. Once the source is turned off, the harvester loses up to 200 uW due to leakage and the quiescent current of the PMU. The self-consumption shown in Figure 10d is highly dependent on the voltage on the storage capacitor, indicating that the leakage current is the dominant factor. In the performed experiments, the efficiency of the harvester is around 40% to 50%. Exact efficiency is highly variable, as it depends on the power available at the source and even on the voltage over the storage capacitor.