## 3 System Implementation
### Solar Energy Harvester
As can be seen in Table 2, by modifying \(\beta\)C and \(\gamma\)C capacitors, different battery voltages, starting from V\({}_{\text{EOD}}\) of 0.9 V up to V\({}_{\text{EOC}}\) of 1.5 V, can be detected. In order to have a temperature-independent voltage reference, \(\alpha\)C should be modified according to the selected \(\beta\)C capacitor. By detecting the battery voltage between 900 mV and 1.1 V, the remaining charge of the battery can be estimated according to the discharge curve of the battery in Figure 4.  
After measuring V\({}_{\text{bat}}\) and estimating the energy stored in the battery, the operating frequency of digital circuits and bias currents of analog circuits are reconfigured according to the remaining charge of the battery. In the current-starved ring oscillator in Figure 6a, the frequency is determined by R\({}_{\text{L}}\) and C\({}_{\text{L}}\) and can be specified as Equation (2). In Equation (2), K\({}_{\text{1}}\) is a constant value that depends on the number of inverter stages in the ring oscillator [17]. By using a digital resistive trimming network to modify R\({}_{\text{L}}\), F\({}_{\text{osc}}\) is reconfigured by an energy harvesting circuit, according to the measured V\({}_{\text{bat}}\). When V\({}_{\text{bat}}\) is low, R\({}_{\text{L}}\) is increased to decrease F\({}_{\text{osc}}\). Four target operating frequencies have been considered, corresponding to four voltage levels that are detected by the LD block, ranging from 125 kHz, corresponding to V\({}_{\text{L}0}\), to 1 MHz corresponding to V\({}_{\text{L}3}\). \[F_{osc}=\ K_{1}/(R_{L}\times C_{L}) \tag{2}\]  
In addition to a fixed 10 nA beta-multiplier (BM) current reference that has been used to provide the required bias current for a solar energy harvester, a switched-capacitor beta-multiplier (SCBM) current source has been designed to generate frequency-proportional bias currents. In this circuit, which can be seen in Figure 6b, SC resistors have been used instead of regular resistors to generate frequency-proportional bias currents [18]. For example, I\({}_{\text{ADC}}\) can be specified as in (3):  
\[I_{ADC}=K_{1}\times K_{2}\times F_{osc}\times(C_{3}+C_{4}) \tag{3}\]  
In Equation (3), K\({}_{\text{1}}\) and K\({}_{\text{2}}\) are constant values that depend on the ratio between the widths of transistors in Figure 6b. K\({}_{\text{1}}\) depends on the ratio between M\({}_{\text{7}}\) and M\({}_{\text{4}}\), and K\({}_{\text{2}}\) depends on the ratio between M\({}_{\text{5}}\) and M\({}_{\text{6}}\). The current ripple of I\({}_{\text{bias}}\) is minimized by using a large decoupling capacitor, C\({}_{\text{2}}\), and two complementary branches charging and discharging C\({}_{\text{3}}\) and C\({}_{\text{4}}\) capacitors in non-overlapping \(\O_{\text{1}}\) and \(\O_{\text{2}}\) clock phases with F\({}_{\text{osc}}\) frequency [18]. As F\({}_{\text{osc}}\) is determined by the oscillator, I\({}_{\text{bias}}\) scales dynamically by changing the frequency of the oscillator. In addition, this current source can be easily deactivated by turning off the \(\O_{\text{1}}\) and \(\O_{\text{2}}\) clocks. In ultra-low power analog circuits, such as the discrete time incremental ADC that has been used here, bias currents should be high enough to guarantee correct operation at the target operating frequency. Generated bias currents (I\({}_{\text{ADC}}\) and I\({}_{\text{Temp}}\)) have been used for the sensor interface circuit. If \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Voltage Level (V\({}_{\text{L}}\))** & **\(\alpha\)C Capacitor** & **\(\beta\)C Capacitor** & **\(\gamma\)C Capacitor** \\ \hline
907 mV (V\({}_{\text{EOD}}\)) & 170 fF & 1230 fF & 230 fF \\
947 mV (V\({}_{\text{L}0}\)) & 170 fF & 1230 fF & 220 fF \\
1002 mV (V\({}_{\text{L}1}\)) & 180 fF & 1300 fF & 220 fF \\
1051 mV (V\({}_{\text{L}2}\)) & 180 fF & 1300 fF & 210 fF \\
1104 mV (V\({}_{\text{L}3}\)) & 190 fF & 1370 fF & 210 fF \\
1509 mV (V\({}_{\text{EOC}}\)) & 160 fF & 1160 fF & 130 fF \\ \hline \hline \end{tabular}
\end{table}