# A Compact Thevenin Model for a Rectenna and Its Application to an RF Harvester with MPPT
## 4 Materials and Methods  
The rectenna shown in Figure 2 was implemented on a printed circuit board with Rogers substrate and with the following components: \(C_{\mathrm{m}}\) = 0.5 pF (AVX, Fountain Inn, SC, USA), \(L_{\mathrm{m}}\) = 27 nH (0603 CS model, Coilcraft, Cary, IL, USA), \(C_{\mathrm{o}}\) = 1 nF, and a Schottky HSMS-2850 diode (Avago Technologies, San Jose, CA, USA) [33]. The selected value of \(C_{\mathrm{o}}\) comfortably accomplished, in order to theoretically have a small ripple (below 1 mV) with the values of \(I_{\mathrm{o}}\) shown later in Section 5, as well as the condition stated in Appendix A (\(C_{\mathrm{o}}>>C_{\mathrm{j}}\)). The circuit of Figure 2 was used for the rectenna characterization, where an RF generator (Agilent E4433B, Santa Clara, CA, USA) was connected at the input instead of the antenna and a Source Measure Unit (SMU, Agilent B2901A, Santa Clara, CA, USA) configured as a voltage sink (quadrant IV) at the output. The generator was set at a tuned optimal frequency of 808 MHz and at different values of \(P_{\mathrm{av}}\) (\(-30\) dBm, \(-20\) dBm, and \(-10\) dBm). For each value of \(P_{\mathrm{av}}\), the SMU was set at different values of \(V_{\mathrm{o}}\) while measuring \(P_{\mathrm{o}}\). Then, \(\eta_{\mathrm{rect}}\) was obtained as \(P_{\mathrm{o}}/P_{\mathrm{av}}\).  
As for the FOCV MPPT, a BQ25504 chip (Texas Instruments, Dallas, TX, USA) was used, and in particular an evaluation board provided by the manufacturer. The chip contains a boost converter with PFM control and the board includes, in reference to Figure 5, \(C_{\mathrm{L}}\) = 4.8 uF (combination of two ceramic capacitors of 4.7 uF and 100 nF placed in parallel), \(C_{\mathrm{REF}}\) = 10 nF, and \(C_{\mathrm{load}}\) = 104.8 uF (combination of three ceramic capacitors of 100 uF, 4.7 uF, and 100 nF placed in parallel). The default values of \(R_{\mathrm{oc1}}\) and \(R_{\mathrm{oc2}}\) were modified to 10 M\(\Omega\) in order to fix \(k\) = 0.5 (the default value is set to 0.78). The sampling and regulation periods are prefixed by the chip to 256 ms and 16 s, respectively. Then, the efficiency of the whole RF harvester (rectenna plus MPPT) was characterized by using the RF generator at the input of the rectenna and the SMU set at 3 V at the output of the MPPT (\(V_{\mathrm{load}}\)). The RF generator was set at different values of \(P_{\mathrm{av}}\), from \(-20\) dBm to \(-5\) dBm in steps of 1 dBm, and for each value the SMU measured the output power \(P_{\mathrm{load}}\). Then, from (23), \(\eta_{\mathrm{T}}\) was estimated.  
For demonstration purposes, the RF harvester including the MPPT was also employed to power a sensor node intended to upgrade a mechanical gas meter to a smart device [38]. For these tests, the node was programmed to stay in a standby mode, consuming 1.4 uA. The input power (\(P_{\mathrm{av}}\)) was set to keep the voltage supply of the sensor node (\(V_{\mathrm{load}}\)) at 3 V, thus \(P_{\mathrm{load}}\) = 4.2 uW. As for the RF harvester input, two configurations were used: (1) an RF generator and (2) a receiving monopole antenna. In the second case, another identical monopole antenna was connected to a nearby RF generator, jointly acting as a wireless energy transmitter. The antennas showed an insertion loss higher than 10 dB at 808 MHz. Figure 6 shows pictures of both setups.  
Figure 6: Picture of the setups for powering the sensor node using, for the RF harvester input, (**left**) the RF generator or (**right**) a monopole antenna.