# A Compact Thevenin Model for a Rectenna and Its Application to an RF Harvester with MPPT
## 3 MPPT and Sensor Node  
In general, a sensor node directly connected to the output of the rectenna will not provide an equivalent resistance \(R_{\rm{o}}=R_{\rm{T}}\), at which the rectenna output operates at the MPP. Thus, an impedance matching stage (in addition to the matching network of the rectenna) is needed between the rectenna output and the sensor node, which can be implemented by a DC/DC converter. An MPPT, which consists of a DC/DC converter plus a tracking algorithm, can be used for automatically searching and settling that optimum value of \(R_{\rm o}\), which also corresponds to \(V_{\rm o}=V_{\rm MPP}\). Thus, the overall power efficiency of the RF harvester will be given by the following:  
\[\eta_{\rm T}=\eta_{\rm rect,max}\eta_{\rm MPPT}, \tag{22}\]  
where \(\eta_{\rm MPPT}\) is the efficiency of the MPPT and \(\eta_{\rm rect}=\eta_{\rm rect,max}\) since the MPPT biases the rectenna at the MPP.  
In this work, the fractional open circuit voltage (FOCV) MPPT technique is used, since it leads to simple and power efficient implementations. In this technique, the open circuit voltage (\(V_{\rm oc}\)) of the energy transducer (a rectenna here) is first measured and a fraction \(k\) of \(V_{\rm oc}\) is used to operate at \(V_{\rm MPP}\) and thus achieve \(\eta_{\rm rect,max}\). Taking into account the analysis in Section 2, a proper choice here is \(k=0.5\) (\(V_{\rm o}=V_{\rm MPP}=0.5V_{\rm oc}\)).  
Figure 5 presents the block diagram for the implementation of the FOCV MPPT technique, where \(C_{\rm L}\), \(C_{\rm REF}\), and \(C_{\rm load}\) are capacitors, \(R_{\rm oc1}\) and \(R_{\rm oc2}\) are resistors, \(S_{1}\) and \(S_{2}\) are switches, \(V_{\rm load}\) is the output voltage used to power the sensor node, and \(P_{\rm load}\) is the power transferred to the sensor node. The operation is the following. First, \(S_{1}\) closes and \(S_{2}\) opens (sampling period). For high values of \(R_{\rm oc1}\) and \(R_{\rm oc2}\), the output of the rectenna can be considered as open and thus \(V_{\rm o}=V_{\rm oc}\). The voltage divider formed by \(R_{\rm oc1}\) and \(R_{\rm oc2}\) fixes \(V_{\rm MPP}=kV_{\rm oc}\), being \(k=0.5\) here (i.e., \(R_{\rm oc1}=R_{\rm oc2}\)). The input capacitor (\(C_{\rm L}\)) momentarily stores the incoming harvested energy. Secondly, \(S_{1}\) opens and \(S_{2}\) closes (regulation period). Thus, \(V_{\rm MPP}\) holds constant thanks to \(C_{\rm REF}\), and the DC/DC converter settles \(V_{\rm o}\) around \(V_{\rm MPP}\) and transfers the harvested energy by the rectenna to the sensor node.  
In order to periodically update \(V_{\rm oc}\) (i.e., a change in \(P_{\rm av}\) changes \(V_{\rm oc}\)), the described sequence is periodically repeated, with the sampling period being much shorter than the regulation period. In this way, \(V_{\rm o}\) will settle most of time at \(V_{\rm MPP}\). To increase the efficiency at light loads, the DC/DC converter uses special control techniques such as pulse frequency modulation (PFM) or burst-mode [36].  
Taking into account (22), \(P_{\rm load}\) can be related with \(P_{\rm av}\) as follows:  
\[P_{\rm load}=\eta_{\rm T}P_{\rm av}. \tag{23}\]  
The value of \(P_{\rm load}\) and thus of \(P_{\rm av}\) must be enough, in average, to power the sensor node, which usually includes a rechargeable storage unit. This unit accounts for the variability of \(P_{\rm av}\), gathering or providing energy whenever \(P_{\rm av}\) is higher or lower than required. Storage units can be supercapacitors, batteries, or a combination of both [37]. On the other hand, the required value of \(P_{\rm load}\) and thus of \(P_{\rm av}\) can be reduced by operating the sensor node in sleep mode most of the time and minimizing its active time.  
Figure 5: Block diagram for the implementation of the fractional open circuit voltage maximum power point tracking technique.