# A Compact Thevenin Model for a Rectenna and Its Application to an RF Harvester with MPPT
## 1 Introduction  
Radio frequency (RF) energy harvesting has been extensively proposed to power tiny devices such as RFID tags, autonomous sensors, or Internet of Things (IoT) nodes. RF energy can be harvested either from dedicated sources, such as in the case of RFID devices [1, 2, 3, 4], or from the RF energy already present in the ambient environment and coming from unintentional sources such as TV, FM radio, cellular, or WiFi emitters [2, 5, 6, 7, 8, 9, 10].  
Figure 1 shows the block diagram of an RF harvester powering a sensor node. The rectenna (rectifying antenna) transforms the RF signal to a DC voltage and the maximum power point tracker (MPPT) provides the optimum load to the rectenna to transfer the maximum power to the sensor node.  
Figure 1: Block diagram of a radio frequency (RF) harvester powering a sensor node.  
The rectenna is composed of an antenna, an impedance matching network, and a rectifier. As the available power at the antenna decreases so does the generated voltage. Whenever this voltage is not high enough to properly bias the diodes of the rectifier, power efficiency severely decreases. Several techniques have been proposed to increase the efficiency at low power levels. One of them consists of using an L-matching network for boosting the voltage at the rectifier input [1, 3, 5, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21]. As for the MPPT, several works propose its use with rectennas using either commercial chips [6, 7] or ad hoc designs [22, 23, 24, 25].  
With the aim of gaining more insight into the performance of the rectennas, different analytical models are proposed. However, the derived expressions, which in some cases seek to model the rectenna output as an equivalent Thevenin circuit, are rather complex and may require additional simulations or extensive calculations, which hide the influence of the different parameters of the rectenna on its performance [12, 18, 26, 27, 28]. At the other extreme, the Thevenin parameters are sometimes inferred by experimental characterization [25, 29, 30, 31, 32]. However, in these cases no relationship with the rectenna parameters is established.  
Taking into account the previous limitations, this paper proposes a compact Thevenin model for the rectenna with the benefit of achieving manageable expressions of the Thevenin parameters as a function of the parameters of the rectenna so as to gain insight into its operation. In particular, the rectenna under study consists of an L-matching network and of a half-wave rectifier. The proposed model is then experimentally verified and the rectenna further tested in a high-efficency RF harvester with MPPT.  
The paper, which continues and expands the work presented in [32], is organized as follows. Section 2 presents the rectenna and the derived Thevenin equivalent. Section 3 describes the MPPT and the sensor node. Section 4 presents the materials and methods and Section 5 provides the experimental results and discussions. Finally, Section 6 concludes the work. Complementarily, two appendices are included. A presents an analytical development useful for the derivation of the Thevenin equivalent and Appendix B shows simulations of the rectenna with and without the matching network.