A Compact Thévenin Model for a Rectenna and Its Application to an RF Harvester with MPPT

Abstract

This paper proposes a compact Thévenin model for a rectenna. This model is then applied to design a high-efficiency radio frequency harvester with a maximum power point tracker (MPPT). The rectenna under study consists of an L-matching network and a half-wave rectifier. The derived model is simpler and more compact than those suggested so far in the literature and includes explicit expressions of the Thévenin voltage (V_oc) and resistance and of the power efficiency related with the parameters of the rectenna. The rectenna was implemented and characterized from −30 to −10 dBm at 808 MHz. Experimental results agree with the proposed model, showing a linear current–voltage relationship as well as a maximum efficiency at V_oc/2, in particular 60% at −10 dBm, which is a remarkable value. An MPPT was also used at the rectenna output in order to automatically work at the maximum efficiency point, with an overall efficiency near 50% at −10 dBm. Further tests were performed using a nearby transmitting antenna for powering a sensor node with a power consumption of 4.2 µW.

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.

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 Thévenin 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 Thévenin 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 Thévenin model for the rectenna with the benefit of achieving manageable expressions of the Thévenin 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 Thévenin 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. Appendix A presents an analytical development useful for the derivation of the Thévenin equivalent and Appendix B shows simulations of the rectenna with and without the matching network.

2. Rectenna and Its Thévenin Model

Figure 2 shows the schematic circuit of the rectenna under study [33], which includes a high-pass L-matching network (composed of a capacitor C_m and an inductor L_m), a half-wave rectifier, and an output filtering capacitor (C_o). The antenna is modelled by a sinusoidal voltage source v_a of amplitude V_ap and frequency f_o with a series radiation resistance R_a. On the other hand, v_in, Z_in, and P_in are, respectively, the sinusoidal voltage, impedance, and power at the input of the rectifier, i_d is the diode current, and V_o, I_o, and P_o are, respectively, the DC voltage, current, and power at the rectenna output. An equivalent resistance R_o is defined as V_o/I_o.

The amplitude V_ap is given by [12] as follows:

$$V_{\mathrm{ap}}=2\sqrt{2R_{\mathrm{a}}{P}_{\mathrm{av}}},$$

(1)

where P_av is the available power at the antenna. The matching network, at matching conditions, that is, Z_m = R_a (where Z_m is defined in Figure 2), boosts the voltage at the input of the rectifier by a voltage gain, G_t, given by [33] as follows:

$$G_{\mathrm{t}}=\frac{V_{\mathrm{inp}}}{V_{\mathrm{ap}}}=\frac{1}{2}\sqrt{\left(1+Q^2\right)},$$

(2)

where V_inp is the voltage amplitude of v_in and Q is the circuit quality factor given by:

$$Q=\frac{1}{{\omega }_{\mathrm{o}}{C}_{\mathrm{m}}{R}_{\mathrm{a}}},$$

(3)

where ω_o = 2πf_o. On the other hand, the value of L_m must comply:

$$L_m=\frac{1}{{\omega }_{\mathrm{o}}^2}\frac{1}{C_{\mathrm{p}}+C_{\mathrm{m}}{Q}^2/\left(1+Q^2\right)},$$

(4)

where C_p models the parasitic capacitance between node A and ground.

To ease the analysis of the proposed rectenna and also gain more insight into its performance, a compact Thévenin model is provided here. First, the left-hand equivalent circuit of Figure 3 accounts for the antenna, the matching network, and the parasitic elements (R_p-C_p) of the coil, diode, and layout of the circuit. These parasitic elements are derived in Appendix A, where R_p models the losses of the coil and diode and C_p includes the parasitic capacitance of the diode, coil, and layout.

Analyzing the left-hand circuit of Figure 3 at f_o, we can achieve the Thévenin equivalent represented by the right-hand circuit of Figure 3, where:

$$\begin{array}{c}{v}_{\mathrm{eq}}=2{\mathrm{G}}_{\mathrm{t}}{v}_{\mathrm{a}}\frac{R_{\mathrm{p}}}{4G_{\mathrm{t}}^2{R}_{\mathrm{a}}+R_{\mathrm{p}}},\\ R_{\mathrm{eq}}=\left(4G_{\mathrm{t}}^2{R}_{\mathrm{a}}\right)\Vert R_{\mathrm{p}},\\ C_{\mathrm{eq}}=C_{\mathrm{m}}\frac{Q^2}{1+Q^2}+C_{\mathrm{p}}.\end{array}$$

(5)

Next, the Thévenin equivalent of Figure 3 is linked to the next stage of the rectenna, the rectifier, resulting in the left-hand circuit of Figure 4, where the diode does not include its parasitic elements since they have been already considered in the previous derivation (they are included in R_eq and C_eq). The diode is forward biased when v_in, assumed sinusoidal, surpasses V_o. As a result, i_d is pulsed and is composed of the fundamental frequency (f_o) as well as its harmonics and a DC component (I_o). Impedance Z_s (defined in the circuit) is zero at DC (due to the coil L_m) and is equal to R_eq at f_o since L_m and C_eq form a parallel resonant circuit presenting an infinite impedance. On the other hand, at the harmonics of f_o we have Z_s << R_eq (due to C_eq) whenever Q is high enough. Therefore, only the current at f_o (i_in) originates a voltage drop and v_in will be sinusoidal, as assumed before. Thus, apart from boosting the voltage, the matching network ideally acts as an input band-pass filter that prevents any of the DC current and harmonics to flow through the antenna resistance and dissipate power. This leads to an ideal rectenna efficiency of 100%, assuming no losses in the circuit components and in the diode [34]. Contrariwise, when no matching network is present, maximum rectenna efficiency decreases to 46%, due to the additional losses at R_a originated by the current harmonics generated by the diode pulsed current, as demonstrated in [35]. Appendix B confirms these results via simulations. Finally, the value of C_o has to be much higher than the diode junction capacitance (C_j), as explained in Appendix A, to keep V_o nearly constant, that is, with a low voltage ripple (ΔV_o). This second condition leads to:

$$C_{\mathrm{o}}>\frac{I_{\mathrm{o}}}{\Delta V_{\mathrm{o}}{f}_{\mathrm{o}}}.$$

(6)

The left-hand circuit of Figure 4 leads to the equivalent Thévenin circuit of the rectenna, represented by the right-hand circuit of Figure 4, by linking their output voltage–current relationship. For the left-hand circuit, we have:

$$V_{\mathrm{o}}=V_{\mathrm{inp}}-V_{\mathsf{\gamma }},$$

(7)

assuming a fixed forward voltage drop V_γ at the diode and:

$$V_{\mathrm{inp}}=V_{\mathrm{eqp}}-R_{\mathrm{eq}}{I}_{\mathrm{inp}},$$

(8)

where V_eqp and I_inp are the amplitudes of v_eq and i_in, respectively. Substituting (8) into (7) provides:

$$V_{\mathrm{o}}=V_{\mathrm{eqp}}-V_{\mathsf{\gamma }}-R_{\mathrm{eq}}{I}_{\mathrm{inp}}.$$

(9)

On the other hand, for the right-hand circuit we have:

$$V_{\mathrm{o}}=V_{\mathrm{oc}}-R_{\mathrm{T}}{I}_{\mathrm{o}}.$$

(10)

Then, by equating powers, we obtain:

$$P_{\mathrm{in}}=P_{\mathrm{o}}+P_{\mathrm{d}},$$

(11)

where

$$\begin{array}{c}{P}_{\mathrm{in}}=\frac{V_{\mathrm{inp}}{I}_{\mathrm{inp}}}{2},\\ P_{\mathrm{o}}=V_{\mathrm{o}}{I}_{\mathrm{o}},\\ P_{\mathrm{d}}=V_{\mathsf{\gamma }}{I}_{\mathrm{o}},\end{array}$$

(12)

and P_d is the average power dissipated across the diode. Thus, replacing (12) into (11) and using (7), we arrive at the following:

$$I_{\mathrm{inp}}=2I_{\mathrm{o}}.$$

(13)

Finally, using (13) in (9) and equating (9) and (10), we obtain the parameters of the Thévenin model:

$$\begin{array}{c}{V}_{\mathrm{oc}}=V_{\mathrm{eqp}}-V_{\mathsf{\gamma }},\\ R_{\mathrm{T}}=2R_{\mathrm{eq}},\end{array}$$

(14)

where V_eqp can be derived from v_eq in (5), using V_ap instead of v_a, resulting in:

$$V_{\mathrm{eqp}}=2{\mathrm{G}}_{\mathrm{t}}{V}_{\mathrm{ap}}\frac{R_{\mathrm{p}}}{4G_{\mathrm{t}}^2{R}_{\mathrm{a}}+R_{\mathrm{p}}}.$$

(15)

Then, using (15) and R_eq of (5) in (14), we have:

$$\begin{array}{c}{V}_{\mathrm{oc}}=2G_{\mathrm{t}}{V}_{\mathrm{ap}}\frac{R_{\mathrm{p}}}{4G_{\mathrm{t}}^2{R}_{\mathrm{a}}+R_{\mathrm{p}}}-V_{\mathsf{\gamma }},\\ R_{\mathrm{T}}=2\left[\left(4G_{\mathrm{t}}^2{R}_{\mathrm{a}}\right)\Vert R_{\mathrm{p}}\right].\end{array}$$

(16)

Therefore, from (16), with an increasing P_av and thus V_ap, V_oc increases whereas R_T holds constant. Next, from (10), we can express I_o as:

$$I_{\mathrm{o}}=\left(V_{\mathrm{oc}}-V_{\mathrm{o}}\right)/R_{\mathrm{T}},$$

(17)

and the output power P_o over a load resistor R_o can be simply calculated as:

$$P_{\mathrm{o}}=V_{\mathrm{o}}{I}_{\mathrm{o}}=\frac{V_{\mathrm{oc}}{V}_{\mathrm{o}}-V_{\mathrm{o}}^2}{R_{\mathrm{T}}},$$

(18)

being the power efficiency of the rectenna as:

$${\eta }_{\mathrm{rect}}=\frac{P_{\mathrm{o}}}{P_{\mathrm{av}}}=\frac{V_{\mathrm{oc}}{V}_{\mathrm{o}}-V_{\mathrm{o}}^2}{P_{\mathrm{av}}{R}_{\mathrm{T}}}.$$

(19)

Applying the maximum power transfer theorem, maximum power is extracted from the rectenna for V_o = 0.5V_oc, which is known as the maximum power point (MPP) voltage (V_MPP). From (19), the resulting efficiency is as:

$${\eta }_{\mathrm{rect},\max }=\frac{V_{\mathrm{oc}}^2}{4P_{\mathrm{av}}{R}_{\mathrm{T}}}.$$

(20)

Thus, using (16) in (20), we arrive at:

$${\eta }_{\mathrm{rect},\max }=\frac{R_{\mathrm{p}}}{4G_{\mathrm{t}}^2{R}_{\mathrm{a}}+R_{\mathrm{p}}}{\left(1-\frac{V_{\mathsf{\gamma }}}{\sqrt{2R_{\mathrm{a}}{P}_{\mathrm{av}}}}\frac{4G_{\mathrm{t}}^2{R}_{\mathrm{a}}+R_{\mathrm{p}}}{4G_{\mathrm{t}}{R}_{\mathrm{p}}}\right)}^2.$$

(21)

As can be seen from (21), η_rect,max increases with increasing P_av. Obviously, with no losses (R_p = ∞ and V_γ = 0) η_rect,max = 1 is obtained. On the other hand, the dependence of η_rect,max on G_t is rather more complex. In [33], an optimum value of G_t was derived arising from the trade-off between the losses introduced by the coil and that due to the voltage drop of the diode. This optimum gain leads, from (16), to a particular value of R_T.

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_o = R_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_o, which also corresponds to V_o = V_MPP. Thus, the overall power efficiency of the RF harvester will be given by the following:

$${\eta }_{\mathrm{T}}={\eta }_{\mathrm{rect},\max }{\eta }_{\mathrm{MPPT}},$$

(22)

where η_MPPT is the efficiency of the MPPT and η_rect = η_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_oc) of the energy transducer (a rectenna here) is first measured and a fraction k of V_oc is used to operate at V_MPP and thus achieve η_rect,max. Taking into account the analysis in Section 2, a proper choice here is k = 0.5 (V_o = V_MPP = 0.5V_oc).

Figure 5 presents the block diagram for the implementation of the FOCV MPPT technique, where C_L, C_REF, and C_load are capacitors, R_oc1 and R_oc2 are resistors, S₁ and S₂ are switches, V_load is the output voltage used to power the sensor node, and P_load is the power transferred to the sensor node. The operation is the following. First, S₁ closes and S₂ opens (sampling period). For high values of R_oc1 and R_oc2, the output of the rectenna can be considered as open and thus V_o = V_oc. The voltage divider formed by R_oc1 and R_oc2 fixes V_MPP = kV_oc, being k = 0.5 here (i.e., R_oc1 = R_oc2). The input capacitor (C_L) momentarily stores the incoming harvested energy. Secondly, S₁ opens and S₂ closes (regulation period). Thus, V_MPP holds constant thanks to C_REF, and the DC/DC converter settles V_o around V_MPP and transfers the harvested energy by the rectenna to the sensor node.

In order to periodically update V_oc (i.e., a change in P_av changes V_oc), the described sequence is periodically repeated, with the sampling period being much shorter than the regulation period. In this way, V_o will settle most of time at V_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_load can be related with P_av as follows:

$$P_{\mathrm{load}}={\eta }_{\mathrm{T}}{P}_{\mathrm{av}}.$$

(23)

The value of P_load and thus of P_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_av, gathering or providing energy whenever P_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_load and thus of P_av can be reduced by operating the sensor node in sleep mode most of the time and minimizing its active time.

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_m = 0.5 pF (AVX, Fountain Inn, SC, USA), L_m = 27 nH (0603CS model, Coilcraft, Cary, IL, USA), C_o = 1 nF, and a Schottky HSMS-2850 diode (Avago Technologies, San Jose, CA, USA) [33]. The selected value of C_o comfortably accomplished, in order to theoretically have a small ripple (below 1 mV) with the values of I_o shown later in Section 5, as well as the condition stated in Appendix A (C_o >> C_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_av (−30 dBm, −20 dBm, and −10 dBm). For each value of P_av, the SMU was set at different values of V_o while measuring P_o. Then, η_rect was obtained as P_o/P_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_L = 4.8 µF (combination of two ceramic capacitors of 4.7 μF and 100 nF placed in parallel), C_REF = 10 nF, and C_load = 104.8 µF (combination of three ceramic capacitors of 100 μF, 4.7 μF, and 100 nF placed in parallel). The default values of R_oc1 and R_oc2 were modified to 10 MΩ 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_load). The RF generator was set at different values of P_av, from −20 dBm to −5 dBm in steps of 1 dBm, and for each value the SMU measured the output power P_load. Then, from (23), η_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 µA. The input power (P_av) was set to keep the voltage supply of the sensor node (V_load) at 3 V, thus P_load = 4.2 µW. 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.

5. Experimental Results and Discussion

As for the proposed rectenna, Figure 7 shows the measured values (in dots) of I_o (blue circles) and η_rect (red squares) as a function of V_o at different values of P_av. A least-squares fitting of (17) to the experimental data of I_o was performed (blue continuous line) to obtain the Thévenin parameters (V_oc and R_T) at each power level, which are shown in

Table 1. Inferred values of V_oc and R_T and calculated values of V_eqp at different values of P_av.

Pav (dBm)	Vap (mV)	Voc (mV)	RT (kΩ)	Veqp (mV)
−10	200 mV	937	3.56	1183
−20	63.2 mV	268	4.29	374
−30	20.0 mV	56.6	5.51	118.3

. Calculated values of V_ap, from (1), and of V_eqp, from (15), are also included in Table 1. This fitting differs from that performed in [32], where the efficiency data (η_rect) were used instead, which leads to slight differences in the Thévenin parameters. The new fitting procedure was considered more convenient as both V_oc and R_T can be more easily inferred from the fitting curve. As can be seen, the fitting curves match well the experimental data, and more at the highest power of −10 dBm, which confirms that the rectenna can be well approximated by a Thévenin equivalent circuit. Then, V_oc and R_T were used to obtain η_rect using (19), and the resulting curves are also represented in Figure 7 (red continuous line). The match with the experimental data is good, and again better at −10 dBm.

With C_m = 0.5 pF, R_a = 50 Ω, and f_o = 808 MHz, Q = 7.88 results from (3), and G_t = 3.97 from (2). Then, from (16) and assuming the value of R_p = 9.21 kΩ derived in Appendix A, R_T = 4.7 kΩ is obtained, which is within the range of values found in Table 1. The inferred values of R_T moderately change with P_av due to the relative low value of Q, which limits the accuracy of the rectenna model proposed in Section 2. However, a higher value of Q, which could be obtained using a lower value of C_m and appropriately readjusting L_m, does not lead to the optimum gain G_t [33], thus decreasing the power efficiency. On the other hand, V_oc in Table 1 increases with increasing P_av and thus V_ap, which agrees with (16). The values of V_oc can be estimated in advance, when necessary, from (16) by calculating V_eqp from (15), shown in Table 1, and inferring a value of V_γ from the manufacturer data or from simulations.

From the measured data of η_rect (red squares in Figure 7),

Table 2. Experimental values of η_rect,max, V_MPP,exp, and V_oc,exp at different values of P_av.

Pav (dBm)	ηrect,max (%)	VMPP,exp (mV)	Voc,exp (mV)
−10	60.3	480	960
−20	39.3	130	280
−30	13.6	27	60

shows the achieved η_rect,max and its corresponding voltage (V_MPP,exp), as well as the experimental open circuit voltage (V_oc,exp) of the rectenna. In Figure 7, η_rect,max, V_MPP,exp, and V_oc,exp are also marked for P_av = −20 dBm. As can be seen, η_rect,max increases with increasing P_av, ranging from 13.6% at −30 dBm to 60.3% at −10 dBm, which agrees with (21). The values of η_rect,max can be estimated in advance, when necessary, from (21) and inferring a value of V_γ from the manufacturer data or from simulations. One particular case is the upper limit, which would be achieved for P_av→∞ (or V_γ→0), in our case 74%. The resulting efficiencies (η_rect,max) are among the highest published in the literature for similar designs [33]. On the other hand, V_oc from Table 1 nearly matches V_oc,exp. Finally, V_MPP,exp equates or nearly matches 0.5 V_oc,exp, the regulated voltage at the input of the MPPT. Thus, the proposed and implemented MPPT will be able to extract the maximum power (or nearly) from the rectenna.

As for the whole RF harvester (rectenna plus the MPPT), Figure 8 shows the experimental values of η_T versus P_av. At −20 dBm, η_rect,max = 39.3% (Table 2) but η_T = 6.5%, resulting, from (22), in η_MPPT = 16.5%. This low value of η_MPPT is due to both a low input voltage value (140 mV = 0.5 V_oc,exp) and a low value of P_o (3.9 µW = η_rect,maxP_av). Contrariwise, at −10 dBm, η_rect,max = 60.3% and η_T = 48.6%, resulting in η_MPPT = 80.6%, which agrees with the data from the BQ25504 chip’s datasheet. At higher values of P_av (−5 dBm), η_T reached a value of 55.6%. Compared to [6], where a similar chip for the MPPT was used, η_T is quite higher.

When powering the sensor node, the required value of P_av was −17.6 dBm. This value fits well with (23), considering the corresponding efficiency in Figure 8 (≈24%). This performance was also tested with the antennas at a distance of 0.5 and 1 m. The power output of the remote RF generator was tuned at appropriate values so as to operate the node, resulting in 8.0 and 13.2 dBm, respectively. These values accounted for the respective link budgets.

6. Conclusions

This work proposed a compact Thévenin model for a rectenna and its application for designing a high-efficiency RF harvester. The rectenna under study consists of an L-matching network and a half-wave rectifier. Explicit expressions for the Thévenin voltage and resistance were derived that offer insight into the operation of the rectenna. An expression was also provided for the power efficiency. The rectenna was implemented and characterized from −30 to −10 dBm at 808 MHz and the results mainly agreed with the derived model, with differences arising from the limited Q factor of the matching network. High efficiencies were obtained, in particular 60% at −10 dBm. Then, an ensuing MPPT was also added, where the behavior of the rectenna as an equivalent Thévenin circuit allowed the use of a simple FOCV technique. The whole RF harvester (rectenna plus MPPT) showed an overall efficiency near 50% at −10 dBm. Further tests were performed with a nearby transmitting antenna for powering a sensor node with a power consumption of 4.2 µW.