Analysis of Passive RF-DC Power Rectification and Harvesting Wireless RF Energy for Micro-watt Sensors

In this paper, analytical modeling of passive rectifying circuits and the harvesting of electromagnetic (EM) power from intentionally generated as well as from ubiquitous sources are presented. The presented model is based on the linearization of rectifying circuits. The model provides an accurate method of determining the output characteristics of rectifying circuits. The model was verified with Advance Design System (ADS) Harmonic balance (HB) simulations and measurements. The results from the presented model were in agreement with simulations and measurements. Consequently design considerations and trade-off of radio frequency (RF) harvesters are discussed. To verify the exploitation of ambient RF power sources for operation of sensors, a dual-band antenna with a size of ~λ/4 at 900 MHz and a passive dual-band rectifier that is able to power a commercial Thermo-Hygrometer requiring ~1.3 V and 0.5 MΩ from a global system for mobile communications (GSM) base station is demonstrated. The RF power delivered by the receiving dual-band antenna at a distance of about 110 m from the GSM base station ranges from −27 dBm to −50 dBm from the various GSM frequency bands. Additionally, wireless range measurements of the RF harvesters in the industrial, scientific and medical (ISM) band 868 MHz is presented at indoor conditions.


Introduction
Recent advances in lowering power demands of wireless remote sensors has afforded the ability to power these sensors with micro-watt power levels.In situations where periodic change of the batteries is not desired, powering the sensors through wireless power sources provides an effective alternative.As a result, wireless RF energy harvesting from ambient sources or from dedicated transmitters has gained research interest for use in these sensor systems.The major challenge in passive wireless energy harvesting is the efficient transformation of the input EM power levels that are less than −10 dBm to the voltage and current demands of the direct current (DC) load.A passive RF to DC power harvester must be optimized at each stage of the circuit design for true implementation of this energy harvesting approach.An RF power harvester consists of a receiving antenna, an impedance matching/transformation network, DC power conditioning and or management and the wireless sensor to be powered.Figure 1 shows a schematic of a passive wireless RF energy harvester.The rectifier may be a single diode or diode-connected transistor, or a cascade of rectifiers.In-between the antenna and the rectifier is an impedance matching or transformation network.The matching network consists of passive components providing inductive or capacitive reactance.The load represents the DC storage or transformation elements and the sensor to be powered.The design of fully passive RF harvesters lies in the accurate modeling of the complete rectifier circuit so that its output performance can be predicted.Harrison et al. [1] used Ritz-Galerkin analysis to present the DC output characteristics of a single diode rectifier with some restrictions.The model neglects the diode junction capacitance and therefore the output DC voltage dependence on the operating frequency.A closed-form equation was presented in [2] that approximates a diode rectifier efficiency and input impedance.In [3,4], models that predict the conversion efficiency of an N-stage full-wave rectifier was presented.However, the DC load current must be determined or maintained to satisfy the constraints in the model.HB simulations using Agilent ADS software can be used to determine the output DC voltage of a rectifier circuit, however it is computationally intensive and do not easily provide the global view of the circuit response [1].
In this paper, a linearized model is presented to determine the output behavior of rectifying circuits.The model assumes steady state conditions and may be applied at various input power levels and connected DC load resistance without neglecting the impedance matching effects and the dynamic influence of the diode impedance on the rectifying process.
With the appropriate design of a rectifier circuit, ambient electromagnetic power harvesters may

Rectifier
η ant η Γ η rect be realized.In our previous work [5,6], wireless RF power transfer were presented in the ISM bands using intentionally generated sources.In [7,8] and [9], ambient RF power harvesters from television (TV) transmitting base stations at the frequency band of (450 to 770) MHz were presented.In [7] for example, the TV base station transmitting about 960 kW was able to power sensors requiring up to 60 µW at a distances of 4.1 km.In [8] and [9], it was shown that a single TV base station can provide multiple TV channels for harvesting.However published work using ambient TV base station signals relies on antenna sizes in the range of 1.5 A4 size or larger for harvesting.These antenna sizes corresponds to at least half of the operating wavelength at (450 to 770) MHz.A rectenna that is larger than A4 size hinder practical integration of the system into modern wireless sensors.In [10], a survey was made to prove the possibility of harvesting RF energy from ambient sources such as GSM.GSM base station transmitters may be the most available in urban environments due to the immense availability of cellular network providers.
In this paper, an ISM band 868 MHz and ambient GSM wireless RF harvester is presented.Planar antenna sizes as small as 6 cm × 8 cm (~λ/4 at 900 MHz) may be used with the rectifier for ubiquitous RF harvesting.The rectifier is designed to operate with dual-band frequency.Using this approach, ubiquitous RF power sources in the range of −27 dBm to −50 dBm and from different frequencies can be utilized for continuous operation of micro-watt sensors.
This paper is structured as follows.Section 2 presents the rectifying circuits and the linearized analytical model.Section 3 presents the verification of the model and its comparison to ADS software HB simulations and measured results.Section 4 presents the design consideration and trade-off when realizing RF power harvesters.The design considerations are based on the presented model.Section 5 presents harvesting RF power from intentionally generated sources at indoor conditions and from ubiquitous sources using a GSM base station at outdoor conditions.Conclusions are given in section 6.

Efficiency versus voltage sensitivity
Efficiency η is defined as in (1), where PL is the output DC power and PA is the input RF power.The voltage sensitivity γ is given by (2), where VL is the output DC voltage.
The current state of the art of low power sensors would require a DC voltage supply of about 1 V and DC current of 10 µA.Therefore, it is necessary to specify the output voltage and current separately rather than the product, the DC output power, when considering RF energy harvesters for remote sensors [4,11].The delivered input RF power PA from the receiving antenna must be transformed to that minimum voltage required to energize the sensor.Although the efficiency is widely presented in literature, its practical use in ambient RF energy harvesting can be limited.This is because an RF harvester can deliver an output DC power more than what is required by a remote sensor but may be unable to energize the sensor due to its specific voltage and input current demands.Therefore, voltage sensitivity of a passive RF harvester may be more important than the output efficiency when powering DC loads from micro-watt RF power levels, as such more emphasis is placed on the γ rather than η in this paper.

RF diode equivalent circuit model
As shown in Figure 1, an impedance transformation network is a sub-system of a wireless RF harvester.The impedance transformation network filters higher order impedances of the diode at the operating frequency.For this reason, only the diodes fundamental impedance at the frequency of operation may be required for its accurate modeling in RF energy harvesting applications.A packaged Schottky diode may be modeled as a nonlinear junction resistance Rj shunted by a non-linear junction capacitance Cj.Vj is the voltage loss at the rectifying junction.RS, LS and CP are the bulk resistance, packaging inductance and capacitance respectively [12].A bare diode may also be modeled as a voltage controlled junction current source in parallel with a controlled capacitance (see Figure 2) and a parasitic bulk resistance [13].IDC is the voltage controlled current source from the rectifying junction.Without neglecting the bulk resistance and the package parasitics, the controlled current source is treated as a DC source in parallel with a conductance G and a susceptance B. RD and XD are the parallel resistance and reactance of the diode respectively.IDC, RD and XD as in the linearized model are variables which depend on the diode parameters, input RF power PA, the connected DC load and the reflection coefficient at the input of the rectifier.From Figure 2 (Left), the admittance of a Schottky diode may be written as in (3), where Ydiode is the diode admittance.
Equation ( 3) can be expanded into the conductance G and susceptance B. The expression for Cj [13] is given by ( 4).Where Q is the charge stored at the rectifying junction.
Rj can be found from Richardson's equation [14], which describes the current voltage relationship at the rectifying junction of a Schottky diode.The current voltage relationship at the rectifying junction is given by (5).
IS is the diode reverse saturation current, . α is the thermal voltage.η0 is the diode ideality factor.q is the charge of an electron.T is the temperature and K is the Boltzmann constant.Since I is an infinite series with higher order values, there are higher order values of the diode junction resistance Rj.
I varies with changes in the input RF power level PA, the losses in the impedance transformation network, rectifier impedance or connected DC load.It is easily deduced from ( 6) that the magnitude of I also affects the junction resistance Rj and consequently the overall impedance of the diode.Due to this, the input impedance of a diode must always be measured at a specified RF power level and DC load conditions.The effect of a Schottky diode equivalent circuit parameters on the parallel resistance is presented.This allow for direct comparison of each diode parasitic parameter on the RD.
The diode parasitic parameters which were used in calculating the diode impedance are shown in Table 1.VBV is the reverse breakdown voltage of the Schottky diode.
Figure 3(Top-left) shows the effect of the saturation current IS on the diode rectifying junction voltage losses Vj, for various values of I.At I in the range of 5 µA, the Vj across both the IS = 0.5 µA and the IS = 50 nA approaches zero.When the I passing through the diode rectifying junction is greater than about 0.05 mA, the efficiency of rectification is skewed to the one with IS = 0.5 µA, since the peak Vj of the diode with IS = 50 nA is much higher at this condition.The results show that the smaller the I that goes through a Schottky diode rectifying junction, the smaller the Vj across it.Therefore the ηrect of a Schottky diode increases with high input voltage instead of high input current.Hence maximum voltage transformation at the input of the diode rectifier is always necessary for its efficient operation.The voltage transformation of the input RF power will reduce the amount of current passing through the diode rectifying junction.3(Top-right), as the IS is increased from 50 nA to 0.5 µA, the RD reduces.From Figure 3(Bottom), as the junction capacitance Cj is increased from 0.18 pF to 1 pF, the RD of the diode reduces.By increasing RS from 6 Ω to 25 Ω, the RD reduces as well.The results shows that a Schottky diode with a low IS, RS and Cj will have high RD.The results also show that at ultra-high frequency (UHF), the RD of a diode is in the range of a few kilo-ohms.

RF power harvesting circuits
Figure 4 shows a fabricated RF harvester realized at 930 MHz on an FR4 printed circuit board using off-the-shelf discrete components.VS is the input RF voltage.RA is the RF source resistance.RL is the DC load resistor.The impedance transformation network is realized with an inductive coil resonator and a chip capacitor.The unloaded quality factor Qu of an impedance transformation element is used as the performance parameter for selection a component.Qu is given by Equation (7), where XCoil and RCoil are the net series reactive and resistive impedance of the inductive transformation element respectively.As can be seen in Figure 3, the RD of a Schottky diode at about 900 MHz is in the range of a few kilo-ohms.The voltage transformation that can be achieved at the input of a Schottky diode is directly proportional to the D R at resonance [5] as in (8).Where VD is the voltage at the input of the diode rectifier.When the RF voltage amplification at the input of the diode is limited due to a lower value of RD, the rectifier efficiency is skewed toward diodes with saturation current IS in the micro-amp range (see Figure 3(Top-left)), since more current I passes through the rectifying junction.Hence the Avago Techologies HSMS-285 series of diodes with IS = 3 µA were used at 930 MHz to realize the RF harvester.

Linearized analysis of the RF harvester
The linearized impedance diagram of the RF rectifier shown in Figure 4 is presented in Figure 5. IDC is the same for each diode since two identical diodes are assumed.IDC may be found from (10).Pin is the power absorbed at Zin plane as in (9).Where Γ is the reflection coefficient at the Zin plane (see Figure 4).N is the number of doubler stages.After the linearized model is setup as in Figure 5, the steady state output voltage VL is found using nodal analysis.From Figure 5, ( 11), ( 12) and ( 13) may be used to determine the voltages at node VIN, VD and VL.
From ( 11) to (13), the minima of VL occurs when IDC in the doubler diodes limits to zero.IDC ≈ 0 implies the diodes are not rectifying at the input RF power level.Hence the output voltage VL approaches (14).The alternating current (AC) output voltage when IDC = 0 is given by VL_AC.
The maxima of the output voltage VL approaches (15).For N number of doublers, the upper limit of the VL is increased by a factor N.

Linearized analysis applied to multipliers and multiple input matching circuits
The RF harvester presented for dual-band applications is realized with a coupled matching to provide the multiple resonant frequencies.The presented dual-band harvester which can harvest from

R Coil
Coil GSM-900 or LTE-800 and GSM-2160 is shown in Figure 6 using a modified voltage quadrupler.The capacitors at the input of the diode chain are connected in parallel, however the capacitors are connected in series at the output of the diode chain.To achieve the additional bands of frequency operation, each input branch into a diode voltage doubler is tuned to a specific frequency; ω1 (at 935 MHz) and ω1 (at 2.2 GHz).The resonant frequencies can be approximated by (16).The employed diodes are the HSMS-285C Schottky diodes.
By replacing the diodes in Figure 6 with its linearized model (see Figure 5), its output DC characteristics can be analyzed with the same approach presented in Section 2.4.

Results of RF to DC power transmission
The presented linearized model, ADS HB simulations and measured voltage sensitivity for the harvesters presented in Figure 4 and Figure 6 are shown in Figure 7.For the harvester presented in Figure 4, a DC voltage of 0.4 V across RL of 0.5 MΩ is measured at −20 dBm input RF power.At −14 dBm input RF power, the harvester as shown in Figure 4 delivers a measured DC voltage of 1 V across a 0.5 MΩ RL.The harvester achieves a peak efficiency of 24% and 41% at −20 dBm and −10 dBm input RF power respectively for about 6 kΩ RL when operating at 930 MHz.
For the harvester shown in Figure 6, a DC voltage of 0.43 V across a 0.5 MΩ RL is measured at −20 dBm input RF power at 935 MHz.At −14.4 dBm input RF power, the harvester as shown in Figure 6 delivers a measured DC voltage of 1 V across a 0.5 MΩ RL.At 5 dBm input RF power, a DC voltage of 6 V is measured across a 0.5 MΩ RL at 935 MHz.The harvester achieves a peak efficiency of 16% and 35% at −20 dBm and −10 dBm input RF power respectively for about 10 kΩ RL when operating at 935 MHz.At 2.2 GHz, an output DC voltage of 0.4 V is measured across a 0.5 MΩ RL at −10 dBm input RF power.At 2.2 GHz, a peak efficiency of 4% is measured at  From the results shown in Figure 7, the maximum calculated deviation between measurements and the presented linearized model is 15%.The 15% maximum difference is as a result of calculating the diode RD and IDC.IDC is dependent on PA, Γ at Zin, RD and RL, as a result any variation such as component tolerances in these parameters affects the estimation of the output DC voltage.RD is also a function of the RL and PA.

Circuit performance parameters
The maximum DC load power from the rectifier may be approximated by (17).Where PLmax is the maximum power delivered to the RL.The DC load resistance that results in the maximum efficiency from the RF harvester is given by (18).RLmax is the DC load resistance RL that results in the maximum η.For Figure 4, RLmax is ~6 kΩ.For Figure 6, RLmax is ~10 kΩ.From ( 8) and ( 17), the diode RD and peak voltage into a diode rectifier VD, must be high as possible for high voltage sensitivity of the RF harvester.
From the linearized transfer functions that describe the performance of an RF harvester, a maxima of PL (PLmax), RL (RLmax), η and γ may be found for any RF harvester topology.

Rectifying diode selection
The harvester shown in Figure 6 is realized to cover the LTE-800 MHz or GSM 900 MHz and GSM 2110 MHz frequency bands (see Figure 8).Hence the realized harvester loaded quality factor ) is low at 935 MHz and 2100 MHz.For RF harvesting applications which require such broad-band operations, diodes with low RD should be considered.Diodes with lower Cj and RS are always preferable in RF energy harvesting applications.RS consumes ohmic power, hence the lower the better.Cj in the range of 1 pF reduces the diodes RD as well as its switching speed.The action of Cj dominates at sufficiently higher diode operating frequencies resulting in lower attainable RD.Since diodes are more sensitive to high voltage at input power levels less than −10 dBm, a low RD results in limited voltage transformation.As a result more current goes through the diode and the diodes voltage losses Vj tend to be maximum.

Multi-band harvester
Hence at low diode input RD, the efficiency of rectifying RF signals is skewed towards the diodes with IS in the micro-amp range (such as HSMS-285x series), since they have lower peak Vj.Impedance transformation components with high unloaded quality factor Qu are always preferable in RF energy harvesting applications.The question always arise whether to use discrete components or transmission lines on a PCB.The unloaded quality factor of a transmission line may be described by (19) [15].Where F0 is the transmission line frequency in mega-hetz, A0 is the attenuation in dB/100 feet at F0 and VF is the velocity factor.
As an example, an inductive or capacitive transmission line on an FR4 PCB has VF of 0.48 and A0 of 132 dB/100 feet at 1 GHz.Using (19) and the values of an FR4 transmission line at 1 GHz gives a Qu of 44.Hence up to 1 GHz, discrete components may be preferred to transmission lines for impedance transformation since chip inductors and capacitors can provide Qu of up to 80 and 1000 at 1 GHz respectively.However, since inductive transmission lines quality factor is directly proportional to the operating frequency, it may be preferred to discrete inductors at frequencies above 3 GHz.
For RF harvesting applications with input power levels greater than −10 dBm, diodes may be cascaded as in multipliers.This is due to the possible constant output voltage or power of a single rectifier stage after a certain threshold input RF power.The appropriate number of diode doubler stages that strikes a good balance between the losses Vj across the diodes in the multiplier and the power saturation of the rectifier stage must be made.Equation (20) may be used as a guide in choosing the number of rectifier voltage doubler stages N and the peak voltage or power handling capabilities of the rectifier.
The maximum DC voltage that can be outputted by a diode is determined by the reverse breakdown voltage VBV.The maximum output DC voltage VL of a single diode rectifier is ~VBV/2 [2].Hence the maximum output DC voltage of a diode voltage doubler is ~VBV and for a multiplier, it is ~NVBV.

Wireless RF energy transfer in the ISM band 868 MHz.
At 868 MHz, the commercially available Huber+Suhner SPA 860 (1308.17.0058) planar antenna [16] was used as a transmitter.The Huber+Suhner SPA 860 has a gain Git of 8 dBi at 868 MHz and measures 20 cm × 20 cm in size.The antenna presented by Homg-Dean Chen et al. [17]   The size of the antenna is 6 cm × 8 cm, λ/4 at 868 MHz.The dual-band rectifier as presented in Figure 6 is used with the antenna for harvesting at 868 MHz.The transmitted RF power Pt was 1 W at 868 MHz.The experimental setup and the wireless range measurements were performed in a warehouse as can be seen in Figure 9 (Left).The sending and the receiving antennas were arranged ~1.5 m above the ground.The rectenna delivered DC voltage was measured with the Keithley 6514 electrometer.
Figure 9(Right) shows the range measurements at 868 MHz.A harvested DC voltage of 0.4 V is measured across a 0.5 MΩ RL at the distance of 20 m.At 13 m, 1 V DC voltage is measured across a 0.5 MΩ RL.The far-field results at 868 MHz show that the received power generally degrades with 1/d 2 as in the Friis equation (21) [18].Where Pr and Pt are the transmitted and received power respectively.λ is the wavelength of the RF signal.ξ as in ( 21) is an additional parameter in the Friis equation which account for reflections and multi-path propagations of the wireless signals.It can be seen from Figure 9 (Right) that the measured output DC power is modulated by the constructive and destructive interferences along 1/d 2 , since there are farther distances where the delivered power is greater than a nearer range.This is evident at a distance d of 15 m, where a DC output voltage of 0.5 V is harvested as compared to 1 V harvested at d of 19 m for 0.5 MΩ RL.At 15 m there is destructive interference from to the reflected signals to the direct signals, hence the harvested power is lower than that predicted by the original Friis formula, however, at 19 m, there is constructive interference and the harvested power is higher than that predicted by the original Friis formula.

Harvesting from ubiquitous GSM signals
To investigate the possible use of ambient RF power sources for operation of remote micro-watt sensors.The RF power levels harvested by a ~λ/4 receiving antenna at 930 MHz was first measured at a distance of about 110 m from a GSM base station.The receiving antenna that was used for this experiment is the dual-band antenna by Homg-Dean Chen et al. [17].
Due to reflections, multi-path propagation and the fact that the transmitting antennas from the GSM base station point at different directions (see Figure 11), the power delivered by the dual-band receiving antenna was not estimated by the Friis formula [18] as in Equation 21.The power delivered by the receiving antenna were made by on-site measurements using a Rohde & Schwarz PR100 RF monitor.From the balcony of a building, about a distance of 110 m from a GSM transceiver base station, the antenna was positioned to harvest the ambient RF power.Figure 10 shows the average (over 5 minutes) harvested RF power levels of the dual-band receiving antenna at a distance of about 110 m from the GSM base station.
The GSM base station is located in the city of Freiburg, Germany at 48.0087,7.829022coordinates.Table 2 shows the transmitting parameters of the GSM base station.Frequency (GHz) Figure 10 shows that the harvested power levels by the dual-band receiving antenna, from the various frequency bands of a GSM base station ranges from −27 dBm to −50 dBm at a distance of about 110 m. Figure 11 shows the output DC voltage from the dual-band rectifier and the dualband [17] receiving antenna.Figure 11 shows a harvested output DC voltage of about 2.3 V across a ~0.5 MΩ resistor is achieved from the several GSM power sources at a distance of 110 m.The RF harvester was also loaded with a commercially available TFA 30.5014.02Thermo-Hygrometer.The Thermo-Hygrometer is normally powered by an LR44 battery requiring 1.3 V to 1.5 V at 3 µA for its continuous operation.It can be seen that the RF harvester was also able to power the sensor through startup-mode and steady state operations (see Figure 12).Since the Thermo-Hygrometer has an input resistance of ~0.5 MΩ and consumes ~1.3 V, the theoretical distance at which the Thermo-Hygrometer may still be powered by the presented RF harvester is about 220 m using the GSM base station.

Conclusions
By using a linearized model of a rectifier, a complete description of an RF harvester can be made without compromise.This analysis is confirmed by measured results and HB computer aided simulations for different RF harvester circuit topologies.It is shown that an RF harvester can be optimized using the equations from a linearized RF harvester model.This provides a unique advantage over computer aided simulations which gives little insight into the design trade-off and the effect of the component parameters on the performance of the harvester.The theory presented in this paper could be used for broad design considerations before a specific RF harvester circuit topology is adapted.The theory has been proved by using low cost off-the-shelf components.However the model is equally applicable to custom made designs based on complementary metal-oxide-semiconductor (CMOS) process.It has been shown that using a dual-band RF harvester, ambient RF power sources in the range of −27 dBm to −50 dBm from different frequency bands can be used to provide perpetual energy for operation of wireless remote sensors requiring 1.3 V at 0.5 MΩ.This has been achieved by using rectenna size of ~λ/4 at 930 MHz.In the ISM 868 MHz frequency band, an operation range of 19 m is demonstrated for DC loads requiring 1 V at 0.5 MΩ from a single transmitted signal at indoor conditions.

Figure 1 .
Figure 1.Block diagram of a passive wireless RF energy harvester.ηant, ηΓ and ηrect are the efficiencies of the receiving antenna, impedance transformation network and the rectifier respectively.

Figure 3 .
Figure 3.The effect of the changes in the equivalent circuit parameters of a Schottky diode on the parallel resistive impedance, RD. (Top-left) Effect of the saturation current IS on the Vj at 25 °C for different currents I passing through the rectifying junction.(Top-right) Schottky diode parallel resistive impedance RD as a function of different IS.(Bottom) Schottky diode parallel resistive impedance RD as a function of different bulk resistances RS, and junction capacitances Cj.

Figure 3 (
Figure3(Top-right) and Figure3(Bottom) show the calculated effect of IS, RS and Cj on the parallel resistive impedance RD of a diode.From Figure3(Top-right), as the IS is increased from 50 nA to 0.5 µA, the RD reduces.From Figure3(Bottom), as the junction capacitance Cj is increased from 0.18 pF to 1 pF, the RD of the diode reduces.By increasing RS from 6 Ω to 25 Ω, the RD reduces as well.The results shows that a Schottky diode with a low IS, RS and Cj will have high RD.The results also show that at ultra-high frequency (UHF), the RD of a diode is in the range of a few kilo-ohms.

Figure 4 .
Figure 4. PCB of the realized RF harvester at 930 MHz using a HSMS-285C diode voltage doubler.The HSMS-285C has the following spice parameters IS = 3 µA, Cj = 0.18 pF and RS = 25.Coil = 38.5 nH at 900 MHz with a Qu of 69.The chip capacitors have Qu of about 1000 at 900 MHz.

Figure 5 .
Figure 5. Linearized model of the RF power harvester at 930 MHz.XDC is the reactance of DC block capacitor.XCC is the reactance of 2.4 pF capacitor.RCoil and XCoil are the series resistive and reactive impedance of the coil respectively.XCL is the reactance of the 100 pF capacitor.RL is the load resistor.

Figure 7 .
Figure 7. Presented linearized model as compared to Agilent ADS HB simulations and measurements.VL is the output DC voltage and PA is the input RF power.(Top-left) Results of the RF harvester as shown in Figure 4. (Top-right) Results of the dual-band RF harvester as shown in Figure 6 at 930 MHz.(Bottom) Results of the dual-band RF harvester as shown in Figure 6 at ~2.2 GHz.

Figure 8 .
Figure 8. Measured open circuit S11 of the dual-band RF harvester.The input RF power level is −15 dBm.The 3-dB return loss frequency bandwidth is 120 MHz around 930 MHz and 200 MHz around 2.2 GHz.
was used to receive the wireless signals at 868 MHz.The antenna by Homg-Dean Chen et al. (see Figure 11) is a dual-band antenna with a 10-dB return loss bandwidth of 90 MHz around 900 MHz and 218 MHz around 1800 MHz.It has a gain Gir of 1 dBi at around 900 MHz and 3 dBi around 1800 MHz.

Figure 9 .
Figure 9. (Left) Picture of the experimental setup for the wireless range measurements at 868 MHz.(Right) Rectenna (antenna + rectifier) receiving range performance by sending Pt of 1 W at 868 MHz.Transmitting antenna size is 20 cm × 20 cm with Git of 8 dBi.Receiving rectenna size is 6 cm × 8 cm.d is the distance between transmitter and rectenna.

Figure 10 .
Figure 10.Average (over 5 minutes) ambient RF power delivered by the dual-band antenna at a distance of about 110 m from a GSM base station.Receiving antenna size is 6 cm × 8 cm (~λ/4 at 930 MHz) with a gain of 1 dBi at 930 MHz and 3 dBi at 1800 MHz.

Figure 11 .
Figure 11.Setup for measuring the power delivered by the GSM base station across a resistive load.The RF to DC rectifier is the circuit as presented in Figure 6 and the antenna is from Homg-Dean Chen et al. [17].RL is ~0.5 MΩ.VL is about 2.3 V.

Figure 12 .
Figure 12.Using ambient RF GSM power to operate Thermo-Hygrometer sensor.The RF to DC rectifier is as presented in Figure 6.