I. INTRODUCTION
Nowadays, sensor nodes require battery power and the node life depends on battery power. However, problems like replacement appear when changing batteries is impractical or impossible, therefore requiring an alternative energy source. Wireless radio-frequency (RF) energy transmission is then an alternative method to avoid conventional power source imbedded inside the structure. A source antenna transmits microwaves to a receiver that is a rectenna (rectifying antenna), integrating the technology to receive and convert the RF energy into dc power. In this study, we focus on the microwaves to dc conversion at 2.45 GHz, frequency greatly used due to its low attenuation through the atmosphere, low-cost technology, and location at the center of un-licensed industrial–scientific–medical frequency band [Reference Brown1].
A rectenna contains a receiving antenna to collect microwave incident power and a rectifying circuit. The rectifier is often made up of a combination of Schottky diodes, an input HF filter, an output bypass capacitor, and a load resistor. The input HF filter localized between the antenna and diodes is a low-pass filter that rejects harmonics created by the nonlinear diode behavior. It also acts as a matching circuit between the antenna and the rectifier [Reference Ren and Chang2, Reference Douyere, Lan Sun Luk and Alicalapa3].
The microwave rectifier can take several configurations. However, the single serial [Reference Douyere, Lan Sun Luk and Alicalapa3–Reference Akkermans, van Beurden, Doodeman and Visser5] and shunt configuration [Reference Ren and Chang2, Reference Strassner and Chang6] are used in most rectifying circuits. To enhance the level of the output dc voltage, a voltage doubler configuration [Reference Ren and Chang2, Reference Heikkinen and Kivikoski7, Reference Heikkinen and Kivikoski8] can also be used. However, to supply high dc output, the rectenna array has to be able to rectify a large amount of incoming power. The rectenna array can be built by using different interconnections in series, or in parallel [Reference Ren and Chang2, Reference Epp, Khan, Smith and Smith9–Reference Shinohara and Matsumoto12] or most rarely in cascaded configuration [Reference Ren and Chang2] and each connection has its own output features.
In this paper, we propose an efficient dual-diode rectifier included on a microstrip rectenna and rectenna arrays combination at 2.45 GHz well suitable for driving smart actuators [Reference Epp, Khan, Smith and Smith9], wireless sensors or sensor nodes [Reference Farinholt, Park and Farrar13]. In general, the RF-to-dc rectifiers proposed in the literature contain an input HF filter [Reference Ren and Chang2–Reference Epp, Khan, Smith and Smith9] but also an output dc filter with, in the most case a shunt capacitor [Reference Ren and Chang2, Reference Zbitou, Latrach and Toutain4, Reference Strassner and Chang6–Reference Epp, Khan, Smith and Smith9], or a microstrip low-pass filter [Reference Douyere, Lan Sun Luk and Alicalapa3], or a radial stub [Reference Akkermans, van Beurden, Doodeman and Visser5]. In addition, vias-hole connections between the rectifier and the ground plane are often used for dc path [Reference Douyere, Lan Sun Luk and Alicalapa3–Reference Epp, Khan, Smith and Smith9]. The proposed rectifier needs neither via-hole connections nor bypass capacitor. In addition, no input HF filter has been used. This makes the circuit very simple, more compact, and low cost.
The RF-to-dc rectifier has been accurately optimized using advanced design system (ADS) commercial software of Agilent Technologies. In order to take into account all the electromagnetic couplings, a global analysis technique [Reference Takhedmit, Merabet, Cirio, Allard, Costa, Vollaire and Picon14] that associates momentum electromagnetic simulator (for the distributed part) and harmonic balance (for lumped linear and nonlinear elements) has been performed. Numerical simulations have also been performed using the 3D-finite difference time domain (FDTD) algorithm extended to lumped circuit elements to accurately describe and analyze the rectenna (including both antenna and rectifier circuit) in term of current distributions [Reference Takhedmit15]. In addition, the total-field/scattered-field formulation has also been included to generate an arbitrary plane wave illumination.
First, four rectifiers based on two different Schottky diodes (HSMS 2860 and 2820) with the same topology have been developed and etched on low-loss Arlon 25N and low-cost FR4 substrates. Simulated and experimental results are then compared.
In a second time, rectenna arrays have been investigated. The rectenna elements are interconnected in series or in parallel. A comparison between series and parallel combinations has been performed in term of efficiencies and voltage ratio (VR) between a measured single rectenna element and the measured rectenna array based on N single rectenna elements. It was shown in [Reference Ren and Chang2, Reference Shinohara and Matsumoto16] that the optimum efficiency is obtained when identical rectenna elements and optimal resistive load are used.
II. DUAL-DIODE MICROWAVE RECTIFIER
A) Description of the structure
The RF-to-dc microwave rectifying circuit shown in Fig. 1 contains two Schottky diodes (D 1 and D 2) mounted with a differential topology. It contains a 50-Ω characteristic impedance microstrip feed line. At point P 0, the RF input power is divided into two equal entities that are rectified by diodes D 1 and D 2. These two diodes have the same impedance at 2.45 GHz and behave identically. The rectifier contains also two folded quarter wavelength open stubs, connected to points P 1 and P 2, which act as short circuits at 2.45 GHz and therefore isolate the resistive load R L during the measurement step. The distance L between stubs (connected to points P 1 and P 2) and diodes D 1 and D 2 has been optimized to tune out the reactances of the diodes and increase their efficiencies. In addition, due to the differential measurement of the output dc voltage over the load (V DC = V 1–V 2), no via-hole connection is necessary. Both diodes exhibit high impedances at 4.9 GHz. At this frequency, the distance between each diode and the point P 0 is equal to a quarter wavelength resulting in a small impedance at the input of the circuit (P 0). The point P 0 behaves like a short circuit at this frequency. Note that the HSMS 286x series is designed to operate from 915 MHz to 5.8 GHz and this circuit has been designed at 2.45 GHz. However, the same rectifier topology can be developed and optimized at other frequencies using when possible another specific Schottky diodes well dedicated in the frequency band of interest.
Layout of the dual-diode rectifier at 2.45 GHz.
B) Numerical simulations
In this study, four dual-diode microwave rectifiers (Table 1) have been developed and compared. Circuits 1 and 2 are etched on Arlon 25N substrate (ε r = 3.38, thickness = 1.524 mm, tan δ = 0.0025). Otherwise, circuits 3 and 4 are printed on low-cost FR4 substrate (ε r = 4.4, thickness = 1.58 mm, tan δ = 0.02). To compare numerical results over a large amount of RF power, the HSMS 2860 and 2820 Schottky diodes in a SOT 23 package are used. Their models are done in [17]. These two diodes are, respectively, characterized by a breakdown voltage B V of 7 and 15 V. The rectifiers have the same topology and have been optimized for an RF input power of 10 mW (circuits 1 and 3) and 20 mW (circuits 2 and 4). The dedicated optimal loads are listed in Table 1.
Parameters of the RF-to-dc rectifiers.
The simulated return loss (S 11) of the rectifiers versus RF frequency is shown in Fig. 2. Simulations are made using ADS software with 10 or 20 mW RF input power. Results clearly show that circuits 1–4 are correctly matched and have a return loss lower than – 20 dB at 2.45 GHz. However, circuit 2 has a minimum of the return loss shifted throughout higher frequencies. Note that the conception of the rectifier is here based on the optimization of its RF-to-dc conversion efficiency at 2.45 GHz. This constraint involves a correct matching at the input of the rectifier but not necessarily a minimum of the return loss at this frequency.
Return loss of the RF-to-dc rectifiers versus RF frequency (ADS simulation).
Figure 3 shows the simulated return loss (S 11) of the rectifiers versus RF input power from 0.1 to 1000 mW at 2.45 GHz using ADS software. Results show that the circuits have a good matching level on the RF input power for which they have been optimized but, as previously mentioned, these values do not correspond to the minimum of the return loss. Return loss is lower than −40 dB at 10 mW for circuits 1 and 3 and lower than −20 dB at 20 mW for circuits 2 and 4.
Return loss of the RF-to-dc rectifiers versus RF power at 2.45 GHz (ADS simulation).
In Table 2, we present the harmonic levels at the input and output of the circuits. All results are normalized with the input RF power at 2.45 GHz. The 4.9 GHz second harmonic is always strongly attenuated at the input of the rectifiers. This is due to the short circuit at point P 0 at this frequency. The 7.35 GHz third-order harmonic is sufficiently attenuated for circuits 2 and 4 (both based on HSMS 2820 diodes). However, circuits 1 and 3 (based on HSMS 2860 diodes) exhibit an attenuation of −20 dB. This can significantly affect the efficiency of the rectifier and then, the overall efficiency of the rectenna. At the output of the circuit, the 2.45 GHz RF component is greatly attenuated. The resistive load is then correctly RF isolated.
Input and output harmonics levels.
Figure 4 shows the simulated RF-to-dc conversion efficiencies of rectifiers when input power varies from 0.1 to 1000 mW at 2.45 GHz. The RF-to-dc conversion efficiency (η) is generally defined as follows:
where P RF is the maximum input RF power toward the rectifier, P DC is the output dc power and V DC is the output dc voltage over the resistive load.
Efficiencies of the RF-to-dc rectifiers (ADS simulation).
The results show that circuits 1 and 3 have maximum efficiencies (75 and 68%, respectively) higher than those obtained with circuits 2 and 4 (68 and 63%, respectively). The efficiencies of rectifiers 1 and 3 roughly decrease from 40 and 32 mW respectively, whereas the efficiencies of rectifiers 2 and 4 decrease from 500 mW. This is due to the breakdown voltage (B V) of diodes which limits the amount of incoming RF input power [Reference Yoo and Chang18]. The rectifier contains two diodes in series. In this case, the maximum RF power that can be converted is defined as follows:
We can also notice that the efficiencies of circuits 2 and 4, both based on HSMS 2820 diodes, slightly vary between 30 and 500 mW. At 2.45 GHz, the diode impedance has been computed as a function of RF input power (Fig. 5) and, unlike the HSMS 2860, the real and imaginary parts of the HSMS 2820 diode vary slowly when the input power increases. This slightly affects the matching of the rectifiers, and then explains the smooth variation of the efficiency.
Impedance of the HSMS 2820 and 2860 diodes (ADS simulation).
Circuits 3 and 4, etched on FR4 substrate, exhibit efficiencies lower than those obtained for circuits 1 and 2. The FR4 has a loss tangent higher (tan δ = 0.02) than the Arlon 25N substrate (tan δ = 0.0025). This directly affects the conversion efficiency of the rectifier.
C) Experimental characterization of the rectifiers
Rectifiers etched on Arlon 25N substrate (circuits 1 and 2) have been realized and experimentally characterized to compare the results with ADS simulations.
Figure 6 shows the output dc voltage and conversion efficiency of circuit 1 when input RF power varies between 0 and 10 mW. At 10 mW RF input power, simulated and measured efficiencies are, respectively, 65 and 58% while the output voltage is 1.7 V over an optimal load of 500 Ω. Simulations agree well with the measured results. However, some differences appear between simulated and measured efficiencies (7–10%). These differences can be mainly explained by the dispersion between the electrical characteristics of the Schottky diodes used in the experiment and the values given by the electrical model provided by ADS. The differences are also due to the tolerances during the fabrication process and the errors during measurements. In addition, the frequency domain simulations performed by harmonic balance (ADS) have a limited accuracy to simulate nonlinear circuits like rectifiers including one or several diodes.
Characterization of circuit 1–simulation and measurements.
Figure 7 shows the output dc voltage and RF-to-dc conversion efficiency of circuit 2 when input power varies from 0 to 250 mW. The measured efficiency varies slightly between 50 and 250 mW (η = 67–72%). DC voltages of 12.9 and 13.7 V have been, respectively, obtained by simulation and measurement across a 1050 Ω optimal resistive load at 250 mW RF input power.
Characterization of circuit 2 – simulation and measurements.
III. RECTENNA ARRAY
When a large dc output (voltage and/or power) is necessary, rectenna arrays are then needed. We focus here on the rectenna arrays with two different interconnections: series and parallel connections (Fig. 8). Rectenna arrays have been realized from the single dual-diode rectifier previously described. Four rectenna arrays containing 2 and 4 single rectenna elements were developed and experimentally characterized in an anechoic chamber at 2.45 GHz.
Layout of the two-elements rectenna array (dimensions in millimeters): (a) series and (b) parallel.
The single rectenna element has been printed on Arlon 25 N substrate with ε r = 3.38 and 1.524 mm thickness. It contains a linearly polarized rectangular patch antenna with notches designed at 2.45 GHz. A 4.7 dB gain and a minimum return loss of −20 dB have been measured. The effective area at its broadside (θ = 0°) is 35.23 cm2. The rectenna contains two HSMS 2860 Schottky diodes in a SOT 23 package. As well described in [Reference Takhedmit15], the length of the feeding line (L 4) between antenna and the input of the rectifier has been accurately adjusted using numerical FDTD simulations in order to match the antenna and the rectifier, and then obtain optimized performances. The 7.35 GHz third-order harmonic at the input of the rectifier has been reduced (−30 dB attenuation) due to the mismatch between the antenna and the rectifier at this frequency. Therefore, the single rectenna exhibits 83% measured efficiency on an optimal load of 1050Ω when the power density is 0.31 mW/cm2 (P RF = 11 mW).
The two-element rectenna array layout with series and parallel interconnections is shown in Fig. 8. The receiving antennas are positioned collinearly along the H-plane. For a spacing between patches larger than 0.10 λ 0, it was shown that the H-plane arrangement exhibits a smaller coupling compared to the E-plane arrangement [Reference Balanis19]. Here, a spacing of 25 mm (λ 0/5) was chosen between patches, resulting in a mutual coupling less than −25 dB. The radiating elements are then correctly isolated.
The overall efficiency has been measured when the resistive load and the power density striking the rectenna panel successively vary. The Friis transmission equation, including effective aperture of the receiving antenna allows to compute the effective received RF power toward the rectifier [Reference Epp, Khan, Smith and Smith9]. Experimental characterizations have been performed using a dedicated measurement setup presented in [Reference Takhedmit20]. Rectenna array is localized in the far field transmitting antenna region (2D 2/λ > 53 cm) at a distance of 70 cm from a linearly polarized horn antenna (G trans = 12 dB) and is illuminated at its broadside. On the transmitter side, a 30 dB gain power amplifier at 2.45 GHz has been connected to a RF signal generator. The output dc voltage across R L has been measured by a voltmeter.
A) Parallel interconnection
Theoretically, in the case of parallel-connected rectennas, the optimal resistive load is divided by the number of single rectenna elements (N) and the dc voltage is the same as a single rectenna. This means that the dc power (and then the dc current) is multiplied by the number of array elements assuming that the rectennas have the same efficiency, that they are illuminated by the same power density and are also correctly isolated to provide the same dc outputs. It has been previously shown in [Reference Shinohara and Matsumoto16] that an imbalance between the characteristics of the single rectenna degrades the performances and the dc output of the rectenna array.
Figure 9 shows the parallel-connected array efficiencies as a function of the resistive load. Measurements have been done considering two power densities: 0.027 and 0.28 mW/cm2. For the two-element array, efficiencies are optimal for a resistive load of 525 Ω (instead of 1050 Ω) and 265 Ω for the four-element rectenna panel. These results show that measurements are in good agreement with the theoretical prediction.
Measured efficiency against resistive load – parallel interconnection.
The measured dc voltage and efficiency as a function of power density (0–0.31 mW/cm2) is shown in Fig. 10. The effective aperture of a rectenna panel is then obtained by multiplying the effective aperture of a unit cell element by the number of elements. Therefore, we assume that the rectenna elements have the same properties and are isolated. The measured dc output of the single rectenna (N = 1) is plotted as a reference and optimal loads are connected in all cases. For N = 2, the dc voltage is close to that provided by the single element and the measured efficiency is about 88% at 0.28 mW/cm2 (P RF = 20 mW). The four-element array provides 3 V output dc voltage across a 265 Ω optimal load when the power density is 0.31 mW/cm2 (P RF = 43.7 mW). It exhibits a maximum efficiency of 78%.
Measured dc voltage efficiency against power density – parallel interconnection.
B) Series interconnection
When a single-rectenna element cannot provide a large dc voltage, the development of series-connected arrays can be an alternative solution. In this case, the optimal load (R L) and the output voltage are multiplied by the number of elements (N). Assuming the previous hypothesis concerning the small mutual coupling between radiating elements and the same properties for each single rectenna, the efficiency should remain constant when the number of elements increases.
To find the optimal loads experimentally, measurements of the efficiency as a function of the output load were performed and results are shown in Fig. 11. Measurements have been performed for the same power densities: 0.027 and 0.28 mW/cm2. For the two-element array, results show that the efficiency is optimal when the output load is close to 2.1 kΩ and it increases when the number of elements increases. An optimal load of 4.2 kΩ has been measured for a panel of four rectennas. Measurements agree well with theoretical predictions and confirm the previous hypothesis. The spacing between each element has been finely adjusted to have a very small coupling. Therefore, we can consider that each element behaves like an independent dc power source.
Measured efficiency against resistive load – series interconnection.
Figure 12 presents the measured dc voltage and efficiency of series-connected arrays (N = 2 and 4) in the power density range of 0–0.31 mW/cm2. The measured output voltage and efficiency of the single-rectenna element are plotted as a reference. The two-element rectenna array provides 6.43 V over a 2.1 kΩ optimal load when the power density is 0.31 mW/cm2 (P RF = 21.9 mW). It exhibits an efficiency of 88%. Under the same power density, when N = 4 (P RF = 43.7 mW), the dc voltage reaches about 11.9 V over a 4.2 kΩ resistive load. The maximum measured efficiency is about 78%.
Measured dc voltage and efficiency against power density – series interconnection.
C) Output VR of the interconnected rectenna arrays
The output VR is defined as the ratio of the dc voltage between the array of rectennas and the single-element rectenna. Figure 13 compares the VR in the case of N = 1, 2, and 4. In the power density range (0–0.31 mW/cm2), the series-connected arrays, with two and four elements, respectively, provide approximately 2.07 and 3.84 times output voltage. However, the parallel-connected arrays generate approximately 1.04 (N = 2) and 0.97 (N = 4) times output voltage whatever the power density striking the rectenna. These results match the theoretical predictions well.
Measured voltage ratio (VR) of the single rectenna element and the interconnected rectenna array.
IV. CONCLUSION
In this paper, a 2.45 GHz efficient dual-diode rectenna and rectenna arrays have been developed. The proposed circuits are simple and compact as they are avoiding the use of input HF filter and via-hole connections. In order to compare and evaluate the performances of a single rectenna element etched on various substrates and using different diodes, two Schottky diodes (HSMS 2860 and 2820) and two substrates (low-loss ARLON 25N and low-cost FR4) were used and results compared. The proposed single rectenna on Arlon 25N can provide a maximum efficiency of 83% under a power density of 0.31 mW/cm2.
Rectenna arrays have been investigated and experimentally characterized. A combination of two and four identical rectenna elements were interconnected either in series or in parallel. Measured results are in good agreement with theoretical predictions, showing that the rectenna elements are equally illuminated, have the same characteristics and are correctly isolated. It has been shown that the choice of the topology of interconnection and the output load can significantly improve the dc power and/or voltage across the load. It is obvious that series connection can give a higher output voltage than the parallel connection but both array interconnections exhibit efficiencies above 78% at a power density of 0.31 mW/cm2. These results can be useful for wireless power transmission applications. The developed rectifier and rectenna arrays are particularly suitable to power remote supply of wireless and low consumption sensors, sensor nodes and actuators.
ACKNOWLEDGEMENT
This project is supported by the “Aeronautic and Space Foundation (FRAE)”.
Hakim Takhedmit received the engineering degree in electronics from the Ecole Nationale Polytechnique, Algiers, Algeria, in 2005, the M.S. degree in microwave communication systems from the Paris-Est Marne-la-Vallée University, Paris, France, in 2007. He is actually a Ph.D. student in electrical engineering at the Ecole Centrale de Lyon, France. He joined in Mars 2007 the ESYCOM Lab and works on the design and modeling of microwave circuits dedicated for wireless power transmission systems. His research interests include passive and active microwave circuits, planar and compact antennas, and numerical methods applied in electromagnetism.
Laurent Cirio was born in Nogent-sur-Marne, France. He received the Ph.D. degree in electrical engineering from the University of Nice-Sophia Antipolis, France, in 1994. In 1996, he joined the ESYCOM Laboratory at the University of Paris-Est Marne-la-Vallée, Marne-la-Vallée, France, as an Assistant Professor. His research focuses on planar antenna with switchable capabilities and dedicated on low power wireless transmission systems. His subject of interest also concerns temporal numerical methods applied on microwave structures such as printed line on silicon substrate and rectenna characterization. He is also involved with experimental characterization and antenna measurement.
Boubekeur Merabet received his engineering degree in electro-mechanic science from the University of Bejaia, Algeria in 2006 and the M.S. degree in electrical engineering from the Ecole Centrale de Lyon, France in 2007. He is actually a Ph.D. student in electrical engineering at the Ecole Normale supérieure de Cachan and works on the development of efficient rectenna circuits. In 2007, he was with the Ampere Lab where he worked on the EMI of power electronic systems dedicated to avionic applications. He Joined in September 2007 the SATIE lab where his main research field was microwave power transmission. He is actually working in the development of power electronic systems.
Bruno Allard received the M.Sc. and Ph.D. degrees in engineering from the Institut National des Sciences Appliquées de Lyon (INSA Lyon), Lyon, France, in 1988 and 1992, respectively. He is currently a full professor at Ampère-lab, in Lyon, France. His research interests include the integration of 3D power systems and low-power monolithic converter design. He has led numerous industrial and academic projects. He is the author and coauthor of more than 60 papers and 90 international conference contributions.
François Costa received the Ph.D. in electrical engineering from University of Paris- Sud, Orsay, France, in 1992. He is also a full professor at the Institut Universitaire de Formation des Maîtres de Créteil, University Paris Est Creteil, France, where he is responsible for the master in teaching sciences and technology. Since 1999, he is the leader of the Power Electronics Team in SATIE Laboratory (SATIE, CNRS UMR 8029). His researches concern high-frequency medium-power converters, the EMI issues and their modeling, the HF instrumentation, the integration in power electronics, and the piezoelectric converters.
Christian Vollaire was born, in 1968. He received his M.S. degree in electrical engineering from the University of Saint Jérôme in Marseille (France) in 1992 and his Ph.D. degree in electrical engineering from the Ecole Centrale de Lyon (France) in 1997. From 1997 to 1998, he worked as graduate research assistant at the Ecole Centrale de Lyon. In 1998, he joined the AMPERE laboratory (UMR CNRS 5005). Since, he carries out its research with AMPERE at the Ecole Centrale de Lyon in the field of the numerical modeling applied to the interaction between electromagnetic field and complex systems. He develops in particular specific formulations and numerical methods for the computation of electromagnetic fields in complex structures. One of the fields of applications relates to electromagnetic compatibility.
Odile Picon was born in Paris, France. She received the doctor degree in external geophysics from Orsay University, France (1980) and a doctorate in electromagnétism University of Rennes (1988). Having been a teacher from 1976 to 1982, she held a position of research engineer in the “Space and Radioelectric Transmission” division of the “Centre National d’études des télécommunications”, from 1982 to 1991. Since 1991, she is a professor of electrical engineering (first at the Paris7-University, then at the Université Paris-Est Marne-la-Vallée (1994)), where she created the “Système de Communication” Laboratory. Her research work focuses on electromagnetic theory, numerical methods for solving field problems, design of millimeter wave passive devices, and electromagnetic compatibility.
