Nonlinear Modeling and Harmonic Recycling of ... - IEEE Xplore

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 63, NO. 3, MARCH 2015

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Nonlinear Modeling and Harmonic Recycling of Millimeter-Wave Rectifier Circuit Shabnam Ladan, Student Member, IEEE, and Ke Wu, Fellow, IEEE

Abstract—This paper presents and demonstrates a harmonic harvesting technique, which aims at rerectifying and recycling the rectifier output harmonics in order to increase the RF-to-dc conversion efficiency. Firstly, an analytical framework is developed based on the Ritz–Galerkin technique to investigate the output power distribution of a simple millimeter-wave rectifier circuit over its dc and generated harmonics components. The numerical results show that about 32% and 66% of the output power is distributed over the dc component and the first harmonic, respectively. In order to recycle and harvest the first harmonic power component, a 35-GHz voltage doubler rectifier implemented in microstrip technology and capable of harmonic harvesting is then studied and designed. To evaluate the performance of the proposed rectifier, the conventional voltage doubler and the harmonic signal rectifiers are fabricated and measured. The measured RF-to-dc conversion efficiencies of 34% at 20-mW input RF power for the harmonic harvester configuration, and 23% at the same input RF power level for the conventional voltage doubler are observed. Moreover, it is shown that the proposed harmonic rectifier suggests about 12% efficiency improvement compared to previously reported millimeter-wave rectifiers at the same level of input power (20 mW). The proposed rectifier configuration can find potential applications in the development of millimeter-wave wireless power transmission devices operating at medium power range (1–100 mW). Index Terms—Harmonic harvester, microwave power transmission, millimeter-wave rectifier, numerical technique, RF-to-dc conversion efficiency, Ritz–Galerkin (RG), Schottky diode, voltage doubler, wireless power transmission.

I. INTRODUCTION

R

APID development of low-power wireless electronic systems has resulted in many research activities focused on the feasibility of a remote powering of these systems. Therefore, RF and microwave power transmission has become a focal point of interest for many years as a promising technique for powering electronic devices over distance [1]. The rectifying antennas known as rectennas are the most important elements in long-range wireless power transmission. The efficiency of rectennas mainly depends on their rectifiers. Therefore, to design a high-efficiency rectenna that guarantees the quality of

Manuscript received October 31, 2014; accepted January 17, 2015. Date of publication February 02, 2015; date of current version March 03, 2015. The authors are with the Poly-Grames Research Center and Center for Radiofrequency Electronics Research of Quebec (CREER), Department of Electrical Engineering, École Polytechnique de Montréal, Montreal, QC, Canada H3V1A2 (e-mail: [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2015.2396043

a wireless power transmission system, more focus needs to be concentrated on the investigation and design of rectifiers with reference to high RF-to-dc conversion efficiency. In rectifier circuits, the rectifying component is also the core element that determines the overall efficiency of the circuits and is normally realized with a diode or a transistor. At low RF frequencies (kilohertz to low megahertz), both transistors and p-n diodes are used as rectifying components. However, at microwave and millimeter-wave frequencies, Schottky diodes (GaAs and Si types) with shorter transit time are better alternatives [2]. The rectification is a nonlinear process in which the final product is a combination of some resulting dc component plus harmonics. This nonlinearity is mainly pronounced as a function of the input power. Although linear and nonlinear circuit models are both used to predict the rectifier behavior, the nonlinear model that considers the nonlinear nature of the diode junction capacitance has better accuracy especially at millimeter-wave frequency since it considers the harmonic oscillation through the nonlinear junction capacitance. In a Schottky diode, the efficiency increment is also observed with increased nonlinearity of the junction capacitance [3]. Therefore, a linear circuit model that ignores the nonlinear behavior of the junction capacitance does not have enough accuracy in predicting the diode conversion efficiency. Just a few studies have thus far been done, evaluating the harmonic effects in connection with the efficiency of a rectifier [4] and [5]. They have had more focus on the harmonics termination technique using stubs (class-F rectifier) as an effective approach to suppressing the generated harmonics and increasing the conversion efficiency of a rectifier [4]. Reference [5] also discussed the power losses of a rectifier because of the diode intrinsic parameters such as series resistance, junction capacitance, built-in potential voltage, and breakdown voltage. Therefore, to yield a better understanding of the rectification process and to evaluate the effect of generated harmonics as well, a closed-form equation describing the nonlinear rectification effects is needed. To obtain such a closed-form solution, the analytical analysis of the nonlinear rectification process of a diode has been studied in [6] and [7]. Due to some simplifications made in truncated series of nonlinear functions, obtained results presented in [6] cannot provide an accurate insight into the rectification behavior. In [7], a numerical approach for the complete dynamic range of a rectifier circuit from “square-law” to “linear” is presented. However, in [7] to simplify the mathematical manipulations, only the dc component has been considered to study the final outcome of rectification process and generated harmonics have been neglected. To ensure the design accuracy, and also to realize the maximum RF-to-dc conversion efficiency, an accurate diode

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model considering harmonics is required. This is essential, especially for millimeter-wave circuit design where the nonlinear effect of diode junction capacitance, leading to a large leakage current, becomes dominant. The frequency-dependent behavior of diode junction capacitance has been investigated in [8]. On the other hand, millimeter-wave rectennas compared to microwave rectennas present the advantages of compact size and higher overall efficiency over a long distance transmission [9]. However, up to now only a few studies have been dedicated to up-microwave frequency and millimeter-wave frequency band. To the best of our knowledge, most of the previous investigation and designs were assumed to operate at a very high RF power level (higher than 100 mW) [8]–[10] while there have been a few reported works for medium- and low-power range in the literature. A 35-GHz rectenna with measured efficiency of 15% for 20-mW input RF power has been discussed in [9]. Two rectennas operating at 10 and 35 GHz with respective 60% RF-to-dc conversion efficiency at 140-mW input power and 39% RF-to-dc conversion efficiency at 120-mW input power have been presented in [8]. A simple substrate integrated waveguide (SIW) rectenna operating at 24 GHz with 15% conversion efficiency with 8-dBm input RF power has been shown in [11]. The design process of a 24-GHz self-biased rectifier with an efficiency of 80% at 5-mW input power has been brought in [12] and [13]. A compact voltage doubler rectifier operating at 24 GHz has been analyzed in [14]. Another structure of a 24-GHz rectifier with 54% of efficiency driven by 130-mW input power and 41% for 50-mW power has been described in [15]. A CMOS rectenna with measured power conversion efficiencies of 53% and 37% in free space at 35 and 94 GHz, respectively, has been reported in [16]. Therefore, the demand for a closed-form solution describing the nonlinear rectification effects, and also a high-efficiency millimeter-wave rectifier design, has motivated our research. Consequently, the contributions of this work are two-fold. • Provide an analytical framework for a rectifier circuit to determine an accurate analysis of the rectification process based on dc component and harmonics of the rectifier output. The extracted equations describing the rectified signal are based on circuit parameters, such as input power, diode series resistance, diode junction capacitance, and optimized resistive load. • Propose a special configuration of a voltage doubler rectifier operating at 35 GHz, which can successfully harvest harmonics generated by the nonlinear effect of rectification to increase the RF-to-dc conversion efficiency. The newly developed rectifier circuit has a compact configuration, which makes it easy to integrate into any kind of antenna and perform the function of a rectenna used in millimeter-wave wireless power transmission systems. This paper is the extended version of our previous work [17], which is organized as follows. Section II discusses the analytical analysis of a rectifier diode. Section III explains the design of a 35-GHz harmonic harvester voltage doubler rectifier. Section IV presents the rectifier design considerations such as diode selection and matching network. Section V demonstrates the measurement result. Finally, a conclusion of the presented results is drawn in Section VI.

Fig. 1. Rectifier simplified equivalent circuit.

II. ANALYTICAL ANALYSIS OF RECTIFIER DIODE In this section, to analyze the contribution of the dc component and relevant harmonics generated through the nonlinear effect of a diode, an analytical framework is presented and discussed. To do so, a Schottky rectifier circuit shown in Fig. 1 is considered, which includes a RF generator, the circuit model of and a Schottky diode considering diode series resistance , and a resistive load at the output. It junction capacitance is worth noting that, in order to simplify the circuit model, the parasitic and packaging effect of the diode are ignored. It is assumed that the diode follows an exponential behavior given by (1) where is the current through the nonlinear diode, is the saturation current, is the voltage across the nonlinear diode and in which is the electronic charge, is the diode ideality factor, is the Boltzmann constant, and is the temperature in Kelvin. In order to obtain a relationship between the input RF power and output power of the circuit, a differential equation of the circuit, shown in Fig. 1, is presented by

(2) where is the input forcing function and the output result, and

is

represents the resistance ratio is the capacitance ratio

Also, primes and denote and , respectively, with . Although the output voltage can be calculated from a numerical integration of (2), the Ritz–Galerkin (RG) technique presented in [7] is adopted to find the closed-form solution. To apply the RG method, the differential equation (2) is represented by (3)

LADAN AND WU: NONLINEAR MODELING AND HARMONIC RECYCLING OF MILLIMETER-WAVE RECTIFIER CIRCUIT

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in which represents the dc component and is the constant coefficient of the first harmonic. Hence, the residual function is presented by

Fig. 2. Power distribution at the output of the rectifier shown in Fig. 1.

(9)

where is a nonlinear operator. Considering the input signal as

In order to reduce the algebraic complexity, it is assumed that , and then the residual function is given by

(4) and . The exact output voltage, while , is then approximated by the following basis function sets:

(10) Therefore, two unknown coefficients, from

and

, can be found

(5)

(11)

where are linearly independent functions, which represent the dc component and different harmonics of the output signal. also signifies adjustable constant coefficients. Since approximates the output voltage, then (5) cannot satisfy the differential equation. Therefore, (3) can be formulated as

(12) By casting (10) into (11) and (12) and after some straightforward multiplications, the resulting equation are given by

(6)

(13)

is called the residual, which is a degree of the in which experienced error. According to [18], the residual is minimized when the Ritz condition of orthogonality is satisfied as (14) (7) Therefore, unknown coefficients, , can be found from a system of equations with the equation and unknown results from (7). In order to determine the number of unknown coefficients, the significant harmonics (which carry more power) of the rectifier output should be determined. To do so, the circuit shown in Fig. 1 is simulated for 10-dBm input power at 35 GHz (Fig. 2). The simulation results are drawn at the output of the Schottky diode without considering the output capacitor (since capacitor is considered as a dc-pass filter). As depicted in Fig. 2, the obtained output power is around 3.2 dBm at dc and 6.6 dBm at the first harmonic (it can be interpreted as or fundamental frequency). Hence, since the injected RF power is set to 10 dBm, it can be concluded that 32% of the output energy is in the dc part and 66% is in the first harmonic, respectively. Also, the second ( ) and third ( ) harmonics (the spectral components at 70 and 110 GHz) have a very small portion of energy ( 15 and 35 dBm, respectively). Consequently, in (5) is considered as (8)

The sum of two trigonometric functions can be expressed as a single trigonometric function to simplify (13) and (14) as follows:

(15)

(16) where (17) (18) The closed-form solution of the above-mentioned equations can be obtained by employing a modified Bessel function defined as follows: (19) (20)

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Fig. 4. Output voltage of the rectifier circuit shown in Fig. 2 versus input power.

Fig. 3. Output voltage of the rectifier circuit shown in Fig. 2.

where and are the modified Bessel function of the first kind of order 0 and 1, respectively. Therefore, (21a) (21b) Since (21) does not have a closed-form solution, an iterative method is used to find and . To do so, for a fixed value of the input voltage, , by iterating the dc component, , a series of first harmonic coefficient, , can be obtained from (21a). The final solution, and , can then be found by satisfying (21b). On the other hand, in order to solve (21a), the inverse of the modified Bessel function is needed, which does not have a closed-form solution. Therefore, a root-finding algorithm called the Secant method [19] is adopted to find the solution of (22a). The Secant method is an iterative root-finding algorithm, which uses a secant line passing through two points of the function to approximate its root. Hence, considering two approximated points and , the Secant algorithm returns an estimate of the function's root as [18]

Fig. 5. Conventional structure of a voltage doubler microwave rectifier circuit.

(22)

In this section, an enhanced rectifier circuit considering millimeter-wave frequency-band requirements with the capability of harmonic harvesting is proposed.

It has been shown that the convergence rate of the Secant method is superlinear with 1.62 [19]. Moreover, it is noted that and ), the Secant algorithm requires two initial points ( which have to be determined cautiously. In order to accelerate the convergence to the optimum solution, the signs of and should be different, and hence, and can be obtained satisfying this condition. Fig. 3 depicts the simulation and analytical results of the dc component and harmonics of the rectifier output voltage for 10-dBm input power, while Fig. 4 shows the generated output voltage at dc and the first harmonic for different level of input power. As observed, there is a good agreement between analytical and simulation results. However, there is a slight difference between two results, which can be traced into the fact that, in simulation, a higher order of harmonics are considered, which increases the accuracy of the obtained results compared to the analytical method where only one harmonic is considered. It is worth noting that, considering higher order of harmonics in (5) leads to more accurate results at the expense of a very high computational complexity.

Fig. 6. Modified structure of the millimeter-wave voltage doubler rectifier.

III. HARMONIC HARVESTER MILLIMETER-WAVE RECTIFIER

A. Voltage Doubler Rectifier Rectifier circuits have different topologies including: a single diode in series or parallel configuration, voltage doubler, and bridge. Among the mentioned architectures, the voltage doubler configuration (Fig. 5) is a very common approach to obtain higher dc voltage. This structure is a full-wave rectifier, which makes at least twice higher dc voltage than the single-diode rectifier, while the size of circuit remains unchanged. Over the millimeter-wave frequency range, the common configuration of rectifiers suffers from electrostatic discharge (ESD) and imperfect output filter drawbacks. Fig. 6 shows the modified configuration of a millimeter-wave voltage doubler rectifier proposed in this study. As observed, a lossy path including a high-value resistor ( k in the proposed design) is considered just after charging capacitor . This resistive path protects the diodes from ESD and prevents them from being burnt out by providing a dc path for accumulated electrical charges [14]. The output filter in a conventional rectifier is also generally made up of a capacitor at a distance


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Fig. 7. Harmonic suppression at the output of the rectifier.

of quarter-wavelength in connection with the operating frequency from the diode. Since at millimeter-wave frequency the impedance of a real capacitor is not zero, then it cannot realize a perfect short circuit. To have a perfect short condition, one solution is using a special quarter-wavelength stub resonator instead of a normal capacitor. This stub resonator prevents RF power to appear across the resistive load. To do so, the output dc-pass filter is realized using a quarter-wavelength open-circuit stub resonator at the fundamental frequency as well as the second harmonic. This output filter is set at the distance of one quarter-wavelength at fundamental frequency from the rectifying diode. The obtained results shown in Fig. 7 justify the resonator structure since it has a superior performance in terms of harmonic suppression compared to a real capacitor. B. Harmonic Harvesting Rectifier Configuration In (5), it was shown that the diode's output can be expressed as a summation of the dc part and the harmonics of the fundamental frequency. It was also explained that, in conventional rectifiers operating at medium range of input RF power (0–100 mW), a substantial portion of energy is wasted in harmonics, which normally are trapped by a dc-pass filter to generate a flat output dc voltage. Therefore, harvesting harmonics instead of suppressing them will result in efficiency increment. Consequently, Fig. 8 presents a modified voltage doubler rectifier with a harmonic harvesting feature. In the proposed structure, diodes and realize a full-wave rectification process. At the output of the voltage doubler (test point A shown in Fig. 8), the dc rectified wave plus some harmonics are available. Capacitor separates harmonics from the dc part by blocking the dc current. Diode then rectifies the harmonics. Fig. 9 shows the spectrum distribution of the rectified signal at the output of the voltage doubler (test point A, Fig. 8) and harmonic harvester (test point B, Fig. 8). As observed, a significant percentage of the available energy existing in harmonics is rectified. The harmonics rectification will result in increasing the dc level. Furthermore, two dc-pass filters in the form of quarter-wavelength resonator stubs are used to reject any RF signals (even though the level of RF signals is very low) and smooth the generated dc voltage. IV. RECTIFIER DESIGN CONSIDERATIONS Designing a high-efficiency rectifier circuit depends on the consideration of two important criteria, namely, choosing an

Fig. 8. Millimeter-wave harmonic harvesting rectifier.

Fig. 9. Distribution of the rectified signal and harmonics at the output of the voltage doubler (test point A, Fig. 8) and harmonic harvesting (test point B, Fig. 8).

appropriate rectifier diode and providing quality matching network. A. Selection of Rectifier Schottky Diode Selecting an appropriate diode is important because in a rectifier circuit, diodes are the main source of loss and their performance determines the overall circuit performance. A closedform equation for the diode conversion efficiency has been derived in [8]. According to [10], the power conversion efficiency of a rectifier depends on three parameters of diode; namely, zero-bias junction capacitance , which determines the oscillation of harmonic currents through a diode, the series resistance , which causes the ohmic loss and restricts the circuit efficiency, and the breakdown voltage , which confines the power-handling capability of a rectifier. An appropriate rectifier diode has low junction capacitance, low series resistance, and high breakdown voltage, which are very difficult to get satisfied simultaneously because of the physical mechanism of diodes and those inter-correlated parameters. For rectification purposes, it is also necessary to choose a diode with the capability of a high-speed switching to follow a high-frequency input signal with low cutoff voltage to operate at low input RF power. Besides, since this study focuses on millimeter-wave frequency design, and more specifically, 35 GHz, the nominated rectifying Schottky diode needs to support this frequency band. Considering the above-mentioned features, commercial Schottky diode MA4E1317 from MACOM with , pF, and V is

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Fig. 10. Real circuit model of the Schottky diode and its measured parasitic and packaging parameters.

selected and used in this study (all the presented simulations and measurements are based on this Schottky rectifier).

Fig. 11. (a) TRL calibration kit. (b) Fabricated harmonic harvesting rectifier without matching. (c) Fabricated modified 35-GHz voltage doubler rectifier. (d) Fabricated 35-GHz harmonic harvesting rectifier. (A: reference plane, B: dc-pass capacitor, C: voltage doubler diodes, D: dc-block capacitor, E: harmonic harvester diode, F: ESD protection resistor, G: load).

B. Matching Network Providing a high-quality matching network guarantees the maximum energy transfer and minimizes the transmission loss. Different techniques are available to determine the input impedance of a rectifier and design the related matching circuit. For example, the equivalent-circuit model of a diode used in the analysis and simulation process can be obtained based on the diode parameters mentioned in the respective datasheet of the candidate diode. This technique is straightforward and accurate at low frequency ( 2.45 GHz). Since the circuit models obtained from datasheets are not accurate enough to contain all parasitic and packaging effects, this technique is not recommended at high-frequency design. Another technique for designing a matching network is to obtain the parameters of a single diode through measurement and extract its real circuit model considering all the parasitic and packaging parameters. The constructed model is then used to design the initial matching network by using an LSSP simulation controller from Advanced Design System (ADS) [14]. At millimeter-wave frequency, circuit models of lumped components similar to diode models do not include real physical and parasitic effects. While at millimeter-wave frequency, the development of an accurate model of diodes and lumped components should be considered in the simulation. Nevertheless, the measured and simulation resonances will occur at different frequencies and the fabricated prototype will have some frequency shift. Therefore, the recommended method to determine the input impedance and design the matching circuit is based on the experimental characterization of lumped components as well as diodes. To do so, the rectifier Schottky diode is firstly measured individually to obtain the parasitic and packaging parameters. The real circuit model of the Schottky diode is shown in Fig. 10 where , the lead inductance, and , the parasitic capacitance, are introducing the packaging effect while and are modeling the effect of the diode pads. The parasitic elements and packaging elements of a diode are voltage-independent parameters and determined by the small-signal measurement explained in [21]. In order to obtain the exact model of the Schottky diode, a microstrip test mount is designed and fabricated for small-signal diode measurement. A thru-reflect-line (TRL) calibration kit is also designed for proper calibration. The S-parameters characterization is performed using an Anritsu 37397C network analyzer from 5 to 40 GHz at a different level of input power. The measured

Fig. 12. Simulation and measurement results of the harmonic harvester rectifier return loss.

frequency range is related to the frequency restriction of the TRL calibration kit. For the small-signal measurement of the selected diode, the S-parameters in the mentioned frequency range are measured and saved as a touchstone format (S2P file). The diode circuit parameters are then obtained through optimization and a tuning process using ADS in order to fit the curves of the diode circuit model to the measured S-parameter data. Consequently, , , , and are extracted and the model shown in Fig. 10 is used for initial design simulation of the rectifier. In the next step, the rectifier circuit without a matching network is designed and the optimization is run to get the maximum efficiency (without matching). The optimization is based on the maximum input power and the dc load. The optimized circuit including Schottky diodes, an ESD protection resistor, an output dc-pass filter, and a dc resistive load is then fabricated [see Fig. 11(b)]. S-parameters of this circuit are measured using an Anritsu network analyzer and saved as an S2P file. Consequently, the obtained result is used as a black box for designing the impedance matching network. Other (TRL) calibration standards [see Fig. 11(a)] are designed and used to relocate reference planes of the structure [i.e., point A in Fig. 11(b)] and remove effects of the microstrip line added to the input of the circuit. This microstrip line keeps the circuit in a proper distance from connectors of the test fixture. V. DESIGN, FABRICATION, AND MEASUREMENT The modified voltage doubler and harmonic harvesting rectifier operating at 35 GHz are designed based on the above-mentioned criteria. Simulations are carried out on both schematic and layout levels. Layout-level simulations are performed using Momentum in ADS. Subsequently, the simulated circuit is brought back to the schematic in order to run co-simulation process. The co-simulation feature is used to reassure that all components show desired performance


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TABLE I COMPARISON AMONG PREVIOUSLY DESIGNED MILLIMETER-WAVE RECTIFIERS

Fig. 13. Output dc voltage versus input RF power.

Fig. 14. Output dc power versus input RF power.

by up to 11%. To the best of our knowledge, the achieved efficiency is the maximum reported to date at this level of input RF power. For a better evaluation, a comparison is given among the documented millimeter-wave rectifier designs (Table I). The RF-to-dc conversion efficiency of the rectifier is defined as the ratio of the output dc power to the incident power [22]. VI. CONCLUSION

Fig. 15. Rectifier efficiency versus input RF power.

at 35 GHz. In order to experimentally test and evaluate the system improvement in a real measurement condition, the optimized circuits (the conventional voltage doubler and the harmonic harvester) are fabricated on a 10-mil-thick high-frequency Rogers 5880 ( and 17 m of copper thickness) [see Fig. 11(c) and (d)]. Simulated and measured impedance matching conditions of the harmonic harvesting rectifier is shown in Fig. 12. Good agreement between simulation and measurement justifies the accuracy of the method used in determining the diode input impedance and designing the related matching network. The small frequency shift (less than 0.25 GHz or 0.35%) between the simulation and measurement results is due to additional tolerance introduced in our in-house fabrication procedure. The signal generator, E8267D from Agilent Technologies, is used to power both rectifiers. Figs. 13–15 show the obtained output dc voltage, dc power and RF-to-dc conversion efficiency of rectifiers, respectively. The maximum measured conversion efficiency of 23% at 20-mW input RF power is reported for the voltage doubler rectifier, while for the harmonic harvesting rectifier, the measured conversion efficiency is 34% for the same level of input power. The obtained results verify that the harmonic harvesting configuration increases the conversion efficiency

An analytical analysis has been developed using an RG method to investigate the nonlinear behavior of the rectification process in a rectifier circuit. According to the obtained equations, it has been shown that the major portion of energy are carried in the first harmonic and dc component. Harvesting harmonics can then increase the efficiency of the rectifier. To justify the idea of harmonic harvesting technique at millimeter-wave applications, a new structure of the full-wave rectifier operating at 35 GHz with the ability of harmonic harvesting is proposed and studied. Subsequently, the performance of the proposed harmonic harvesting structure is compared with the modified voltage doubler configuration. Both structures are studied by full-wave simulations using ADS software and also experimentations. The measured efficiency of 34% at 20-mW RF power level is obtained for the harmonic harvesting rectifier that is compared to the voltage doubler model with measured efficiency of 23% for the same input power level. This shows a significant enhancement in terms of conversion efficiency. According to the state-of-the-art millimeter-wave rectifier reported in the literature, the proposed structure is believed to exhibit the highest conversion efficiency at medium power range. ACKNOWLEDGMENT The authors would like to thank Dr. F. Sarabchi for his invaluable advice on analytical analysis of this work. Special thanks is extended to T. Antonescu, M. Thibault, S. Dubé, and J. Gauthier, all with the Poly-Grames Research Center, École Polytechnique de Montréal, Montreal, QC, Canada, for their help

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and support in the fabrication and measurement of the circuit prototypes.

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Shabnam Ladan (S'10) received the M.Sc. degree in telecommunication-wave engineering from the K. N. Toosi University of Technology, Tehran, Iran, in 2006, and is currently working toward the Ph.D. degree in microwave engineering at the École Polytechnique de Montréal, Montreal, QC, Canada. She is currently with the Poly-Grames Research Center and the Center for Radiofrequency Electronics Research of Quebec, Department of Electrical Engineering, École Polytechnique de Montréal. Her main research interests include far-field wireless power transmission and energy harvesting, high-efficiency rectennas including antenna and rectifier design and characterization, and modeling and measurement of nonlinear active components at millimeter-wave frequencies. Ms. Ladan was the recipient of first place honors of the Student Design Competition “Wireless Energy Harvesting,” IEEE Microwave Theory and Techniques Society (IEEE MTT-S) International Microwave Symposium (IMS) 2012. She was also a member of the second finalist team of the Student Design Competition “Wireless Energy Harvesting,” IEEE MTT-S IMS 2013. Ke Wu (M'87–SM'92–F'01) received the B.Sc. degree (with distinction) in radio engineering from the Nanjing Institute of Technology (now Southeast University), Nanjing, China, in 1982, and the D.E.A. and Ph.D. degrees in optics, optoelectronics, and microwave engineering (with distinction) from the Institut National Polytechnique de Grenoble (INPG) and University of Grenoble, Grenoble, France, in 1984 and 1987, respectively. He is currently a Professor of electrical engineering and Tier-I Canada Research Chair in RF and millimeter-wave engineering with the École Polytechnique de Montréal, Montreal, QC, Canada, where he has also been the Director of the Poly-Grames Research Center. He was the Founding Director of the Center for Radiofrequency Electronics Research of Quebec (Regroupement stratégique of FRQNT). He has also held guest, visiting, and honorary professorship at many universities around the world. He has authored or coauthored over 1000 referred papers and a number of books/book chapters. He has filed over 30 patents. His current research interests involve substrate integrated circuits (SICs), antenna arrays, advanced computer-aided design (CAD) and modeling techniques, wireless power transmission and harvesting, and development of low-cost RF and millimeter-wave transceivers and sensors for wireless systems and biomedical applications. He is also interested in the modeling and design of microwave and terahertz photonic circuits and systems. Dr. Wu is a member of the Electromagnetics Academy, Sigma Xi, and URSI. He has held key positions in and has served on various panels and international committees including the chair of Technical Program Committees, international Steering Committees and international conferences/symposia. In particular, he was the general chair of the 2012 IEEE Microwave Theory and Techniques Society (IEEE MTT-S) International Microwave Symposium (IMS). He has served on Editorial/Review Boards of many technical journals, transactions, proceedings, and letters, as well as scientific encyclopedia as an editor or guest editor. He is currently the chair of the joint IEEE chapters of MTTS/APS/ LEOS, Montreal, QC, Canada. He is an elected IEEE MTT-S Administrative Committee (AdCom) member for 2006–2015 and served as chair of the IEEE MTT-S Transnational Committee, Member and Geographic Activities (MGA) Committee and Technical Coordinating Committee (TCC) among many other AdCom functions. He is the 2015 IEEE MTT-S president-elect and will become the 2016 IEEE MTT-S president. He is the inaugural three-year representative of North America as a Member of the European Microwave Association (EuMA) General Assembly. He is a Fellow of the Canadian Academy of Engineering (CAE) and the Royal Society of Canada (The Canadian Academy of the Sciences and Humanities). He was an IEEE MTT-S Distinguished Microwave Lecturer from 2009 to 2011. He was the recipient of many awards and prizes including the first IEEE MTT-S Outstanding Young Engineer Award, the 2004 Fessenden Medal of IEEE Canada, the 2009 Thomas W. Eadie Medal of the Royal Society of Canada, the Queen Elizabeth II Diamond Jubilee Medal in 2013, the 2013 FCCP Education Foundation Award of Merit, the 2014 IEEE MTT-S Microwave Application Award, and the 2014 Marie-Victorin Prize (Prix du Quebec—the highest distinction of Québec in the natural sciences and engineering).