# Study on Millimeter-Wave Vivaldi Rectenna and Arrays with High Conversion Efficiency

Authors: Guan-Nan Tan; Xue-Xia Yang; Huan Mei; Zhong-Liang Lu
Journal: International Journal of Antennas and Propagation
 (2016)

---

## Abstract

A novel Vivaldi rectenna operated at 35 GHz with high millimeter wave to direct current (MMW-to-DC) conversion efficiency is presented and the arrays are investigated. The measured conversion efficiency is 51.6% at 35 GHz and the efficiency higher than 30% is from 33.2 GHz to 36.6 GHz when the input MMW power is 79.4 mW. The receiving Vivaldi antenna loaded with metamaterial units has a high gain of 10.4 dBi at 35 GHz. A SIW- (substrate integrated waveguide-) to-microstrip transition is designed not only to integrate the antenna with the rectifying circuit directly but also to provide the DC bypass for the rectifying circuit. When the power density is 8.7 mW/cm2, the received MMW power of the antenna is 5.6 mW, and the maximum conversion efficiency of the rectenna element is 31.5%. The output DC voltage of the element is nearly the same as that of the parallel array and is about half of the series array. The DC power obtained by the 1 × 2 rectenna arrays is about two times as much as that of the element. The conversion efficiencies of the arrays are very close to that of the element. Large scale arrays could be expended for collecting more DC power.


---

## Body

## 1. Introduction

WPT (wireless power transmission) technology is used to deliver electric power without wires. It can date back to 1960s when Brown carried out the first WPT experiment [1]. To solve the energy crises, the concept of space-based SSP (space solar power) was conceived by Dr. Peter Glaser in 1968 [2], promoting the development of WPT technology [3, 4]. Compared to the microwave WPT systems, the millimeter-wave systems have the advantages of smaller size and higher system transmission efficiency for long distance WPT, which can be applied in the space where there is no atmosphere loss [5]. The rectenna, consisting of a receiving antenna and a rectifying circuit, plays an important role in the WPT systems.Many rectennas at microwave bands have been developed [6–11], and the RF-to-DC conversion efficiency can reach about 80% when the rectifying circuits obtain about 100 mW input power. Until now, only a few millimeter-wave rectennas have been reported [12–16], which are listed in Table 1. The reported CPS (coplanar strip line) rectenna and patch rectenna operated at 35 GHz obtain the measured conversion efficiencies of 38% and 29%, respectively, when the input MMW power is 120 mW [12, 13]. To obtain the enough input power for the rectifying circuit, the transmitted millimeter-wave power is high for the above two rectennas because of the low gain of the receiving antennas. In order to lessen the transmitting power demand and supply the required input power for the rectifying circuit, the 1 × 2 antenna array is designed for the rectifying circuit [14]. The rectenna element and the 2 × 2 series array obtain an efficiency of 35% when the power density is 30 mW/cm2. However, the length of the rectifying circuit is longer than 2λ0. Reference [15] reports a dual-band rectenna operated at 35 and 94 GHz with the conversion efficiency of 53% and 37%, respectively, under the power density of 30 mW/cm2. The circuit is based on the CMOS 0.13-μm technology, which is more expensive and complex to design comparing to the standard PCB technology. In [16], the voltage doubling rectifying circuit obtains measured conversion efficiency of 34% at 35 GHz when the input power is 20 mW.Table 1
Performances of the reported rectifying circuits/rectennas and this work.
References f (GHz) Diode connect P i n (mW) rectifying circuit P d (mW/cm2) rectenna eff (%) [12] 35 Parallel 120 — 38 [13] 35 Series 120 — 29 [14] 35 Parallel — 30 35 [15] 3594 Parallel — 30 5337 [16] 35 Doubling 20 — 34 This work 35 Series 20 — 43.7 79.4 51.6 — 8.7 31.5In this paper, a novel Vivaldi rectenna operated at 35 GHz with high MMW-to-DC conversion efficiency is presented and the array design is investigated. The rectifying circuit adopts the series-mounted diode topological structure and has small and simple structure. The receiving antenna is a broadband end-fire Vivaldi antenna with high gain and harmonic suppression function and could be integrated directly to the rectifying circuit to form the rectenna. The performances of the rectifying circuit, rectenna element, and arrays are verified by the measurements. The rectenna element has high conversion efficiency and compact structure and could be extended to large arrays. Table1 summarizes the performances of the reported rectifying circuits or rectennas and this work.


## 2. Rectenna Design

### 2.1. Rectifying Circuit Design

To design the rectifying circuit, it is essential to determine the diode’s input impedance. At microwave band, the diode’s input impedance could be obtained from the closed-form equation [6, 7] or the commercial software of ADS (Advanced Design System) and AWR Microwave Office [8–11], in which the parameters of the diode model provided by the datasheet are accurate. However, at millimeter-wave bands, the equivalent circuit parameters of the diode model are inaccurate and the simulated results will not be precise enough, so the conversion efficiencies of the designed rectifying circuits are low [12–14, 16]. In this study, the proposed rectifying circuit is designed by the experimental method.


#### 2.1.1. Rectifying Circuit Configuration

The geometrical structure of the proposed rectifying circuit operating at 35 GHz is shown in Figure1, which consists of a diode in series configuration, an open-circuit match branch, a quarter-wave microstrip line impedance transformer, a microstrip-SIW-microstrip transition, two radial stubs, and a resistance load RL. The resistive load RL is used to collect the DC power. The rectifying circuit is designed on Rogers 5880 substrate with the relative permittivity of 2.2, the loss tangent of 0.0009, and the thickness of 0.254 mm.Figure 1
Structure of the rectifying circuit.The commercial Schottky diode of MA4E1317 is used for rectifying. The diode has the forward and breakdown voltages of 0.7 V and 7 V, respectively. The zero-bias junction capacitanceCj is 0.02 pF and the series resistance is 4 Ω. The diode’s input impedance Zd is a complex due to the junction capacitance Cj. The open-circuit match branch with the length of Lm is inserted between the diode and the DC-pass filter to eliminate the imaginary part of the diode’s input impedance Zd. The quarter-wave microstrip line impedance transformer with the width of Wt is used to convert the real part of Zd into Z1, which is designed to be 50 Ω.To integrate the rectifying circuit with the following SIW receiving Vivaldi antenna, the microstrip-SIW-microstrip transition with zero-phase shift is designed. With this transition, the input impedance and the conversion efficiency of the proposed rectifying circuit can be measured in experiment. The vias in SIW also provide the DC bypass to collect the DC power because of the series configuration of the diode. The simulatedS-parameters of the microstrip-SIW-microstrip transition are shown in Figure 2. It can be observed that the reflection coefficient S11 is less than −15 dB and the insert loss S21 is lower than 0.6 dB within the bandwidth from 30 GHz to 40 GHz, which ensures the good passband performance of the transition. Meanwhile, the simulated phase shift of the designed transition at 35 GHz is about 0°, which indicates that the input impedance Zin of the rectifying circuit shown in Figure 1 is equal to Z1.Figure 2
SimulatedS-parameters of the microstrip-SIW-microstrip transition.The two radial stubs with the lengths ofLs1 and Ls2 are designed as a DC-pass filter to prevent the unwanted fundamental wave and the second harmonic from passing the resistive load RL. The simulated S parameters of the DC-pass filter are shown in Figure 3. It can be found that the filter shows good DC-pass performance with the attenuations of 35 dB and 38 dB at 35 GHz and 70 GHz, respectively.Figure 3
SimulatedS-parameters of the DC-pass filter.


#### 2.1.2. Rectifying Circuit Experiments

The exact sizes of the high efficiency rectifying circuit shown in Figure1 are determined by the experimental method. The two parameters, the length Lm of the open-circuit match branch and the width Wt of the quarter wavelength transformer, are optimized to cancel the imaginary part of the diode’s input impedance Zd and match the real part of Zd to 50 Ω. Several circuits with the same length Lm and different width Wt are fabricated. The initial length Lm is λg/2, and λg is the waveguide wavelength in the microstrip line. To eliminate the imaginary part of the input impedance Zin of the rectifying circuit, the length of Lm in each circuit is adjusted. When the input impedance Zin is matched to 50 Ω, which is measured by the Agilent VNA (Vector Network Analyzer) of N5227A, the sizes of Lm and Wt are determined, and the high efficiency rectifying circuit is obtained. The final dimensions of the rectifying circuit are given in Table 2. The measured reflection coefficient S11 versus frequency is shown in Figure 4. It can be seen that when the input power is 10 dBm and the load is 550 Ω, the measured S11 is −19.6 dB at 35 GHz and the corresponding Zin is (46+j6.7)Ω which can be found in the Smith chart of the VNA. The diode’s input impedance Zd calculated from Zin is (22.7-j3.3)Ω. It is observed that the imaginary part of Zd is small and the open-circuit match branch works well.Table 2
Dimensions of the rectifying circuit and the microstrip-SIW-microstrip transition.
L m W t L s 1 L s 2 L c W S I W 2.02 1.4 0.6 1.12 7 4.55  P D W 1 W 2 L 1 L 2 0.8 0.5 0.78 1 3.1 1.55Figure 4
Measured reflection coefficient|S11| versus frequency, Pin=10dBm, and RL=550Ω.The MMW-DC conversion efficiencyη of the rectifying circuit can be calculated by(1)η=VdcRLPin×100%,where RL is the resistance load, Vdc is the output DC voltage on the load that can be read by a voltmeter, and Pin is the input MMW power of the circuit. When the input power is 10 dBm, the measured output DC voltages and the conversion efficiencies versus the load at 35 GHz are shown in Figure 5. It can be seen that the conversion efficiency increases with the load and gets the peak of 38.6% at 550 Ω. When the load keeps on increasing, the output DC voltage continues to increase while the efficiency decreases. So the optimal load resistance is 550 Ω.Figure 5
Measured output DC voltages and conversion efficiencies versus loadRL, Pin=10dBm, and f=35 GHz.When the load resistance is 550 Ω, the measured output DC voltages and conversion efficiencies versus the input power are plotted in Figure6. It is found that the output DC voltage and the conversion efficiency increase with the input power. When the input power is 19 dBm (79.4 mW), the output voltage and conversion efficiency are 4.75 V and 51.6%, respectively. When the input power continues to increase, the maximum voltage will exceed the breakdown voltages and the conversion efficiency decreases. The conversion efficiency is higher than 30% when the input power is higher than 7 dBm (5 mW). Figure 7 shows the measured output DC voltages and conversion efficiencies versus the frequency at the input power of 19 dBm when the load resistance is 550 Ω. The efficiencies are all higher than 30% from 33.2 GHz to 36.6 GHz, which exhibits a relatively broadband performance.Figure 6
Measured output DC voltages and conversion efficiencies versus input power,RL=550Ω, and f=35 GHz.Figure 7
Measured output DC voltage and conversion efficiency versus frequency,Pin=19dBm, and RL=550Ω.


### 2.2. Receiving Antenna Design

A novel Vivaldi slot is used as the receiving antenna, which is shown in Figure8. It has the characteristics of high gain, broad bandwidth, and harmonic suppression. The Vivaldi slot is excited by a SIW, which is formed by two extra rows of metal vias to bound the energy within the SIW tightly and enhance the transmission performance. The center-symmetric metamaterial units with zero effective permittivity at 35 GHz are loaded on the Vivaldi slot to improve the antenna gain. The microstrip-to-SIW transformer is designed to feed the antenna, and the characteristic impedance of the microstrip line is 50 Ω. In order to prevent the second harmonics generated by the nonlinear diode from reradiating by the antenna, the SRR (split ring resonator) units are etched on the ground of the microstrip feed line to act as a low pass filter. The substrate used for the receiving antenna is the same as that for the rectifying circuit.Figure 8
Structure of receiving antenna (units: mm).The simulated and measured reflection coefficients and gains of the proposed Vivaldi antenna are plotted in Figure9. The antenna exhibits a broad bandwidth of 38.5% ranging from 26.5 GHz to 40 GHz with the reflection coefficient less than −10 dB. The gain varies from 9.3 dBi to 10.4 dBi within the Ka band and the highest gain is 10.4 dBi at 35 GHz.Figure 9
Simulated and measured reflection coefficients and gains of the receiving Vivaldi antenna.


## 2.1. Rectifying Circuit Design

To design the rectifying circuit, it is essential to determine the diode’s input impedance. At microwave band, the diode’s input impedance could be obtained from the closed-form equation [6, 7] or the commercial software of ADS (Advanced Design System) and AWR Microwave Office [8–11], in which the parameters of the diode model provided by the datasheet are accurate. However, at millimeter-wave bands, the equivalent circuit parameters of the diode model are inaccurate and the simulated results will not be precise enough, so the conversion efficiencies of the designed rectifying circuits are low [12–14, 16]. In this study, the proposed rectifying circuit is designed by the experimental method.


### 2.1.1. Rectifying Circuit Configuration

The geometrical structure of the proposed rectifying circuit operating at 35 GHz is shown in Figure1, which consists of a diode in series configuration, an open-circuit match branch, a quarter-wave microstrip line impedance transformer, a microstrip-SIW-microstrip transition, two radial stubs, and a resistance load RL. The resistive load RL is used to collect the DC power. The rectifying circuit is designed on Rogers 5880 substrate with the relative permittivity of 2.2, the loss tangent of 0.0009, and the thickness of 0.254 mm.Figure 1
Structure of the rectifying circuit.The commercial Schottky diode of MA4E1317 is used for rectifying. The diode has the forward and breakdown voltages of 0.7 V and 7 V, respectively. The zero-bias junction capacitanceCj is 0.02 pF and the series resistance is 4 Ω. The diode’s input impedance Zd is a complex due to the junction capacitance Cj. The open-circuit match branch with the length of Lm is inserted between the diode and the DC-pass filter to eliminate the imaginary part of the diode’s input impedance Zd. The quarter-wave microstrip line impedance transformer with the width of Wt is used to convert the real part of Zd into Z1, which is designed to be 50 Ω.To integrate the rectifying circuit with the following SIW receiving Vivaldi antenna, the microstrip-SIW-microstrip transition with zero-phase shift is designed. With this transition, the input impedance and the conversion efficiency of the proposed rectifying circuit can be measured in experiment. The vias in SIW also provide the DC bypass to collect the DC power because of the series configuration of the diode. The simulatedS-parameters of the microstrip-SIW-microstrip transition are shown in Figure 2. It can be observed that the reflection coefficient S11 is less than −15 dB and the insert loss S21 is lower than 0.6 dB within the bandwidth from 30 GHz to 40 GHz, which ensures the good passband performance of the transition. Meanwhile, the simulated phase shift of the designed transition at 35 GHz is about 0°, which indicates that the input impedance Zin of the rectifying circuit shown in Figure 1 is equal to Z1.Figure 2
SimulatedS-parameters of the microstrip-SIW-microstrip transition.The two radial stubs with the lengths ofLs1 and Ls2 are designed as a DC-pass filter to prevent the unwanted fundamental wave and the second harmonic from passing the resistive load RL. The simulated S parameters of the DC-pass filter are shown in Figure 3. It can be found that the filter shows good DC-pass performance with the attenuations of 35 dB and 38 dB at 35 GHz and 70 GHz, respectively.Figure 3
SimulatedS-parameters of the DC-pass filter.


### 2.1.2. Rectifying Circuit Experiments

The exact sizes of the high efficiency rectifying circuit shown in Figure1 are determined by the experimental method. The two parameters, the length Lm of the open-circuit match branch and the width Wt of the quarter wavelength transformer, are optimized to cancel the imaginary part of the diode’s input impedance Zd and match the real part of Zd to 50 Ω. Several circuits with the same length Lm and different width Wt are fabricated. The initial length Lm is λg/2, and λg is the waveguide wavelength in the microstrip line. To eliminate the imaginary part of the input impedance Zin of the rectifying circuit, the length of Lm in each circuit is adjusted. When the input impedance Zin is matched to 50 Ω, which is measured by the Agilent VNA (Vector Network Analyzer) of N5227A, the sizes of Lm and Wt are determined, and the high efficiency rectifying circuit is obtained. The final dimensions of the rectifying circuit are given in Table 2. The measured reflection coefficient S11 versus frequency is shown in Figure 4. It can be seen that when the input power is 10 dBm and the load is 550 Ω, the measured S11 is −19.6 dB at 35 GHz and the corresponding Zin is (46+j6.7)Ω which can be found in the Smith chart of the VNA. The diode’s input impedance Zd calculated from Zin is (22.7-j3.3)Ω. It is observed that the imaginary part of Zd is small and the open-circuit match branch works well.Table 2
Dimensions of the rectifying circuit and the microstrip-SIW-microstrip transition.
L m W t L s 1 L s 2 L c W S I W 2.02 1.4 0.6 1.12 7 4.55  P D W 1 W 2 L 1 L 2 0.8 0.5 0.78 1 3.1 1.55Figure 4
Measured reflection coefficient|S11| versus frequency, Pin=10dBm, and RL=550Ω.The MMW-DC conversion efficiencyη of the rectifying circuit can be calculated by(1)η=VdcRLPin×100%,where RL is the resistance load, Vdc is the output DC voltage on the load that can be read by a voltmeter, and Pin is the input MMW power of the circuit. When the input power is 10 dBm, the measured output DC voltages and the conversion efficiencies versus the load at 35 GHz are shown in Figure 5. It can be seen that the conversion efficiency increases with the load and gets the peak of 38.6% at 550 Ω. When the load keeps on increasing, the output DC voltage continues to increase while the efficiency decreases. So the optimal load resistance is 550 Ω.Figure 5
Measured output DC voltages and conversion efficiencies versus loadRL, Pin=10dBm, and f=35 GHz.When the load resistance is 550 Ω, the measured output DC voltages and conversion efficiencies versus the input power are plotted in Figure6. It is found that the output DC voltage and the conversion efficiency increase with the input power. When the input power is 19 dBm (79.4 mW), the output voltage and conversion efficiency are 4.75 V and 51.6%, respectively. When the input power continues to increase, the maximum voltage will exceed the breakdown voltages and the conversion efficiency decreases. The conversion efficiency is higher than 30% when the input power is higher than 7 dBm (5 mW). Figure 7 shows the measured output DC voltages and conversion efficiencies versus the frequency at the input power of 19 dBm when the load resistance is 550 Ω. The efficiencies are all higher than 30% from 33.2 GHz to 36.6 GHz, which exhibits a relatively broadband performance.Figure 6
Measured output DC voltages and conversion efficiencies versus input power,RL=550Ω, and f=35 GHz.Figure 7
Measured output DC voltage and conversion efficiency versus frequency,Pin=19dBm, and RL=550Ω.


## 2.1.1. Rectifying Circuit Configuration

The geometrical structure of the proposed rectifying circuit operating at 35 GHz is shown in Figure1, which consists of a diode in series configuration, an open-circuit match branch, a quarter-wave microstrip line impedance transformer, a microstrip-SIW-microstrip transition, two radial stubs, and a resistance load RL. The resistive load RL is used to collect the DC power. The rectifying circuit is designed on Rogers 5880 substrate with the relative permittivity of 2.2, the loss tangent of 0.0009, and the thickness of 0.254 mm.Figure 1
Structure of the rectifying circuit.The commercial Schottky diode of MA4E1317 is used for rectifying. The diode has the forward and breakdown voltages of 0.7 V and 7 V, respectively. The zero-bias junction capacitanceCj is 0.02 pF and the series resistance is 4 Ω. The diode’s input impedance Zd is a complex due to the junction capacitance Cj. The open-circuit match branch with the length of Lm is inserted between the diode and the DC-pass filter to eliminate the imaginary part of the diode’s input impedance Zd. The quarter-wave microstrip line impedance transformer with the width of Wt is used to convert the real part of Zd into Z1, which is designed to be 50 Ω.To integrate the rectifying circuit with the following SIW receiving Vivaldi antenna, the microstrip-SIW-microstrip transition with zero-phase shift is designed. With this transition, the input impedance and the conversion efficiency of the proposed rectifying circuit can be measured in experiment. The vias in SIW also provide the DC bypass to collect the DC power because of the series configuration of the diode. The simulatedS-parameters of the microstrip-SIW-microstrip transition are shown in Figure 2. It can be observed that the reflection coefficient S11 is less than −15 dB and the insert loss S21 is lower than 0.6 dB within the bandwidth from 30 GHz to 40 GHz, which ensures the good passband performance of the transition. Meanwhile, the simulated phase shift of the designed transition at 35 GHz is about 0°, which indicates that the input impedance Zin of the rectifying circuit shown in Figure 1 is equal to Z1.Figure 2
SimulatedS-parameters of the microstrip-SIW-microstrip transition.The two radial stubs with the lengths ofLs1 and Ls2 are designed as a DC-pass filter to prevent the unwanted fundamental wave and the second harmonic from passing the resistive load RL. The simulated S parameters of the DC-pass filter are shown in Figure 3. It can be found that the filter shows good DC-pass performance with the attenuations of 35 dB and 38 dB at 35 GHz and 70 GHz, respectively.Figure 3
SimulatedS-parameters of the DC-pass filter.


## 2.1.2. Rectifying Circuit Experiments

The exact sizes of the high efficiency rectifying circuit shown in Figure1 are determined by the experimental method. The two parameters, the length Lm of the open-circuit match branch and the width Wt of the quarter wavelength transformer, are optimized to cancel the imaginary part of the diode’s input impedance Zd and match the real part of Zd to 50 Ω. Several circuits with the same length Lm and different width Wt are fabricated. The initial length Lm is λg/2, and λg is the waveguide wavelength in the microstrip line. To eliminate the imaginary part of the input impedance Zin of the rectifying circuit, the length of Lm in each circuit is adjusted. When the input impedance Zin is matched to 50 Ω, which is measured by the Agilent VNA (Vector Network Analyzer) of N5227A, the sizes of Lm and Wt are determined, and the high efficiency rectifying circuit is obtained. The final dimensions of the rectifying circuit are given in Table 2. The measured reflection coefficient S11 versus frequency is shown in Figure 4. It can be seen that when the input power is 10 dBm and the load is 550 Ω, the measured S11 is −19.6 dB at 35 GHz and the corresponding Zin is (46+j6.7)Ω which can be found in the Smith chart of the VNA. The diode’s input impedance Zd calculated from Zin is (22.7-j3.3)Ω. It is observed that the imaginary part of Zd is small and the open-circuit match branch works well.Table 2
Dimensions of the rectifying circuit and the microstrip-SIW-microstrip transition.
L m W t L s 1 L s 2 L c W S I W 2.02 1.4 0.6 1.12 7 4.55  P D W 1 W 2 L 1 L 2 0.8 0.5 0.78 1 3.1 1.55Figure 4
Measured reflection coefficient|S11| versus frequency, Pin=10dBm, and RL=550Ω.The MMW-DC conversion efficiencyη of the rectifying circuit can be calculated by(1)η=VdcRLPin×100%,where RL is the resistance load, Vdc is the output DC voltage on the load that can be read by a voltmeter, and Pin is the input MMW power of the circuit. When the input power is 10 dBm, the measured output DC voltages and the conversion efficiencies versus the load at 35 GHz are shown in Figure 5. It can be seen that the conversion efficiency increases with the load and gets the peak of 38.6% at 550 Ω. When the load keeps on increasing, the output DC voltage continues to increase while the efficiency decreases. So the optimal load resistance is 550 Ω.Figure 5
Measured output DC voltages and conversion efficiencies versus loadRL, Pin=10dBm, and f=35 GHz.When the load resistance is 550 Ω, the measured output DC voltages and conversion efficiencies versus the input power are plotted in Figure6. It is found that the output DC voltage and the conversion efficiency increase with the input power. When the input power is 19 dBm (79.4 mW), the output voltage and conversion efficiency are 4.75 V and 51.6%, respectively. When the input power continues to increase, the maximum voltage will exceed the breakdown voltages and the conversion efficiency decreases. The conversion efficiency is higher than 30% when the input power is higher than 7 dBm (5 mW). Figure 7 shows the measured output DC voltages and conversion efficiencies versus the frequency at the input power of 19 dBm when the load resistance is 550 Ω. The efficiencies are all higher than 30% from 33.2 GHz to 36.6 GHz, which exhibits a relatively broadband performance.Figure 6
Measured output DC voltages and conversion efficiencies versus input power,RL=550Ω, and f=35 GHz.Figure 7
Measured output DC voltage and conversion efficiency versus frequency,Pin=19dBm, and RL=550Ω.


## 2.2. Receiving Antenna Design

A novel Vivaldi slot is used as the receiving antenna, which is shown in Figure8. It has the characteristics of high gain, broad bandwidth, and harmonic suppression. The Vivaldi slot is excited by a SIW, which is formed by two extra rows of metal vias to bound the energy within the SIW tightly and enhance the transmission performance. The center-symmetric metamaterial units with zero effective permittivity at 35 GHz are loaded on the Vivaldi slot to improve the antenna gain. The microstrip-to-SIW transformer is designed to feed the antenna, and the characteristic impedance of the microstrip line is 50 Ω. In order to prevent the second harmonics generated by the nonlinear diode from reradiating by the antenna, the SRR (split ring resonator) units are etched on the ground of the microstrip feed line to act as a low pass filter. The substrate used for the receiving antenna is the same as that for the rectifying circuit.Figure 8
Structure of receiving antenna (units: mm).The simulated and measured reflection coefficients and gains of the proposed Vivaldi antenna are plotted in Figure9. The antenna exhibits a broad bandwidth of 38.5% ranging from 26.5 GHz to 40 GHz with the reflection coefficient less than −10 dB. The gain varies from 9.3 dBi to 10.4 dBi within the Ka band and the highest gain is 10.4 dBi at 35 GHz.Figure 9
Simulated and measured reflection coefficients and gains of the receiving Vivaldi antenna.


## 3. Measurement of Rectenna and Arrays

The rectifying circuit and the receiving antenna are integrated directly because they are all fed by the microstrip lines with the input impedances of 50 Ω. Figure10 shows the structure of the proposed rectenna. The SIW in the receiving antenna is used not only to feed the Vivaldi slot but also to provide the DC bypass to the rectifying circuit so the rectenna structure is simplified. The total length Lc of the rectifying circuit is 7 mm, which is only about 0.82λ0. The photographs of the fabricated rectenna are given in Figure 11.Figure 10
Structure of the proposed rectenna.Figure 11
Photograph of the fabricated rectenna.
(a)
Top view (b)
Bottom viewThe conversion efficiency of the rectenna is also calculated by (1), while Pin is the MMW power received by the antenna. The output DC voltage Vdc is also read by a voltmeter. According to the Friis transmission equation, Pin is calculated by(2)Pin=λ04πr2PtGtGr,where λ0 is the free space wavelength, r is the propagation distance, and Pt is the transmitting MMW power. The MMW signal source is Agilent E8257D. The MMW power is amplified by the amplifier with the saturation power of 36 dBm at 35 GHz. A horn is used as the transmitting antenna, whose gain Gt is 20.7 dBi at 35 GHz. The measured gain of the receiving antenna is Gr of 10.4 dBi. The rectenna is fixed at the distance of r=58 cm, and the rectenna is in the far field region.In order to collect more DC power, rectenna arrays could be designed. The configuration of the 1 × 2 rectenna array is shown in Figure12(a) and the photograph of the fabricated one is given in Figure 12(b). The space S between the two rectenna elements is 8.5 mm (≈λ0.). The series and parallel DC combiner circuits are shown in Figure 13. The load resistances of the series and the parallel arrays are RLs and RLp, which is calculated by RLs=2·RL=1100 Ω and RLp=RL/2=275 Ω, respectively. The rectenna element and the arrays are measured at 35 GHz.Figure 12
1 × 2 rectenna arrays.
(a)
Configuration of 1 × 2 rectenna array (b)
Photograph of fabricated 1 × 2 rectenna arrayFigure 13
The series and parallel DC combiner circuits.
(a)
Series layout (b)
Parallel layoutThe measured output DC voltage, DC power and the MMW-to-DC conversion efficiency of the rectenna element, and series and parallel arrays versus the power densityPd are shown in Figures 13-14. Due to the limited MMW output power of the amplifier and the measurement system errors, the maximum power density is only 8.7 mW/cm2 at the far field of 58 cm. From Figure 14, it is observed that the output DC voltages increase with the power density. When the power density Pd is 8.7 mW/cm2, the output DC voltages of the rectenna element and parallel-connected and series-connected rectenna arrays are 0.99 V, 0.93 V, and 1.87 V, respectively. The output DC voltages of the rectenna element are very close to the parallel-connected rectenna array and are about half of the series-connected rectenna array.Figure 14
Measured output DC voltage.As shown in Figure15, the rectenna arrays obtain nearly double DC power comparing to the element, and the conversion efficiencies of the arrays and the element are nearly the same. When the power density Pd is 8.7 mW/cm2, the received MMW power of the antenna element is 5.6 mW and the maximum conversion efficiency of the element is 31.5% while that of the arrays is about 4% less. The differences of the conversion efficiencies are mainly caused by the fabrication and measurement errors. It can be predicable that the conversion efficiencies of the rectenna element and arrays will continue to increase with the power density. From the measured results, it can be concluded that the rectenna arrays show good array performances and large scale arrays could be expanded to obtain more DC power.Figure 15
Measured output DC power and conversion efficiency.


## 4. Conclusion

In this paper, a novel high efficiency rectenna operated at 35 GHz is proposed. The rectifying circuit exhibits a measured MMW-to-DC conversion efficiency higher than 30% from 33.2 GHz to 36.6 GHz when the input MMW power is 79.4 mW, and the peak efficiency reaches 51.6% at 35 GHz. The receiving antenna with broad bandwidth, harmonic suppression, and high gain is integrated directly to the rectifying circuit to form the rectenna. The rectenna element and series-connected and parallel-connected rectenna arrays have been measured and the maximum conversion efficiency of 31.5% is obtained at a low power density of 8.7 mW/cm2. The efficiency would increase under a higher power density condition. Compared to the rectenna element, the 1 × 2 arrays obtain nearly double DC power. The developed rectenna has the merits of low profile, small size, and low cost. It is easy to form large scale rectenna arrays to collect more MMW power suitable for millimeter-wave energy harvesting and wireless power transmission applications.



---

*Source: 1897283-2016-12-15.xml*