On Design and Verification of an Efficient Microwave Wireless Power Transmission System

. We report on the theoretical design and experimental verifcation of a high efciency microwave wireless power transmission (MWPT) system operating in the Fresnel region. To achieve high conversion efciency over a transmit distance of 11meters, the transmit refector antenna was optimized to locate the focal point at 11 m. Te size of the receive antenna was decided by calculating the feld distribution and the received power at diferent positions in the receive antenna aperture. Furthermore, an accurate model of the diode is presented, which was imported into the ADS software for high-precision rectifying circuit design. As a result, an overall DC-DC conversion efciency of 20% was achieved, as measured in an anechoic chamber at a given distance of 11m. Te experimental results validated the proposed method.


Introduction
Microwave wireless power transmission (MWPT) has attracted increasing attention, owing to its capability of charging mobile phones and laptops, electric vehicles, and unmanned aerial vehicles (UAV) [1].Moreover, it is one of the key technologies to realize space solar power satellites (SSPS).MWPT technologies can be broadly divided into radiative and nonradiative power transfer methods.As for the former, if the distance between transmit and receive antenna satisfying far-feld (FF) condition long range MWPT can be achieved by means of microwave or laser sources [2,3].However, the achievable radiative power transmission efciency in the FF region is often unacceptably low, mainly because of the size limitation of transmit and receive antennas.Nonradiative power transfer methods mainly include near-feld magneto-inductive coupling [4] and Fresnel felds [5].Systems operating in the reactive near-feld zone can achieve high conversion efciency since power is transferred between resonant circuits via magneto-inductive coupling.However, their efciency decrease as 1 � d6 [6], where d is the distance between transmit and receive antennas.In the Fresnel region, the Friis transmission equation is invalid since the FF pattern is not formed.In this case, the power transmission efciency can be improved by focusing the feld intensity from the source, and therefore, increasing the amount of power received by a receive antenna aperture placed at the focal point power received by a receiving antenna aperture placed at the focal point.
It is worth noting that in many applications, such as mobile devices, Internet of things, and sensors, do not require a long power transfer distance, but only a few meters, typically around 10 m [7].In this case, to increase the power transmission efciency, the aperture of the transmit antenna should be enlarged in order to narrow the beamwidth.Te receive antenna is placed in the Fresnel zone rather than in the far-feld region, at a mid-range of several meters.In recent years, MWPT systems and methods operating in the Fresnel feld have gained much attention due to their good conversion efciency, medium-range distance, and acceptable antenna size [8][9][10][11][12].In [8], the infuence of the beam focus, and the taper distribution of the radiating feld in the Fresnel zone have been discussed.In [9,10], the designs of Fresnel MWPT systems which can achieve 66.5% and 33.2% RF-DC efciency, respectively, have been reported.However, in both cases, the operating distance is only about 10λ, and the feeding network is complicated and easy to make systems defocus for a larger array.In [11], an MWPT system equipped with an optimal number of rectenna array elements for mid-range application and a parallel DC combing circuit is designed to improve conversion efciency.Nevertheless, only a 5.01% RF-DC efciency can be achieved at a distance of 1 m.Based on Bezier curves [12], a method for antenna aperture illumination design for MWPT in the Fresnel zone is reported in [13].As a result, a larger aperture power coefcient can be achieved, with a slight reduction of the beam collection efciency [14].Publication [15] reports a compact, polarization-insensitive rectenna based on metasurface at a frequency of 5.8 GHz, it can reach the maximum conversion efciency measured 66% under a 500 Ω load.Article [16] proposes a highly integrated multipolarization wideband rectenna for simultaneous wireless information and power transfer, the wireless power receiving port has conversion efciency up to 76.5%.
In this paper, a new design of MWPTsystem operating in the Fresnel zone is presented.Te main features of the proposed MWTP system can be summarized as follows: (i) a refector antenna is deployed as the transmit antenna, which can enjoy advantages of low cost and no feeding network; (ii) an air-supported microstrip antenna is used as the receive antenna to reduce substrate loss; (iii) twoelement series fed and four-element cascaded arrays are introduced such that diferent power densities can be adapted; (ii) and (iii) have been introduced in article [17]; (iv) a diode model is implemented to get its optimal characteristic and parameters, and a high-precision rectifying circuit model is designed accordingly; and (v) a parallel DC combing circuit is designed.By means of the proposed design, the resulting experimental conversion efciency is 20%, as measured in an anechoic chamber at a distance of 11 m.

MWPT System Design
Figure 1 illustrates a schematic diagram of the MWPT system.It mainly includes microwave transmitter, transmit antenna, the receive antenna, rectifying, and the DC combiner circuits.It is known that the overall efciency of the system relates to each of the aforementioned components.Tus, each component of the MWPT system should be carefully designed, and we shall discuss this in the sequal.

Te Microwave
Transmitter.In the MWPT system, the DC energy should be frst converted to RF power, which is then radiated to the free space by the transmit antenna.In our designed system, a GaN power amplifer is introduced to achieve high output power, as illustrated in Figure 2. Te maximum DC-RF conversion efciency is 59.3% when the input power is 88 W.

Transmit Antenna Design.
Since high DC-DC conversion efciency is a primary objective for our MWPT system, a narrow beam width of the transmit antenna is expected.It is known that antenna array can be employed for this purpose.However, in our design, a refector antenna was selected because of its low cost and no feeding network.In our design, the distance between the transmit antenna and the receive antenna is fxed at 11 meters.
Since the position of the focus is dependent on the antenna dimension, the size of the refector antenna should be determined.To this end, we frst give the power density S(ρ) of the refector antenna as where η is the wave impedance and in free space we have η � 120π, ρ indicates the distance between the feld point and the center in the transmit antenna aperture, and | E(ρ)| means the electric feld strength.Figure 3 shows a diagrammatic sketch relevant to these parameters.Te total energy within the antenna aperture can be expressed as where D denotes the diameter of the refector antenna, P t is the transmit power, and η a is the antenna efciency excluding leakage.In our design, a −10 dB aperture feld distribution of the refector is assumed.Letting η � 120π and substituting (1) into (2), one obtains Te feld in the axial direction E(z) can be obtained by integrating the |E(ρ)| feld distribution at z position according to the following equation ( 5): where z is the distance from the refector antenna in the axial direction.Figure 4 displays the distribution of the normalized electric feld along z, for diferent refector antenna diameters D � 2.0 m, D � 2.4 m, and D � 2.8 m.As it can be observed in the fgure, the electric feld focuses at 11 m when D � 2.4 m.Te transmit antenna size is therefore selected as 2.4 m in the designed WPT system.

Design of the Receiving Antenna.
A low profle airsupported microstrip antenna is chosen as the receiving antenna element in order to reduce substrate loss and withstand high power.Moreover, two-element 2 International Journal of Antennas and Propagation series-fed and four-element cascaded arrays are introduced in order to adapt diferent power densities.Tis section was also introduced in the previous article [17].
Te comparative results among antenna element, twoelement series-fed array, and four-element cascaded array are presented in Table 1.

Signal source (GaN) Amplifier
Microwave transmitter DC energy  International Journal of Antennas and Propagation 2.4.Calculation of Received Power.Te Friis transmission equations are not suitable for computing the RF power captured by the receiving antenna because the distance between the transmitting and the receiving antenna does not satisfy the FF condition.Te received RF power can be computed by

RF power Antenna
where P r (x, y) denotes the power received by the antenna, whose efective receiving area is A e (x, y) at position (x, y), and p(x, y) is the power density at position (x, y).p(x, y) can be expressed as follows: where p m is the maximum power density, and a(x, y) is the normalized relative power density distribution.Finally, the following equation can be formulated: According to equation (3), we can write where η tr is the transmission efciency between the transmitting antenna and the receiving antenna, including cable loss, coaxial connector loss, space transmission loss, polarization mismatch, feld mismatch, and so on.Terefore, p m can be expressed as P r (x, y) can be reformulated as and a(x, y) can be computed by where ρ is the distance between the feld point and the center in the transmitting antenna aperture (see equation ( 1)), (x, y, z) means the position in the receiving antenna aperture, and r is the distance between the source point and the feld point.
According to equation (10), if the transmitted power P t , the normalized relative power density distribution at a fxed distance from the transmitting antenna a(x, y), and the efective receiving area A e (x, y) at position (x, y) are given, the received power can be computed.Figure 5 shows the normalized near feld amplitude distribution at center row and at center column, at a distance of 11 m (z � 11 m in equation ( 12)) from the transmitting antenna.Te size of the plotted near feld area is 3 m × 3 m.A −10 dB aperture feld distribution of the refector is assumed for computations.As it can be seen from the plots, the feld strength at a distance of 1.2 m from the center is about −10 dB, so the size of the receiving antenna is selected as 2.4 m.It is worth to point out that since the rectifying efciency is related to the input power to the rectifying circuit, input power should be kept as stable as possible.Te gain of the antenna element can be related to the efective receiving area A e by the following equation: Te computed gain of the simulated antenna element is 8.6 dBi, as obtained by HFSS software, so A e can be calculated as 0.0086 m 2 according to equation (13).Substituting A e � 0.0086 m 2 , P t � 50 W, and η tr � 0.5 into equation (10), the distribution of P r can be obtained (see Figure 6).Te maximum received power by the antenna element is 22.6 dBm.Within the receiving area, a single antenna element is conveniently adopted where P r is between 20 dBm and 22.6 dBm; two-element series-fed antenna array is a better choice where P r is between 17 dBm and 20 dBm; four-element cascaded array is adopted where P r is between 10 dBm and 17 dBm; the place is vacant where P r is less than 10 dBm.According to this idea, the schematic view of the resulting antenna placement is shown in Figure 7. Green, red, and blue portions, respectively, indicate the single antenna elements, the two-element series-fed antenna arrays, and the four-element cascaded antenna arrays, each of them being connected to a single rectifying circuit.As a result, there are a total of 214 RF ports.

Rectifying Circuit Design
. In a MWPT system, the rectifying circuit is one of the crucial components since the overall system efciency mainly depends on the characteristics of the rectifying circuit [18].An accurate model of the rectifying circuit is therefore mandatory.Te accuracy of the model is mainly determined by the parameter acquisition of the diode, since other passive parts of the circuit can be easily modeled and simulated.Terefore, the diode model is of Figure 8 shows schematic and photographs of the diode measurement setup, which include straight calibration, refection calibration, transmission calibration, and diode measurement circuit.Te diode parameters can be obtained using the method introduced in Ref. [19].Measured junction current I j and junction capacitance C j were ftted according to this model.Te best ft curves and the measured data are shown in Figure 9. Te fnal equivalent circuit model of the HSMS-282b diode is displayed in Figure 10.Terefore, the calculated diode parameters can be imported into the ADS software for the rectifying circuit design.
According to the received power analysis reported in Section 2.4, the input power to the rectifying circuit is approximately between 20 dBm and 22.6 dBm.Terefore, the expected input power to the rectifying circuit is around 21 dBm.Te conversion efciency of the rectifying circuit (η r ) is defned as Te detailed design has been presented in the previous article [17]. Figure 11 shows the fnal rectifying circuit.

DC Combiner Circuit Design.
In order to improve the power transfer efciency, the receiver must collect as much wireless power as possible from the transmitter.Te conventional method consists in RF-power combing by means of a power divider, but this technique results efective on condition that the RF power waves follow into the power divider in-phase condition.However, in the Fresnel region the received phase of the power changes at each point of the receiver because of the diferent path lengths from the transmitter to the receiver.Indeed, a DC combiner circuit must be designed if there is more than one rectifying circuit.Te value of the rectifying circuit load must be optimized since it will afect the overall conversion efciency.Assuming that the load value is R when the conversion efciency of a single rectifying circuit reaches the maximum, then the load value is n • R when n-th rectifying circuits are in series, and the load value is R/m when m-th rectifying circuits are in parallel.Terefore, the ultimately optimized load value is n • R/m in hybrid circuits.Figure 11 shows a photograph of the DC combiner circuit comprising four parallel rectifying circuits.

MWPT System Measurement
Te experimental verifcation of the designed MWPT system is mainly aimed to illustrate the key factors which afect the WPT conversion efciency.Te WPT system is placed in an anechoic chamber, with the purpose of avoiding the electromagnetic interference.In order to reduce the transmission loss as much as possible, the connection path between the microwave transmitter and the transmitting antenna is short.Figure 12 shows a photo of the designed MWPT system during testing, the transmitting distance is 11 m. Figure 13 shows the back view of the receiving antenna.All the rectifying circuits, as well as the 214 RF ports, have been tested individually by means of a power sensor, and the total RF output power is 24.3 W.Based on the above analysis, the RF-DC conversion efciency is strictly related to the load resistance.In the proposed design, 214 rectifying circuits are connected in parallel, so the DC load is estimated as 3500/214 Ω � 16.4 Ω. Te key factors afecting the conversion efciency are: the DC-RF conversion efciency (η s ), the transmission efciency (η tr ), the rectifying efciency (η rect ), and the DC combing efciency (η pc ).Teir values are 59.3%, 46.8%, 77.2%, and 90%, respectively, according to the measurement results.Figure 14 shows the efciency confguration of the designed WPT system, and the overall conversion efciency can be obtained by (15) based on the efciency of each component: During measurements, the infuence of the DC load on the overall conversion efciency has been investigated, and the results are shown in Figure 15.Te plot indicates that the maximum efciency can reach 20% when the DC load is 16 Ω.In this condition, the measured DC output voltage is   2 summarizes the conversion efciency achieved in the present work with that by other reported designs.Te results show that the measured RF-DC and DC-DC conversion efciencies can reach 37.5% and 20%, respectively, at a given distance of 11 m.Te RF-DC conversion efciency is higher than that reported in References [10,11]; lower than that reported in Reference [9], but in that work the transmission distance was only 1 m.Furthermore, the mentioned references do not give the DC-DC conversion efciency.

Conclusion
Tis paper presents the theoretical design and the experimental verifcation of a high-efciency MWPT system operating in the Fresnel zone.Te design principle and the corresponding equations are elaborated in detail.Finally, the MWPT system is tested in an anechoic chamber, and the total DC-DC conversion efciency can reach 20% at a distance of 11 m.Te proposed method can be useful for the applications of high-efciency, high-power, mediumdistance MWPT system operating in the Fresnel region.

Figure 2 :Figure 4 :
Figure 2: Sketch of the basic structure of the microwave transmitter.

Figure 5 :
Figure 5: Te computed amplitude distribution at center row and at center column.(a) Te computed near feld amplitude distribution at center row.(b) Te computed near feld amplitude distribution at center column.

Figure 6 :
Figure 6: Received power (Pr) by the antenna element.

Figure 7 :Figure 8 :Figure 9
Figure 7: Schematic view of the antenna placement.

Figure 9 :
Figure 9: Results from diode measurements and ftting procedure.(a) Y-parameters of remaining voltage-dependent components when when bias voltage is −0.4 V. (b) Y-parameters of remaining voltage-dependent components bias voltage is 0.1 V. (c) Measured I j as a function of applied voltage and best ft curve of measured data.(d) Measured C j as a function of applied voltage and best ft curve of measured data.

Figure 11 :
Figure 11: Photograph of the DC combiner circuit comprising four parallel rectifer circuits.

Figure 13 :Figure 14 :
Figure 13: Back view of the receiving during testing antenna.

Figure 15 :
Figure 15: Te DC-to-DC conversion efciency as a function of the load resistance.

Table 1 :
Comparison among antenna parameters for the evaluated receiving antenna designs.
primary importance in the rectifying circuit design, and its inaccurate model would lead to a deviation of measurements from simulated results.

Table 2 :
Comparison of the proposed MWPT design with other designs reported in literature.