CN112531924B - Method for rapidly designing antenna array based on maximum wireless energy transmission efficiency - Google Patents

Method for rapidly designing antenna array based on maximum wireless energy transmission efficiency Download PDF

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CN112531924B
CN112531924B CN202011089224.6A CN202011089224A CN112531924B CN 112531924 B CN112531924 B CN 112531924B CN 202011089224 A CN202011089224 A CN 202011089224A CN 112531924 B CN112531924 B CN 112531924B
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殷丹
杨钊
赵发定
文光俊
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University of Electronic Science and Technology of China
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J50/00—Circuit arrangements or systems for wireless supply or distribution of electric power
    • H02J50/20—Circuit arrangements or systems for wireless supply or distribution of electric power using microwaves or radio frequency waves
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
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    • G06F30/20—Design optimisation, verification or simulation
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01Q—ANTENNAS, i.e. RADIO AERIALS
    • H01Q21/00—Antenna arrays or systems
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J50/00—Circuit arrangements or systems for wireless supply or distribution of electric power
    • H02J50/20—Circuit arrangements or systems for wireless supply or distribution of electric power using microwaves or radio frequency waves
    • H02J50/23—Circuit arrangements or systems for wireless supply or distribution of electric power using microwaves or radio frequency waves characterised by the type of transmitting antennas, e.g. directional array antennas or Yagi antennas
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J50/00—Circuit arrangements or systems for wireless supply or distribution of electric power
    • H02J50/20—Circuit arrangements or systems for wireless supply or distribution of electric power using microwaves or radio frequency waves
    • H02J50/27—Circuit arrangements or systems for wireless supply or distribution of electric power using microwaves or radio frequency waves characterised by the type of receiving antennas, e.g. rectennas

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Abstract

The invention discloses a method for rapidly designing an antenna array based on maximum wireless energy transmission efficiency. The invention only needs to solve the problem of full electromagnetic wave of the transmitting and receiving antenna array separately and estimate the gain directional diagram of each unit in the finite array, thus obtaining the maximum energy transmission efficiency and the corresponding antenna array excitation coefficient. By the method, the complexity of calculation can be obviously reduced, and the calculation time is greatly shortened.

Description

Method for rapidly designing antenna array based on maximum wireless energy transmission efficiency
Technical Field
The invention belongs to the wireless energy transmission technology, and particularly relates to a method for rapidly designing an antenna array based on maximum wireless energy transmission efficiency.
Background
The design work of wireless energy transmission systems is a complex process that has received a lot of attention from the last century to date. Given the long-range wireless energy transfer based on the radiation mechanism, such systems often consist of a dc power source, a dc-to-rf conversion stage, a transmitting antenna, a receiving antenna, and an rf-to-dc conversion stage.
The main performance index of a wireless energy transmission system is system efficiency, which is defined as the ratio of the total receiving power at the load end to the total input power at the transmitting end. Since the dc-rf conversion stage (formed by a solid state device or magnetron) and the rf-dc conversion stage (formed by a transistor or diode) are designed using non-linear devices, the system efficiency is a non-linear function of power. In addition, the design of the wireless energy transmission system is a multidisciplinary task, and relates to full electromagnetic wave, circuit simulation and the like. These factors make the design process very complex and time consuming, especially when we optimize the overall efficiency of the system.
One of the difficulties in the design of wireless energy transmission systems is the simulation of the wireless link, i.e., the design of the transmitting and receiving antennas and the estimation of the air channel between the transmitting and receiving antennas and the simulation of the transmission efficiency. For the far field, the well-known Friis formula can describe various influencing factors and can optimize the caliber excitation coefficients according to the methods described in the documents "g.oliver, l.poli, and a.massa," Maximum efficacy understanding beam synthesis of radial planar array for wireless power transmission, "IEEE trans.antennas pro ag., vol.61, No.5, pp.2490-2499, May 2013".
The documents "A.F.Kay", "Near-field gain of adaptation antennas", "IRE Trans. antennas Propag, vol.AP-8, pp.586-593 Nov.1960" and "G.V.Borgiotti", "Maximum power transfer between plane antennas adapters in the Fresnel Zone", "IRE Trans. antennas Propag, vol.AP-14, No.8, pp-158-163, Mar.1966" theoretically estimate the highest energy transfer efficiency for two given transmitting and receiving apertures in the Fresnel Zone. But the formula therein is only suitable for the case of a continuous caliber. Since efficiency optimization requires an optimal design of the aperture distribution and this is usually achieved by the antenna array aperture, the results obtained in these two documents can be considered as the upper efficiency limit.
The documents "W.Geyi," provisions of applied electrical properties ". New York, NY, USA: Wiley,2010(pp.273-275)," and "L.Shan and W.Geyi," Optimal design of focused antenna array, "IEEE trans. antennas Propag., vol.62, No.11, pp.5565-5571, Nov.2014" provide a method of evaluating the efficiency of wireless energy transfer between antenna arrays that can take into account the mutual coupling effect between antenna elements. However, this method needs to calculate the complete wireless energy transmission system composed of two antenna arrays separated by a certain distance through full electromagnetic wave simulation, which is a very large power system, and thus the calculation amount is very large. Although there are some full electromagnetic wave simulation environments that can provide advanced mixed finite element method-integral equation solutions to solve such problems faster, such as HFSS, it is necessary to optimize the transmit and receive antenna arrays, and the amount of computation is still large.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a method for rapidly designing an antenna array based on the maximum wireless energy transmission efficiency.
The purpose of the invention is realized by the following technical scheme: a method for rapidly designing an antenna array based on maximum wireless energy transmission efficiency is characterized in that wireless energy transmission is carried out between a transmitting antenna array and a receiving antenna array in an electromagnetic radiation mode, the wireless energy transmission efficiency between the calibers of the two antenna arrays is calculated according to a scattering matrix to obtain the maximum energy transmission efficiency, and an excitation coefficient is obtained according to the maximum energy transmission efficiency.
Further, the scattering matrix is represented as:
Figure BDA0002721505670000021
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0002721505670000022
Figure BDA0002721505670000023
representing scattering momentsArraying; [ b ] Atx]、[brx]Normalized reflected and incident wave vectors, respectively, of the transmit antenna array, [ a ]tx]、[arx]Respectively receiving normalized reflected wave and incident wave vector of antenna array;
btx，1、btx，2、...、
Figure BDA0002721505670000024
respectively, the normalized reflected waves of the 1 st, 2 nd, … th and Nth antenna elements of the transmitting antenna array, brx，1、brx，2、...、
Figure BDA0002721505670000025
Normalized incident waves of the 1 st, 2 nd, … th and Nth antenna units of the transmitting antenna array are respectively represented; a is atx，1、atx，2、...、
Figure BDA0002721505670000026
Respectively represent the normalized reflected waves of the 1 st, 2 nd, … th and Nth antenna elements of the receiving antenna array, arx，1、arx，2、...、
Figure BDA0002721505670000027
Respectively representing normalized incident waves of 1 st antenna unit, 2 nd antenna unit, … th antenna unit and Nth antenna unit of the receiving antenna array;
obtaining the wireless energy transmission efficiency etaairComprises the following steps:
Figure BDA0002721505670000028
by assuming impedance matching, equation (3) is rewritten in the form of a eigenvalue problem as:
([Srx-tx]H[Srx-tx])[atx]＝ηair[atx] (4)
let [ A ]]＝([Srx-tx]H[Srx-tx]) Then [ A ]]The corresponding maximum characteristic value is the energy transmission efficiency etaairAnd its corresponding eigenvector is the optimal excitation vector atx]。
The beneficial effects of the invention are: the invention does not need to calculate the scattering matrix by carrying out full-wave electromagnetic simulation on the whole wireless energy transmission system, but provides a method for carrying out far-field approximation on each group of transmitting and receiving antenna units, so that the maximum energy transmission efficiency and the corresponding antenna array excitation coefficient can be obtained by only separately solving the problem of full electromagnetic waves of transmitting and receiving antenna arrays and estimating the gain directional diagram of each unit in a finite array. By the method, the complexity of calculation can be obviously reduced, the calculation time is greatly shortened, and the calculation amount is reduced.
Drawings
FIG. 1 illustrates a general wireless energy transfer system;
fig. 2 shows a wireless energy transmission environment of a transmitting antenna array and a receiving antenna array, and corresponding equivalent network input ports;
fig. 3 shows two antenna arrays facing each other, and transmit-receive antenna element coupling distance vectors;
figure 4 illustrates an equivalent antenna array for estimating an embedded gain pattern;
fig. 5 illustrates a transmit/receive antenna array and a patch antenna unit structure for estimating wireless energy transfer efficiency in fig. 6;
fig. 6 shows the results of wireless energy transfer efficiency calculations using different methods: (a) simulating the whole wireless energy transmission system by full electromagnetic waves (solving by using a mixed finite element-integral equation method in HFSS); (b) the invention provides a method;
fig. 7 shows the workflow of matrix computation by different methods: (a) simulating the whole wireless energy transmission system by full electromagnetic waves; (b) the invention provides a method.
Detailed Description
The technical scheme of the invention is further explained by combining the attached drawings.
The invention provides a method for rapidly designing an antenna array based on maximum wireless energy transmission efficiency.
Fig. 1 shows a schematic diagram of a conventional wireless energy transmission system. A DC power source 1 supplies a certain power to a DC-RF conversion stage 2, wherein 2 converts the DC power to a frequency f0Of the radio frequency signal. The radio frequency signal is radiated to a receiving end located in a certain direction by the transmitting antenna device 3 and received by the receiving antenna 4. The received power is received in the form of a radio frequency signal and passed through a radio frequency-to-dc conversion stage 5 to a dc load 6.
Each power conversion process can be characterized by a power conversion efficiency, and the total transmission efficiency can be approximated as (assuming an ideal radiation aperture for simplifying the expression):
Figure BDA0002721505670000041
symbol ηDC-RFAnd ηRF-DCDc-rf and rf-dc power conversion stage efficiencies are characterized separately and are non-linear functions of input power, operating frequency, voltage/current wave.
The main research of the invention is etaair. It is assumed that the rf system of the present embodiment is composed of antenna arrays 7 and 8 of N and M patch antenna units 9, respectively, and the antenna arrays 7 and 8 are separated by a certain distance d, as shown in fig. 2. The whole system can be regarded as an N + M port network, and can pass through a scattering matrix (the working frequency is set to be f)0) The description is as follows:
Figure BDA0002721505670000042
wherein the content of the first and second substances,
Figure BDA0002721505670000043
Figure BDA0002721505670000044
representing a scattering matrix; [ b ] Atx]、[brx]Respectively, normalized reflected and incident wave vectors of the transmit antenna array, [ a ]tx]、[arx]Respectively receiving normalized reflected wave and incident wave vector of antenna array;
btx，1、btx，2、...、
Figure BDA0002721505670000045
respectively, the normalized reflected waves of the 1 st, 2 nd, … th and Nth antenna elements of the transmit antenna array, brx，1、brx，2、...、
Figure BDA0002721505670000046
Normalized incident waves of the 1 st, 2 nd, … th and Nth antenna units of the transmitting antenna array are respectively represented; a istx，1、atx，2、...、
Figure BDA0002721505670000047
Respectively represent the normalized reflected waves of the 1 st, 2 nd, … th and Nth antenna elements of the receiving antenna array, arx，1、arx，2、...、
Figure BDA0002721505670000048
Normalized incident waves of the 1 st, 2 nd, … th and Nth antenna units of the receiving antenna array are respectively shown;
obtaining the wireless energy transmission efficiency etaairComprises the following steps:
Figure BDA0002721505670000049
assuming impedance matching (i.e. transmitting and receiving antenna elements andthe source (and load) have perfect impedance matching, so [ a ]rx]＝0、[btx]0), in which case equation (7) can be expressed as:
Figure BDA00027215056700000410
in conjunction with equation (5), equation (7) can be rewritten in the form of a eigenvalue problem as:
([Srx-tx]H[Srx-tx])[atx]＝ηair[atx] (8)
let [ A]＝([Srx-tx]H[Srx-tx]) Then [ A ] is]The corresponding maximum characteristic value is the energy transmission efficiency etaairAnd its corresponding feature vector is the optimal excitation vector atx]The values in the optimal excitation vector are the corresponding excitation coefficients.
The scattering matrix S can be calculated by Computer Aided Design (CAD) tools, such as IE3D or HFSSrx-tx]And this method takes into account the mutual coupling effect between the antenna elements and environmental factors. Since this method is used to calculate the wireless energy transfer efficiency of the fresnel region, however, wherein,
Figure BDA0002721505670000051
(where D is the transmit antenna array size and λ is the wavelength), causing the all electromagnetic wave problem to be a huge power problem, increasing the amount of computation and simulation time.
For any practical situation, we can ensure that the receiving antenna array is located in the fresnel region of the transmitting antenna array, while ensuring that the receiving array antenna elements are located in the far field region of the transmitting array antenna elements. [ P.Lemaitre-Auger, S.Abielrona, and C.Caloz, "Generation of Bessel beams by two-dimensional anti-enrna arrays using sub-sampled distributions," IEEE transactions. antennas Propag, vol.61, No.4, pp.1838-1849, 2013]. According to this assumption, the scattering matrix [ S ]rx-tx]Can be written as
Figure BDA0002721505670000052
Wherein
Figure BDA0002721505670000053
ψn，mAccording to the electromagnetic wave transmission distance r from the nth transmitting array unit to the mth receiving array unitn，m＝|| n，mrThe calculated phase, and Gtx，i( n，mr) And Grx，j( n，mr) Is the independent antenna gain of the ith element in the transmit array and the jth element in the receive array, whose direction is the distance vector n，mr10, in the direction indicated by 10.
Obviously, when the antenna array element distance is smaller, the mutual coupling effect between the elements can significantly affect the antenna performance, especially the gain pattern. To in the scattering matrix [ Srx-tx]Taking into account the mutual coupling effect, single antenna gain
Figure BDA0002721505670000056
And
Figure BDA0002721505670000057
(since the antenna elements are located in the far field region, the gain depends only on the angular position and is independent of distance) is assumed to be an embedded antenna gain, i.e. a gain pattern is obtained by the array elements shown in fig. 3. The embedded gain pattern of a cell is calculated by feeding 11 the cell individually and ensuring that the other cell input ports are connected to a reference load impedance 12 (fig. 4) [ r.c. hansen, "phase Array Antennas" (Chapter 7 and 8), John Wiley&Sons Inc.，2nd Edition，1998]. Furthermore, to account for Hannan's embedded cell efficiency (antenna Array gain is always less than the sum of all cell gains p.lemiree-Auger, s.abielmona, and c.caloz, "Fundamental Directivity Limitations of Dense Array antennas：A Numerical Study Using Hannan’s Embedded Element Efficiency，”IEEE Antennas Wireless Propag.Lett，vol.15，pp.766-769，2016]) And carrying out normalization processing on the gain of the embedded antenna by using the corresponding maximum antenna array gain during uniform excitation. When the array is large, according to practical application experience, because the edge effect can be ignored, the method can obtain more accurate result.
The method is based on the known excitation profile [ a ]tx]And [ b)rx]In the case of (3), the efficiency η in the formula (7) can be effectively evaluatedairThe efficiency η can also be corrected by estimating the eigenvalue problem in equation (8) and taking into account the scattering matrix in equation (9)airAnd (6) optimizing. This approach requires full electromagnetic wave simulations of both far fields, estimation of the embedded gain pattern and post-processing in equation (9).
By solving the transmit and receive antenna array in fig. 5 (two arrays have the same size D, and D is 124.14mm, the number of elements N of the two arrays M is 4, the element spacing is 0.6 λ, the operating frequency f is05.8 GHz; the two arrays use two different probe fed microstrip patch elements: #1 is a 13.4mm square patch on a 0.508mm thick substrate of Rogers 4003C; #2 is a stacked square patch in which the lower patch has a length of 13.06mm and is positioned on a 0.508mm thick Rodges 4003C substrate, the upper patch is separated from the lower patch by air by 2mm, has a length of 14.02mm, and is positioned on the same substrate as the lower patch), and the optimum efficiency η is calculated from the characteristic value problem (8) corresponding to the different distances dairThe results are shown in FIG. 6. Efficiency can be calculated by solving the all-electromagnetic wave problem (a) using the hybrid finite element-integral equation method in HFSS, and (b) using the approximation method in equation (6). From the observation, it can be seen that the results obtained using the approximation method are very similar to those obtained by the method (a), but the approximation method uses less computational resources and is faster. In fact, in the case of (a) d being 200mm, the Intel Xeon E5-2630 v32.40ghz workstation takes 15h18min and takes up 41.6GB RAM to calculate the matrix Srx-tx](note that each distance d requires one full electromagnetic wave simulation); use of(b) In the method, the same workstation only needs 1h23min and occupies 13.6GB RAM to calculate to obtain an array structure solution, and then each embedded gain directional diagram is calculated in 5 seconds, which means that the calculation efficiency eta is calculatedairDoes not exceed 3h (and calculates an approximation matrix Stx-rx]The post-treatment process of (2) is fast). Because the embedded gain pattern is independent of distance d, for any distance d, the efficiency η can be calculated by only two full electromagnetic wave simulationsair(Once the full electromagnetic wave simulation is complete, the matrix [ S ] can be expressed by calculating the matrix elements in equation (9) through a fast post-processing procedurerx-tx])。
The workflow corresponding to solutions (a)13 and (b)14 is shown in fig. 7.
It should be noted that the number of target far field solutions can be further reduced by taking into account the symmetry of the antenna array structure. By way of example, with reference to FIG. 5, a similarity can be written
Figure BDA0002721505670000061
Of (c) is calculated.
Therefore, when the result needs to be calculated quickly, for example, when the size of the wireless energy transmission array antenna is large or the effect of the wireless energy transmission link needs to be considered in the complete optimization process, the calculation can be completed quickly by using the method and a very ideal approximate result can be obtained.
It will be appreciated by those of ordinary skill in the art that the embodiments described herein are intended to assist the reader in understanding the principles of the invention and are to be construed as being without limitation to such specifically recited embodiments and examples. Those skilled in the art can make various other specific changes and combinations based on the teachings of the present invention without departing from the spirit of the invention, and these changes and combinations are within the scope of the invention.

Claims (1)

1. A method for rapidly designing an antenna array based on maximum wireless energy transmission efficiency is characterized in that wireless energy transmission is carried out between a transmitting antenna array and a receiving antenna array in an electromagnetic radiation mode, the wireless energy transmission efficiency between the calibers of the two antenna arrays is calculated according to a scattering matrix to obtain the maximum energy transmission efficiency, and an excitation coefficient is obtained according to the maximum energy transmission efficiency;
the scattering matrix is represented as:
Figure FDA0003683190970000011
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003683190970000012
Figure FDA0003683190970000013
representing a scattering matrix; [ b ] atx]、[brx]Normalized reflected and incident wave vectors, respectively, of the transmit antenna array, [ a ]tx]、[arx]Respectively receiving normalized reflected wave and incident wave vector of antenna array;
Figure FDA0003683190970000014
respectively representing the normalized reflected waves of the 1 st, 2 nd, … th and nth antenna elements of the transmit antenna array,
Figure FDA0003683190970000015
respectively representing normalized incident waves of 1 st antenna unit, 2 nd antenna unit, … th antenna unit and Nth antenna unit of the transmitting antenna array;
Figure FDA0003683190970000016
respectively representing the normalized reflected waves of the 1 st, 2 nd, … th and nth antenna elements of the receive antenna array,
Figure FDA0003683190970000017
respectively representReceiving normalized incident waves of the 1 st, 2 nd, … th and Nth antenna units of the antenna array;
obtaining the wireless energy transmission efficiency etaairComprises the following steps:
Figure FDA0003683190970000018
by assuming impedance matching, equation (3) is rewritten in the form of a eigenvalue problem as:
([Srx-tx]H[Srx-tx])[atx]＝ηair[atx] (4)
let [ A ]]＝([Srx-tx]H[Srx-tx]) Then [ A ] is]The corresponding maximum characteristic value is the energy transmission efficiency etaairAnd its corresponding feature vector is the optimal excitation vector atx]；
Scattering matrix [ S ]rx-tx]Writing as follows:
Figure FDA0003683190970000021
wherein
Figure FDA0003683190970000022
λ is the wavelength, #n，mAccording to the electromagnetic wave transmission distance r from the nth transmitting array unit to the mth receiving array unitn，m＝||r n，m Calculated phase, and Gtx，i(r n，m ) And Grx，j(r n，m ) Is the independent antenna gain of the ith element in the transmitting array and the jth element in the receiving array, and the direction of the independent antenna gain is a distance vector n，mrThe direction represented.
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