Modular design method of microwave wireless energy transmission active phased array transmitting antenna

Abstract

The application discloses a microwave wireless transmission energy active phased array transmitting antenna modular design method, and the method comprises the following steps: obtaining a highest radiation level constraint outside a receiving area, an aperture field amplitude distribution function of a transmitting antenna with a maximum beam collection efficiency as a target; designing physical size and arrangement mode of a subarray, establishing a radiation model of the subarray, and obtaining subarray excitation coefficients according to the physical size and the arrangement mode and the aperture field amplitude distribution function; classifying the subarrays based on the subarray excitation coefficients, dividing each class of subarrays into a module, and calculating module excitation coefficients; and optimizing the module excitation coefficients to maximize the beam collection efficiency while suppressing the highest radiation level of the radiation model radiated to the outside of the receiving area. The application reduces the engineering implementation difficulty and manufacturing cost of the transmitting antenna under the condition of meeting high transmission efficiency, and the active phased array transmitting antenna with high beam collection efficiency, high safety and low cost can be effectively designed by the method.

Description

Technical Field

[0001] The present invention belongs to the technical field of antenna design, and in particular relates to a modular design method for a microwave wireless energy transmission active phased array transmitting antenna. Background Art

[0002] Microwave wireless energy transfer (MWET) involves transmitting electrical energy in the form of microwaves through a transmitting antenna to a target area. A receiving rectenna intercepts the microwave energy and converts it back into electrical energy. This technology has broad application prospects. It can facilitate power transmission to disaster areas, large offshore platforms, islands, remote mountainous areas, and other locations where laying cables is difficult. It can also provide flexible power supply to mobile targets such as satellite platforms, drones, and airships. Active phased array antennas, with their flexible beamforming and beam pointing capabilities, are considered the preferred transmitting antenna for MWET. However, if each radiating antenna element in an MWET antenna is connected to a transmitting component, the high cost of manufacturing hinders the widespread application of MWET technology. Modular design can significantly reduce the number and variety of transmitting components and is one means of reducing the cost of MWET antennas. Therefore, developing a modular design approach for MWET antennas has important engineering applications.

[0003] At present, there are several main approaches to the design of microwave wireless energy transmission antennas at home and abroad: (1) Optimize the excitation amplitude and phase of each radiating unit of the transmitting antenna to achieve the highest beam collection efficiency: For active phased array antennas, if each radiating unit is connected to a transmitting component with different output power, the engineering implementation is difficult and the cost is high. (2) Divide the transmitting antenna into regular sub-arrays and excite all sub-arrays uniformly to reduce costs: Since all sub-arrays are uniformly excited, the beam collection efficiency is low, which affects the energy transmission efficiency of the system. (3) Use irregular sub-arrays and optimize the sub-array excitation coefficient to improve the beam collection efficiency: The feeding network of irregular sub-arrays is complex and the engineering implementation is difficult.

[0004] Cost and efficiency are two key metrics for microwave wireless energy transmission systems. In practical engineering, both efficiency and cost must be considered when designing a transmitting antenna. Therefore, a high-efficiency, low-cost design method for active phased array transmitting antennas is urgently needed. Summary of the Invention

[0005] In order to solve the technical problems of low efficiency and high cost of microwave wireless energy transmission in the prior art, the present invention provides a modular design method for microwave wireless energy transmission active phased array transmitting antenna, the technical solution adopted is:

[0006] A modular design method for a microwave wireless energy transmission active phased array transmitting antenna includes the following steps:

[0007] S1, obtaining an aperture field amplitude distribution function of a transmitting antenna;

[0008] S2, designing physical size and arrangement of a subarray, establishing a radiation model of the subarray, and obtaining subarray excitation coefficients according to the physical size and arrangement and the aperture field amplitude distribution function;

[0009] S3, classifying the subarrays based on the subarray excitation coefficients, dividing each class of subarrays into a module, and calculating module excitation coefficients;

[0010] S4, optimizing the module excitation coefficients to maximize beam collection efficiency while suppressing the highest radiation level of the radiation model radiated to an outside of a receiving area.

[0011] In an embodiment of the present application, the step S1 comprises:

[0012] S11, determining a normalized aperture field amplitude distribution function E t (ρ,ψ) of the transmitting antenna;

[0013] S12, determining a beam collection efficiency function BEC;

[0014] S13, obtaining an aperture field amplitude distribution function f(ρ) of the transmitting antenna, and obtaining a transmitting antenna aperture field distribution and a maximum beam collection efficiency at which the beam collection efficiency is maximum;

[0015] S14, determining a transmitting antenna aperture field distribution design without considering a constraint of the highest radiation level outside the receiving area;

[0016] S15, considering the constraint of the highest radiation level outside the receiving area, suppressing the highest radiation level outside the receiving area, and realizing high beam collection efficiency.

[0017] In an embodiment of the present application, the step S11 comprises:

[0018] Let E t (ρ,ψ) be the normalized aperture field amplitude distribution function of the transmitting antenna, and be expressed as:

[0019] E t (ρ,ψ)=f(ρ)exp[jψ(ρ)] (1)

[0020] In formula (1), f(ρ) is the aperture field amplitude distribution function of the transmitting antenna, ψ(ρ) is the phase distribution function of the transmitting antenna, and ρ=r / R t is the normalized radius of the transmitting antenna, and r is the distance from the center of the transmitting antenna to any point on the aperture surface of the transmitting antenna;

[0021] In the Fresnel field region, in order to focus the transmit beam on the receiving port surface at a distance L, the transmitting antenna should have a spherical phase distribution: k is the wave constant, k = 2π / λ.

[0022] In one embodiment of the present invention, step S12 includes:

[0023] The beam collection efficiency is the ratio of the microwave power focused by the transmitting antenna on the receiving antenna to the total radiated power of the transmitting antenna, expressed as:

[0024]

[0025] In formula (2),

[0026]

[0027] In formula (2) and formula (3), BEC is the beam collection efficiency, J0(·) is the first-order zero-order Bessel function, and u = kR t sinθ, sinθ≈r′ / L, r′ is the distance from the center of the receiving antenna to any point on the aperture, u0=kR t sinθ0≈kR t R r / L, θ0 is the angle between the transmitting antenna and the receiving antenna.

[0028] In one embodiment of the present invention, step S13 includes:

[0029] Determine the number of basis functions used to describe the aperture field amplitude distribution function f(ρ), and express the aperture field amplitude distribution f(ρ) of the transmitting antenna as:

[0030]

[0031] In formula (4), (1-ρ 2 ) n-1 and x n are basis functions and control coefficients respectively;

[0032] Let x=[x1,…,x N ] T ,A=[1,…,(1-ρ 2 ) B-1 ] T , then formula (4) is expressed as:

[0033] f(ρ)=x T A (5)In formula (5), the superscript “ T ” indicates matrix transpose;

[0034] Substituting formula (5) into the denominator of formula (2), we get:

[0035]

[0036] In formula (6),

[0037]

[0038] Substituting formula (4) into formula (3), F(u) is expressed as:

[0039]

[0040] The nth integral in formula (8) is expressed as:

[0041]

[0042] In formula (9), J n (·) represents the nth order of the first kind Bessel function, and the symbol “!” represents factorial; let Formula (8) can be written as:

[0043] F(u)=x T B

[0044] (10) Based on formula (10), the numerator of formula (2) is expressed as:

[0045]

[0046] In formula (11),

[0047]

[0048] Substituting formula (11) and formula (6) into formula (2), we obtain:

[0049]

[0050] Based on formula (13), the transmit antenna aperture field distribution that maximizes the beam collection efficiency is obtained, which is expressed as finding the optimal coefficient vector x opt , expressed as:

[0051]

[0052] Determine the corresponding maximum eigenvalue λ through matrix C and matrix D max And the corresponding eigenvector is expressed as:

[0053] Cx opt =λ max Dx opt (15)

[0055] In formula (15), the maximum beam collection efficiency is equal to λmax , the corresponding optimal aperture field amplitude distribution f(ρ)=(x opt ) T A.

[0056] In one embodiment of the present invention, step S14 includes:

[0057] The maximum radiation level outside the receiving area is expressed as:

[0058]

[0059] In formula (16), PRL is the highest radiation level outside the receiving area;

[0060] The aperture field distribution design problem of the transmitting antenna is converted into:

[0061]

[0062] In formula (17), C0 is the maximum allowable radiation level outside the receiving area. Without the constraint of the maximum radiation level outside the receiving area, the beam collection efficiency is maximized, and the corresponding optimal aperture field amplitude distribution and radiation pattern are obtained.

[0063] In one embodiment of the present invention, step S15 includes:

[0064] The constraint on the maximum radiation level outside the receiving area is directly incorporated into the objective function, transforming it into an unconstrained optimization problem, which can be expressed as:

[0065]

[0066] In formula (18), Is a penalty parameter used to control the impact of the penalty term;

[0067] Suppresses the highest radiation levels outside the receiving area and achieves high beam collection efficiency.

[0068] In one embodiment of the present invention, step S2 includes:

[0069] Based on the transmitting antenna aperture field amplitude distribution function f(ρ), for an aperture size of R t The transmitting antenna is located at (x p ,y p ) position, is expressed as:

[0070]

[0071] In formula (19), f(·) refers to the aperture field amplitude distribution function f(ρ).

[0072] In one embodiment of the present invention, step S3 includes:

[0073] Based on the excitation coefficient matching principle, the subarray is classified into Q class according to the subarray excitation coefficient, which is expressed as:

[0074]

[0075] In formula (20), I ref =[I1,I2,…,I P ] T is the reference subarray excitation coefficient, I ref The pth element in is obtained by formula (19), where P is the number of subarrays contained in the transmitting antenna;

[0076] is the module excitation coefficient, Q is the number of modules, R is a matrix with P rows and Q columns, where R pq It represents the relationship between the p-th sub-matrix and the q-th module, satisfying:

[0077]

[0078] and

[0079]

[0080] The excitation coefficient of module q is approximately expressed as:

[0081]

[0082] The k-means clustering method is used to solve formula (20) to obtain the optimal module division method, and then the excitation coefficient of each module is obtained according to formula (23).

[0083] In one embodiment of the present invention, step S4 includes:

[0084] Based on the module division method in step S3, the radiation pattern of the transmitting antenna is expressed as:

[0085]

[0086] In formula (24), is the radiation pattern of the p-th sub-array, is the direction cosine;

[0087] The beam collection efficiency of the system and the maximum level of radiation outside the receiving area are expressed as:

[0088]

[0089] In formula (26), r0 = sinθ0, θ0 is the maximum angle between the transmitting antenna and the receiving antenna;

[0090] The optimization model is expressed as:

[0091]

[0092] The module excitation coefficient is optimized using the GWO algorithm to improve the beam collection efficiency, while constraining the highest level outside the receiving area.

[0093] Beneficial effects of the present invention:

[0094] The modular design method for a microwave wireless energy transmission active phased array transmitting antenna of the present invention first designs the aperture field amplitude distribution function of the transmitting antenna with the goal of maximizing beam collection efficiency. It then obtains the subarray excitation coefficients, divides the antenna into modules, calculates the module excitation coefficients, and optimizes the module excitation coefficients to maximize the beam collection efficiency (BCE) while suppressing the maximum radiation level (PRL) of the radiation model outside the receiving area. Through modular division, the present invention brings the performance of the transmitting array close to that of a continuous aperture field. Optimizing the module excitation coefficients improves the maximum BCE while suppressing the PRL. Therefore, by simultaneously considering both beam collection efficiency and the safety of radiation outside the receiving area, the present invention can reduce the engineering difficulty and manufacturing cost of the transmitting antenna while maintaining high transmission efficiency, effectively designing an active phased array transmitting antenna with high BCE, high safety, and low cost. BRIEF DESCRIPTION OF THE DRAWINGS

[0095] Figure 1 This is a flow chart of a modular design method for a microwave wireless energy transmission active phased array transmitting antenna provided by an embodiment of the present invention;

[0096] Figure 2 is the normalized aperture field amplitude distribution under different PRL constraints (unconstrained and constrained) provided by the embodiment of the present invention;

[0097] Figure 3 The embodiment of the present invention provides Figure 2 The antenna normalized radiation pattern with the aperture field amplitude distribution given in;

[0098] Figure 4 is a schematic diagram of a 2×2 patch unit subarray provided by an embodiment of the present invention;

[0099] Figure 5 is a schematic diagram of a SICL structure provided by an embodiment of the present invention;

[0100] Figure 6 2 is a schematic diagram of an optimized 2×2 sub-array structure provided by an embodiment of the present invention;

[0101] Figure 7 is a simulated S11 curve diagram of a 2×2 sub-array designed according to an embodiment of the present invention;

[0102] Figure 8 is an AR curve diagram of a 2×2 sub-array designed according to an embodiment of the present invention;

[0103] Figure 9 is a gain diagram of a 2×2 sub-array designed according to an embodiment of the present invention;

[0104] Figure 10 Schematic diagram of a transmitting array with a diameter of 2.3 meters provided in an embodiment of the present invention;

[0105] Figure 11 The optimal module partitioning layout under unconstrained PRL is provided by an embodiment of the present invention when the number of modules is (a) Q = 2, (b) Q = 3, and (c) Q = 4;

[0106] Figure 12 is a schematic diagram of a 5×5 array and a gain pattern of the effective radiation pattern (EEP) of a 2×2 patch subarray provided by an embodiment of the present invention;

[0107] Figure 13 The embodiments of the present invention provide an optimal module partition layout under a constrained PRL when the number of modules is (a) Q=2, (b) Q=3, and (c) Q=4. DETAILED DESCRIPTION

[0108] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0109] The present invention provides a modular design method for a high-efficiency, low-cost active phased array transmitting antenna for microwave wireless energy transmission. This method can reduce the difficulty of implementing the transmitting antenna project and the manufacturing cost while meeting high transmission efficiency.

[0110] Refer to the attached Figure 1 The modular design method of the microwave wireless energy transmission active phased array transmitting antenna of the present invention comprises the following steps:

[0111] S1. Obtain the aperture field amplitude distribution function of the transmitting antenna;

[0112] S2. Design the physical size and arrangement of the sub-array, establish the radiation model of the sub-array, and obtain the sub-array excitation coefficient based on the physical size and arrangement, as well as the aperture field amplitude distribution function;

[0113] S3. Based on the subarray excitation coefficients, the subarrays are classified, each type of subarray is divided into a module, and the module excitation coefficients are calculated;

[0114] S4. Optimize the module excitation coefficient to maximize the beam collection efficiency while suppressing the radiation model from radiating to the highest radiation level outside the receiving area.

[0115] Step S1 of the present invention comprises:

[0116] S11. Determine the normalized aperture field amplitude distribution function E of the transmitting antenna t (ρ,ψ).

[0117] Let E t (ρ, ψ) is the normalized aperture field amplitude distribution function of the transmitting antenna, expressed as:

[0118] E t (ρ,ψ)=f(ρ)exp[jψ(ρ)] (1)

[0120] In formula (1), f(ρ) is the aperture field amplitude distribution function of the transmitting antenna, ψ(ρ) is the phase distribution function of the transmitting antenna, and ρ = r / R t is the normalized radius of the transmitting antenna, r is the distance from the center of the transmitting antenna to any point on the transmitting antenna aperture;

[0121] In the Fresnel field region, in order to focus the transmit beam on the receiving port surface at a distance L, the transmitting antenna should have a spherical phase distribution: k is the wave constant, k = 2π / λ.

[0122] S12. Determine the beam collection efficiency function BEC.

[0123] Beam Collection Efficiency (BCE) is the ratio of the microwave power focused by the transmitting antenna on the receiving antenna to the total radiated power of the transmitting antenna, expressed as:

[0124]

[0125] In formula (2),

[0126]

[0127] In formula (2) and formula (3), BEC is the beam collection efficiency, J0(·) is the first-order zero-order Bessel function, and u = kR t sinθ, sinθ≈r′ / L, r′ is the distance from the center of the receiving antenna to any point on the aperture, u0=kR t sinθ0≈kR t R r / L, θ0 is the angle between the transmitting antenna and the receiving antenna.

[0128] S13. Obtain the aperture field amplitude distribution function f(ρ) of the transmitting antenna, and calculate the transmitting antenna aperture field distribution with the maximum beam collection efficiency and the maximum beam collection efficiency.

[0129] Determine the number of basis functions used to describe the aperture field amplitude distribution function f(ρ), and express the aperture field amplitude distribution f(ρ) of the transmitting antenna as:

[0130]

[0131] In formula (4), (1-ρ 2 ) n-1 and x n are basis functions and control coefficients respectively;

[0132] Let x=[x1,…,x N ] T ,A=[1,…,(1-ρ 2 ) N-1 ] T , then formula (4) is expressed as:

[0133] f(ρ)=x T A (5)

[0135] In formula (5), the superscript " T ” indicates matrix transpose;

[0136] Substituting formula (5) into the denominator of formula (2), we get:

[0137]

[0138] In formula (6),

[0139]

[0140] Substituting formula (4) into formula (3), F(u) is expressed as:

[0141]

[0142] The nth integral in formula (8) is expressed as:

[0143]

[0144] In formula (9), J n (·) represents the nth order of the first kind Bessel function, and the symbol “!” represents factorial; let Formula (8) can be written as:

[0145] F(u)=x T B

[0146] (10) Based on formula (10), the numerator of formula (2) is expressed as:

[0147]

[0148] In formula (11),

[0149]

[0150] Substituting formula (11) and formula (6) into formula (2), we obtain:

[0151]

[0152] Based on formula (13), the transmit antenna aperture field distribution that maximizes the beam collection efficiency is obtained, which is expressed as finding the optimal coefficient vector x opt , expressed as:

[0153]

[0154] Determine the corresponding maximum eigenvalue λ through matrix C and matrix D max And the corresponding eigenvector is expressed as:

[0155] Cx opt =λ max Dx opt (15)

[0157] In formula (15), the maximum beam collection efficiency is equal to λ max , the corresponding optimal aperture field amplitude distribution f(ρ)=(x opt ) T A.

[0158] S14. Without considering the maximum radiation level constraint (PRL) outside the receiving area, determine the aperture field distribution design of the transmitting antenna.

[0159] For some microwave wireless power transfer (MWPT) applications, the transmission power is very high. Therefore, radiation safety must be considered, that is, the maximum radiation level outside the receiving area must be considered.

[0160] The maximum radiation level outside the receiving area is expressed as:

[0161]

[0162] In formula (16), PRL is the highest radiation level outside the receiving area;

[0163] The aperture field distribution design problem of the transmitting antenna is converted into:

[0164]

[0165] In formula (17), C0 is the maximum allowable radiation level outside the receiving area. Without the constraint of the maximum radiation level outside the receiving area, the beam collection efficiency is maximized, and the corresponding optimal aperture field amplitude distribution and radiation pattern are obtained.

[0166] Specifically, in this embodiment, the aperture field distribution design constraint optimization problem of the transmitting antenna is solved by solving the eigenvalue problem in formula (15) without PRL constraints to obtain the maximum BCE. The schematic diagrams of the optimal aperture field amplitude distribution diagram and radiation diagram are shown in the attached figure. Figure 2 (blue solid line) and attached Figure 3 The blue solid line shows the edge of the receiving aperture field, where the black dashed line indicates the edge of the receiving aperture field. It is observed that a very high PRL (PRL = -12.58 dB) appears at the edge of the receiving aperture field. This high PRL may pose a problem to the environment or human safety.

[0167] S15. Considering the constraint of the maximum radiation level outside the receiving area, the maximum radiation level outside the receiving area is suppressed and high beam collection efficiency is achieved.

[0168] Since high PRL may pose a problem to the environment or human safety, it is necessary to constrain the maximum radiation level outside the receiving area. In order to further deal with this constrained optimization problem, the constraint on the maximum radiation level outside the receiving area is directly incorporated into the objective function, transforming it into an unconstrained optimization problem, which can be expressed as:

[0169]

[0170] In formula (18), Is a penalty parameter used to control the impact of the penalty term;

[0171] A powerful GWO-NM algorithm is used to handle the optimization problem, suppressing the highest radiation levels outside the receiving area and achieving high beam collection efficiency.

[0172] In this embodiment, the penalty function Set to 106, and set the PRL threshold to C0 = -17.5dB. This paper uses the GWO-NM algorithm to obtain BCE and the corresponding PRL. The optimized control coefficient vector x opt As shown in the third row and second column of Table I, the optimal aperture field amplitude distribution is f(ρ)=(x opt ) T A, where A=[1,…,(1-ρ 2 ) N-1 ] T The corresponding schematic diagrams of the optimal aperture field amplitude distribution diagram and radiation diagram are attached. Figure 2 (red dotted line) and attached Figure 3(red dashed line) is shown.

[0173] Further, in order to better reduce the PRL, the threshold of the PRL is updated constantly, the maximum BCE under different threshold constraints is obtained by using the GWO-NM algorithm, and several groups of maximum BCE / PRL threshold are compared to show the relationship between the maximum BCE and the suppression of PRL under different thresholds. In the case of maximizing the BCE, the value of suppressing the PRL is determined, and then the optimized aperture field amplitude distribution function f(p) is finally determined.

[0174] In an optional embodiment, step S2 comprises:

[0175] According to the actual engineering needs, i.e. the working frequency and bandwidth requirements of the antenna, the physical size (such as length, width or diameter) of each subarray is designed; according to the application scenario (such as radar, communication, etc.), the arrangement mode of the subarray is designed. Common arrangement modes include rectangular grid, triangular grid, circular array, etc.

[0176] In this embodiment, patch antennas are used because of their small size, low profile and easy integration. Among them, LP and WP are the length and width of the patch, LG and WG represent the length and width of the substrate, L0 refers to the distance from the center of the patch to the feed point, E0 represents the size of the cut edge, and D is the distance between two adjacent patches. It should be noted that by cutting the edges of the patch, the subarray realizes circular polarization, and the subarray structure design is shown in FIG. 2. Figure 4

[0177] At the same time, according to the mutual coupling effect between the array subarrays, the substrate integrated coaxial line (SICL) technology is used to design the feed network in this embodiment. The SICL structure is composed of five layers from top to bottom, as shown in FIG. 3. The first and fifth layers are metal plates, the second and fourth layers are dielectric substrates, and the third layer contains metal conductors and connecting media. The schematic diagram of the SICL structure is shown in FIG. 4. Figure 4 Figure 5 Figure 5 In FIG. 4, W represents the width of the metal conductor, S represents the distance between the metal vias, and A represents the distance between the metal vias on both sides of the conductor.

[0178] In order to fully utilize the non-scanning characteristics of the array, the spacing between two adjacent units is set to 47 mm (about 0.9λ), which is relatively large compared to the wavelength. FIG. 5 shows the optimized 2x2 subarray structure. Figure 6

[0179] According to the designed subarray structure, the radiation model of the subarray is established by using simulation software, and the element factor is calculated. The element factor describes the radiation pattern characteristics of a single subarray and is the basis for subsequent array factor calculation.​​​​

[0180] In this embodiment, a radiation model of the sub-array is established based on the designed sub-array structure. The simulated S11 curve is shown in the attached figure. Figure 7 As shown in the attached figure, the axial ratio (AR) curve is shown in the attached figure. Figure 8 The actual gain diagram is shown in the attached Figure 9 shown.

[0181] Designing an aperture antenna with a specific radiation aperture is generally difficult. Therefore, in this invention, the continuous distribution function of the aperture field amplitude, f(ρ), is sampled and discretized to obtain the excitation coefficients for a circular antenna array. These coefficients are then applied to the subarrays (i.e., the repeating radiating elements) of the circular array antenna, thereby approximating the performance of an aperture antenna.

[0182] In this embodiment, a circular array antenna with a diameter of 2.3 meters is constructed with the designed sub-array as a repeating unit, which consists of 464 sub-arrays, as shown in the attached figure. Figure 10 shown.

[0183] For the aperture size R t The transmitting antenna has a radius of R t Array, find the location (x p ,y p ) position, is expressed as:

[0184]

[0185] In formula (19), f(·) refers to the aperture field amplitude distribution function f(ρ).

[0186] In an optional embodiment, step S3 includes:

[0187] Based on the aperture field amplitude distribution function f(ρ), the structure of the subarray, and the structure of the large array, the excitation coefficient of each subarray can be calculated. Based on the excitation coefficient matching principle, the subarray is classified into Q class according to the subarray excitation coefficient, which is expressed as:

[0188]

[0189] In formula (20), I ref =[I1,I2,…,I P ] T is the reference subarray excitation coefficient, I ref The pth element in is obtained by formula (19), where P is the number of subarrays contained in the transmitting antenna.

[0190] is the module excitation coefficient, Q is the number of modules, R is a matrix with P rows and Q columns, where R pq It represents the relationship between the p-th sub-matrix and the q-th module, satisfying:

[0191]

[0192] and

[0193]

[0194] Specifically, in this embodiment, we first consider the optimal f(ρ) that produces the maximum BCE without PRL constraints. At the same time, in order to study the relationship between the achievable BCE and the number of modules, this embodiment sets different numbers of modules, namely (a) Q = 2, (b) Q = 3, and (c) Q = 4, and uses the k-means clustering method to solve the problem. The optimal module partitioning result is shown in the attached figure. Figure 11 As shown in the figure, blocks with the same color form a module.

[0195] Specifically, in this embodiment, for simplicity, the excitation coefficient of module q is approximately expressed as:

[0196]

[0197] The k-means clustering method is used to solve formula (20) to obtain the optimal module division method, and then the excitation coefficient of each module is obtained according to formula (23).

[0198] It should be noted that in order to accurately estimate the performance of a large array, such as BCE and PRL, it is necessary to consider the mutual coupling effect. However, using a full-wave simulator to analyze such a large array is very time-consuming. Therefore, in this embodiment, the embedded element pattern (EEP) method is used to simulate and model a large array, that is, a 5×5 array is used, as shown in the attached figure. Figure 12 (a); and considering the coupling effect of adjacent elements, the gain pattern of the embedded element is plotted as shown in the attached figure. Figure 12 (b) shown.

[0199] The radiation pattern of an array can be approximated by multiplying the array factor by the EEP, expressed as:

[0200]

[0201] It is worth noting that the 3D radiation pattern of the transmitting array is obtained without considering the maximum radiation level constraint (PRL) outside the receiving area. However, the PRLs obtained by the three array module division modes are very high, which is not ideal in actual engineering. Therefore, the optimized amplitude distribution with PRL constraint given in step 1.3 is used. Specifically, in this embodiment, the constraint PRL: C0 = -18.5dB is used as an example. The optimal module division result is shown in the attached figure. Figure 13 shown.

[0202] In an optional embodiment, step S4 includes:

[0203] Based on the module division method in step S3, the radiation pattern of the transmitting antenna is expressed as:

[0204]

[0205] In formula (24), is the radiation pattern of the p-th sub-array, is the direction cosine.

[0206] Correspondingly, the system's beam collection efficiency and the maximum level radiated outside the receiving area are expressed as:

[0207]

[0208] In formula (26), r0=sinθ0, θ0 is the maximum angle between the transmitting antenna and the receiving antenna.

[0209] When the module partitioning is given, both BCE and PRL are determined by the module excitation coefficient. Due to the use of subarrays, the spacing between two adjacent subarrays is large relative to the wavelength, which causes sampling errors. The module partitioning design of the present invention further exacerbates the sampling errors.

[0210] Therefore, the GWO algorithm is used to optimize the module excitation coefficient to improve the beam collection efficiency while constraining the maximum level outside the receiving area. The optimization model is expressed as:

[0211]

[0212] Specifically, in this embodiment, only the module partitioning result obtained by constraining PRL: C0=-18.5dB in step 3.2 is optimized using the GWO algorithm to improve the module excitation coefficient and BCE.

[0213] This invention first proposes a low-cost, high-efficiency modular design method for microwave wireless energy transmission active phased array transmitting antennas. Specifically, this method offers three advantages: First, the number of transmitting components required for the transmitting antenna is reduced to one-quarter that of traditional methods; second, the number of types of transmitting components required for the transmitting antenna is significantly reduced (e.g., two or three); and third, this method simultaneously considers both beam collection efficiency and the safety of radiation outside the receiving area.

[0214] Furthermore, the modular design method and effect of the microwave wireless energy transmission active phased array transmitting antenna are explained through specific simulation experiments.

[0215] 1. Simulation parameters

[0216] A fixed point-to-point microwave wireless power transmission system with circular transmitting and receiving antennas is used. The aperture sizes of the transmitting and receiving antennas are D t =2.3m and D r =5.0m, the distance between the transmitting and receiving antennas is L=100m, and the operating frequency is 5.8GHz. Table 1 summarizes the MWPT system parameters.

[0217] Table 1

[0218] f (GHz) 5.8 <![CDATA[D t (m)]]> 2.3 <![CDATA[D r (m)]]> 5.0 L (m) 100

[0219] 2. Simulation content and results

[0220] First, the continuous aperture field distribution with and without PRL constraints is designed and simulated, and the results are shown in Table 2.

[0221] Table 2

[0222]

[0223] Without constraining PRL, the maximum BCE of 94.48% is obtained, while the maximum radiation level outside the receiving area is PRL = -12.58dB. Further, adding PRL constraints, respectively C0 = -17.5dB, C0 = -18.0dB, C0 = -18.5dB and C0 = -19.0dB, the optimized BCE are 90.0%, 89.29%, 88.58% and 87.76%, respectively. The corresponding PRL is exactly equal to the PRL constraint value, and the obtained excitation coefficient x is opt See the second column of Table 1. The continuous aperture field amplitude distribution and radiation pattern of the above parameter settings are shown in the attached Figure 2 and attached Figure 3 From the results, we can find that suppressing PRL comes at the expense of reducing BCE, and as the PRL value decreases, the main lobe becomes narrower and the other side lobes become higher.

[0224] Secondly, the subarray structure is determined according to the actual engineering requirements. Patch antennas are used to design a 2×2 patch unit subarray. Figure 4 Considering the mutual coupling effect between array sub-arrays, the embodiment of the present invention adopts substrate integrated coaxial line (SICL) technology to design the feeding network. At the same time, in order to fully utilize the non-scanning characteristics of the array, the spacing between two adjacent units is set to 47 mm (about 0.9λ). The optimized 2×2 sub-array structure is shown in the attached figure. Figure 6 , and the relevant parameters are shown in Table 3.

[0225] Table 3

[0226] LP WP L0 WG LG 16.39 mm 16 mm 3.59 mm 94 mm 94 mm E0 W S A D 2.4 mm 1.4 mm 5 mm 5 mm 47 mm

[0227] Next, the excitation coefficient of each subarray is obtained according to the calculation formula of the subarray excitation coefficient. The subarray is divided into Q categories based on the excitation coefficient matching principle, with (a) Q = 2, (b) Q = 3, and (c) Q = 4 set. Under the constraints of not considering the PRL constraint and considering the PRL constraint (C0 = -18.5 dB), the k-means clustering method is used to solve the optimal module division results and related parameters, as shown in Table 4.

[0228] Table 4

[0229]

[0230] The optimal module division results are shown in the attached Figure 11 and attached Figure 13 shown.

[0231] From the analysis of the results, it can be seen that without considering the PRL constraint, the highest radiation level PRL outside the receiving area divided by the three modules is very high. By comparing the performance indicators of the discrete array in Table 2 with the performance indicators of the continuous aperture field in Table 2, as the number of modules increases, the performance of the transmitting array is getting closer and closer to the performance of the continuous aperture field. Figure 11 and attached Figure 13 It can be seen that the radiation power is mainly concentrated in the receiving area, and the grating lobes are effectively suppressed.

[0232] Finally, the PRLs for the three modularization methods described above are higher than -18.5dB. The continuous distribution reduces the PRL to below -18.5dB due to the modularization and sampling error. Therefore, the GWO algorithm is used to optimize the modular excitation coefficients (with the PRL constraint of C0 = -18.5dB). The results are shown in Table 5.

[0233] Table 5

[0234]

[0235]

[0236] It's important to note that when using two modules, the -18.5dB PRL constraint is not met. Comparing the results in Tables 4 and 5, we see that the achievable BCE values ​​are improved by 0.92% and 0.87%, respectively, and the PRL is reduced to below -18.5dB in both cases. This improves the maximum BCE while suppressing the PRL. These results demonstrate that the method presented in this paper can effectively design active phased array transmit antennas with high BCE, high security, and low cost.

[0237] The above description is only a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions and improvements made by any technician familiar with this technical field within the technical scope disclosed by the present invention and within the spirit and principles of the present invention should be covered by the scope of protection of the present invention.

Claims

1. A modular design method for microwave wireless energy transmission active phased array transmitting antenna, characterized in that: Including steps: S1. Obtain the aperture field amplitude distribution function of the transmitting antenna; S2. Design the physical size and arrangement of the sub-array, establish a radiation model of the sub-array, and obtain the sub-array excitation coefficient based on the physical size and arrangement, and the aperture field amplitude distribution function; S3. Classify the subarrays based on the subarray excitation coefficients, divide each type of subarray into a module, and calculate the module excitation coefficients; S4. Optimizing the module excitation coefficient to maximize the beam collection efficiency while suppressing the radiation model from radiating to the highest radiation level outside the receiving area; The step S2 comprises: Based on the transmitting antenna aperture field amplitude distribution function , for aperture size The transmitting antenna is located at The first position The sub-array excitation coefficient is expressed as: （19） In formula (19), f(∙) Refers to the aperture field amplitude distribution function ; The step S3 comprises: Based on the excitation coefficient matching principle, the subarray is classified into Q class according to the subarray excitation coefficient, which is expressed as: （20） In formula (20), is the reference subarray excitation coefficient, The p The elements are obtained by formula (19), is the number of sub-arrays contained in the transmitting antenna; is the module excitation coefficient, is the number of modules, For one P OK Q A matrix of columns, where It means the p The sub-array and q The relationship between the modules satisfies: （21） and （22） Module q The excitation coefficient is approximately expressed as: （23） The k-means clustering method is used to solve formula (20) to obtain the optimal module division method, and then the excitation coefficient of each module is obtained according to formula (23); The step S4 comprises: Based on the module division method in step S3, the radiation pattern of the transmitting antenna is expressed as: （24） In formula (24), For the p The radiation pattern of the sub-array, is the direction cosine; The beam collection efficiency of the system and the maximum level of radiation outside the receiving area are expressed as: （25） （26） In formula (26), , , is the maximum angle between the transmitting antenna and the receiving antenna; The optimization model is expressed as: st （27） The module excitation coefficient is optimized using the GWO algorithm to improve the beam collection efficiency, while constraining the highest level outside the receiving area.

2. The modular design method for microwave wireless energy transmission active phased array transmitting antenna according to claim 1 is characterized in that: The step S1 comprises: S11. Determine the normalized aperture field amplitude distribution function of the transmitting antenna ; S12. Determine beam collection efficiency function ; S13. Obtain the aperture field amplitude distribution function of the transmitting antenna , find the transmit antenna aperture field distribution and maximum beam collection efficiency with the maximum beam collection efficiency; S14. Determine the aperture field distribution design of the transmitting antenna without considering the maximum radiation level constraint outside the receiving area; S15. Considering the constraint of the maximum radiation level outside the receiving area, the maximum radiation level outside the receiving area is suppressed and high beam collection efficiency is achieved.

3. The modular design method for microwave wireless energy transmission active phased array transmitting antenna according to claim 2 is characterized in that: The step S11 includes: make is the normalized aperture field amplitude distribution function of the transmitting antenna, expressed as: （1） In formula (1), is the aperture field amplitude distribution function of the transmitting antenna, is the phase distribution function of the transmitting antenna, is the normalized radius of the transmitting antenna, is the distance from the center of the transmitting antenna to any point on the transmitting antenna aperture; In the Fresnel field, in order to focus the transmit beam at a distance of On the receiving port surface, the transmitting antenna should have a spherical phase distribution: , .

4. The modular design method for microwave wireless energy transmission active phased array transmitting antenna according to claim 3 is characterized in that: The step S12 includes: The beam collection efficiency is the ratio of the microwave power focused by the transmitting antenna on the receiving antenna to the total radiated power of the transmitting antenna, expressed as: （2） In formula (2), （3） In formula (2) and formula (3), BEC is the beam collection efficiency, is the zero-order Bessel function of the first kind, , , is the distance from the center of the receiving antenna to any point on the aperture surface, , is the angle between the transmitting antenna and the receiving antenna.

5. The modular design method for microwave wireless energy transmission active phased array transmitting antenna according to claim 4 is characterized in that: The step S13 includes: Determine the amplitude distribution function used to describe the aperture field The number of basis functions is used to distribute the aperture field amplitude of the transmitting antenna Expressed as: （4） In formula (4), and are basis functions and control coefficients respectively; make , , then formula (4) is expressed as: （5） In formula (5), the superscript " T ” indicates matrix transpose; Substituting formula (5) into the denominator of formula (2), we get: （6） In formula (6), （7） Substituting formula (4) into formula (3), Expressed as: （8） The first n The integral is expressed as: （9） In formula (9), represents the first kind of Bessel function n The symbol "!" represents factorial; make , formula (8) can be written as: （10） Based on formula (10), the numerator of formula (2) is expressed as: （11） In formula (11), （12） Substituting formula (11) and formula (6) into formula (2) yields: （13） Based on formula (13), the transmit antenna aperture field distribution that maximizes the beam collection efficiency is obtained, which is expressed as finding the optimal coefficient vector , expressed as: （14） Determine the corresponding maximum eigenvalue through matrix C and matrix D And the corresponding eigenvector is expressed as: （15） In formula (15), the maximum beam collection efficiency is equal to , the corresponding optimal aperture field amplitude distribution .

6. The modular design method for microwave wireless energy transmission active phased array transmitting antenna according to claim 5, characterized in that: The step S14 includes: The maximum radiation level outside the receiving area is expressed as: （16） In formula (16), PRL is the highest radiation level outside the receiving area; The aperture field distribution design problem of the transmitting antenna is converted into: st （17） In formula (17), For the highest allowable radiation level outside the receiving area, without the constraint of the highest radiation level outside the receiving area, the beam collection efficiency is maximized, and the corresponding optimal aperture field amplitude distribution and radiation pattern are obtained.

7. The modular design method for microwave wireless energy transmission active phased array transmitting antenna according to claim 6, characterized in that: The step S15 includes: The constraint on the maximum radiation level outside the receiving area is directly incorporated into the objective function, transforming it into an unconstrained optimization problem, which can be expressed as: （18） In formula (18), Is a penalty parameter used to control the impact of the penalty term; Suppresses the highest radiation levels outside the receiving area and achieves high beam collection efficiency.

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