A three-dimensional flexible magnetic metamaterial structure regulated by magnetic field and a design method thereof

Abstract

This invention discloses a three-dimensional flexible hybrid magnetic metamaterial structure and design method with magnetic field control, relating to the field of implantable wireless charging technology. The structure includes a -3 and -2 permeability hybrid array, a -2 and 0 permeability hybrid array, and a side-mounted 0 permeability array. Magnetic field focusing and constraint are achieved by arranging the permeability primitives. A design method for the three-dimensional flexible hybrid magnetic metamaterial with magnetic field control is also provided, including (1) constructing a mutual inductance model between coils of different shapes based on the Neumann formula, analyzing the variation law of the coupling coefficient when the coil is offset, and determining the primitive shape as a regular hexagon or rectangle; (2) optimizing the regular hexagonal primitives using a genetic algorithm with transmission efficiency, quality factor, and surface area as objective functions; (3) specifying the optimization objective constraint range; (4) designing rectangular primitives; and (5) matching the equivalent permeability of each primitive to construct the three-dimensional flexible hybrid magnetic metamaterial. This invention improves transmission performance and effectively suppresses magnetic leakage by controlling the system's magnetic field.

Description

Technical Field

[0001] This application relates to the field of implantable wireless charging technology, and in particular to a three-dimensional flexible hybrid magnetic metamaterial structure and design method for magnetic field control. Background Technology

[0002] Active implantable devices generally rely on battery power, which presents problems such as large size, limited lifespan, and the risk of replacement via secondary surgery. This not only increases the physical burden on patients but also significantly raises medical costs. [1] The emergence of magnetically coupled resonance wireless power transfer (MCR-WPT) technology has provided new possibilities for powering implantable devices. [2-3] The MCR-WPT system achieves efficient and stable energy transmission through contactless power supply, avoiding the probability of complications during battery replacement surgery and reducing the risks caused by sudden battery depletion. In practical applications, the system is susceptible to strong attenuation, multipath scattering, and conductivity losses in complex biological tissue environments, inevitably facing multiple challenges to transmission performance and patient safety. Therefore, effectively enhancing the system's power transmission efficiency, alignment tolerance, and magnetic leakage suppression capabilities, while considering different patient body shapes, is of great significance.

[0003] Electromagnetic metamaterials, as functional materials designed to achieve specific electromagnetic response characteristics, are composed of metallic conductors and dielectric materials arranged in a certain periodic pattern. Chinese invention patent CN202510025157.8 discloses a design method for small-sized shielded electromagnetic metamaterials in the kHz band. By changing its unit structure and electromagnetic parameters, electromagnetic properties such as negative permeability and near-zero permeability can be achieved in specific frequency bands, realizing magnetic field focusing or magnetic field shielding functions, improving the coupling strength between coils, and providing an innovative solution for optimizing the overall performance of the system. According to relevant literature [4-5], flexible, wearable metamaterials can be used as body surface devices to focus magnetic fields and improve the transmission performance of implantable wireless charging systems. However, the single permeability structure limits the metamaterial's ability to control the magnetic field, and the design of metamaterial structural parameters usually relies on experience or single parameter optimization methods, lacking a systematic multi-parameter collaborative optimization strategy.

[0004] Therefore, we designed a metamaterial structure with high degree of freedom that can achieve multidimensional magnetic field control, and constructed a comprehensive optimization method based on multiple performance indicators such as the transmission efficiency of the implantable wireless power transmission system, the metamaterial quality factor, and the surface area, to solve the problems of low system efficiency, insufficient system stability, and serious magnetic leakage, thereby improving the overall system performance and application reliability.

[0005] [1] Wörmann J, Strik M, Jurisic S, et al. Occurrence of prematurebattery depletion in a large multicentre registry of subcutaneouscardioverter-defibrillator patients[J]. Europace, 2024, 26(7): euae170.

[0006] [2] Abbas N, Basir A, Ali Shah I, et al. Development of an efficientmid-field wireless power transmission system for biotelemetric IoT medicaldevices[J]. Scientific Reports, 2025, 15(1): 14889.

[0007] [3] Rodriguez-Fuentes A, Carrizosa M J, Ramos R. Neural Network-BasedDesign of Wireless Power Transfer Systems for Implantable Medical Devices[J].IEEE Transactions on Power Electronics, 2025, 41(2): 3011-3024.

[0008] [4] Ahmad A, Choi D. Efficient Metamaterial-Integrated RadiativeNear-Field Wireless Power Transfer System for Scalp-Implantable Devices inIoMT Applications[J]. IEEE Internet of Things Journal, 2025, 12(13): 25879-25891.

[0009] [5] Shah IA, Zada ​​M, Shah SAA, et al. Flexible metasurface-coupledefficient wireless power transfer system for implantable devices[J]. IEEETransactions on Microwave Theory and Techniques, 2023, 72(4): 2534-2547. Summary of the Invention

[0010] This application proposes a three-dimensional flexible hybrid magnetic metamaterial structure and design method for magnetic field control, which aims to solve the problems of low efficiency, poor stability and serious magnetic leakage in traditional two-coil implanted wireless power transmission systems.

[0011] On one hand, according to the embodiments of this application, a three-dimensional flexible hybrid magnetic metamaterial structure with magnetic field control is provided. The three-dimensional flexible hybrid magnetic metamaterial structure includes a -3 and -2 permeability hybrid array, a -2 and 0 permeability hybrid array, and a side-mounted 0 permeability array. The -3 and -2 permeability hybrid array consists of a central hexagonal -2 permeability element and six peripheral hexagonal -3 permeability elements. The -2 and 0 permeability hybrid array consists of a central hexagonal 0 permeability element and six peripheral hexagonal -2 permeability elements. The two hybrid arrays achieve magnetic field focusing through a negative permeability gradient distribution. The side-mounted 0 permeability array consists of 18 rectangular 0 permeability elements, placed sideways on both sides of the hybrid array to constrain the system's magnetic field. The hexagonal and rectangular elements are based on a polyimide flexible dielectric substrate, and are constructed by connecting an upper layer of spiral copper wire and a lower layer of lumped capacitance in series. The permeability of the elements is achieved by adjusting the lumped capacitance.

[0012] According to one aspect of the embodiments of this application, the three-dimensional flexible hybrid magnetic metamaterial structure is arranged coaxially with the transmitting and receiving coils, and the transmitting and receiving coils are spiral circular coils of the same size; the -3, -2 permeability hybrid array and the -2, 0 permeability hybrid array are arranged symmetrically along the axis of the transmitting and receiving coils, wherein the former is adjacent to the transmitting coil and the latter is adjacent to the receiving coil, and the two are connected by a side-mounted 0 permeability array to form the three-dimensional flexible hybrid magnetic metamaterial structure.

[0013] On the other hand, this application proposes a magnetic field-controlled three-dimensional flexible hybrid magnetic metamaterial design method for designing the aforementioned metamaterial, including the following steps: S1: Set the size and spacing of the transmitting and receiving coils and the system operating frequency f; measure the self-inductance L of the transmitting and receiving coils. T LR resistance R T R R Based on the changes in mutual inductance between planar spiral coils of different shapes under offset conditions, the basic shapes of the three-dimensional flexible hybrid magnetic metamaterial are determined to be regular hexagons and rectangles; S2: Evaluate the size of the regular hexagonal spiral coil and determine the constraints of its maximum side length a, line width w, gap s, and number of turns N; S3: Construct an equivalent circuit model, with system transmission efficiency, metamaterial quality factor and metamaterial surface area as objective functions, and use a multi-objective genetic algorithm for global optimization; S4: Based on the optimized metamaterial primitives, different array structures were constructed, the changes in system transmission performance under each array structure were analyzed, the 7-primary-unit array structure was determined, and the coaxial arrangement spacing characteristics of the hybrid permeability dual arrays were further studied. Based on the spatial arrangement and structural dimensions of the dual arrays, a side-mounted 0-permeability rectangular metamaterial primitive structure was designed. S5: Based on the relationship between magnetic permeability and refraction angle, a three-dimensional flexible hybrid magnetic metamaterial structure is constructed, and the lumped capacitance corresponding to the required magnetic permeability is determined at the target resonant frequency by calculating the self-inductance of each element.

[0014] According to one aspect of the present application, in step S1, the geometric parameters of the transmitting and receiving coils are determined based on the size constraints of the implanted device, wherein the geometric parameters include the coil diameter D. T / R The number of turns, copper wire diameter, and turn spacing are consistent, and the structural parameters of the transmitting and receiving coils are identical. To optimize the shape of the metamaterial element, mutual inductance models of single-turn circle-circle, circle-rectangle, and circle-regular hexagon under coaxial and lateral offset conditions are established based on the transmitting coil. The mutual inductance value M between the coils is calculated under different spatial positions. The circumcircle diameters of the rectangle and the regular hexagon are equal to D. T The shape of the basic element is determined by comparing and analyzing the rate of change of mutual inductance and the coupling strength between coils. The rate of change of mutual inductance is defined as:

[0015] Where M0 is the mutual inductance value when the coaxial alignment is complete, M offset The lateral offset distance between the two coils is D. T Based on the principle of minimizing ΔM and maximizing M0, the mutual inductance value at / 2 is used to determine the basic shapes of the building blocks used to construct the three-dimensional flexible hybrid magnetic metamaterial as regular hexagons and rectangles.

[0016] According to one aspect of the present application, the constraint ranges for the optimization parameters of the regular hexagonal primitives—side length a, line width w, gap s, and number of turns N—in step S2 are as follows:

[0017] Among them, wmax The size is constrained by the compactness of the basic structure, the quality factor, and the electromagnetic coupling requirements. min a max These are the minimum and maximum boundaries of the implantable device size, which depend on the external dimensions of the implantable device.

[0018] According to one aspect of the present application, the system transmission efficiency η, metamaterial quality factor Q, and metamaterial surface area S are calculated in step S3, and the above parameters are normalized to construct a comprehensive weighted evaluation function F(η, Q, S), the expression of which is:

[0019] Where α, β, and γ are weighting coefficients, and satisfy α + β + γ = 1; a multi-objective genetic algorithm is used to globally optimize the design parameters, thereby obtaining the optimal parameter combination that maximizes system transmission efficiency, maximizes metamaterial quality factor, and minimizes structural size. The expressions for the objective functions η, Q, and S are as follows:

[0020] Where ω = 2πf is the operating angular frequency, μ0 is the permeability of free space, and M is the mutual inductance between the regular hexagonal metamaterial and the transmitting and receiving coils. TR For the mutual inductance between the transmitting and receiving coils, R T Let L be the internal resistance of the transmitting coil, L be the self-inductance of the regular hexagonal element, A be the inner radius of the regular hexagonal element, and R be the equivalent resistance of the element, which includes the DC resistance component R. dc With AC resistance component R s +R p .

[0021] According to one aspect of the present application, the different array structures in step S4 include: single element, 3-element array, 7-element array, 9-element array, and 11-element array; the optimization indicators of the array structure include: transmission efficiency within the lateral offset range of 0-30mm and average magnetic flux density on the surface of the receiving coil. The number of array elements is determined based on the principle of maximizing transmission efficiency and average magnetic flux density on the surface of the receiving coil; and the influence of the relative spacing between the two arrays on the system performance is further analyzed through parametric scanning to determine the relative spacing between the two arrays. Finally, the length and width of the rectangular element are formed by a and the relative spacing between the two arrays.

[0022] This application belongs to the field of implantable wireless charging, and particularly relates to a three-dimensional flexible hybrid magnetic metamaterial structure and design method of magnetic field control. The purpose is to solve the problems of low efficiency, serious magnetic leakage, and poor alignment tolerance of traditional implantable wireless power transmission systems with two coil resonances, and the unstable transmission efficiency caused by the dynamic fluctuations of the human body. The beneficial effects are as follows: (1) By combining and arranging different magnetic permeability elements, the magnetic field is focused and guided, which enhances the magnetic coupling between the transmitting coil and the receiving coil, effectively improving the energy transmission efficiency of the implantable wireless charging system. When the receiving coil is offset, it can still maintain a high magnetic coupling effect, reduce efficiency fluctuations, and improve system stability. The side-mounted zero magnetic array reduces the potential impact of magnetic field leakage on surrounding tissues by suppressing the magnetic field in non-target areas, thus improving the safety of system application. (2) By introducing a multi-objective optimization method, transmission efficiency, basic quality factor and structural surface area are taken as the synergistic optimization objectives to achieve a balance between multiple performance indicators, avoid the performance imbalance caused by single indicator optimization, and enhance the global optimality and stability of the design results, and improve the scientificity and repeatability of structural parameter selection. Attached Figure Description

[0023] The accompanying drawings are incorporated in and form part of this specification. The drawings illustrate several embodiments of the present application and are used to further explain the technical solutions and principles of the present application. It should be understood that the drawings are merely illustrative and do not constitute an undue limitation on the scope of protection of this application.

[0024] Figure 1 This is a schematic diagram of the three-dimensional flexible hybrid magnetic metamaterial structure of the present invention;

[0025] Figure 2 This is a flowchart illustrating the optimization steps of the three-dimensional flexible hybrid magnetic metamaterial structural elements of the present invention.

[0026] Figure 3 This is a schematic diagram of the equivalent circuit of the implantable wireless power transmission system of the present invention;

[0027] Figure 4 This is a graph showing the equivalent magnetic permeability of the three-dimensional flexible hybrid magnetic metamaterial elements of the present invention.

[0028] Figure 5 This is a magnetic field distribution diagram of the system when the three-dimensional flexible hybrid magnetic metamaterial structure of the present invention is involved;

[0029] Figure 6 This is a comparison of efficiency and power with and without three-dimensional flexible hybrid magnetic metamaterials as a function of the receiving coil offset. Detailed Implementation

[0030] To enable those skilled in the art to more clearly and completely understand the technical solution of this application, the features and exemplary embodiments of various aspects of this application will be described in detail below, in conjunction with the appendix. Figures 1-6 The present application will be described in further detail below with reference to specific embodiments. It should be understood that the specific embodiments described herein are intended to explain the application only and not to limit it. Those skilled in the art will recognize that the present application can be implemented without some of these specific details. The following description of the embodiments is merely to provide a better understanding of the present application by illustrating examples.

[0031] This invention relates to implantable wireless charging systems, specifically to electromagnetic metamaterial structures used in implantable wireless charging systems.

[0032] On the one hand, the following combination Figures 1-6 The present invention provides a detailed description of a magnetic field-controlled three-dimensional flexible hybrid magnetic metamaterial structure and its design method, based on embodiments of this application.

[0033] See appendix Figure 1 The three-dimensional flexible hybrid magnetic metamaterial structure 0103 is coaxially arranged with the transmitting coil 0101 and the receiving coil 0102. 0104 is the side length *a* of a regular hexagonal element, 0105 is the linewidth *w* of a regular hexagonal element, 0106 is the turn gap *s* of a regular hexagonal element, and 0107 is the width *x* of a rectangular element. s 0108 represents the line width w of the rectangular primitive. s 0109 represents the rectangular element turn gap s s 0110 is the diameter D of the transmitting coil. T 0111 represents the diameter D of the receiving coil. R 0112 represents the distance D between the transmitting and receiving coils.

[0034] Specifically, the three-dimensional flexible hybrid magnetic metamaterial structure includes a -3, -2 permeability hybrid array, a -2, 0 permeability hybrid array, and a side-mounted 0 permeability array; the three-dimensional flexible hybrid magnetic metamaterial structure includes a -3, -2 permeability hybrid array, a -2, 0 permeability hybrid array, and a side-mounted 0 permeability array; the -3, -2 permeability hybrid array is composed of a central hexagonal -2 permeability element and six peripheral hexagonal -3 permeability elements; the -2, 0 permeability hybrid array is composed of a central hexagonal -2 permeability element and six peripheral hexagonal -3 permeability elements; the -2, 0 permeability hybrid array is composed of a central hexagonal -2 permeability element and a peripheral hexagonal -3 permeability element; the -2, 0 permeability hybrid array is composed of a central hexagonal -2 permeability element and a peripheral hexagonal -3 permeability element; the -3, -2 ... The system consists of a regular hexagonal zero-permeability element and six surrounding regular hexagonal -2-permeability elements; the two hybrid arrays achieve magnetic field focusing through a negative permeability gradient distribution; the side-mounted zero-permeability array consists of 18 rectangular zero-permeability elements, which are placed on both sides of the hybrid array to constrain the system's magnetic field; the regular hexagonal elements and rectangular elements are based on a polyimide flexible dielectric substrate, and are composed of an upper layer of spiral copper wire and a lower layer of lumped capacitor connected in series, with the permeability of the elements being adjusted by adjusting the lumped capacitor.

[0035] Furthermore, the three-dimensional flexible hybrid magnetic metamaterial structure is arranged coaxially with the transmitting and receiving coils, and the transmitting and receiving coils are spiral circular coils of the same size; the -3 and -2 permeability hybrid array and the -2 and 0 permeability hybrid array are arranged symmetrically along the axis of the transmitting and receiving coils, wherein the former is adjacent to the transmitting coil and the latter is adjacent to the receiving coil, and the two are connected by a side-mounted 0 permeability array to form the three-dimensional flexible hybrid magnetic metamaterial structure.

[0036] See appendix Figure 2 This invention presents a design method for three-dimensional flexible hybrid magnetic metamaterials with magnetic field control, and its optimization process steps are as follows: S1: Set the size and spacing of the transmitting and receiving coils and the system operating frequency f; measure the self-inductance L of the transmitting and receiving coils. T L R resistance R T R R Based on the changes in mutual inductance between planar spiral coils of different shapes under offset conditions, the basic shapes of the three-dimensional flexible hybrid magnetic metamaterial are determined to be regular hexagons and rectangles; S2: Evaluate the size of the regular hexagonal spiral coil and determine the constraints of its maximum side length a, line width w, gap s, and number of turns N; S3: Construct an equivalent circuit model, with system transmission efficiency, metamaterial quality factor and metamaterial surface area as objective functions, and use a multi-objective genetic algorithm for global optimization; S4: Based on the optimized metamaterial primitives, different array structures were constructed, the changes in system transmission performance under each array structure were analyzed, the 7-primary-unit array structure was determined, the coaxial arrangement spacing characteristics of the hybrid permeability dual arrays were further studied, and the side-mounted 0 permeability rectangular metamaterial primitive structure was designed according to the spatial arrangement and structural dimensions of the dual arrays. S5: Based on the relationship between magnetic permeability and refraction angle, a three-dimensional flexible hybrid magnetic metamaterial structure is constructed, and the lumped capacitance corresponding to the required magnetic permeability is determined at the target resonant frequency by calculating the self-inductance of each element.

[0037] Specifically, the planar coils of different shapes in S1 are circle-circle, circle-rectangle, and circle-hexagon, respectively, and the circumcircle diameters of the rectangle and the regular hexagon are equal to D. T The formula for calculating the mutual inductance between coils is as follows:

[0038] In the formula, r is the radius of the transmitting and receiving coils, d is the offset distance, D is the distance between the transmitting and receiving coils, and M is the distance between the transmitting and receiving coils. R-A M R-B M R-C M R-D For the mutual inductance between the sides of the square and the circle, M H-A M H-B M H-C M H-D M H-E M H-F For the mutual inductance of each side of a regular hexagon and the circle, r i This represents the distance from each side to the coil.

[0039] Furthermore, the shape of the basic element is determined by comparing and analyzing the mutual inductance change rate and coupling strength between the coils, wherein the mutual inductance change rate is defined as:

[0040] Where M0 is the mutual inductance value when the coaxial alignment is complete, M offset The lateral offset distance between the two coils is D. T Based on the principle of minimizing ΔM and maximizing M0, the mutual inductance value at / 2 is used to determine the basic shapes of the building blocks used to construct the three-dimensional flexible hybrid magnetic metamaterial as regular hexagons and rectangles.

[0041] See appendix Figure 3 The transmitting coil, the three-dimensional flexible hybrid magnetic metamaterial, and the receiving coil are analyzed as equivalent to an RLC series circuit, where 0301 is the AC source. 0302 is the transmitter current. 0303 is the equivalent resistance R of the transmitter. T 0304 is the transmitter tuning capacitor C. T 0305 is the equivalent inductance L of the transmitting coil. T 0306 represents the mutual inductance M between the transmitting coil and the mixed permeability array of -3 and -2. T-1 The mutual inductance M between the 0307 transmitting coil and the side-mounted zero permeability array T-s0308 is the mutual inductance M between the transmitting coil and the -2, 0 permeability hybrid array. T-2 0309 is the mutual inductance M between the transmitting coil and the receiving coil. TR 0310 represents the mutual inductance M between the -3 and -2 permeability hybrid array and the side-mounted 0 permeability array. 1-s 0311 represents the mutual inductance M between the -3, -2 permeability mixed array and the -2, 0 permeability mixed array. 1-2 0312 represents the mutual inductance M between the -3 and -2 permeability hybrid array and the receiving coil. 1-R 0313 represents the mutual inductance M between the side-mounted 0 permeability array and the mixed array of -2 and 0 permeability. s-2 0314 represents the mutual inductance M between the side-mounted zero-permeability array and the receiving coil. s-R 0315 represents the mutual inductance M between the -2, 0 permeability hybrid array and the receiving coil. 2-R 0316 is the equivalent inductance L of the receiving coil. R 0317 is the equivalent resistance R at the receiving end. R 0318 is the receiving end current. 0319 is the load resistor R L 0320 is a -2 permeability element tuning capacitor, 0321 is a regular hexagonal element equivalent inductance, 0322 is a -3 permeability element tuning capacitor, 0323 is a regular hexagonal element equivalent resistance, 0324 is a rectangular element equivalent inductance, 0325 is a rectangular element equivalent resistance, 0326 is a rectangular 0 permeability element tuning capacitor, and 0327 is a regular hexagonal 0 permeability element tuning capacitor.

[0042] Specifically, according to Kirchhoff's voltage law, the system satisfies the following equivalent relationship: Where Z represents impedance, the subscripts corresponding to each variable are T (representing the transmitting coil), 1 (representing a mixed array of -3 and -2 permeability), s (representing a side-mounted 0 permeability array), 2 (representing a mixed array of -2 and 0 permeability), R (representing the receiving coil), and M... 1i-sn M 1i-2i M 2i-sn For the mutual inductance between the three array elements, X I X2, X s for Equivalent impedance networks for three arrays.

[0043] Furthermore, the expression for the self-inductance L of the metamaterial element is:

[0044] Furthermore, the equivalent resistance R of the metamaterial element includes a DC resistance component R0. dc With AC resistance component R s +R pThe expression is as follows:

[0045] In the formula, ρ c Let σ be the resistivity of copper, σ be the conductivity of copper, and l be the total length of the coil. n Let t be the length of the nth turn of the coil. c δ represents the coil thickness, and δ represents the skin depth of the copper.

[0046] Furthermore, according to Match the compensation capacitors at the transmitter and receiver.

[0047] Furthermore, the mutual inductance M between the transmitting coil, the receiving coil, and the metamaterial element is calculated according to the following formula. TR M:

[0048] Where, N Tx l is the number of turns of the transmitting coil. an l bn l cn l dn l en l fn The distance d from the side of a regular hexagon to the circular coil is defined as d. an d bn d cn d dn d en d fn dr Tx =(-r Tx sinθ, cosθ, 0)dθ, dl an - dl fn The parameter expression is based on x = x i +t ( x i+1 - x i ), y = y i +t ( y i+1 - y i Solving for x, we get x i y i It refers to the vertex of a regular hexagon.

[0049] Furthermore, the constraints on the maximum side length a, line width w, gap s, and number of turns N of the regular hexagon are as follows:

[0050] Furthermore, the system transmission efficiency η, the metamaterial element quality factor Q, and the surface area S are expressed as follows:

[0051] in, Let a be the inner radius of the regular hexagonal element. avg The average diameter of the metamaterial element is given by ρ = (a - A) / (a ​​+ A), which is the filling factor determined by the diameter of its circumcircle.

[0052] Furthermore, η, Q, and S are normalized to construct a comprehensive weighted evaluation function F(η, Q, S), whose expression is:

[0053] Wherein, α, β and γ are weight coefficients, and satisfy α + β + γ = 1; a multi-objective genetic algorithm is used to globally optimize the design parameters, thereby obtaining the optimal parameter combination that maximizes system transmission efficiency, maximizes metamaterial quality factor and minimizes structural size.

[0054] See appendix Figure 4 It can be seen that each element achieves permeability of -3, -2, and 0 at 150kHz. At this time, the metamaterial has negative magnetic properties and can achieve the control of the system's magnetic field.

[0055] Specifically, through equivalent simplification and numerical extraction methods, the distribution of induced current and magnetic field in the metamaterial unit is analyzed, forming an equivalent magnetic response inside the structure. Combining this with the conservation relationship of magnetomotive force, the expressions for the equivalent permeability and lumped capacitance can be obtained as follows:

[0056] In the formula, ω0 is the resonant angular frequency of the metamaterial, and S i V is the area enclosed by the i-th spiral. unit The volume of the basic unit.

[0057] See appendix Figure 5 The magnetic field distribution of the system with and without three-dimensional flexible hybrid magnetic metamaterial was compared. The left side shows the magnetic flux density distribution in the plane of the receiving coil, and the right side shows the three-dimensional magnetic flux density distribution in the non-working area 80 mm away from the center, perpendicular to the plane of the transmitting coil. The results show that compared with the wireless charging system based on three-dimensional flexible hybrid magnetic metamaterial, the average magnetic flux density generated by the two coils in the receiving plane is lower and the magnetic field is more divergent. There is a large magnetic leakage in the non-working area. The intervention of three-dimensional flexible hybrid magnetic metamaterial effectively improves the magnetic flux density passing through the receiving coil and effectively suppresses magnetic field leakage in the non-working area.

[0058] See appendix Figure 6 It can be seen that as the offset distance of the receiving coil increases, the transmission efficiency and output power of the system with and without three-dimensional flexible hybrid magnetic metamaterials gradually decrease. However, the intervention of metamaterials effectively improves the transmission efficiency of the system and effectively improves the alignment tolerance of the system.

[0059] Table 1. Parameters of Basic Structure Parameter Regular hexagon (mm) Rectangle (mm) Parameter Regular hexagon (mm) Rectangle (mm) Substrate size 27 mm 27×4 Substrate thickness 0.8 0.2 Copper wire maximum side length 25.9 mm 26×3.2 Gap 0.1 0.1 Inner diameter 0.495 mm 23.2×0.4 Number of turns 13 3 Wire width 1.6 mm 0.4 Coil thickness 0.28 0.035

[0060] This application relates to a three-dimensional flexible hybrid magnetic metamaterial structure and design method for magnetic field control. The method uses the side length, linewidth, turn gap, and number of turns of the three-dimensional flexible hybrid magnetic metamaterial unit as decision variables, and optimizes its design with transmission efficiency, unit quality factor, and surface area as objective functions. By combining and arranging units with different permeabilities, the magnetic field of an implantable wireless charging system can be focused and constrained. The relationships between the system's magnetic field distribution and the changes in system transmission efficiency and output power with and without the three-dimensional flexible hybrid magnetic metamaterial as a function of the receiving coil movement are shown below. Figure 5 , 6 As shown, the intervention of three-dimensional flexible hybrid magnetic metamaterials significantly increased the magnetic flux density at the receiving plane, effectively suppressed the magnetic flux density diffusion of the two-coil system into non-target regions, improved the transmission efficiency and alignment tolerance of the system, and suppressed magnetic field leakage.

[0061] The above description, in conjunction with specific embodiments, provides a detailed account. However, the scope of protection of this invention is not limited thereto. This invention can be implemented in other specific forms without departing from its spirit or essential characteristics. The described embodiments are considered to be illustrative rather than restrictive in all respects. For example, the structural parameters of the three-dimensional flexible hybrid magnetic metamaterial structure and the combination and arrangement of different permeability primitives are not limited to those described in the embodiments; the application methods, placement positions, and control methods of the magnetic field distribution of the three-dimensional flexible hybrid magnetic metamaterial in implantable wireless charging systems are not limited to those described in the embodiments; the optimization design method with transmission efficiency, primitive quality factor, and surface area as objective functions, including the selection of objective functions, weight settings, and optimization algorithm forms, are not limited to those described in the embodiments.

[0062] Therefore, the scope of this invention is indicated by the appended claims rather than the foregoing description. All variations falling within the meaning and scope of equivalent technical solutions of the claims are included within its scope.

Claims

1. A magnetic field-controlled three-dimensional flexible hybrid magnetic metamaterial structure, characterized in that, The three-dimensional flexible hybrid magnetic metamaterial structure includes a -3 and -2 permeability hybrid array, a -2 and 0 permeability hybrid array, and a side-mounted 0 permeability array. The -3 and -2 permeability hybrid array consists of a central hexagonal -2 permeability element and six peripheral hexagonal -3 permeability elements. The -2 and 0 permeability hybrid array consists of a central hexagonal 0 permeability element and six peripheral hexagonal -2 permeability elements. The two hybrid arrays achieve magnetic field focusing through a negative permeability gradient distribution. The side-mounted 0 permeability array consists of 18 rectangular 0 permeability elements, which are placed on both sides of the hybrid arrays to constrain the system's magnetic field. The hexagonal and rectangular elements are based on a polyimide flexible dielectric substrate and are composed of an upper layer of spiral copper wire connected in series with a lower layer of lumped capacitance. The permeability of the elements is achieved by adjusting the lumped capacitance.

2. The magnetic field-controlled three-dimensional flexible hybrid magnetic metamaterial structure according to claim 1, characterized in that, The three-dimensional flexible hybrid magnetic metamaterial structure is arranged coaxially with the transmitting and receiving coils, which are spiral circular coils of the same size. The -3 and -2 permeability hybrid array and the -2 and 0 permeability hybrid array are arranged symmetrically along the axis of the transmitting and receiving coils, with the former adjacent to the transmitting coil and the latter adjacent to the receiving coil. The two are connected by a side-mounted 0 permeability array to form the three-dimensional flexible hybrid magnetic metamaterial structure.

3. A method for designing a magnetically modulated three-dimensional flexible hybrid magnetic metamaterial, comprising the magnetically modulated three-dimensional flexible hybrid magnetic metamaterial structure as described in any one of claims 1-2, characterized in that, Includes the following steps: S1: Set the size and spacing of the transmitting and receiving coils and the system operating frequency f; measure the self-inductance L of the transmitting and receiving coils. T L R resistance R T R R Based on the changes in mutual inductance between planar spiral coils of different shapes under offset conditions, the basic shapes of the three-dimensional flexible hybrid magnetic metamaterial are determined to be regular hexagons and rectangles; S2: Evaluate the size of the regular hexagonal spiral coil and determine the constraints of its maximum side length a, line width w, gap s, and number of turns N; S3: Construct an equivalent circuit model, with system transmission efficiency, metamaterial quality factor and metamaterial surface area as objective functions, and use a multi-objective genetic algorithm for global optimization; S4: Based on the optimized metamaterial primitives, different array structures were constructed, the changes in system transmission performance under each array structure were analyzed, the 7-primary-unit array structure was determined, and the coaxial arrangement spacing characteristics of the hybrid permeability dual arrays were further studied. Based on the spatial arrangement and structural dimensions of the dual arrays, a side-mounted 0-permeability rectangular metamaterial primitive structure was designed. S5: Based on the relationship between magnetic permeability and refraction angle, a three-dimensional flexible hybrid magnetic metamaterial structure is constructed, and the lumped capacitance corresponding to the required magnetic permeability is determined at the target resonant frequency by calculating the self-inductance of each element.

4. The design method according to claim 3, characterized in that, In step S1, the geometric parameters of the transmitting and receiving coils are determined based on the size constraints of the implanted device. These geometric parameters include the coil diameter D. T / R The number of turns, copper wire diameter, and turn spacing are consistent, and the structural parameters of the transmitting and receiving coils are identical. To optimize the shape of the metamaterial element, mutual inductance models of single-turn circle-circle, circle-rectangle, and circle-regular hexagon under coaxial and lateral offset conditions are established based on the transmitting coil. The mutual inductance value M between the coils is calculated under different spatial positions. The circumcircle diameters of the rectangle and the regular hexagon are equal to D. T The shape of the basic element is determined by comparing and analyzing the rate of change of mutual inductance and the coupling strength between coils. The rate of change of mutual inductance is defined as: Where M0 is the mutual inductance value when the coaxial alignment is complete, M offset The lateral offset distance between the two coils is D. T Based on the principle of minimizing ΔM and maximizing M0, the mutual inductance value at / 2 is used to determine the basic shapes of the building blocks used to construct the three-dimensional flexible hybrid magnetic metamaterial as regular hexagons and rectangles.

5. The design method according to claim 3, characterized in that, In step S2, the constraints on the side length a, line width w, gap s, and number of turns N of the regular hexagonal primitive optimization parameters are as follows: Among them, w max The size is constrained by the compactness of the basic structure, the quality factor, and the electromagnetic coupling requirements. min a max These are the minimum and maximum boundaries of the implantable device size, which depend on the external dimensions of the implantable device.

6. The design method according to claim 3, characterized in that, In step S3, the system transmission efficiency η, metamaterial quality factor Q, and metamaterial surface area S were calculated, and the above parameters were normalized to construct a comprehensive weighted evaluation function F(η, Q, S), the expression of which is: Where α, β, and γ are weighting coefficients, and satisfy α + β + γ = 1; a multi-objective genetic algorithm is used to globally optimize the design parameters, thereby obtaining the optimal parameter combination that maximizes system transmission efficiency, maximizes metamaterial quality factor, and minimizes structural size. The expressions for the objective functions η, Q, and S are as follows: Where ω = 2πf is the operating angular frequency, μ0 is the permeability of free space, and M is the mutual inductance between the regular hexagonal metamaterial and the transmitting and receiving coils. TR For the mutual inductance between the transmitting and receiving coils, R T Let L be the internal resistance of the transmitting coil, L be the self-inductance of the regular hexagonal element, A be the inner radius of the regular hexagonal element, and R be the equivalent resistance of the element, which includes the DC resistance component R. dc With AC resistance component R s +R p .

7. The design method according to claim 3, characterized in that, The different array structures in step S4 include: single element, 3-element array, 7-element array, 9-element array, and 11-element array; the optimization indicators of the array structure include: transmission efficiency within the 0-30mm lateral offset range and average magnetic flux density on the surface of the receiving coil. Based on the principle of maximizing transmission efficiency and average magnetic flux density on the surface of the receiving coil, the number of array elements is determined; and the influence of the relative spacing between the two arrays on the system performance is further analyzed through parametric scanning to determine the relative spacing between the two arrays. Finally, the length and width of the rectangular element are formed by 'a' and the relative spacing between the two arrays.

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