Design method of differential compensation electromagnetic metamaterial array

Abstract

The invention discloses a design method of a differential compensation electromagnetic metamaterial array, and belongs to the technical field of artificial electromagnetic materials. Firstly, basic structure parameters of the electromagnetic metamaterial are calculated according to a selected structure and resonance frequency, element simulation is carried out in Maxwell to obtain self-inductance of the electromagnetic metamaterial, and differential capacitance compensation is carried out according to the electromagnetic effect of elements. According to the invention, the low-frequency electromagnetic metamaterial is introduced into the magnetic coupling resonant wireless power transmission system, and through a differential compensation strategy, the overall resonant frequency deviation of the array is effectively suppressed, so that the system stably works at a target frequency and shows a stable negative magnetic conductivity characteristic; the problems of low transmission efficiency and poor stability under low frequency caused by coupling change between coils are solved.

Description

Technical Field

[0001] This invention belongs to the field of artificial electromagnetic materials technology, and relates to an electromagnetic metamaterial array for use in magnetically coupled resonant wireless power transmission systems, and more particularly to a metamaterial array structure and its design method that can compensate for inter-unit coupling effects to stabilize the operating frequency. Background Technology

[0002] Magnetic-coupled resonant wireless power transfer technology, as an efficient and convenient contactless power transfer method, shows broad application prospects in consumer electronics, medical implants, industrial robots, and wireless charging for electric vehicles. However, in practical deployments, its transmission performance is extremely sensitive to changes in distance and position. As the transmission distance between the transmitting and receiving coils increases, or if lateral, angular, or axial positional shifts occur, the system's coupling coefficient decreases significantly, leading to a weakening of the magnetic coupling strength and a sharp drop in transmission efficiency. This instability severely restricts the large-scale application of this technology in dynamic or complex environments.

[0003] To overcome these limitations, researchers have recently introduced electromagnetic metamaterials as an effective means to improve system performance. Electromagnetic metamaterials are functional materials with special artificial structures that enable the artificial manipulation of electromagnetic field distribution. When designed to possess negative permeability in a specific frequency band and strategically placed in the magnetic field region between the transmitting and receiving coils, the metamaterial can effectively converge and guide magnetic field lines, enhancing the magnetic flux connection between the two coils. This, to some extent, compensates for the weakening of coupling caused by increased distance or positional shift, significantly improving the system's energy transmission efficiency and effective transmission distance.

[0004] However, existing technologies still have significant drawbacks in the practical application of metamaterials. Due to the limited effective range of a single metamaterial unit, multiple units are typically arranged in a planar or three-dimensional array to cover a sufficient energy transfer area in practical systems. However, the mutual inductive coupling effect between units in such a densely packed array is often overlooked. The magnetic coupling between units significantly alters the equivalent inductance parameter of each metamaterial unit, causing the resonant frequency of the entire array to deviate from the resonant point designed for the unit in its isolated state. Consequently, at the actual operating frequency of the system, the metamaterial array fails to exhibit the expected negative permeability, its magnetic field focusing ability is greatly reduced, and its effect on improving system transmission performance is significantly weakened.

[0005] Invention patent CN113193666A proposes a novel dual-frequency negative permeability metamaterial plate for wireless power transmission, which changes the resonant frequency by adjusting the compensation capacitor or inductor. However, this scheme is mainly designed for a single plate and does not systematically analyze the impact of mutual inductive coupling between units in the metamaterial array on the equivalent inductance and resonant frequency shift. Utility model patent CN206059650U proposes an NFC antenna device and electronic device with adjustable self-resonant frequency, which achieves frequency correction by adjusting the resonant point through connecting capacitors, but does not address the coupling behavior between multiple resonant units. Utility model patent CN222776014U proposes a metamaterial unit and wireless power transmission system for wireless power transmission, providing a compact hexagonal open-loop metamaterial unit suitable for arraying, but similarly does not address the equivalent parameter changes and compensation methods caused by internal array coupling. Invention patent CN106340973A proposes an implantable wireless power transmission device based on metamaterials, which enhances magnetic field focusing through negative permeability metamaterials, but its scale is small and does not consider the coupling effect between units in a large-area array.

[0006] Current mainstream design methods either completely ignore the coupling effects between elements during modeling and optimization, or adopt an overall homogeneous approximation design, failing to provide effective analysis and compensation methods for coupling effects. This gap between the idealized design and the actual physical response leads to unstable performance of metamaterial arrays in practical applications, poor adaptability to transmission distance, positional changes, and operating frequency fluctuations, limiting their reliability and practicality in complex application scenarios.

[0007] The above background information is provided only to aid in understanding the inventive concept and technical solution of this invention. It does not necessarily belong to the prior art of this patent application. In the absence of clear evidence that the above information was disclosed on the filing date of this patent application, the above background information should not be used to evaluate the novelty and inventiveness of this application. Summary of the Invention

[0008] This invention addresses the shift in the resonant frequency of an electromagnetic metamaterial system caused by the coupling effect between basic elements. It provides a design method for electromagnetic metamaterial arrays that differentiates the coupling effect between units, accurately determines the compensation parameters, stabilizes the resonant frequency, and significantly improves the efficiency of wireless power transmission systems.

[0009] To achieve the above objectives, the present invention adopts the following technical solution:

[0010] A design method for a differentially compensated electromagnetic metamaterial array includes the following steps:

[0011] Step 1: Based on the equivalent circuit method, the electromagnetic metamaterial is simplified into an RLC model consisting of a resistor R, an inductor L, and a capacitor C. The structural parameters of the electromagnetic metamaterial are initially designed according to the target resonant frequency.

[0012] Step 2: Based on the structural parameters, establish a basic model in electromagnetic simulation software, extract its permeability and resonant frequency using the quality factor method, and optimize the basic structure.

[0013] Step 3: Establish the lumped parameter equivalent circuit model of the metamaterial array, and introduce the mutual inductance coefficient M to describe the electromagnetic coupling between the elements. ij ;

[0014] Step 4: Based on the model described in Step 3, simulate the array in the uncompensated state using electromagnetic field simulation software to obtain the equivalent inductance L of each element at different spatial locations. eff ;

[0015] Step 5, based on the target resonant frequency f0 and the equivalent inductance L eff Calculate the initial compensation capacitance required for the corresponding element to achieve resonance;

[0016] Step 6: With the optimization objective of the real part of the equivalent relative permeability of the array at the target frequency f0 being close to -1, the initial compensation capacitor obtained in step 5 is iteratively optimized to obtain the final differentiated compensation capacitor values ​​of the basic elements at different positions in the array, so that the entire array can work stably at the target frequency and obtain a stable negative permeability.

[0017] Furthermore, the electromagnetic metamaterial described in step 1 is simplified into an equivalent circuit model consisting of a resistor R, an inductor L, and a capacitor C, as shown in the following equation:

[0018]

[0019] in Where is the vacuum permeability; N is the number of turns of the copper cladding layer; The average diameter of the resonant unit. and These are the outer and inner diameters of the resonant unit, respectively. , , The linewidth of the copper layer, The turn spacing; For fill rate, ; , and These are the dielectric constants of air, substrate, and vacuum, respectively. The thickness of the copper cladding layer; The thickness is the substrate thickness. The length of the gap between copper layers. .

[0020] Furthermore, the electromagnetic metamaterial is a copper wire printed on both sides of the substrate and connected in series with a lumped capacitor through a metallized via.

[0021] Furthermore, the substrate adopts a square structure.

[0022] Furthermore, the substrate has a thickness h of 1 mm, a coil outer diameter D of 120 mm, a coil inner diameter d of 60.8 mm, a coil width w of 1.6 mm, a coil spacing s of 0.4 mm, a coil thickness t of 0.035 mm, and a coil number of turns N of 8.

[0023] Furthermore, the metamaterial units are arranged in a planar array, and the capacitance values ​​of the compensation capacitors connected in series to the metamaterial units located at different spatial positions in the array are configured to be different for each other, in order to compensate for the differences in equivalent parameters caused by the different degrees of electromagnetic coupling between the units.

[0024] Furthermore, the stronger the electromagnetic coupling between a metamaterial unit and its surrounding units, the greater the reduction in its equivalent inductance value relative to the inductance in the isolated state. The configuration rule for the compensation capacitor is: for unit positions where the reduction in equivalent inductance due to inter-unit coupling is greater, the value of the compensation capacitor should be larger, thereby ensuring that the resonant frequency of the unit circuit is stable at the design target value.

[0025] Furthermore, the array described in step 4 is divided into a central region, an edge region, and a corner region; wherein the compensation capacitor configured in the central region unit has a first capacitance value, the compensation capacitor configured in the corner region unit has a second capacitance value, and the compensation capacitor configured in the edge region unit has a third capacitance value, and the second capacitance value < the third capacitance value < the first capacitance value.

[0026] Furthermore, step 5 calculates the compensation capacitance of each element based on the coupling effect between metamaterial elements, including the following steps:

[0027] Step 5-1: Establish the lumped parameter equivalent circuit model of the metamaterial array, the model including the mutual inductance coefficient M used to characterize the coupling relationship between adjacent metamaterial units. ij This allows for a precise description of the electromagnetic interactions within the array;

[0028] Step 5-2: Based on the equivalent circuit model or through electromagnetic field simulation, obtain the equivalent inductance parameter L of the metamaterial unit at different locations in the array under uncompensated conditions. eff ;

[0029] Step 5-3: Based on the target resonant frequency and the equivalent inductance parameters obtained in step S2, calculate the initial compensation capacitance value required to make each unit at each position resonate.

[0030] Step 5-4: Using the real part of the equivalent permeability of the array at the target frequency as the optimization target, iteratively optimize the initial compensation capacitance value obtained in step 5-3, and finally determine the optimal compensation capacitance value of the metamaterial unit at different positions in the array.

[0031] Furthermore, the real part of the equivalent relative permeability of the optimization target at the target frequency is made as close as possible to -1.

[0032] Compared with the prior art, the present invention has the following technical advantages:

[0033] (1) By configuring different compensation capacitors for units at different positions, the present invention actively cancels the changes in equivalent parameters caused by the coupling between units, so that the overall resonant frequency of the array is accurately stabilized at the system operating frequency, thus solving the detuning problem.

[0034] (2) Significant performance improvement: The array of the present invention can provide a stable and strong negative permeability response at the system operating frequency, effectively reconstruct the magnetic field distribution, and concentrate more magnetic flux to the receiving end, thereby greatly improving the transmission efficiency of the system.

[0035] (3) By introducing low-frequency electromagnetic metamaterials into the magnetically coupled resonant wireless power transmission system, the present invention effectively suppresses the overall resonant frequency shift of the array through a differentiated compensation strategy, so that it can work stably at the target frequency and exhibit stable negative permeability characteristics, thus solving the problems of low transmission efficiency and poor stability at low frequencies caused by the coupling changes between coils. Attached Figure Description

[0036] Figure 1 Flowchart for the design of electromagnetic metamaterial units.

[0037] Figure 2 This is a three-dimensional structural diagram of the metamaterial unit in an embodiment of the present invention.

[0038] Figure 3 A schematic diagram showing the configuration of different compensation capacitors for different regional units.

[0039] Figure 4 The image shows the electromagnetic parameters of the electromagnetic metamaterial. Detailed Implementation

[0040] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. It should be noted that the following embodiments are for illustrative purposes only and do not constitute a limitation on the scope of protection of the present invention.

[0041] See Figure 1 A design method for a differentiated compensation electromagnetic metamaterial array includes the following steps:

[0042] Step 1: Based on the equivalent circuit method, the electromagnetic metamaterial element is equivalent to an RLC model composed of a resistor R, an inductor L, and a capacitor C connected in series. The structural parameters of the element are initially determined according to the target resonant frequency.

[0043] The electromagnetic metamaterial can be simplified into an equivalent circuit model consisting of a resistor R, an inductor L, and a capacitor C, as shown in the following equation:

[0044]

[0045] in Where is the vacuum permeability; N is the number of turns of the copper cladding layer; The average diameter of the resonant unit. and These are the outer and inner diameters of the resonant unit, respectively. , , The linewidth of the copper layer, The turn spacing; For fill rate, ; , and These are the dielectric constants of air, substrate, and vacuum, respectively. The thickness of the copper cladding layer; The thickness is the substrate thickness. The length of the gap between copper layers. ;

[0046] Step 2: Based on the structural parameters, establish a basic model in HFSS software, extract its permeability and resonant frequency using the quality factor method, and optimize the basic structure.

[0047] Step 3: Establish the lumped parameter equivalent circuit model of the metamaterial array, and introduce the mutual inductance coefficient M to describe the electromagnetic coupling between the elements. ij ;

[0048] Step 4: Based on the model described in Step 3 or in electromagnetic field simulation software, simulate the array in the uncompensated state in Maxwell software to obtain the equivalent inductance L of each element at different spatial locations. eff ;

[0049] The metamaterial units are arranged in a planar array, and the capacitance values ​​of the compensation capacitors connected in series to the metamaterial units located at different spatial positions in the array are configured to be different for each other, so as to compensate for the difference in equivalent parameters caused by the different electromagnetic coupling between the units.

[0050] The stronger the electromagnetic coupling between a metamaterial unit and its surrounding units, the greater the reduction in its equivalent inductance value relative to the inductance in the isolated state. The configuration rule of the compensation capacitor is: for the unit position where the reduction in its equivalent inductance due to inter-unit coupling is greater, the value of the compensation capacitor configured is larger, so as to ensure that the resonant frequency of the unit circuit is stable at the design target value.

[0051] The basic metamaterial unit of the present invention includes an FR4 dielectric substrate, on which planar square spiral copper metal coils are printed respectively on the front and back sides. The substrate has a thickness h of 1 mm, an outer diameter D of 120 mm, an inner diameter d of 60.8 mm, a width w of 1.6 mm, a spacing s of 0.4 mm, a thickness t of 0.035 mm, and a number of turns N of 8.

[0052] The ends of the coils on both sides are connected by metallized vias to form a continuous inductor structure. A lumped capacitor is also connected in series in this circuit; this capacitor is the key component for realizing the compensation function described in this invention.

[0053] Step 5, based on the target resonant frequency f0 and the equivalent inductance L eff Calculate the initial compensation capacitance required for the corresponding element to achieve resonance;

[0054] The compensation capacitance of each element is calculated based on the coupling effect between metamaterial elements, including the following steps:

[0055] Step 5-1: Establish the lumped parameter equivalent circuit model of the metamaterial array, the model including the mutual inductance coefficient M used to characterize the coupling relationship between adjacent metamaterial units. ij This allows for a precise description of the electromagnetic interactions within the array;

[0056] Step 5-2: Based on the equivalent circuit model or through electromagnetic field simulation, obtain the equivalent inductance parameter L of the metamaterial unit at different locations in the array under uncompensated conditions. eff ;

[0057] Step 5-3: Based on the target resonant frequency and the equivalent inductance parameters obtained in step S2, calculate the initial compensation capacitance value required to make each unit at each position resonate.

[0058] Step 5-4: Using the real part of the equivalent permeability of the array at the target frequency as the optimization target, iteratively optimize the initial compensation capacitor value obtained in step 5-3, and finally determine the optimal compensation capacitor value of the metamaterial unit at different positions in the array.

[0059] The real part of the equivalent relative permeability of the optimization target at the target frequency is made as close as possible to -1;

[0060] Step 6: With the optimization objective of the real part of the equivalent relative permeability of the array at the target frequency f0 being close to -1, the initial compensation capacitor obtained in step 5 is iteratively optimized to obtain the final differentiated compensation capacitor values ​​of the basic elements at different positions in the array, so that the entire array can work stably at the target frequency and obtain a stable negative permeability.

[0061] See Figure 2 and Figure 3 Let's take a 3×3 array as an example. This array can be clearly divided into three types of regions: a central region containing one cell; an edge region containing four cells; and a corner region containing four cells. According to the core concept of this invention, since the central region cells are surrounded by the most adjacent cells, their equivalent inductance is reduced the most due to coupling, thus requiring the smallest compensation capacitor (first capacitance value). The edge region cells require the next largest compensation capacitor (second capacitance value). The corner region cells are least affected by coupling, therefore requiring the largest compensation capacitor (third capacitance value), satisfying the condition that second capacitance value < third capacitance value < first capacitance value. This differentiated configuration of increasing capacitance values ​​from "center-edge-corner" effectively compensates for coupling differences caused by different locations, enabling the entire array to work collaboratively at the target frequency.

[0062] Each unit is equivalent to a series RLC circuit, and the mutual inductance M between adjacent units is introduced to establish the impedance matrix equation for the entire array. The impact of coupling on the equivalent inductance is theoretically analyzed. An initial array model with all units temporarily having the same capacitance is established using electromagnetic simulation software. Through simulation, the average equivalent inductance values ​​of the center unit, typical edge units, and typical corner units under coupled conditions are extracted. Based on the target resonant frequency and the LC resonance formula... The initial compensation capacitance values ​​for the three types of elements were calculated separately. These calculated initial capacitance values ​​were then assigned to the corresponding elements in the simulation model. Frequency domain simulation was performed to extract the S-parameters of the array and inversely calculate its equivalent relative permeability curve. The value of the curve at the target resonant frequency was observed. .by To achieve the desired result, the three types of capacitance values ​​were fine-tuned and iterated repeatedly until the requirements were met, ultimately yielding the optimized combination of capacitance values.

[0063] See Figure 4 The permeability of the electromagnetic metamaterial in this case was calculated. The vertical axis represents the value of the permeability of the electromagnetic metamaterial, and the horizontal axis represents the frequency range. When the permeability is -1, the frequency is approximately 85kHz, which meets the target design performance.

[0064] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A design method for a differentiated compensation electromagnetic metamaterial array, characterized in that, Includes the following steps: Step 1: Based on the equivalent circuit method, the electromagnetic metamaterial element is equivalent to an RLC model composed of a resistor R, an inductor L, and a capacitor C connected in series. The structural parameters of the element are initially determined according to the target resonant frequency. Step 2: Based on the structural parameters, establish a basic model in electromagnetic simulation software, extract its permeability and resonant frequency using the quality factor method, and optimize the basic structure. Step 3: Establish the lumped parameter equivalent circuit model of the metamaterial array, and introduce the mutual inductance coefficient M to describe the electromagnetic coupling between the elements. ij ; Step 4: Based on the model described in Step 3 or in electromagnetic field simulation software, simulate the array in the uncompensated state to obtain the equivalent inductance L of each element at different spatial locations. eff ; Step 5, based on the target resonant frequency f0 and the equivalent inductance L eff Calculate the initial compensation capacitance required for the corresponding element to achieve resonance; Step 6: With the optimization objective of the real part of the equivalent relative permeability of the array at the target frequency f0 being close to -1, the initial compensation capacitor obtained in step 5 is iteratively optimized to obtain the final differentiated compensation capacitor values ​​of the basic elements at different positions in the array, so that the entire array can work stably at the target frequency and obtain a stable negative permeability.

2. The design method for the differentiated compensation electromagnetic metamaterial array according to claim 1, characterized in that, The electromagnetic metamaterial described in step 1 can be simplified into an equivalent circuit model consisting of a resistor R, an inductor L, and a capacitor C, as shown in the following equation: ； in Where is the vacuum permeability; N is the number of turns of the copper cladding layer; The average diameter of the resonant unit. and These are the outer and inner diameters of the resonant unit, respectively. , , The linewidth of the copper layer, The turn spacing; For fill rate, ; , and These are the dielectric constants of air, substrate, and vacuum, respectively. The thickness of the copper cladding layer; The thickness is the substrate thickness. The length of the gap between copper layers. .

3. The design method for differentiated compensation electromagnetic metamaterial arrays according to claim 2, characterized in that, The electromagnetic metamaterial is a copper wire printed on both sides of a substrate and connected in series with a lumped capacitor through metallized vias.

4. The design method for differentiated compensation electromagnetic metamaterial arrays according to claim 3, characterized in that, The substrate has a square structure, and multiple elements are arranged in a planar array.

5. The design method for differentiated compensation electromagnetic metamaterial arrays according to claim 4, characterized in that, The substrate has a thickness h of 1 mm, an outer diameter D of 120 mm, an inner diameter d of 60.8 mm, a width w of 1.6 mm, a spacing s of 0.4 mm, a thickness t of 0.035 mm, and a number of turns N of 8.

6. The design method for differentiated compensation electromagnetic metamaterial arrays according to claim 1, characterized in that, The metamaterial units are arranged in a planar array, and the capacitance values ​​of the compensation capacitors connected in series to the metamaterial units located at different spatial positions in the array are configured to be different for each other, in order to compensate for the differences in equivalent parameters caused by the different degrees of electromagnetic coupling between the units.

7. The design method for differentiated compensation electromagnetic metamaterial arrays according to claim 6, characterized in that, The stronger the electromagnetic coupling between a metamaterial unit and its surrounding units, the greater the reduction in its equivalent inductance value relative to the inductance in the isolated state. The configuration rule for the compensation capacitor is: for the unit position where the reduction in its equivalent inductance due to inter-unit coupling is greater, the value of the compensation capacitor should be larger, so as to ensure that the resonant frequency of the unit circuit is stable at the design target value.

8. The design method for differentiated compensation electromagnetic metamaterial arrays according to claim 1, characterized in that, In step 4, the array is divided into a central region, an edge region, and a corner region; wherein, the compensation capacitor configured in the central region unit has a first capacitance value, the compensation capacitor configured in the corner region unit has a second capacitance value, and the compensation capacitor configured in the edge region unit has a third capacitance value, and the second capacitance value < the third capacitance value < the first capacitance value.

9. The design method for differentiated compensation electromagnetic metamaterial arrays according to claim 1, characterized in that, Step 5 calculates the compensation capacitance of each element based on the coupling effect between metamaterial elements, including the following steps: Step 5-1: Establish the lumped parameter equivalent circuit model of the metamaterial array, the model including the mutual inductance coefficient M used to characterize the coupling relationship between adjacent metamaterial units. ij This allows for a precise description of the electromagnetic interactions within the array; Step 5-2: Based on the equivalent circuit model or through electromagnetic field simulation, obtain the equivalent inductance parameter L of the metamaterial unit at different locations in the array under uncompensated conditions. eff ; Step 5-3: Based on the target resonant frequency and the equivalent inductance parameters obtained in step S2, calculate the initial compensation capacitance value required to make each unit at each position resonate. Step 5-4: Using the real part of the equivalent permeability of the array at the target frequency as the optimization target, iteratively optimize the initial compensation capacitance value obtained in step 5-3, and finally determine the optimal compensation capacitance value of the metamaterial unit at different positions in the array.

10. The design method for differentiated compensation electromagnetic metamaterial arrays according to claim 9, characterized in that, The goal is to make the real part of the equivalent relative permeability of the optimization target at the target frequency as close as possible to -1.

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