A low-frequency receiving antenna based on a gradient metamaterial with critical coupling

Abstract

This invention relates to a low-frequency receiving antenna based on a gradient metamaterial with critical coupling, belonging to the field of low-frequency magnetic induction communication technology. The low-frequency receiving antenna includes: a receiving coil connected in series with a capacitor and connected to a receiver load via the capacitor; and a gradient metamaterial composed of multiple concentric resonant units with size gradients, each resonant unit consisting of a coil and a capacitor connected in series to form an independent resonant circuit. The receiving coil and the gradient metamaterial are concentrically nested, with the receiving coil located on the innermost side. This invention's low-frequency receiving antenna achieves matching between the antenna output impedance and the receiver load by precisely controlling the coupling strength between the gradient metamaterial and the receiving coil, as well as the capacitor configuration parameters. Simultaneously, the wide spacing between adjacent coils significantly reduces proximity losses. With the optimal combination of impedance matching and loss performance, the antenna reaches a critical coupling state. Combined with the increasing equivalent permeability distribution from the outside to the inside formed by the gradient metamaterial, it effectively converges low-frequency magnetic fields, improving the pickup capability of weak low-frequency electromagnetic signals. This invention maintains a compact size for the low-frequency antenna while possessing high receiving sensitivity, making it suitable for low-frequency magnetic field communication and detection in complex environments such as underwater and underground.

Description

Technical Field

[0001] This invention belongs to the field of low-frequency magnetic induction communication technology, and particularly relates to a low-frequency receiving antenna based on a gradient metamaterial with critical coupling. Background Technology

[0002] Magnetic induction communication based on coil coupling is a commonly used cross-medium wireless communication technology. To achieve high power density and data transmission rates, current research on magnetic induction communication largely operates in the MHz band. However, magnetic fields in the MHz band still exhibit significant eddy current losses and rapid signal attenuation in conductive media such as seawater and building structures. To extend communication distances in lossy media, the operating frequency needs to be extended to lower frequencies (below 300 kHz). Due to its strong penetration and low attenuation characteristics, low-frequency communication has become a key technology in fields such as underwater wireless communication, ground-penetrating communication, and geophysical exploration.

[0003] In low-frequency magnetic induction communication, receiving antennas typically employ multi-turn coils connected in series with capacitors to form a resonant circuit. By adjusting the capacitor, the coil resonates at the operating frequency to compensate for the coil's inductive reactance and achieve frequency-selective reception. However, when the antenna size is much smaller than the wavelength, this design faces two key challenges. First, the extremely low coil resistance leads to a severe mismatch between the antenna output impedance and the standard 50 Ω receiver impedance. Using additional matching devices introduces further insertion loss and thermal noise. Second, the compact and dense arrangement of the coil wires causes significant proximity loss, further increasing the coil's equivalent resistance and reducing the quality factor of the resonant circuit. Therefore, there is a need to research a low-frequency receiving antenna that balances impedance matching and low loss to meet the application requirements of underwater and underground cross-medium communication. Summary of the Invention

[0004] The purpose of this invention is to provide a low-frequency receiving antenna based on a gradient metamaterial with critical coupling, solving the problems of impedance mismatch and high proximity loss in low-frequency magnetic induction receiving antennas with small electrical dimensions. This antenna offers advantages such as compact structure, high sensitivity, and no need for an additional matching network. To achieve the above objective, this invention provides the following solution:

[0005] The present invention provides a low-frequency antenna based on critical coupling and a gradient metamaterial, comprising a receiving coil and a gradient metamaterial. The receiving coil is connected in series with a capacitor, which is then connected to a receiver load to form a closed loop. The gradient metamaterial is composed of multiple concentric resonant units with a size gradient, each resonant unit consisting of a coil and a capacitor connected in series to form an independent resonant circuit. The receiving coil is concentrically nested with the gradient metamaterial, with the receiving coil located at the innermost edge. The coil radii of the receiving coil and all resonant units increase from the inside out by a predetermined arithmetic progression, forming a size gradient; this size gradient allows for a wide spacing between adjacent coils, reducing proximity losses between coils.

[0006] In its working principle, by configuring the value of the series capacitor of the receiving coil, the imaginary part of the antenna output impedance can be changed, which is used for imaginary part adjustment of impedance matching. By configuring the values ​​of the capacitors in each resonant unit, the overall resonant frequency of the gradient metamaterial can be adjusted. By adjusting the size gradient value, the coupling strength between the gradient metamaterial and the receiving coil can be controlled, thereby changing the real part of the antenna output impedance, which is used for real part adjustment of impedance matching. By adjusting the size gradient and the parameters of each capacitor, the antenna can obtain the maximum size gradient under the premise of satisfying impedance matching, thereby achieving the minimum proximity loss and reaching the optimal combination of impedance matching and loss performance. At this time, the antenna enters the critical coupling state. In the critical coupling state, the gradient metamaterial forms an equivalent permeability distribution that increases from the outside to the inside, effectively converging low-frequency magnetic fields and enhancing the receiving coil's ability to pick up weak signals.

[0007] The low-frequency antenna based on critical coupling using gradient metamaterials proposed in this invention has the following advantages:

[0008] 1. No additional matching network is required. By adjusting the size gradient and capacitance parameters, a good match between the antenna output impedance and the receiver load can be achieved, avoiding additional insertion loss and thermal noise.

[0009] 2. The wide-spacing structure formed by the size gradient significantly reduces the adjacent losses between coils and improves the quality factor of the resonant circuit;

[0010] 3. Under critical coupling conditions, gradient metamaterials form an increasing equivalent permeability distribution, effectively concentrating low-frequency magnetic fields and further improving receiving sensitivity;

[0011] 4. The antenna has a compact overall structure and high sensitivity, making it suitable for applications such as underwater communication and ground-penetrating communication. Attached Figure Description

[0012] Figure 1 Schematic diagram of a gradient metamaterial low-frequency receiving antenna structure based on critical coupling;

[0013] Figure 2 Equivalent circuit diagram of a gradient metamaterial low-frequency receiving antenna based on critical coupling;

[0014] Figure 3 Received voltage simulation results diagram;

[0015] Figure 4 Antenna output impedance diagram;

[0016] Figure 5 The result of the receiver performance test is shown in the figure.

[0017] Explanation of reference numerals in the attached diagram: 100, receiving coil; 101, capacitor; 102, receiver; 200, resonant unit coil; 201, resonant unit capacitor. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described below in conjunction with the accompanying drawings and embodiments. The present invention includes, but is not limited to, the following embodiments.

[0019] Example 1:

[0020] This embodiment provides a gradient metamaterial low-frequency receiving antenna based on critical coupling to illustrate the basic structure and impedance matching mechanism of the antenna.

[0021] like Figure 1 As shown, the gradient metamaterial low-frequency receiving antenna based on critical coupling proposed in this invention consists of a receiving coil 100 and a gradient metamaterial. The figure illustrates this using three resonant units as an example. A capacitor 101 is connected in series with the receiving coil 100 and then connected to the receiver 102 via the capacitor 101. The gradient metamaterial consists of multiple concentric resonant units with a size gradient. Each resonant unit is an independent resonant circuit formed by a coil 200 and a capacitor 201 connected in series. The receiving coil 100 and the gradient metamaterial are concentrically nested, with the receiving coil 100 located on the innermost side. The radii of the receiving coil 100 and all the resonant unit coils 200 increase from the inside out by a preset equal arithmetic progression, forming a size gradient.

[0022] The equivalent circuit diagram of a gradient metamaterial low-frequency receiving antenna based on critical coupling is shown below. Figure 2 As shown. The receiving coil circuit and each resonant unit circuit are coupled through mutual inductance, forming a multi-coil coupled system. In the receiving coil circuit, L0 is the self-inductance of the receiving coil, R0 is the resistance of the receiving coil, C0 is the series capacitance, and R... L The receiver load resistance is given. For the gradient metamaterial section, the i-th resonant unit (i=1, 2, ..., n) is determined by the coil's self-inductance L. i Resistance R i and series capacitor C i This forms a resonant circuit. Magnetic coupling exists between the coils of each resonant unit and the receiving coil; the mutual inductance is denoted as M. 0i (i=1, 2, ..., n); magnetic coupling also exists between any two resonant units, and the mutual inductance is denoted as M. ij (i, j = 1, 2, ..., n; i ≠ j). The values ​​of each mutual inductance are determined by the spatial relationship between the coils. In the concentric nested structure of this embodiment, the mutual inductance M... 0i and M ij It decreases as the size gradient Δr increases. By reasonably setting the size gradient, the mutual inductance values ​​can be precisely controlled, thereby adjusting the coupling strength between each resonant unit and the receiving coil, as well as the coupling strength between each resonant unit and each other.

[0023] For this multi-unit coupled system, direct solution is quite complex. To facilitate the explanation of the basic principle of impedance matching and critical coupling in this invention, we first analyze the simplified case of a single resonant unit (n=1), in which the system contains only a receiving coil and one resonant unit. For the desired operating frequency ω0 and a given coil geometry, the adjustable parameters in the circuit are capacitors C0 and C1. The antenna output impedance can be expressed as:

[0024] (1)

[0025] Where Z0 and Z1 are functions of C0 and C1 respectively: Z0 = R0 + jωL0 + 1 / (jωC0), Z1 = R1 + jωL1 + 1 / (jωC1). As can be seen from equation (1), capacitor C0 adjusts the imaginary part of the antenna output impedance by changing the imaginary part of Z0, so that it is canceled at the operating frequency f0; capacitor C1 adjusts the self-resonant frequency of the resonant unit by changing Z1, so that the entire coupling system presents a matched real part of impedance at f0. By configuring capacitors C0 and C1 to the optimized values ​​respectively, impedance matching can be achieved simultaneously at the target operating frequency.

[0026] Besides impedance matching, proximity loss also affects the antenna's receiving performance. Coil losses include the conduction loss of the conductor itself and proximity loss between adjacent coils, the latter caused by eddy currents induced by the coupling of the coil magnetic fields. In the equivalent circuit, proximity loss manifests as an additional induced resistance, and this additional resistance increases with the smaller the coil spacing. The antenna of this invention employs a concentric nested structure, with each coil arranged coaxially, and the radial dimension determines the coil spacing. In this embodiment, the radius r1 of the resonant unit coil is kept constant, while the radius r0 of the receiving coil is reduced, resulting in a radial dimension difference Δr = r1 - r0. This Δr is the specific manifestation of the aforementioned dimension gradient. Increasing Δr can increase the radial distance between coils without changing the overall antenna size, thereby reducing proximity loss. However, increasing Δr also brings another effect: increased magnetic flux leakage between the receiving coil and the resonant unit, leading to increased mutual inductance M... 01 Decrease. From equation (1), it can be seen that the peak real part of the antenna output impedance is reduced by ω. 2 M 01 2 / R1 determines this value, which varies with M. 01 As Δr decreases, the peak real part of the antenna output impedance gradually decreases, causing the antenna to transition from an impedance-matched state to a mismatched state. During this transition, there exists a critical point where the peak real part of the antenna output impedance is exactly equal to the load impedance R. L ,satisfy:

[0027] (2)

[0028] Therefore, by adjusting the size gradient Δr, the coupling strength between the receiving coil and the resonant unit can be controlled, thereby changing the real part of the antenna output impedance. When the value of Δr makes the coupling reach the critical point (2), the antenna enters the critical coupling state. In this state, the value of Δr is the maximum size gradient that can be allowed under the premise of ensuring impedance matching, corresponding to the minimum proximity loss. The antenna thus obtains the optimal combination of impedance matching and loss performance.

[0029] Example 2:

[0030] This embodiment provides a gradient metamaterial low-frequency receiving antenna based on critical coupling, which is used to illustrate the multi-element gradient design and receiving performance of the antenna.

[0031] The single-unit structure in Example 1 is extended to a gradient metamaterial composed of n resonant units. In a multi-unit system, the responses generated by each resonant unit under external magnetic field excitation act on the receiving coil through mutual inductance coupling. Its impedance adjustment mechanism is completely consistent with the single-unit case: the series capacitor C0 of the receiving coil adjusts the imaginary part of the antenna output impedance, causing it to cancel out at f0; the capacitors C of each resonant unit... i The function of (i=1, 2, ..., n) is to adjust the overall resonant frequency of the gradient metamaterial, and in conjunction with the size gradient to control the coupling strength, thereby presenting the desired real part of the impedance at f0. When entering the critical coupling state, the real part of the antenna output impedance reaches its peak at the operating frequency and is matched with the load impedance. To verify the performance advantages of the multi-element gradient metamaterial antenna, a finite element electromagnetic simulation is performed with n=3 as an example. The antenna is optimized to the critical coupling state, at which point the parameters are: the radius of the receiving coil r0=8.4 cm, the radii of the three resonant coils from the inside out are r1=10.6 cm, r2=12.8 cm, and r3=15.0 cm, forming a size gradient Δr=2.2 cm; the number of turns of each coil is N=10, the wire diameter is 1.5 mm, and the turn spacing is 0.5 mm. At this point, the receiving coil has a self-inductance L0 = 26.94 μH, a resistance R0 = 0.101 Ω, and a series capacitance C0 = 500 nF; the self-inductances of each resonant unit are L1 = 40.08 μH, L2 = 54.11 μH, and L3 = 68.85 μH, respectively; the resistances are R1 = 0.145 Ω, R2 = 0.185 Ω, and R3 = 0.220 Ω, respectively; and the series capacitances are C1 = 365 nF, C2 = 267 nF, and C3 = 246 nF, respectively; the mutual inductance between the receiving coil and each resonant unit is M, respectively. 01 =12.72 μH, M 02 =8.76 μH, M 03 =7.70 μH, the mutual inductance between each resonant unit is M respectively. 12 =21.32 μH, M13 =15.56 μH, M 23 =29.72 μH; operating frequency f0=30kHz, load resistance R L =50 Ω. Figure 3 The receiving voltage comparison curves of a multi-element (n=3) gradient metamaterial antenna and a single-element (n=1) antenna under critical coupling are presented. At the operating frequency f0=30 kHz, the receiving voltage of the n=3 structure is significantly higher than that of the n=1 case, indicating that increasing the number of resonant elements can effectively enhance the response of the gradient metamaterial to the magnetic field and improve the receiving sensitivity. Figure 4 The output impedance curve of the gradient metamaterial antenna under critical coupling conditions is presented. At the operating frequency, the real part of the impedance is equal to 50 Ω and the imaginary part is zero, indicating good impedance matching. Furthermore, the impedance matching frequency is equal to the peak frequency of the real part of the impedance, satisfying the critical coupling characteristics.

[0032] Under critical coupling conditions, the gradient metamaterial exhibits an equivalent permeability distribution that increases from the outside in. According to metamaterial theory, the resonant unit can be considered a medium, and its electromagnetic properties can be expressed by its equivalent permeability μ. eq Quantitative description. For the concentric gradient structure with n=3 in this embodiment, the equivalent permeability of a certain layer is the sum of the equivalent magnetization current contributions of that layer and all the outermost resonant units. Simulation extraction of the current in each resonant unit yields the calculated permeability amplitudes of the three equivalent media layers as follows: outermost layer |μ eq |=226.9, intermediate layer|μ eq |=426.8, innermost layer|μ eq |=561.3. This gradient permeability distribution, increasing from the outside in, amplifies the low-frequency magnetic field layer by layer within the metamaterial and guides it to the innermost receiving coil, enhancing the antenna's ability to pick up weak magnetic signals. Simultaneously, the permeability phase of all three layers is 90° at the operating frequency, indicating that each layer resonates at the same frequency without frequency detuning, and the metamaterial as a whole exhibits a unified electromagnetic response.

[0033] Receiver performance testing is a crucial step in evaluating the actual working capability of an antenna. The main indicators examined include magnetic field sensitivity (S0). m Detection limit LOD and equivalent magnetic noise N mBased on the optimized parameters, a prototype gradient metamaterial low-frequency receiving antenna with n=3 elements was fabricated. All coils were wound with 1.5 mm diameter enameled copper wire, and the coils were precisely positioned and fixed using a 3D-printed plastic skeleton to ensure concentricity and spacing between the coils. Testing was conducted in a low-magnetic-noise laboratory environment. The transmitting end generated a sinusoidal signal at its operating frequency, which was then amplified and fed into the transmitting coil, radiating a low-frequency magnetic field. The gradient metamaterial antenna under test received this magnetic field signal and converted it into an electrical signal. A lock-in amplifier was used at the receiving end to extract the weak signal. Figure 5 The curves showing the variation of received voltage with applied magnetic field strength are presented. The measured data points exhibit a clear linear relationship, and the slope obtained from the linear fitting is the antenna's magnetic field sensitivity S. m =3.728×10 6 V / T. Based on the measured noise voltage of 142.22 nV, the detection limit LOD of the antenna is obtained as 38.15 fT. Under the condition of turning off magnetic field excitation, the equivalent magnetic noise spectral density of the antenna is measured to be 88.2 nV / Hz. 1 / 2 The corresponding equivalent magnetic noise N m =23.66 fT / Hz 1 / 2 .

[0034] This embodiment demonstrates that the gradient metamaterial low-frequency receiving antenna based on critical coupling proposed in this invention has three synergistic advantages: First, the capacitor configuration enables a good match between the antenna output impedance and the load impedance; second, the wide-spacing structure formed by the size gradient effectively reduces proximity losses between coils; and third, the gradient permeability distribution formed under critical coupling enables effective focusing of low-frequency magnetic fields. These three synergistic effects allow the antenna to achieve high magnetic field sensitivity and a low detection limit within a compact size, making it suitable for low-frequency magnetic field detection in complex environments such as underwater communication and ground-penetrating communication.

[0035] The above description and embodiments are merely some preferred embodiments of the present invention and should not be construed as limiting the scope of the present invention. Various modifications and variations can be made to this application by those skilled in the art, but modifications and alterations based on the inventive concept are still within the protection scope of the claims of the present invention.

Claims

1. A low-frequency antenna based on a gradient metamaterial with critical coupling, characterized in that, include: A receiving coil is connected in series with a capacitor, which is then connected to the receiver load. A gradient metamaterial is composed of multiple concentric resonant units with size gradients; each resonant unit consists of a coil and a capacitor connected in series to form an independent resonant circuit. The receiving coil and the gradient metamaterial are concentrically nested, with the receiving coil located on the innermost side.

2. The gradient metamaterial low-frequency antenna based on critical coupling according to claim 1, characterized in that, By configuring the capacitance value connected to the receiving coil, the imaginary part of the antenna output impedance can be changed for impedance matching adjustment of the imaginary part.

3. The gradient metamaterial low-frequency antenna based on critical coupling according to claim 1, characterized in that, The overall resonant frequency of the gradient metamaterial can be adjusted by configuring the capacitance values ​​in each of the resonant units.

4. The gradient metamaterial low-frequency antenna based on critical coupling according to claim 1, characterized in that, The radius of the receiving coil and the coils of all resonant units in the gradient metamaterial increases from the inside out by a preset arithmetic increment, forming a size gradient. By adjusting the size gradient value, the coupling strength between the gradient metamaterial and the receiving coil can be controlled, thereby changing the real part of the antenna output impedance for impedance matching adjustment of the real part.

5. A gradient metamaterial low-frequency antenna based on critical coupling according to claim 4, characterized in that, The size gradient makes the spacing between adjacent coils much larger than the wire diameter of the coil conductor, forming a wide-spacing structure, thereby significantly reducing the proximity loss between coils.

6. A gradient metamaterial low-frequency antenna based on critical coupling according to claim 4, characterized in that, By adjusting the size gradient and various capacitor parameters, the antenna can achieve the maximum size gradient while satisfying impedance matching, thereby minimizing proximity loss and achieving the optimal combination of impedance matching and loss performance. At this point, the antenna enters the critical coupling state.

7. A gradient metamaterial low-frequency antenna based on critical coupling according to claim 6, characterized in that, In the critical coupling state, the gradient metamaterial forms an equivalent permeability distribution that increases from the outside to the inside, thereby achieving effective focusing of low-frequency magnetic fields.

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