APT symmetric sensing system and method based on singular point degeneracy

Abstract

The invention discloses an APT symmetric sensing system and method based on singular point degeneracy. The APT symmetric sensing system comprises a reader and two sensors. The reader comprises an inductor, a capacitor and a negative resistor; each sensor comprises an inductor, a capacitor and a loss resistor; and respectively applying disturbance to the two sensors according to the detected parameters, and detecting the working frequency of the wireless sensing system to obtain the corresponding detected parameters. Through degeneracy of different types of singular points, system frequency splitting is in direct proportion to a quarter of perturbation, so that the detection sensitivity of the system is greatly improved, the sensor can detect obvious changes under tiny disturbance, and especially in an application scene needing to accurately detect tiny changes, the detection sensitivity is greatly improved. Meanwhile, the singular junction with the high sensitivity characteristic is obtained only in a third-order system through regulation and control over the singular points, and compared with an existing fourth-order system for achieving the singular junction, the number of resonators is reduced.

Description

Technical Field

[0001] The invention belongs to the technical field of wireless sensors, and in particular relates to an APT symmetric sensing system and method based on singular point degeneration. Background Art

[0002] In standard quantum mechanics, the Hamiltonian describing a physical system is generally Hermitian to ensure that the system has a real energy spectrum and unitary evolution of the system. The pioneering research of Bender, Boettcher and others has aroused people's interest in non-Hermitian Hamiltonians. The work of Bender and others shows that Hermitianity is not a necessary condition for the generation of real eigenspectra. They first proposed the concept of parity time (PT) symmetry in the context of quantum mechanics, and proved that there is a special type of non-Hermitian system that still retains some properties of the Hermitian system. The non-Hermitian Hamiltonian that obeys PT symmetry still has real eigenvalues, which has opened up a wave of research on non-Hermitian systems.

[0003] With further research on non-Hermitian systems, it was found that there is a novel non-Hermitian singular point (Exceptional Point, EP) between the PT symmetric phase and the PT symmetry breaking phase. At this point, the eigenvalues ​​of two or more eigenstates and their corresponding eigenvectors merge, which is not present in the Hermitian system. With the in-depth study of the PT symmetric system, people have proposed a new system with anti-parity time (Anti-PT, APT) symmetry characteristics, which shows the characteristics of the PT symmetric system dual, and it is found that there is also an EP between the APT symmetric phase and the broken phase.

[0004] Since EP exists in PT symmetric and APT symmetric systems, it has important application value in the field of precision sensing. In Hermitian systems, the shift or split (Δω) of the eigenfrequency caused by a perturbation (|ε|<<1) is at most one order with the perturbation ε itself; while in non-Hermitian systems, the eigenvalues ​​of the system near EP are more sensitive to the perturbation, and the eigenvalues ​​near the Nth-order non-Hermitian singularity (EPN) corresponding to the merger of N modes have an eigenfrequency splitting of ε under a small perturbation ε. 1 / N The dependence of 1 / N It can be seen that when the perturbation effect is the same and small enough, the EP vicinity of the non-Hermitian system can greatly improve the detection sensitivity to external perturbations compared with the Hermitian system, which provides a theoretical idea for the design of high-sensitivity sensors.

[0005] With the in-depth study of EP points, more and more researchers have begun to explore the possibility of higher-order EPs, and discovered exceptional structures of different dimensions such as exceptional arcs (EA), exceptional surfaces (ES) and exceptional nexus (EX). It was found that the degeneration of multiple low-order EPs can form high-order EPs, which greatly promoted the study of high-order EPs.

[0006] However, although the response of the system is greatly enhanced at high-order singular points, most studies have only achieved third-order singular points or even second-order singular points due to the influence of system noise and topological structure limitations. How to achieve higher-order singular points is crucial to the future development of electronic sensors. At the same time, most high-order singular points are realized based on PT symmetry, while the realization of high-order singular points through nonlinear EX and singular point degeneration is limited to applying perturbations to the capacitors on the sensing side; in addition, the different devices in the existing sensor systems that realize high-order singular points are wired and have a small scope of application. Summary of the invention

[0007] The object of the present invention is to provide an APT symmetric sensing system and method based on singular point degeneration.

[0008] In a first aspect, the present invention provides an APT symmetric sensing system based on singular point degeneration, which includes a reader and a sensor; the reader includes an inductor, a capacitor and a negative resistor; the sensors each include an inductor, a capacitor and a loss resistor; the number of the reader is one; the number of the sensors is two; the natural resonant frequency ω1 of the reader and the natural resonant frequencies ω2 and ω3 of the two sensors satisfy the following relationship: ; The coupling ratios between the two sensors and the reader are equal, and the coupling ratio between the two sensors is zero; The loss ratios of the two sensors are equal.

[0009] Preferably, the coupling ratio between the two sensors and the reader is adjusted to be equal to a reference coupling ratio κ0, and the reference coupling ratio κ0 satisfies ; where δ is the natural frequency difference, ; The loss rate of the two sensors is equal to the reference loss rate γ0, ; By setting the reference coupling rate κ0 and the natural frequency difference δ, different types of singular points are degenerated, and the system frequency splitting is proportional to the quarter power of the perturbation.

[0010] As a preference, the operating frequency after disturbance as follows: Among them, ω0 is the center frequency; ε γ is the disturbance amount.

[0011] Preferably, the negative resistance is measured using a network analyzer or an impedance analyzer.

[0012] Preferably, the inductance, capacitance and negative resistance in the reader are connected in series; the inductance, capacitance and loss resistance in the sensor are connected in series.

[0013] Preferably, the inductances of the two sensors are equal, and the loss resistances of the two sensors are equal.

[0014] In the second aspect, the present invention provides an APT symmetric sensing method based on singular point degeneracy, which adopts the above-mentioned APT symmetric sensing system; the sensing method is specifically as follows: disturbances are applied to two sensors respectively according to the measured parameters, the working frequency of the wireless sensing system is detected, and the corresponding measured parameters are obtained.

[0015] Preferably, the disturbance is applied to loss resistors in both sensors.

[0016] Preferably, the disturbances applied to the two loss resistors are identical.

[0017] Preferably, the disturbance applied to the two loss resistors is less than zero.

[0018] The present invention has the following beneficial effects: 1. The present invention realizes that the system frequency splitting is proportional to the fourth power of the perturbation, compared with the Hermitian system that only realizes the system frequency splitting is proportional to the disturbance and the non-Hermitian system that realizes the second-order singular points and the third-order singular points through the degeneracy of different types of singular points. This greatly improves the detection sensitivity of the system, allowing the sensor to detect significant changes under tiny disturbances, especially in application scenarios that require accurate detection of tiny changes, which has important practical significance.

[0019] 2. The present invention constructs a sensing system through two sensors and a reader. Compared with the wireless APT symmetrical system with two gains and one loss, the present technology does not require the two gains to be completely equal, but only requires the two losses to be equal, which has lower requirements on the system and is conducive to implementation; at the same time, the present invention obtains a singular junction with high sensitivity characteristics only in a third-order system by regulating the singular point. Compared with the existing fourth-order system for realizing the singular junction, the present invention reduces the number of resonators.

[0020] 3. The present invention directly applies the disturbance to the load itself. Compared with the sensing system in which the disturbance is applied to the capacitance on the sensing side, the present invention can cope with various environmental conditions more flexibly, and improves the adaptability and accuracy of the sensor in different applications. At the same time, the present invention adopts a network analyzer or an impedance analyzer as a negative resistor, which can act as a negative resistor and also as a detection instrument to detect the zero-crossing point of the imaginary part of the input impedance, and can effectively detect the changes of the load with the environment. This simple operation method makes the experimental process faster, and can detect all characteristic frequencies in the working process, ensuring the accuracy of the measurement results. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 Schematic diagram of the circuit of the sensing system in the present invention.

[0022] Figure 2 It is a schematic diagram of the structure of the sensor system in the present invention.

[0023] Figure 3 It is a schematic diagram of characteristic frequencies corresponding to different loss rates and coupling rates in the present invention.

[0024] Figure 4 It is a schematic diagram of characteristic frequencies corresponding to different loss rates in the present invention.

[0025] Figure 5 It is a simulation diagram of the changing relationship between the normalized frequency splitting and the normalized disturbance amount in the present invention.

[0026] Figure 6 Schematic diagram of the sensor system experimental platform in the present invention.

[0027] Figure 7 This is an experimental diagram of the relationship between the normalized frequency splitting and the normalized disturbance amount in the present invention. DETAILED DESCRIPTION

[0028] The present invention will be further described below in conjunction with the accompanying drawings.

[0029] like Figure 1 and Figure 2 As shown, an APT symmetric sensing system based on singular point degeneration includes a reader and two sensors; both the reader and the sensor are resonators; the reader includes an inductor, a capacitor and a negative resistor connected in series; the sensor includes an inductor, a capacitor and a loss resistor connected in series. The reader is used to provide energy for the system, and its gain rate is g1, and its natural resonant frequency is ω1; the loss rates of the two sensors are γ2 and γ3, and the natural resonant frequencies are ω2 and ω3, respectively; the natural resonant frequency is ω1, which is equal to the center frequency ω0, and there is a frequency offset between the natural resonant frequency ω1 and the natural resonant frequencies ω2 and ω3, that is, there is a natural frequency difference δ, so that ; The coupling rates between the two sensors and the reader are κ 12 and κ 13 .

[0030] Based on the coupled mode theory, the Hamiltonian equation of the sensing system is obtained as follows: Special styles Where H is the Hamiltonian of the sensor system; a=[a1,a2,a3] T are the energy modes of the reader and the two sensors respectively, a1 is the energy mode of the reader, and a2 and a3 are the energy modes of the sensors.

[0031] The third-order Hamiltonian H is converted into a second-order form as follows: In steady-state analysis, the energy norm a follows e iωt By substituting da / dt = iωa into formula (1), we get: Special styles Where ω is the system characteristic frequency.

[0032] According to formula (2), the expression of energy modulus a1 is obtained as follows: Special styles Substituting a1 obtained from equation (3) into equation (2), we get a system of equations only about a2 and a3. If κ 12 = κ 13 = κ0, γ2=γ3 = γ0, and the second-order Hamiltonian H′ is obtained as: Special styles Among them, κ0 is the reference coupling rate; γ0 is the reference loss rate; H′ is the second-order Hamiltonian.

[0033] The Hamiltonian of the APT symmetric system forms a conjugate phenomenon with the behavior mode of the non-Hermitian Hamiltonian in the PT symmetric system. The Hamiltonian of the APT symmetric system requires that the Hamiltonian of the APT symmetric system will characterize the opposite of the original form under the joint operation of space reversal (P) and time reversal (T). When the system characteristic frequency ω is close to the intermediate frequency ω0, that is, ω ≈ ω0, the result of the combined operation of the Hamiltonian of the system under space reversal P and time reversal T is opposite to the original Hamiltonian, that is, PTH′(PT) -1 =-H′, which is consistent with the properties of APT symmetry, indicating that the system is a high-order APT symmetric sensing system.

[0034] Solving the characteristic equation det(ΔωI+H′)=0, where I is the unit matrix, we can obtain the characteristic frequency ω of the system, which satisfies the following equation: Special styles Where Δω is the characteristic frequency splitting, Δω= ω-ω0.

[0035] By separating the real and imaginary parts of formula (5), the real number solution of the characteristic frequency can be obtained as: Special styles Among them, g 1(1) and g 1(2) is different values ​​of the gain rate.

[0036] From formula (6), we can see that different values ​​of gain g1 will correspond to different characteristic frequencies. , gain rate g 1(2) becomes a complex number, the system will only obtain the gain rate g 1(1) , at this time the system has only one characteristic frequency, ω = ω0. , the gain rate g 1(2) Substituting into formula (6), we get four different characteristic frequencies:

[0037] Special styles in, Represents these four different characteristic frequencies, Δ1 and Δ2 are intermediate variables, and their expressions are: Special styles Special styles The four different characteristic frequencies in formula (7) Arrange in the following order: (+,+), (+,-), (-,-), (-, +); the first and second symbols in the brackets represent the choice of the first and second symbols in equation (7); characteristic frequency is the state with the highest real frequency.

[0038] According to formula (7), the intermediate variables Δ1 and Δ2 will affect the characteristic frequency of the system, resulting in the coalescence of different states (CS), and two different types of singular points will appear: single singular point (single EP2) and paired singular point (pairedEP2). In single EP2, the two eigenvectors will degenerate at the eigenvalue ω0; in paired EP2, two singular points will appear at the same time under the same parameter conditions, and the eigenvalues ​​of the two singular points are opposite in sign. According to the different values ​​of the intermediate variables, the singular points include the following three states:

[0039] 1. CS-1: When Δ1= 0 and Δ2≠ 0, we get ; At this time, the characteristic frequency and characteristic frequency exist At the same time, the characteristic frequency and characteristic frequency exist The type of singular point is paired EP2.

[0040] 2. CS-2: When When Δ1≠ 0, Δ2≠ 0, we get , then the characteristic frequency and characteristic frequency It is degenerate at ω0, and the type of singular point is single EP2; when When Δ1≠ 0, Δ2≠ 0, , then the characteristic frequency and characteristic frequency It is degenerate at ω0, and the singular point type is single EP2. In the CS-2 state, only when , single EP2 will appear; if , .

[0041] 3. CS-3: When Δ1=Δ2= 0, we get , , at this time, all characteristic frequencies will degenerate at ω0, and single EP2 and paired EP2 will degenerate into a higher-order singular knot, which is not only the endpoint of an unclosed line composed of continuous trajectories of multiple EP2s, but also a higher-order singular point.

[0042] At the center frequency ω0 is 3.55×10 7 rad / s, the natural frequency difference δ is 0.5×10 6 rad / s, the characteristic frequencies corresponding to different loss rates γ0 and coupling rates κ0 are as follows: Figure 3 In three-dimensional space, an infinite number of singular points form singular lines. Figure 3 It can be clearly observed that there are two different types of singular lines. The black solid line represents paired EL, and the red dotted line represents single EL. When the paired EL and single EL converge together (at the yellow star in the figure), EX is formed.

[0043] According to the coupling ratio and coupling ratio Get coupling ratio Different ranges of values ​​are taken to further analyze the singular point states of CS-1, CS-2 and CS-3, where the coupling rate The value of is divided into the following five cases: (a) ; (b) ; (c) ; (d) ; (e) ; At the center frequency ω0 is 3.55×10 7 rad / s, the natural frequency difference δ is 0.5×10 6 rad / s, the characteristic frequencies corresponding to different loss rates γ0 are as follows: Figure 4 As shown. The pink line, blue line, black line and green line in the figure represent , , and ; From the figure, it can be seen that when When , only two paired EP2s will appear, and Slowly increasing, two singleEP2s will gradually appear; when When , the two paired EP2s and one of the single EP2s degenerate to form an EX; and when When , at the two paired EP2s, the characteristic frequencies become a pair of conjugate complex numbers. As the value decreases slowly, the phenomenon of two paired EP2s with complex conjugate eigenvalues ​​and one single EP2 degenerating into EX will also occur. It can be seen that EX is formed only when paired EP2s and single EP2 degenerate.

[0044] The sensitivity of the sensor system working in the EX state is analyzed, and the analysis process is as follows: Apply a disturbance to the loss rate γ0 at EX, and the disturbance amount is ε γ ; Because when ε γ > 0, g 1(2) becomes a complex number, so the perturbation ε γ < 0, get the system operating frequency ω after disturbance εγ,j for: Special styles Satisfied at EX , , substituting into (10), we get Special styles If the disturbance ε γ Much smaller than the natural frequency difference δ (ε γ<< δ), then the frequency splitting after disturbance is Δω εγ for: Special styles Among them, "+" means ,"-"express .

[0045] From (12), we can see that , the frequency splitting phenomenon of the system and the disturbance ε γ This characteristic shows that when the disturbance ε γ When the loss is small, the EX formed by the degenerate paired EP2s and single EP2 has a very high sensitivity compared to EP2 and EP3 (second-order and third-order singular points). This means that at the EX point, the system is extremely sensitive to small perturbations of the loss, and this sensitivity has a significant improvement in the performance of the sensor.

[0046] When the same type of EP2 is degenerated together, such as Figure 4 In (b), , Substituting into (10), we get the frequency splitting Δω εγ satisfy: Special styles Among them, "+" means ,"-"express .

[0047] According to formula (13), when two single EP2s are degenerated together, , the frequency splitting of the system is proportional to the disturbance, and the same type of EP2 degeneracy does not lead to a significant improvement in the system sensitivity. Only when two different types of EP2 degenerate together, it has extremely high sensitivity. This high sensitivity is crucial for accurate measurement and early detection, especially in applications that require high resolution and fast response, such as biosensors, environmental monitoring, and precision instruments.

[0048] The scheme of the present invention is verified by simulation experiments: The gain and loss in the sensing system are realized by negative resistance and loss resistance respectively. Negative resistance provides gain energy to the system by using a network analyzer or impedance analyzer. To simplify the analysis, the parasitic loss of inductance and capacitance in the loop is not considered. The inductance L2 and L3 of the two sensors are set equal to the reference inductance L0, and the loss resistance R2 and R3 of the two sensors are set equal to the reference resistance R0.

[0049] Therefore, the self-resonant frequency of each resonant circuit satisfies: Special styles The expression of reference loss rate γ0 is: Special styles Among them, Γ2 and Γ3 are the loss coefficients of the two sensors respectively.

[0050] Coupling rate κ 12 and κ 13 The expression is: Special styles Among them, k 12 and k 13 are the coupling coefficients between the reader and the sensor, k 12 = k 13 ;M 12 and M 13 are the mutual inductance between the reader and the sensor, respectively.

[0051] Assuming that the inductance of each resonant circuit remains unchanged, the same disturbance is applied to the resistance of the two sensors at the same time. From equation (15), it can be seen that this is equivalent to applying a disturbance to the loss rate γ0 of the two circuits. Since the characteristic frequency of the system corresponds to the input impedance Z of the reader in The imaginary part of the zero crossing point is simulated in Advanced Design System (ADS) as the resistance R0 changes Z in The imaginary part of the zero crossing point is shown in Figure 2. The sensor coil inductance L2 = L3 = L0 = 10uH, the reader coil inductance L1 = 13uH, the two sensor capacitors C2 = 77.16pF, C3 = 81.63pF and the reader capacitor C1 = 61.04pF are set, and the self-resonant frequencies of each coil are ω1 = 35.5Mrad / s, ω2 = 36Mrad / s and ω3 = 35Mrad / s, respectively. The natural frequency difference δ = 0.5Mrad / s can be obtained. When single EP2 and paired EP2s are degenerated to form EX, , And equations (15) and (16), the corresponding reference resistance R0 = 24.5 ohms and coupling coefficient k are obtained. 12 =k 13 =0.0619.

[0052] At the center frequency ω0 is 3.55×10 7 rad / s, the natural frequency difference δ is 0.5×10 6 rad / s, changing the value of resistor R0, we get the normalized frequency splitting of the system ( ) and the normalized perturbation ( ) Figure 5 The red solid line in the figure is the theoretical curve calculated according to formula (11). In logarithmic coordinates, the slope of the curve is one quarter. The blue asterisk represents the simulation value. The simulation value and the theoretical value fit well, indicating that the frequency splitting phenomenon of the system is related to the disturbance ε γ It is proportional to the fourth power of , which verifies the accuracy of the theoretical model and proves the effectiveness of the simulation method.

[0053] In order to further verify the feasibility of this scheme, a high-sensitivity APT symmetric sensing system experimental platform based on singular point degeneration was built. Figure 6 As shown. Since the coupling rate between the reader and the two sensors is equal, the reader coil is designed to be connected with two coils of the same size and coaxially aligned with the two sensor coils. The two coils of the sensor are placed side by side so that the coupling rate between them is approximately zero. The coupling rate between the reader and the sensor is obtained by adjusting the distance between the two PCB boards, which is achieved here by controlling the number of gaskets with a thickness of 1mm. Two identical resistor arrays are installed under the two sensor coils to simulate the change of load when the environmental parameters change. Through this resistor array, the value of the reference resistor R0 can be accurately controlled to simulate different load conditions.

[0054] The design of each parameter in the experiment is shown as follows. Since there is parasitic capacitance between the PCB board and each component, the size of the parasitic capacitance cannot be accurately obtained. Therefore, each resonant circuit adjusts the resonant frequency through a patch adjustable capacitor so that the self-resonant frequency of each circuit meets the requirements of the APT symmetric system. The specific experimental parameters are shown in Table 1. The distance between the reader and the sensor and the size of the reference resistor approximately meet the conditions for the existence of a singular junction. The parasitic resistance of the PCB board and each component is 7.5 ohms, and the resistance in the resistor array is 16.9 ohms, which together form the reference resistor R0.

[0055] Table 1 Experimental parameters of high-sensitivity APT symmetric sensing system based on singular point degeneration parameter Numeric <![CDATA[Reader coil inductance L1]]> 12uH <![CDATA[Reader coil inductances L2, L3]]> 6uH <![CDATA[Self-resonant frequencies ω1, ω2, and ω3]]> 20.5Mrad / s, 21Mrad / s and 20Mrad / s Distance between reader and sensor 9mm <![CDATA[Reference resistor R0]]> 24.4 Euro Under this parameter condition, by adjusting the position of the jumper cap in the resistor array to change the value of resistor R0, the simulated load changes with the environmental parameters, with a step of 0.1 ohm, and the normalized frequency splitting of the system is obtained ( ) and the normalized perturbation ( ) Figure 7 As shown, where ω0=2.05×10 7 rad / s,δ=0.5×10 6 rad / s.

[0056] from Figure 7It can be seen that the theory and experiment are highly consistent, which shows that the frequency splitting phenomenon of the system is related to the disturbance ε γ The system has a high sensitivity to resistance changes, allowing significant changes to be detected with very small disturbances. This is critical to improving the resolution and detection capabilities of sensors, especially in environments where small changes need to be detected, such as environmental monitoring, medical diagnostics, and precision engineering.

Claims

1. An APT symmetric sensing system based on singular point degeneration, comprising a reader and a sensor; the reader comprises an inductor, a capacitor and a negative resistor; the sensors each comprise an inductor, a capacitor and a loss resistor; characterized in that: The number of the readers is one; the number of the sensors is two; the natural resonant frequency ω1 of the reader and the natural resonant frequencies ω2 and ω3 of the two sensors satisfy: ; The coupling ratios between the two sensors and the reader are equal, and the coupling ratio between the two sensors is zero; The loss ratios of the two sensors are equal.

2. The APT symmetric sensing system based on singular point degeneration according to claim 1, characterized in that: The coupling ratio between the two sensors and the reader is equal to the reference coupling ratio κ0, which satisfies ; where δ is the natural frequency difference, ; The loss rate of the two sensors is equal to the reference loss rate γ0, .

3. The APT symmetric sensing system based on singular point degeneration according to claim 2, characterized in that: Working frequency after disturbance as follows: Among them, ω0 is the center frequency; ε γ is the disturbance amount.

4. The APT symmetric sensing system based on singular point degeneration according to claim 1, characterized in that: The negative resistance is measured by a network analyzer or an impedance analyzer.

5. The APT symmetric sensing system based on singular point degeneration according to claim 1, characterized in that: The inductance, capacitance and negative resistance in the reader are connected in series; the inductance, capacitance and loss resistance in the sensor are connected in series.

6. The APT symmetric sensing system based on singular point degeneration according to claim 1, characterized in that: The inductances of the two sensors are equal, and the loss resistances of the two sensors are equal.

7. An APT symmetric sensing method based on singular point degeneration, characterized in that: An APT symmetric sensing system based on singular point degeneration as described in claim 1 is adopted; the sensing method is specifically as follows: disturbances are applied to two sensors respectively according to the measured parameters, the working frequency of the wireless sensing system is detected, and the corresponding measured parameters are obtained.

8. The APT symmetric sensing method based on singular point degeneration according to claim 7, characterized in that: The perturbation is applied to the loss resistors in both sensors.

9. The APT symmetric sensing method based on singular point degeneration according to claim 8, characterized in that: The perturbation applied to both loss resistors is the same.

10. The APT symmetric sensing method based on singular point degeneration according to claim 8, characterized in that: The disturbance applied to the two loss resistors is less than zero.

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