Wireless sensing system and sensing method for realizing APT symmetry based on unidirectional coupling

Abstract

The invention discloses a wireless sensing system and a sensing method for realizing APT symmetry based on unidirectional coupling. The wireless sensing system comprises four resonators, a reading end follower and a sensing end follower, by adding a reading end follower and a sensing end follower in a wireless sensing system, imaginary number coupling between resonators in a traditional APT symmetric system is replaced by real number coupling, so that wireless connection between different resonators in the APT symmetric system is realized. Meanwhile, when the system works around an EP point, the number of working frequencies of the system is remarkably changed, so that the two working frequencies of the wireless sensing system can be located at the overlapped and bifurcated junction by adjusting the coupling rate of the reading end follower and the sensing end follower, calibration of the EP point is completed, and the wireless sensing system works in a high-sensitivity state.

Description

Technical Field

[0001] The present invention belongs to the technical field of wireless sensing, and in particular relates to a wireless sensing system and a sensing method for realizing APT symmetry based on unidirectional coupling. Background Art

[0002] Non-Hermitian Hamiltonians can be used to describe open quantum systems and classical wave systems. The non-Hermitian property of a Hamiltonian usually means that its eigenvalues ​​are complex. However, a class of non-Hermitian systems that satisfy parity-time (PT) symmetry can have real eigenvalues, and their Hamiltonian (H PT ) remains unchanged under the combined action of the space reversal operator (P) and the time reversal operator (T), namely PTH PT (PT) −1 = H PT . Various exotic phenomena of PT symmetric systems have been widely studied in fields such as optics, electronics, and acoustics. The eigenvalues ​​and eigenstates of PT symmetric systems merge simultaneously at special points (EPs), thereby distinguishing PT symmetry states from broken states. At EPs, the system exhibits ultra-high sensitivity to perturbations. This response usually follows ~ε 1 / n (i.e., 1 / nth order), where ε is the disturbance and n is the number of eigenvalues. In the field of electronics, PT-symmetrical sensors that construct gain-loss distributions by coupling RLC resonators have been successfully applied to detect quantities such as pressure, humidity, or distance with high sensitivity. A vector network analyzer (VNA) is usually used to detect the system response and act as a system gain to provide a drive signal. However, the bulky VNA is not suitable for use outside the laboratory. Although low-cost and portable alternatives exist, they often do not provide sufficient output power or the flexible frequency sweeping capabilities required for different applications. By implementing a time-domain self-oscillating gain (usually using a positive feedback operational amplifier built in the nonlinear saturation region), the operating frequency can be adaptively matched to the eigenvalue, thereby avoiding the use of a VNA for frequency scanning.

[0003] However, the existing VNA-free detection methods based on self-oscillation gain are limited in practical applications by the difficulty of calibrating the sensor to the EP before the sensing operation. S. Assawaworrarit et al., in the paper “Robust wireless power transfer using a nonlinear parity-time-symmetric circuit”, showed in simulation and experiment of a PT-symmetric bistable system containing coupled RLC resonators that the transition between the PT symmetric state and the broken state is gradual rather than abrupt when adjusting the coupling coefficient. This is attributed to the nonlinear characteristics of the gain, which leads to a mismatch between the operating frequency and the inherent resonant frequency of the resonator. In addition, due to the bistable characteristics of the system and the single gain, there is only one operating frequency in the system, although there are two possible operating frequencies in the PT symmetric state. Therefore, there is a lack of a clear EP position to distinguish the PT symmetric state from the broken state. In the existing detection methods based on self-oscillation circuits, the theoretical 1 / 2 order sensitivity of the PT symmetric sensor cannot be clearly observed in simulation and experiment. In addition, in the existing PT-symmetric sensors, most of them complete the calibration of the EP point by moving the distance between the devices, which is a mechanical adjustment method. In addition, the limitation of the wired resistance coupling (imaginary coupling) used to connect the two gains in the existing APT symmetric structure is that it is a wired connection structure and only relies on the distance between the resonators to mechanically adjust the EP point, which is difficult to adjust. Summary of the invention

[0004] The object of the present invention is to provide a wireless sensing system and a sensing method for realizing APT symmetry based on unidirectional coupling.

[0005] In the first aspect, the present invention provides a wireless sensing system for realizing APT symmetry based on unidirectional coupling, which includes a resonator Y1, a resonator Y2, a resonator Y3, a resonator Y4, a read-end follower and a sensing-end follower; the resonator Y1 includes an inductor L1, a capacitor C1 and a negative resistor R1; the resonator Y2 includes an inductor L2, a capacitor C2 and a negative resistor R2; the resonator Y3 includes an inductor L3 and a capacitor C3; the resonator Y4 includes an inductor L4 and a capacitor C4; the read-end follower includes an operational amplifier AMP1, a resistor R 31 and resistor R 32 ; The sensor follower includes an operational amplifier AMP2, a resistor R 41 and resistor R 42 The positive input port of the operational amplifier AMP1 is connected to the ground wire through the inductor L1, the capacitor C1 and the negative resistor R1; the negative input port of the operational amplifier AMP1 is connected to the ground wire through the resistor R 31connected to the ground wire; the output port of the operational amplifier AMP1 is connected to the ground wire through the inductor L3 and the capacitor C3 respectively; the reverse input port and the output port of the operational amplifier AMP1 are connected through the resistor R 32 The positive input port of the operational amplifier AMP2 is connected to the ground wire through the inductor L2, the capacitor C2 and the negative resistor R2; the negative input port of the operational amplifier AMP2 is connected to the ground wire through the resistor R 41 connected to the ground wire; the output port of the operational amplifier AMP2 is connected to the ground wire through the inductor L4 and the capacitor C4 respectively; the reverse input port and the output port of the operational amplifier AMP2 are connected through the resistor R 42 connection; the resonant frequency of resonator Y1 is the same as that of resonator Y3, and the same resonant frequency is used as the natural resonant frequency ω1; the resonant frequency of resonator Y2 is the same as that of resonator Y4, and the same resonant frequency is used as the natural resonant frequency ω2; the coupling rate between resonator Y1 and resonator Y4 and the coupling rate between resonator Y2 and resonator Y3 are both κ, with opposite polarities.

[0006] Preferably, the resonator Y1 and the resonator Y2 are two active resonators, which are driven by two negative resistors respectively; the resonator Y3 and the resonator Y4 are neutral resonators, which are driven by a read-end follower and a sensor-end follower respectively.

[0007] Preferably, the gain coefficient of the read-end follower is adjusted by adjusting the resistor R 31 With R 32 The gain coefficient of the sensor follower is adjusted by adjusting the resistor R 41 With R 42 The ratio is adjusted.

[0008] Preferably, the gain coefficient of the read-end follower is equal to the gain coefficient of the sensing-end follower.

[0009] Preferably, the operating frequency ω of the wireless sensor system is expressed as: Where δ is the difference frequency, δ=(ω1−ω2) / 2; c is the gain coefficient of the read-end follower and the sensor-end follower; ε ω is a negative disturbance.

[0010] Preferably, when the wireless sensing system is at the EP point and in the APT symmetric state, the operating frequency ω has only one solution.

[0011] Preferably, the negative resistor adopts a feedback operational amplifier.

[0012] Preferably, the difference frequency δ of the wireless sensing system is 1.3% to 1.5% of the average frequency ω0; ω0=(ω1+ω2) / 2; δ=(ω1−ω2) / 2.

[0013] In a second aspect, the present invention provides a sensing method for realizing unidirectional coupling based on APT symmetry, which adopts the above-mentioned wireless sensing system; the sensing method is specifically as follows: By adjusting the gain coefficients of the reading-end follower and the sensing-end follower, the two operating frequencies of the wireless sensor system are placed at the junction of overlap and bifurcation; according to the disturbance imposed on the resonator Y2 by the measured parameter, the operating frequency of the wireless sensor system is detected to obtain the corresponding measured parameter.

[0014] Preferably, the disturbance is applied to the capacitor C2 of the resonator Y2.

[0015] The present invention has the following beneficial effects: 1. The present invention replaces the imaginary coupling between resonators in the traditional APT symmetric system with real coupling by adding a reading end follower and a sensing end follower in the wireless sensing system, thereby realizing wireless connection between different resonators in the APT symmetric system.

[0016] 2. The present invention can adjust the gain coefficients of the reading end follower and the sensing end follower so that the two operating frequencies of the wireless sensor system are at the junction of overlap and bifurcation, complete the calibration of the EP point, and make the wireless sensor system work in a high-sensitivity state. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 It is a schematic diagram of the overall circuit of the present invention.

[0018] Figure 2 Schematic diagram of the Hamiltonian in the traditional APT system.

[0019] Figure 3 Schematic diagram of the Hamiltonian of the present invention; wherein, (a) is the circuit principle diagram of the present invention; and (b) is the equivalent APT symmetric dimer model.

[0020] Figure 4 This is a diagram showing the placement of the coupling coil in the present invention.

[0021] Figure 5 The figure is a comparison diagram between the simulation value and the theoretical value of the system frequency under different amplification factors of the present invention.

[0022] Figure 6 This is a comparison diagram between the system frequency simulation value and the theoretical value when the amplification factor is 1 of the present invention. DETAILED DESCRIPTION

[0023] The present invention will be further described below in conjunction with the accompanying drawings.

[0024] like Figure 1 As shown, a wireless sensing system and sensing method for realizing APT symmetry based on unidirectional coupling include a resonator Y1, a resonator Y2, a resonator Y3, a resonator Y4, a read-end follower and a sensing-end follower. Resonator Y1 includes an inductor L1, a capacitor C1 and a negative resistor R1; resonator Y2 includes an inductor L2, a capacitor C2 and a negative resistor R2; resonator Y3 includes an inductor L3 and a capacitor C3; resonator Y4 includes an inductor L4 and a capacitor C4; the read-end follower includes an operational amplifier AMP1, a resistor R 31 and resistor R 32 ; The sensor follower includes an operational amplifier AMP2, a resistor R 41 and resistor R 42

[0025] The positive input port of the operational amplifier AMP1 is connected to the ground wire through the inductor L1, the capacitor C1 and the negative resistor R1; the negative input port of the operational amplifier AMP1 is connected to the ground wire through the resistor R 31 connected to the ground wire; the output port of the operational amplifier AMP1 is connected to the ground wire through the inductor L3 and the capacitor C3 respectively; the reverse input port and the output port of the operational amplifier AMP1 are connected through the resistor R 32 The positive input port of the operational amplifier AMP2 is connected to the ground wire through the inductor L2, the capacitor C2 and the negative resistor R2; the negative input port of the operational amplifier AMP2 is connected to the ground wire through the resistor R 41 connected to the ground wire; the output port of the operational amplifier AMP2 is connected to the ground wire through the inductor L4 and the capacitor C4 respectively; the reverse input port and the output port of the operational amplifier AMP2 are connected through the resistor R 42 connection; the resonant frequency of resonator Y1 is the same as that of resonator Y3, and the same resonant frequency is used as the natural resonant frequency ω1; the resonant frequency of resonator Y2 is the same as that of resonator Y4, and the same resonant frequency is used as the natural resonant frequency ω2; the coupling rate between resonator Y1 and resonator Y4 and the coupling rate between resonator Y2 and resonator Y3 are both κ, with opposite polarities. Resonators Y1 and Y2 are two active resonators, driven by two gains respectively; resonators Y3 and resonator Y4 are neutral resonators, driven by the read-end follower and the sensing-end follower respectively.

[0026] like Figure 2As shown, the two resonators of the existing APT symmetric system are imaginary coupled; when the working state of the existing wireless sensor system based on APT symmetry changes, the number of working frequencies changes; when working in the APT broken state, the gains of the two resonators oscillate at their respective natural frequencies, and when working in the EP or APT symmetric state, the frequencies of the two resonators are the same. Therefore, the EP of the gain-gain characteristic APT symmetric system is easy to determine. However, the PT symmetric dimer can only provide one working frequency by one gain in the PT broken state or the PT symmetric state. Although the working frequency is bifurcated into two values ​​in the PT symmetric state, due to the bistable characteristics, the gain-loss PT symmetric system selects one frequency as the working frequency; the present invention realizes wireless connection between APT symmetric systems by adding a read-end follower and a sensor-end follower for real number coupling. Based on the coupled mode theory, the state equation of the wireless sensor system is obtained as follows:

[0027] Formula (1) Wherein, ω is the operating frequency; g1 and g2 are the gain rates of resonators Y1 and Y2 respectively; a1, a2, a3, a4 are the energy modes of resonators Y1, Y2, Y3, Y4 respectively; c is the gain coefficient of the read-end follower and the sensor-end follower.

[0028] The energy mode of the resonator m Follow jωt Rule, m = 1, 2, 3, 4; According to the third and fourth lines of equation (1), we can get a3 = a1 + κa2 / ω and a4 = a2 – κa1 / ω. Substituting a3 and a4 into the other expressions of equation (1), we get the following expressions:

[0029] Formula (2) When the APT symmetric sensor works near EP, the operating frequency ω is close to the average frequency ω0, and the coupling rate cκ is close to the difference frequency δ; the average frequency ω0=(ω1+ω2) / 2; the difference frequency δ=(ω1−ω2) / 2. Since δ<<ω0, the difference frequency δ is 1.3%~1.5% of the average frequency ω0; when c≥1, the gain rates g1 and g2 are approximately equal. Since resonators Y3 and Y4 are neutral resonators, if parasitic losses are ignored, g1≈g2≈0. Further simplifying equation (2) to obtain the Schrodinger type state equation is:

[0030] Formula (3) By energy model a m Apply a rotation transformation −jω0t , a m ′=e −jω0t am Substituting into formula (3) we obtain: Formula (5) Among them, H′ APT is the Hamiltonian.

[0031] like Figure 3 As shown, the Hamiltonian H′ APT It becomes −H′ under the operations of parity reversal (swapping diagonal and anti-diagonal elements) and time reversal (changing the sign of j) APT The coupling rates cκ and −cκ are opposite real numbers and are exchanged only under parity reversal operations, not under time reversal operations. In the conventional APT symmetric Hamiltonian H APT In the example, the coupling rate jκ becomes −jκ under the time reversal operation, but not under the parity reversal operation. After the joint parity and time reversal operation, H′ APT and H APT Have the same symmetry. Real matrix H′ APT It is a new paradigm that satisfies the APT symmetry.

[0032] By solving det(xI+H APT )=0 to obtain the operating frequency ω of the APT symmetric system + ,ω - The expression is: Formula (6) Where x=ω−ω0 and I is the identity matrix.

[0033] When cκ=δ, a special point (EP) is observed. When cκ>δ, the system is in an APT symmetric state, where the two resonators are attracted to the same frequency. When cκ<δ, the system is in an APT broken state, where the two resonators oscillate around their own natural resonant frequencies. When the operating state crosses EP, the number of operating frequencies changes abruptly. If a negative perturbation ε is applied to the resonant frequency ω2 of resonator Y2 ω , the expression of the operating frequency ω of the APT symmetric system is:

[0034] Formula (7) Frequency deviation Δω, defined as Δω=ω′ + −ω′ − , which can be approximated as Δω≈2(−δε ω ) 0.5 Near EP. Note that cκ=δ is satisfied at EP. The frequency response follows ∼|ε ω | 0.5, which is the same as the conventional PT or APT symmetric dimer. The perturbation can be measured by taking the operating frequency ω as the readout.

[0035] like Figure 4 As shown in the figure, the wireless sensor system based on anti-parity time symmetry to achieve unidirectional coupling is designed using Pspice simulation software; due to the long distance between coil 1 and coil 2 and between coil 1 and coil 4, their mutual coupling is negligible. Only the mutual coupling between coil 2 and coil 3 and between coil 1 and coil 4 is considered. The coupling coefficient k 14 and k 23 Designed to be k 14 = −k 23 =k. All capacitors are initially set to 1.4 nF. The inductance of inductors L1 and L3 is 2.6 μH; the inductance of inductors L2 and L4 is 2.75 μH; the natural resonant frequencies ω1 and ω2 are 16.57 Mrad / s and 16.12 Mrad / s, respectively. Therefore, ω0=16.345 Mrad / s and δ=0.225 Mrad / s. The negative resistance of the wireless sensor system is achieved by connecting an amplifier (LM7171AIM) with positive feedback, and the resistor R 11 , R 12 and R 13 The resistance values ​​of are 50 Ω, 470 Ω and 4.7 kΩ respectively. The voltage on capacitors C1 and C2 is amplified by voltage followers to drive resonators Y3 and Y4 respectively. The energy mode is a m =(C m / 2) 0.5 V m , where V m is the capacitance C m Then, energy modes a3 and a4 are copied from a1 and a2 respectively, with a gain factor c equal to 1+R 32 / R 31 . Add a disturbance at capacitor C2 and then read the frequency change of the system. Figure 5 The data graph of the frequency changing with the coupling coefficient under different gain coefficients c. The calculated theoretical value and the recorded simulation value are consistent with each other in the frequency value under different coupling coefficients. Figure 6 The results of theoretical analysis and simulation under this series of parameters show that the theoretical value is consistent with the simulation value, and under a small disturbance (gray circle cover), it can be found that the system is disturbed and the frequency response Δω∼|ε ω | 0.5 .

Claims

1. A wireless sensing system based on unidirectional coupling to achieve APT symmetry, characterized by: The invention comprises a resonator Y1, a resonator Y2, a resonator Y3, a resonator Y4, a read-end follower and a sensing-end follower; the resonator Y1 comprises an inductor L1, a capacitor C1 and a negative resistor R1; the resonator Y2 comprises an inductor L2, a capacitor C2 and a negative resistor R2; the resonator Y3 comprises an inductor L3 and a capacitor C3; the resonator Y4 comprises an inductor L4 and a capacitor C4; the read-end follower comprises an operational amplifier AMP1, a resistor R 31 and resistor R 32 ; The sensor follower includes an operational amplifier AMP2, a resistor R 41 and resistor R 42 The positive input port of the operational amplifier AMP1 is connected to the ground wire through the inductor L1, the capacitor C1 and the negative resistor R1; the negative input port of the operational amplifier AMP1 is connected to the ground wire through the resistor R 31 connected to the ground wire; the output port of the operational amplifier AMP1 is connected to the ground wire through the inductor L3 and the capacitor C3 respectively; the reverse input port and the output port of the operational amplifier AMP1 are connected through the resistor R 32 The positive input port of the operational amplifier AMP2 is connected to the ground wire through the inductor L2, the capacitor C2 and the negative resistor R2; the negative input port of the operational amplifier AMP2 is connected to the ground wire through the resistor R 41 connected to the ground wire; the output port of the operational amplifier AMP2 is connected to the ground wire through the inductor L4 and the capacitor C4 respectively; the reverse input port and the output port of the operational amplifier AMP2 are connected through the resistor R 42 connection; the resonant frequency of resonator Y1 is the same as that of resonator Y3, and the same resonant frequency is used as the natural resonant frequency ω1; the resonant frequency of resonator Y2 is the same as that of resonator Y4, and the same resonant frequency is used as the natural resonant frequency ω2; the coupling rate between resonator Y1 and resonator Y4 and the coupling rate between resonator Y2 and resonator Y3 are both κ, with opposite polarities.

2. The wireless sensing system for achieving APT symmetry based on unidirectional coupling according to claim 1, characterized in that: The resonator Y1 and the resonator Y2 are two active resonators, which are driven by two negative resistors respectively; the resonator Y3 and the resonator Y4 are neutral resonators, which are driven by a read-end follower and a sensing-end follower respectively.

3. The wireless sensing system for achieving APT symmetry based on unidirectional coupling according to claim 1, characterized in that: The gain coefficient of the read-end follower is adjusted by the resistor R 31 With R 32 The ratio is adjusted; The gain coefficient of the sensor follower is adjusted by adjusting the resistor R 41 With R 42 The ratio is adjusted.

4. The wireless sensing system for achieving APT symmetry based on unidirectional coupling according to claim 1, characterized in that: The gain factor of the read-end follower is equal to the gain factor of the sensing-end follower.

5. The wireless sensing system for achieving APT symmetry based on unidirectional coupling according to claim 4, characterized in that: The expression of the operating frequency ω of the wireless sensor system is: Where δ is the difference frequency, δ=(ω1−ω2) / 2; c is the gain coefficient of the read-end follower and the sensor-end follower; ε ω is a negative disturbance.

6. The wireless sensing system for achieving APT symmetry based on unidirectional coupling according to claim 5, characterized in that: The wireless sensor system is at the EP point and in the APT symmetric state, and the operating frequency ω has only one solution.

7. The wireless sensing system for achieving APT symmetry based on unidirectional coupling according to claim 1, characterized in that: The negative resistor adopts a feedback operational amplifier.

8. The wireless sensing system for achieving APT symmetry based on unidirectional coupling according to claim 1, characterized in that: The difference frequency δ of the wireless sensor system is 1.3%~1.5% of the average frequency ω0; ω0=(ω1+ω2) / 2; δ=(ω1−ω2) / 2.

9. A sensing method for realizing unidirectional coupling based on APT symmetry, characterized in that: The wireless sensing system for realizing APT symmetry based on unidirectional coupling as described in claim 1 is adopted; the sensing method is specifically as follows: By adjusting the gain coefficients of the reading-end follower and the sensing-end follower, the two operating frequencies of the wireless sensor system are placed at the junction of overlap and bifurcation; according to the disturbance imposed on the resonator Y2 by the measured parameter, the operating frequency of the wireless sensor system is detected to obtain the corresponding measured parameter.

10. The sensing method for realizing unidirectional coupling based on APT symmetry according to claim 9, characterized in that: The disturbance is applied to the capacitor C2 of the resonator Y2.

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