Displacement sensing system and displacement measuring method based on PT symmetry

Abstract

The invention discloses a displacement sensing system based on PT symmetry and a displacement measurement method, the displacement sensing system detects displacement by arranging a three-order PT symmetry system, and high sensitivity can be realized without limiting the system to work at a singular point, so that the system can realize more flexible sensing setting with a larger operation area; meanwhile, under the condition that the initial coupling coefficient between the sensor and the transmitter is known, the sensitivity of displacement detection can be improved by setting the distance between the transmitter and the receiver. Besides, displacement is detected in a voltage amplitude ratio detection mode, compared with traditional frequency and impedance detection modes, the voltage detection mode is simpler and more convenient, use of instruments large in size and expensive is avoided, the operation difficulty is greatly lowered, and portability is improved; meanwhile, the detection frequency deviation is replaced by detecting the voltage ratio between the readers, so that the experimental phenomenon has better observability.

Description

Technical Field

[0001] The present invention belongs to the technical field of displacement detection, and in particular relates to a displacement sensing system and a displacement measurement method based on PT symmetry. Background Art

[0002] With the continuous advancement of science and technology, various sensors for detecting and real-time monitoring of chemical or physical quantities in gas or liquid environments (such as temperature, humidity, pressure, etc.) have made significant progress and have been widely used in many industries. However, with the continuous increase in application scenarios, wireless high-precision sensing measurement of displacement is a major demand for applications such as industrial control, aerospace, and healthcare.

[0003] The non-contact displacement measurement methods are mainly based on laser, ultrasonic and electromagnetic wave sensing technologies. However, in practical applications, laser and ultrasonic ranging technologies are easily affected by obstacles and smoke, dust and other air debris around the target, thus affecting the accuracy of the measurement. Displacement sensors based on microwaves such as radio frequency electromagnetic waves can overcome the application limitations of the first two technologies due to their better penetration ability. Especially for the near field area, when the object is blocked by a non-metallic obstacle, the magnetic field coupling between the two coils is suitable for non-contact measurement of the object's displacement.

[0004] As one of the main requirements for sensing applications, wireless displacement sensors have always been the focus of researchers. Therefore, LC passive wireless displacement sensor systems based on PT symmetry have also developed rapidly. The latest research on parity-time (PT) symmetry shows that applying PT symmetry to LC passive wireless sensor systems can significantly improve the sensitivity of the system. The eigenvalues ​​and eigenvectors of the PT symmetric system will be degenerate at the same time at the exceptional point (EP), making the system extremely sensitive to disturbances applied to the EP point. When the system is biased at the EP point, the frequency splitting of the system is proportional to the square root of the small disturbance near the EP point, that is, Δω~(ε k ) 0.5 , which shows that the system has ultra-high sensitivity to tiny displacement disturbances, which provides new ideas for the research of displacement sensors.

[0005] Mehdi Hajizadegan et al. proposed and experimentally verified an ultra-sensitive wireless displacement sensing technology based on PT symmetry. The system diagram is as follows: Figure 1As shown in the figure, the PT symmetric telemetry sensing system includes a fixed reader and a movable sensor. A negative impedance converter is constructed using a Colpitts oscillator to balance the gain and loss in the system so that the system satisfies PT symmetry. A VNA is connected to the readout coil to detect the frequency offset. The experimental results show that the system reflection coefficient changes with displacement. Figure 2 As shown in the figure, the experimental results show that the PT symmetric LC passive wireless displacement sensor system has higher sensitivity than the traditional system. The article also points out that when the system is operated near the EP, it can achieve a dramatic frequency response and high sensitivity. John S. Ho and other researchers proposed a special type of EP-based LC passive wireless sensor system, which also achieved ultra-sensitive displacement sensing. The system is shown in the figure. Figure 3 As shown. Unlike traditional EP-based wireless sensors, the reader in this system is a system with PT symmetry locked to EP, while the sensor is an additional resonant system. The only function of the sensor is to generate an external perturbation to the coupling strength k through inductive coupling with the reader, which is an innovative attempt in the design of LC passive wireless sensor systems.

[0006] Although the PT-symmetric LC wireless passive displacement sensor can show high sensitivity at the EP point, there are still many shortcomings. First, for the PT-symmetric LC resonator, when the system deviates from the EP point, sensitivity degradation will inevitably occur, so that Δω will follow ~ε k changes; secondly, the EP point of the PT symmetric system is fuzzy, and the state switching on both sides of the EP point is gradual rather than sudden, which makes it difficult to calibrate in the experiment. Although hardware and algorithms with EP locking function can be developed, this increases the complexity of the system and may deteriorate the response time of the system. The system is also very susceptible to uncertain external environmental influences (such as component temperature drift), causing the system to deviate from the EP point again; finally, the method of using expensive and bulky detection equipment such as VNA to monitor frequency offset has limitations for different applications. All VNAs need to be calibrated before measurement, which also reduces their appeal to non-technical users. Summary of the invention

[0007] The object of the present invention is to provide a displacement sensing system and a displacement measuring method based on PT symmetry.

[0008] In a first aspect, the present invention provides a displacement sensing system based on PT symmetry, which includes a sensor, a transmitter and a receiver. The sensor includes a parallel resonant capacitor C S 、Inductor L S and resistor R S ; The transmitter includes a parallel resonant capacitor C T 、Inductor LT and negative resistance R T ; The receiver includes a parallel resonant capacitor C R 、Inductor L R and resistor R R ; Resonant capacitor C S , resonant capacitor C T , resonant capacitor C R The capacitance value is the same; the inductor L S 、Inductor L T 、Inductor L R The inductance value and polarity are the same; the resistance R S With resistor R R The resistance value is the same; the distance d between the sensor and the transmitter TS By the voltage amplitude ratio between the transmitter and the receiver V Rn Get;

[0009] During operation, the sensor only moves in the direction close to the transmitter, and the sensor and receiver are combined into an energy module. SR The virtual resonator maintains the equivalent coupling coefficient k between the virtual resonator and the transmitter. TSR Greater than or equal to the reference gain coefficient Γ0; so that the sensor, transmitter and receiver work in a PT symmetric state.

[0010] The key condition for the sensor, transmitter and receiver to work in the PT symmetric state is: the inductor L S 、Inductor L T and the inductor L R The polarity is the same; the sensor and receiver are combined into a SR The virtual resonator, the equivalent coupling coefficient k between the virtual resonator and the transmitter TSR Greater than or equal to the reference gain factor Γ0; the sensor only moves in the direction closer to the transmitter.

[0011] As a preference, if the coupling coefficient k between the sensor and the transmitter before movement is TS >(2 / 3) 0.5 Γ0, then set the coupling coefficient between the transmitter and the receiver to k TS / 2 0.5 Otherwise, the coupling coefficient between the transmitter and the receiver is set to

[0012] As a preference, the equivalent coupling rate κ TSR The expression is:

[0013]

[0014] Among them, k TRis the coupling coefficient between the transmitter and the receiver; k TS is the coupling coefficient between the transmitter and the sensor.

[0015] Preferably, the operating frequency ω of the wireless passive displacement sensing system is as follows:

[0016]

[0017] Where ω0 is the reference resonant frequency of the sensor, transmitter and receiver; κ TS is the coupling ratio between the transmitter and the sensor; κ TR is the coupling rate between the transmitter and the receiver; γ0 is the reference loss rate between the sensor and the receiver.

[0018] Preferably, the expression of the reference loss rate γ0 is:

[0019]

[0020] The expression of reference gain coefficient Γ0 is:

[0021]

[0022] Among them, L0 is the inductance coil L S 、Inductor L T 、Inductor L R Same inductance value; R0 is the resistance R S With resistor R R Same resistance value.

[0023] Preferably, the negative resistance is realized by a self-excited oscillation amplifier with a positive feedback structure.

[0024] In a second aspect, the present invention provides a displacement measurement method, which uses the above-mentioned displacement sensing system. The displacement measurement method is specifically as follows:

[0025] The sensor is placed on the target, and the transmitter and receiver are placed in the moving direction of the target. During the movement of the target, the equivalent coupling coefficient k between the virtual resonator and the transmitter is maintained. TSR Greater than or equal to the reference gain factor Γ0. By the voltage amplitude ratio V between the transmitter and the receiver Rn Get the distance d between the sensor and the transmitter TS , thereby obtaining the displacement of the target being measured.

[0026] Preferably, the distance d between the acquisition sensor and the transmitter is TS The method is as follows:

[0027] Build voltage amplitude ratio V RnThe relationship with the coupling coefficient k is:

[0028]

[0029] Among them, k TS is the coupling coefficient between the transmitter and the sensor; k TR is the coupling coefficient between the transmitter and the receiver.

[0030] According to the distance d between the transmitter and the receiver TR Get the corresponding coupling coefficient k TR Then, substitute into the above formula to obtain the coupling coefficient k between the transmitter and the sensor. TS , using the coupling coefficient k TS Get the distance d between the sensor and the transmitter TS .

[0031] The present invention has the following beneficial effects:

[0032] 1. The present invention detects displacement by setting a third-order PT symmetric system, and can achieve high sensitivity without limiting the system to work at a singular point, so that the system can achieve a more flexible and larger operating area sensing setting; at the same time, when the initial coupling coefficient between the sensor and the transmitter is known, the sensitivity of displacement detection can be improved by setting the distance between the transmitter and the receiver.

[0033] 2. The present invention detects displacement by detecting the voltage amplitude ratio. Compared with the traditional detection frequency and impedance, the voltage detection method is simpler and avoids the use of bulky and expensive instruments, greatly reducing the difficulty of operation and improving portability. At the same time, the voltage ratio between the detection readers replaces the detection frequency offset, making the experimental phenomenon more observable. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 Schematic diagram of PT-symmetrical ultra-sensitive wireless displacement sensing technology; (a) is the system schematic diagram; (b) is the measurement device schematic diagram.

[0035] Figure 2 Schematic diagram of the change of reflection coefficient with displacement in PT-symmetrical ultra-sensitive wireless displacement sensing technology.

[0036] Figure 3 Schematic diagram of a wireless microsensor with an EP lock reader; wherein (a) is a system schematic diagram; and (b) is a circuit schematic diagram.

[0037] Figure 4 It is a circuit schematic diagram of the present invention.

[0038] Figure 5 It is the work flow chart of the present invention.

[0039] Figure 6 is the different coupling coefficients k in the present invention TS and k TR The voltage under V Rn Schematic diagram of changes.

[0040] Figure 7 is the different coupling coefficients k in the present invention TR and k TS The sensitivity S v Schematic diagram of changes.

[0041] Figure 8 Schematic diagram of the experimental platform of the displacement sensor system in Example 1 of the present invention.

[0042] Fig. 9 This is a circuit diagram of a voltage-controlled negative resistor in Example 1 of the present invention.

[0043] Fig.10 Schematic diagram of the relationship between the coupling coefficient and the distance in Example 1 of the present invention.

[0044] Fig.11 The different coupling rates κ in Comparative Example 1 of the present invention TS and κ TR The corresponding schematic diagram of the normalized characteristic frequency change is shown below.

[0045] Fig.12 is the sensitivity S of the detection voltage ratio in comparative example 1 of the present invention V and the sensitivity of detecting frequency deviation S ω Relative to k TS A holistic view of change.

[0046] Fig.13 Schematic diagram of the change of voltage amplitude ratio offset and frequency ratio offset under different coupling coefficient offsets in comparative example 1 of the present invention; wherein (a) is the initial distance d TS (a) is a schematic diagram of the change of voltage amplitude ratio offset and frequency ratio offset at 40 mm; (b) is a schematic diagram of the change of voltage amplitude ratio offset and frequency ratio offset at the initial distance d TS This is a schematic diagram of the changes in voltage amplitude ratio offset and frequency ratio offset at 36mm. DETAILED DESCRIPTION

[0047] The present invention will be further described below in conjunction with the accompanying drawings.

[0048] like Figure 4 and Figure 5 As shown, a displacement sensing system based on PT symmetry includes a reader and a sensor; the reader includes a transmitter (Tx) and a receiver (Rx); the sensor, the transmitter and the receiver are all LC resonators; the sensor is composed of a resonant capacitor CS 、Inductor L S and resistor R S Parallel connection; the transmitter consists of a resonant capacitor C T 、Inductor L T and negative resistance R T Parallel connection; the receiver consists of a resonant capacitor C R 、Inductor L R and resistor R R When the distance d between the sensor and the transmitter is TS When the coupling coefficient k between the sensor and the transmitter changes TS The voltage between the transmitter and the receiver changes accordingly. Rn The voltage amplitude ratio V Rn It can reflect the displacement change of the sensor and realize displacement sensing.

[0049] The inductor coils and resonant capacitors of the sensor, transmitter, and receiver are the same. The reference inductor L0 and the reference capacitor C0 represent the same inductance and capacitance of the sensor, transmitter, and receiver. The resistance of the sensor and receiver are both set to the reference resistance R0. The resistance of the transmitter is a negative resistance, set to -R T Based on coupled mode theory, the state equation of the displacement sensing system is as follows:

[0050]

[0051] Where a is the energy mode in the transmitter, sensor and receiver; a T is the energy mode of the transmitter; a S is the energy mode of the sensor; a R is the energy mode in the receiver; H is the Hamiltonian of the displacement sensing system; ω0 is the reference resonant frequency of the sensor, transmitter and receiver; g T is the gain rate of the transmitter; κ TS is the coupling ratio between the transmitter and the sensor; κ TR is the coupling rate between the transmitter and the receiver; γ0 is the reference loss rate between the sensor and the receiver.

[0052] Gain rate g T And the expression of reference loss rate γ0 is:

[0053]

[0054] Among them, G T is the gain coefficient, Γ0 is the reference gain coefficient.

[0055] Coupling rate κ TS and κ TR The expression is:

[0056]

[0057] Among them, k TS is the coupling coefficient between the transmitter and the sensor; k TR is the coupling coefficient between the transmitter and the receiver; M TS Mutual inductance between transmitter and sensor; M TR Mutual inductance between transmitter and receiver.

[0058] The Hamiltonian H in the displacement sensing system should remain unchanged under the combined operation of parity change P and time reversal T. Since the PT symmetry of the third-order Hamiltonian is not easy to observe, converting the third-order Hamiltonian into a second-order form is a more intuitive way to observe its PT symmetry. In steady-state analysis, the energy norm a follows e iωt By substituting da / dt=iωa into formula (1), we can obtain:

[0059]

[0060] Where ω is the system characteristic frequency.

[0061] According to formula (4), the energy modulus a is obtained S and a R The expression is:

[0062]

[0063] According to formula (5), the energy modulus a is obtained S and a R The relationship is:

[0064]

[0065] From formula (6), we can see that if the coupling rate κ TS and κ TR The polarity is the same, then the energy modulus a S and a R are in phase, that is, they are synchronized in phase; if the coupling rate κ TS and κ TR The polarity is opposite, then the energy module a S and -a R Synchronization. Under the premise of phase synchronization, it has energy mode a S and a R The sensors and receivers can be combined into a SR The virtual resonator has an equivalent coupling rate with the transmitter of κ TSR , then the displacement sensing system can be further described as:

[0066]

[0067] According to formulas (4) and (7), the equivalent coupling rate κ is obtained TSR The expression is:

[0068]

[0069] Define a′=[a T ,a SR ] T , the state equation of the displacement sensing system can be further described as:

[0070]

[0071] The Hamiltonian H′ in equation (9) remains unchanged under the combined operation of parity change P and time reversal T, which shows that the system has PT symmetry. According to |ωI-H′|=0, the characteristic frequency ω of the displacement sensing system satisfies the following equation:

[0072]

[0073] Among them, I is the unit matrix; Δω is the frequency difference, Δω=ω-ω0.

[0074] Separating the real and imaginary parts of equation (10), the real number solution of the characteristic frequency ω is obtained as:

[0075]

[0076] Among them, κ c is the critical coupling rate, κ c =γ0.

[0077] When TSR ≥κ c When g T =γ0. When κ TSR <κ c When the system works in the PT symmetry breaking state (i.e., weak coupling region), the system gain g T =κ 2 TSR / γ0. The adaptive adjustable gain is realized by using the nonlinear gain saturation mechanism of the operational amplifier and a linear amplifier with positive feedback structure. In the PT symmetry breaking state, the eigenfrequency is degenerated to ω0.

[0078] Using the voltage amplitude ratio as a detection parameter to sense the distance change between the transmitter coil and the sensor coil actually introduces the coupling rate κ TSFor an RLC resonator, the energy mode can be expressed as |a| = (C0 / 2) 0.5 V; therefore, the voltage amplitude V represents the amplitude information of the energy mode |a|. Substituting the eigenfrequency value of equation (11) into equation (5), we get the voltage amplitude ratio V Rn The expression is:

[0079]

[0080] Among them, k TSR is the equivalent coupling coefficient,

[0081] Different coupling coefficients k TS and k TR The voltage amplitude under the condition is V Rn like Figure 6 As shown. Figure 6 In the symmetric state (k TSR ≥Γ0), if k TR remains unchanged, the voltage amplitude ratio V Rn Direct monitoring of the coupling coefficient k TS The displacement change of the sensor is first reflected as the coupling coefficient k TS The change is then converted into a voltage amplitude ratio V Rn When the system is in the PT-breaking state (k TSR <Γ0), the voltage amplitude is greater than V Rn =k TR / Γ0, its effect on k TS Not sensitive to changes.

[0082] Define the voltage amplitude ratio V Rn For the coupling coefficient k TS The sensitivity is S v =|ΔV Rn / Δk TS |; where ΔV Rn is the voltage amplitude ratio V Rn The deviation of Δk TS is the coupling coefficient k TS When the offset Δk TS Small enough, sensitivity S v By the voltage amplitude ratio V Rn Derivation to obtain, sensitivity S v The expression is:

[0083]

[0084] At EP, a positive offset Δk is required TS To ensure that the system is not in a PT destruction state. From formula (13), it can be seen that the sensitivity S v Depends on the coupling coefficient k TR , which can be obtained by the coupling coefficient k between the transmitter and the receiver TR To adjust the sensitivity S v .pass Get the maximum sensitivity S v,max , maximum sensitivity S v,max The expression is:

[0085]

[0086] Different coupling coefficients k TR and k TS Lower sensitivity S v like Figure 7 As shown, the color bar on the right shows the sensitivity S v The red solid line in the figure shows the size of the coupling coefficient k. TS Maximum sensitivity under conditions S v,max And the corresponding coupling coefficient k TR , the point marked with a star is S v,max The peak value S v,peak Therefore, given the reference gain coefficient Γ0 and coupling coefficient k TS In the case of TR Make the system work in PT symmetric state while achieving maximum sensitivity requirement, peak value S v,peak The expression is:

[0087]

[0088] The initial coupling coefficient k TS The best coupling coefficient k under the condition TR The design is summarized into two cases listed in Table 1:

[0089] Table 1 Initial coupling coefficient k TS The best coupling coefficient k under the condition TR

[0090]

[0091] Example 1

[0092] like Figure 8As shown in Figure 1, a third-order PT symmetric LC passive wireless displacement sensor system experimental platform was built. In this model, the sensor, transmitter, and receiver are implemented by using the same LC resonator, and are coaxially aligned in sequence and fixed on a guide rail (with an accuracy of 0.1 mm) to accurately control the distance between the coils. The negative resistance in the transmitter is implemented by a self-excited oscillation amplifier with a positive feedback structure and connected in parallel with the LC resonator, as shown in Figure 1. Fig. 9 shown.

[0093] Each resonator consists of an identical printed spiral coil with an inductance of 22.3μH measured by an impedance analyzer (E4990A). Each coil is tuned to a natural resonant frequency of 2.14MHz (f0=ω0 / 2π). The inductor parallel parasitic resistance measured at 2.14MHz is 12.5kΩ. When the sensor perturbation is small, the operating frequency is close to the natural resonant frequency, so the parasitic resistance can be considered a constant. This parasitic resistance, together with the additional 20kΩ resistor in parallel with the LC resonator, forms a loss of Γ0≈0.03898. The parasitic resistance loss of the transmitter can be absorbed into a negative resistance, which is obtained by using a self-oscillating amplifier (LM7171) and three feedback resistors (R f1 =30Ω, R f2 =510Ω, R f3 =5.1kΩ). The amplifier is powered by a ±5V DC power supply (UTP8305C). The coupling coefficient k (k TS or k TR ) at different distances d(d TS or TR )like Fig.10 shown.

[0094] When the sensor moves toward the transmitter, the equivalent coupling coefficient k between the virtual resonator and the transmitter is maintained. TSR Greater than or equal to the reference gain coefficient Γ0, coupling coefficient k TR remains unchanged by detecting the voltage amplitude ratio V between the transmitter and the receiver Rn Get the distance d between the sensor and the transmitter TS .

[0095] Comparative Example 1

[0096] Compared with Example 1, the present invention uses frequency to detect displacement in the PT symmetric working state; Fig.11 As shown, different coupling rates κ are measured in the working state of the present invention. TS and κ TR The corresponding normalized characteristic frequency (ω n=ω / ω0). From the figure, we can clearly see the abnormal line with phase change. We can also see the high sensitivity of frequency change around the abnormal line. This characteristic has also been applied to the sensor system in previous research to realize an ultra-high sensitivity sensor.

[0097] from Fig.12 It can be seen from the figure that, except at the abnormal line EL or in the extreme area outside the abnormal line EL, the sensitivity S of the detection voltage amplitude ratio is V Almost in the entire PT symmetry area, it is higher than the sensitivity S for detecting frequency shift ω In addition, in certain applications, for a given k TS and Γ0, we can design a suitable k TR , which can further improve the sensitivity of the system and ensure that the system is TS It always works in the PT symmetric state within the range of change.

[0098] For a specific k TR , choose the appropriate k TS , and then gradually reduce the distance between the transmitter and the sensor, and measure the voltage amplitude ratio or frequency across the receiver and the transmitter in the two cases in Table 1. Fig.13 As shown, although different d TR and d TS , but the measured results are consistent with the experimental results. At the same time, the detection voltage amplitude ratio shifts ΔV Rn is the detection frequency offset Δω n For Δk TS Ten times the response, ΔV Rn and Δω n All follow ~Δk TS This is due to the fuzziness of the EP points, and the fuzzy EP properties will not affect ΔV Rn The application of detection has too great an impact. This further verifies the feasibility and superiority of the present invention.

Claims

1. A displacement sensing system based on PT symmetry, characterized in that: It includes a sensor, a transmitter and a receiver; the sensor includes a parallel resonant capacitor C S 、Inductor L S and resistor R S ; The transmitter includes a parallel resonant capacitor C T 、Inductor L T and negative resistance R T ; The receiver includes a parallel resonant capacitor C R 、Inductor L R and resistor R R ; Resonant capacitor C S , resonant capacitor C T , resonant capacitor C R The capacitance value is the same; the inductor L S 、Inductor L T 、Inductor L R The inductance value and polarity are the same; the resistance R S With resistor R R The resistance value is the same; the distance d between the sensor and the transmitter TS By the voltage amplitude ratio between the transmitter and the receiver V Rn Get; During operation, the sensor only moves in the direction close to the transmitter, and the sensor and receiver are combined into an energy module. SR The virtual resonator maintains the equivalent coupling coefficient k between the virtual resonator and the transmitter. TSR Greater than or equal to the reference gain coefficient Γ0; so that the sensor, transmitter and receiver work in a PT symmetric state.

2. A displacement sensing system based on PT symmetry according to claim 1, characterized in that: During operation, if the coupling coefficient k between the sensor and the transmitter before moving TS >(2 / 3) 0.5 Γ0, then set the coupling coefficient between the transmitter and the receiver to k TS / 2 0.5 ; Otherwise, the coupling coefficient between the transmitter and the receiver is set to 3. The displacement sensing system based on PT symmetry according to claim 1, characterized in that: The equivalent coupling coefficient k TSR The expression is: Among them, k TR is the coupling coefficient between the transmitter and the receiver; k TS is the coupling coefficient between the transmitter and the sensor.

4. The displacement sensing system based on PT symmetry according to claim 1, characterized in that: The operating frequency ω of the displacement sensing system based on PT symmetry is as follows: Where ω0 is the reference resonant frequency of the sensor, transmitter and receiver; κ TS is the coupling ratio between the transmitter and the sensor; κ TR is the coupling rate between the transmitter and the receiver; γ0 is the reference loss rate between the sensor and the receiver.

5. A displacement sensing system based on PT symmetry according to claim 4, characterized in that: The expression of the reference loss rate γ0 is: Among them, L0 is the inductance coil L S 、Inductor L T 、Inductor L R The inductance value.

6. The displacement sensing system based on PT symmetry according to claim 4, characterized in that: The expression of the reference gain coefficient Γ0 is: Where R0 is the resistance R S With resistor R R Same resistance value.

7. The displacement sensing system based on PT symmetry according to claim 1, characterized in that: The negative resistance R T This is achieved through a self-oscillating amplifier with a positive feedback structure.

8. The displacement sensing system based on PT symmetry according to claim 1, characterized in that: The receiver is placed on the side of the transmitter facing away from the sensor.

9. A displacement measurement method, characterized in that: Using the PT symmetry-based displacement sensing system described in claim 1, the displacement measurement method is as follows: The sensor is placed on the target, and the transmitter and receiver are placed on the side of the target close to the moving direction. During the movement of the target, the equivalent coupling coefficient k between the virtual resonator and the transmitter is maintained. TSR Greater than or equal to the reference gain factor Γ0; by the voltage amplitude ratio V between the transmitter and the receiver Rn Get the distance d between the sensor and the transmitter TS , thereby obtaining the displacement of the target being measured.

10. A displacement measurement method according to claim 9, characterized in that: The distance d between the sensor and the transmitter is obtained TS The method is as follows: Voltage Amplitude Ratio V Rn The relationship with the coupling coefficient k is: Among them, k TS is the coupling coefficient between the transmitter and the sensor; k TR is the coupling coefficient between the transmitter and the receiver; According to the distance d between the transmitter and the receiver TR Get the corresponding coupling coefficient k TR Then, substitute into the above formula to obtain the coupling coefficient k between the transmitter and the sensor. TS , using the coupling coefficient k TS Get the distance d between the sensor and the transmitter TS .

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