Compact three-order PT symmetrical wireless sensing system and method based on capacitive coupling

Abstract

The invention discloses a compact three-order PT symmetrical wireless sensing system and method based on capacitive coupling. The wireless sensing system comprises a reader and a sensor. The reader comprises a resonant capacitor C1, a transmitting coil L1 and a negative resistor R1; the sensor comprises a resonant capacitor C4, a resistor R2, a receiving coil L3, a resonant capacitor C2, a resonant capacitor C3 and a receiving coil L2, wherein the resonant capacitor C3 can be used as a capacitance sensing element to sense the change of other physical quantities; the resonant capacitor C3, the resonant capacitor C2 and the receiving coil L2 are connected in series to form an LC resonant circuit; the resonant capacitor C4, the resonant capacitor C2, the receiving coil L3 and the resistor R2 are sequentially connected in series to form an LRC resonant circuit; by introducing an internal bypass capacitor, a PT symmetric system with a third-order exception point is synthesized in a single-coil resonator, so that the system is more compact in size space, and the requirements of design flexibility and miniaturization are met.

Description

Technical Field

[0001] The invention belongs to the technical field of wireless sensing, and in particular relates to a compact third-order PT symmetric wireless sensing system and method based on capacitive coupling. Background Art

[0002] The concept of parity time (PT) symmetry first appeared in the fields of quantum mechanics and optics. In the 1990s, Professor Bender CM and his research team in the United States pioneered the PT symmetry theory, revealing the phenomenon that a class of non-Hermitian Hamiltonian operators that satisfy PT symmetry have real eigenvalues. PT symmetry refers to the property of a system that remains unchanged after parity transformation and time reversal. The discovery of PT symmetry has led to its wide application in many different fields. In electronics research, gain / loss type resonators and their couplings can be designed to meet the conditions of PT symmetry, thereby realizing a PT symmetric system.

[0003] In the PT symmetric system, there is a non-Hermitian special degenerate point, namely the exceptional point (EP). EP is the critical point where the PT symmetry is broken, which will cause the n eigenvalues ​​of the system and their corresponding eigenvectors to merge at the same time, making the eigenvalues ​​of the system particularly sensitive to external disturbances. ω When the disturbance is ω 1 / n Theoretically, even with a tiny disturbance, the degenerate eigenvalues ​​of the system will show a strong response. This provides a new idea for research in the field of electronic sensing.

[0004] Taking advantage of the EP's ability to enhance sensor sensitivity, researchers have implemented many EP-based sensor systems that have shown extremely high sensitivity in practice. Based on this background, most electronic sensors use magnetic induction coupling between multiple resonant coils to achieve wireless sensing applications. In order to further improve the sensitivity, existing solutions increase the sensitivity order by increasing the number of magnetically coupled resonant coils, resulting in a larger system size. This spatial configuration limits the flexibility and miniaturization of PT symmetric system design to a certain extent. Figure 1 As shown in the figure, the existing three-order PT symmetric sensing system requires three coils arranged in this way to form two coupling coefficients of equal size in turn to satisfy the PT symmetry, which undoubtedly takes up a large space and even makes it unusable in some occasions. Therefore, how to minimize the system size without affecting the order of sensor sensitivity is a problem worth exploring. Summary of the invention

[0005] The object of the present invention is to provide a compact third-order PT symmetric wireless sensing system and method based on capacitive coupling.

[0006] In the first aspect, the present invention provides a compact third-order PT symmetrical wireless sensing system based on capacitive coupling, which includes a reader and a sensor; the reader includes a resonant capacitor C1, a transmitting coil L1 and a negative resistor -R1; the sensor includes a resonant capacitor C4, a resistor R2, a receiving coil L3, a resonant capacitor C2, a resonant capacitor C3 and a receiving coil L2; the resonant capacitor C3, the resonant capacitor C2 and the receiving coil L2 are connected in series to form an LC resonant circuit; the resonant capacitor C4, the resonant capacitor C2, the receiving coil L3 and the resistor R2 are connected in series in sequence to form an LRC resonant circuit; the wireless sensing system operates at an exceptional point.

[0007] As a preference, the conditions for working at the exceptional point are: the capacitance value of the resonant capacitor C1 is equal to the equivalent capacitance value of the resonant capacitor C2 and the resonant capacitor C3 in series; the capacitance values ​​of the resonant capacitor C3 and the resonant capacitor C4 are equal; the inductance values ​​of the transmitting coil L1, the receiving coil L2 and the receiving coil L3 are equal; the resistance values ​​of the negative resistor -R1 and the resistor R2 are equal; the coupling rate κ between the transmitting coil L1 and the receiving coil L2 12 Equal to the coupling ratio κ between the receiving coil L2 and the receiving coil L3 23 ; The reference coupling rate κ and loss rate γ satisfy 2κ 2 =γ 2 ; Reference coupling rate κ and coupling rate κ 12 equal.

[0008] Preferably, the resonant capacitor C3 is a capacitive sensing element disturbed by the measured environmental parameters.

[0009] Preferably, the capacitive sensing element is a capacitive position sensor, a capacitive pressure sensor, a capacitive liquid level sensor, or a variable area capacitive sensor.

[0010] Preferably, the resonant capacitor C1, the transmitting coil L1 and the negative resistor -R1 in the reader are connected in series.

[0011] Preferably, the negative resistor -R1 is measured using a vector network analyzer.

[0012] Preferably, the coupling rate κ 12 and coupling rate κ 23 The way to obtain is as follows:

[0013]

[0014] Wherein, M is the mutual inductance between the transmitting coil L1 and the receiving coil L2; ω is the operating frequency of the system; and L is the equivalent resonant inductance equal to the inductance of the transmitting coil L1.

[0015] Preferably, the mutual inductance M is obtained as follows:

[0016]

[0017] Wherein, C is an equivalent resonant capacitor having the same capacitance value as the resonant capacitor C1.

[0018] In the second aspect, the present invention provides a compact third-order PT symmetric wireless sensing method based on capacitive coupling, which adopts the above-mentioned wireless sensing system; the sensing method is specifically as follows: adjusting the distance between the reader and the sensor so that the wireless sensing system works at an exceptional point; when the environmental change causes the disturbance applied to the sensor to change, the characteristic frequency of the system will also change accordingly, by detecting the deepest drop point of the reflection coefficient and frequency relationship diagram of the system and the input impedance Z in The imaginary part of the signal is used to monitor environmental changes by crossing the zero point.

[0019] As an example, the deepest drop point of the reflection coefficient and frequency relationship diagram is detected by a vector network analyzer; the input impedance Z in The zero crossing point of the imaginary part is detected by an impedance analyzer.

[0020] The present invention has the following beneficial effects:

[0021] 1. The present invention synthesizes a PT symmetric system with a third-order exceptional point (EP3) in a single-coil resonator by introducing an internal bypass capacitor. Compared with the existing third-order relay PT symmetric sensing system, the present invention reduces the number of coils and makes the sensor system more compact.

[0022] 2. The present invention applies disturbance to the capacitor in the LC resonant circuit, so that the maximum sensitivity of the system is better than that of the traditional third-order relay PT symmetrical sensing system; at the same time, the present invention only needs a vector network analyzer to provide energy to the system and monitor frequency changes, making the measurement results faster and ensuring the accuracy of the measurement results. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 This is the circuit schematic diagram of the third-order relay PT symmetrical wireless sensing system.

[0024] Figure 2 This is a circuit schematic diagram of the wireless sensor system in the present invention.

[0025] Figure 3 It is a comparison diagram between the frequency simulation value and the theoretical value of the present invention.

[0026] Figure 4 The figure is a relationship diagram between the frequency splitting and the disturbance amount of the wireless sensor system of the present invention in logarithmic coordinates.

[0027] Figure 5 This is a graph showing the relationship between the frequency splitting and the disturbance amount of the third-order relay PT symmetric sensing system in logarithmic coordinates. DETAILED DESCRIPTION

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

[0029] like Figure 2 As shown, a compact three-order PT symmetrical wireless sensing system based on capacitive coupling includes a reader and a sensor; the reader includes a resonant capacitor C1, a transmitting coil L1 and a negative resistor -R1 connected in series; the negative resistor -R1 adopts a vector network analyzer, which is used to provide energy for the system and also serves as a detection instrument; the sensor includes a resonant capacitor C2, a resonant capacitor C3, a resonant capacitor C4, a receiving coil L2, a receiving coil L3 and a resistor R2; the resonant capacitor C3, the resonant capacitor C2 and the receiving coil L2 connected in series in sequence constitute an LC resonant circuit; the resonant capacitor C4, the resonant capacitor C2, the receiving coil L3 and the resistor R2 connected in series in sequence constitute an LRC resonant circuit; the capacitance value of the resonant capacitor C1 is equal to the equivalent capacitance value of the resonant capacitor C2 and the resonant capacitor C3 connected in series; the capacitance values ​​of the resonant capacitor C3 and the resonant capacitor C4 are equal; the inductance values ​​of the transmitting coil L1, the receiving coil L2 and the receiving coil L3 are equal; the resistance values ​​of the negative resistor -R1 and the resistor R2 are equal.

[0030] In this embodiment, the resonant capacitor C3 is used as a capacitive sensing element to sense changes in other physical quantities. The capacitive sensing element is a capacitive position sensor, a capacitive pressure sensor, a capacitive liquid level sensor, or a variable area capacitive sensor.

[0031] Circuit analysis of wireless sensor systems based on Kirchhoff’s laws:

[0032]

[0033] Wherein, ω is the operating frequency; M is the mutual inductance between the transmitting coil L1 and the receiving coil L2, M=C / C2L; C is the equivalent resonant capacitance equal to the capacitance of the resonant capacitor C1; L is the equivalent resonant inductance equal to the inductance of the transmitting coil L1; I1, I2 and I3 are the currents on the transmitting coil L1, the receiving coil L2 and the receiving coil L3 respectively.

[0034] Define a = [a1, a2, a3] T System energy mode vector, where a1 is the energy mode of the reader, a2 and a3 are the energy modes of the LC resonant circuit and LRC resonant circuit in the sensor respectively; energy mode an Represented as a n =-iL n dI n / dτ, where n = 1, 2, 3. When the system operating frequency ω is approximately equal to the reference frequency ω0 (ω≈ω0), the sensor operates near EP; where ω0 = 1 / (LC) 1 / 2 . From this we get ω0 2 –ω 2 ≈2ω(ω0–ω). Let τ=ωt, and equation (1) can be rearranged as:

[0035]

[0036] Wherein, Z is an impedance having the same resistance value as negative resistor -R1 and resistor R2.

[0037] Formula (2) can be rewritten into the matrix form of formula (3):

[0038]

[0039] Where γ is the loss rate of the sensor, γ = Z / 2L; κ 12 is the coupling ratio between the transmitting coil L1 and the receiving coil L2, κ 12 =Mω / 2L;κ 23 is the coupling ratio between the receiving coil L2 and the receiving coil L3, κ 23 =1 / 2ωC2L.

[0040] When the system achieves coupling matching, κ=Cω / 2C2, and the solution of the system characteristic frequency ω is:

[0041]

[0042] Where κ is the reference coupling ratio.

[0043] If the system characteristic frequency ω works at the reference frequency ω0, the reference coupling rate κ and loss rate γ should satisfy: 2κ 2 =γ 2 When a disturbance ε is added to capacitor C3 ω When the equivalent resonant capacitance C of the LC resonant circuit where C3 is located will become C', 1 / C'=1 / C2+1 / (C3+ΔC), where ΔC is the change in capacitance C3, and the resonant frequency of the circuit becomes ω0+ε ω =1 / (LC') 1 / 2 , formula (3) can be rewritten as:

[0044]

[0045] Let Δω=ω0–ω, expand equation (5) and separate the real and imaginary parts, and we get:

[0046]

[0047] If equation (6) holds true, the real part of the equation can be rewritten as:

[0048] Δω 3 +ε ω Δω 2 +2κ 2 ε ω =0 (7)

[0049] Solve the real part offset formula of the system characteristic frequency:

[0050] Re(Δω)=2 1 / 3 κ 2 / 3 ε ω 1 / 3 (8)

[0051] It can be seen from equation (8) that when the receiving resonator C3 is disturbed in this sensor system, the real part of the characteristic frequency (reflection valley frequency) of the sensing mode shifts by approximately Re(Δω)=2 1 / 3 κ 2 / 3 ε ω 1 / 3 , the imaginary part is always zero. Therefore, the characteristic frequency response of the system at EP is Δω~ε ω 1 / 3 In the traditional third-order relay PT symmetric sensing system, the capacitance C3 of the perturbation receiving resonator is about Re(Δω)=κ 2 / 3 ε ω 1 / 3 It can be seen that the system proposed in this patent not only has a more compact size, but also has a higher sensitivity.

[0052] To verify the above theoretical results, a simulation circuit was built in the simulation software Advanced Design System (ADS). The reader coil inductance L1 = 10μH, the sensor coil inductance L2 = L3 = 10μH, the reader capacitance C1 = 1nF, the sensor capacitance C2 = 28.082nF, and C3 = C4 = 1.037nF were set. To simplify the analysis, the parasitic losses of the inductance and capacitance in the loop are not considered for the time being. C3 is the sensing capacitor, which is used to sense the small disturbance ε ω The negative resistance of the reader is realized by a vector network analyzer, which provides energy for the system and also serves as a detection instrument. The load of the sensor is R2 = 5.036Ω. At this time, the two coils have almost the same resonant frequency at f0 = ω0 / 2π = 1.592MHz. The coupling coefficient k at the EP point is obtained by κ = Cω0 / 2C2 12 =k 23=0.03561. According to formula (4), Figure 3 As shown, the relationship between the frequency and the coupling coefficient in such a compact third-order PT symmetric wireless sensing system can be verified.

[0053] It can be seen from equation (5) that changing the capacitance C3 is equivalent to applying a disturbance to the reference frequency ω0. At this time, it can be observed on the reflected impedance spectrum at the reader end that the steep depression of the reflected spectrum will shift, which corresponds to the characteristic situation where the imaginary part of the characteristic frequency is the smallest. Figure 4 The relationship between the frequency splitting and the disturbance of the compact third-order PT symmetric wireless sensor system in logarithmic coordinates is given. The straight line is the calculated theoretical data, and the square mark is the obtained simulation data. The simulation results are consistent with the theoretical results, and the obtained function slope is close to 1 / 3. It can be seen that the frequency offset response of the system is related to the disturbance ε ω The relationship is 1 / 3, which verifies the correctness of the theoretical model.

[0054] Figure 5 The relationship between the frequency splitting and the disturbance amount of the traditional third-order relay PT symmetrical sensing system in logarithmic coordinates is given. The parameter values ​​of the resonant capacitor, resonant inductor and load resistance of the circuit are consistent with those of the compact third-order PT symmetrical wireless sensing system. The resonant capacitor C1=C2=C3=1nF, the resonant inductor L1=L2=10μH, and the load R2=5.036Ω of the system are set. Figure 5 The solid line is the theoretical data obtained, and the square marks are the simulation data obtained. Figure 4 By comparison, it can be seen that the compact third-order PT symmetrical wireless sensing system has higher sensitivity.

[0055] The sensing method of this compact third-order PT symmetric wireless sensing system is as follows:

[0056] The EP of the system is regulated by adjusting the distance between the reader and the sensor. The system initially works at the EP point. When the environment changes and the disturbance applied to the resonant capacitor C3 changes, the characteristic frequency of the system will also change, which is reflected in the reflection coefficient (S 11 ) and the deepest dip in the frequency graph and the input impedance Z in The imaginary part of the zero crossing point changes, and the reflection coefficient (S 11 ) is the deepest drop point in the frequency relationship graph, and the impedance analyzer detects the input impedance Z in The disturbance change is monitored by the zero crossing point of the imaginary part of

Claims

1. A compact third-order PT symmetrical wireless sensing system based on capacitive coupling, comprising a reader and a sensor; the reader comprises a resonant capacitor C1, a transmitting coil L1 and a negative resistor -R1; the sensor comprises a resonant capacitor C4, a resistor R2 and a receiving coil L3; characterized in that: The sensor also includes a resonant capacitor C2, a resonant capacitor C3 and a receiving coil L2; the resonant capacitor C3, the resonant capacitor C2 and the receiving coil L2 are connected in series to form an LC resonant circuit; the resonant capacitor C4, the resonant capacitor C2, the receiving coil L3 and the resistor R2 are connected in series in sequence to form an LRC resonant circuit; the wireless sensing system works at an exceptional point.

2. The compact third-order PT symmetric wireless sensing system based on capacitive coupling according to claim 1 is characterized in that: The conditions for working at the exception point are: the capacitance value of the resonant capacitor C1 is equal to the equivalent capacitance value of the resonant capacitor C2 and the resonant capacitor C3 in series; the capacitance values ​​of the resonant capacitor C3 and the resonant capacitor C4 are equal; the inductance values ​​of the transmitting coil L1, the receiving coil L2 and the receiving coil L3 are equal; the resistance values ​​of the negative resistor -R1 and the resistor R2 are equal; the coupling rate κ between the transmitting coil L1 and the receiving coil L2 12 Equal to the coupling ratio κ between the receiving coil L2 and the receiving coil L3 23 ; The reference coupling rate κ and loss rate γ satisfy 2κ 2 =γ 2 ; Reference coupling rate κ and coupling rate κ 12 equal.

3. The compact third-order PT symmetric wireless sensing system based on capacitive coupling according to claim 1 is characterized in that: The resonant capacitor C3 is a capacitive sensing element that is disturbed by the measured environmental parameters.

4. The compact third-order PT symmetric wireless sensing system based on capacitive coupling according to claim 1 is characterized in that: The capacitive sensing element is a capacitive position sensor, a capacitive pressure sensor, a capacitive liquid level sensor, or a variable area capacitive sensor.

5. The compact third-order PT symmetric wireless sensing system based on capacitive coupling according to claim 1 is characterized in that: The resonant capacitor C1, the transmitting coil L1 and the negative resistor -R1 in the reader are connected in series.

6. The compact third-order PT symmetric wireless sensing system based on capacitive coupling according to claim 1 is characterized in that: The negative resistor -R1 is measured using a vector network analyzer.

7. The compact third-order PT symmetric wireless sensing system based on capacitive coupling according to claim 1 is characterized in that: The coupling ratio κ 12 and coupling rate κ 23 The way to obtain is as follows: Wherein, M is the mutual inductance between the transmitting coil L1 and the receiving coil L2; ω is the operating frequency of the system; and L is the equivalent resonant inductance equal to the inductance of the transmitting coil L1.

8. The compact third-order PT symmetric wireless sensing system based on capacitive coupling according to claim 7 is characterized in that: The mutual inductance M is obtained as follows: Wherein, C is an equivalent resonant capacitor having the same capacitance value as the resonant capacitor C1.

9. A compact third-order PT symmetric wireless sensing method based on capacitive coupling, characterized in that: The compact third-order PT symmetrical wireless sensing system based on capacitive coupling as described in claim 1 is adopted; the sensing method is as follows: adjusting the distance between the reader and the sensor so that the wireless sensing system works at the exceptional point; when the environmental change causes the disturbance applied to the sensor to change, the characteristic frequency of the system will also change accordingly, by detecting the deepest drop point of the reflection coefficient and frequency relationship diagram of the system and the input impedance Z in The imaginary part of the signal is used to monitor environmental changes by crossing the zero point.

10. The compact third-order PT symmetric wireless sensing method based on capacitive coupling according to claim 9 is characterized in that: The deepest drop point of the reflection coefficient and frequency relationship diagram is detected by a vector network analyzer; the input impedance Z in The zero crossing point of the imaginary part is detected by an impedance analyzer.

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