CN114812622A - High-sensitivity circuit based on third-order exception points - Google Patents

High-sensitivity circuit based on third-order exception points Download PDF

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CN114812622A
CN114812622A CN202210548850.XA CN202210548850A CN114812622A CN 114812622 A CN114812622 A CN 114812622A CN 202210548850 A CN202210548850 A CN 202210548850A CN 114812622 A CN114812622 A CN 114812622A
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CN114812622B (en
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王侍川
曹云姗
严鹏
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University of Electronic Science and Technology of China
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Abstract

The invention belongs to the technical field of electronic circuits, and particularly relates to a three-order exception point-based high-sensitivity circuit. The circuit model is a circuit with anti-PT symmetry and comprises a first unit, a second unit and a third unit, wherein each unit is formed by connecting an inductor, a resistor and a capacitor in parallel, the first unit and the second unit are connected with the second unit through resistors, and circuit parameters are configured based on a third-order exception, so that a high-sensitivity circuit is obtained. According to the invention, through different coupling modes among the three units, both the wired sensor and the wireless sensor can be designed, the ultra-sensitive response and the ultra-high resolution are shown, and the non-linear response to external disturbance can be generated according to the non-Hermite degeneracy on an abnormal point, so that the sensitivity is improved.

Description

High-sensitivity circuit based on third-order exception points
Technical Field
The invention belongs to the technical field of electronic circuits, and particularly relates to a three-order exception point-based high-sensitivity circuit.
Background
In recent decades, sensors with high sensitivity and high quality factor have attracted much attention in the fields of health inspection, environmental monitoring, etc. due to their wide application.
The sensor is a detection device which can sense the measured information and convert the sensed information into an electric signal or other information in a required form according to a certain rule to output so as to meet the requirements of information transmission, processing, storage, display, recording, control and the like. Collins realized the first compact passive wireless sensor based on inductive (L) and capacitive (C) resonant circuits in 1967. With the development of the technology, wireless sensors based on passive LC oscillation circuits are increasingly popular and can be used for measuring pressure, temperature, chemical reactions and the like.
Parity-time (PT) symmetric systems are a class of non-hermitian hamiltonian systems that are symmetric under the combined action of parity P and time reversal T, which have received a great deal of attention due to their interesting fundamental nature and promising applications. Such systems have been studied in many fields, such as quantum mechanics, optics, electronic circuits, and magnetic systems. PT symmetric non-hermitian quantities can exhibit a break in full real harmonics and spontaneous symmetry, with harmonic phase changes occurring at both real and complex numbers at the Exception Point (EP). EP is a spectral singularity in parameter space where two or more eigenvalues and their corresponding eigenvectors are merged simultaneously. In the vicinity of EP, the intrinsic frequency difference obeys the 1/N power exponential relation of external disturbance, wherein N is the order of EP, namely the number of combined eigenvalues is N, and the theory is verified through experiments in optical and electronic circuits. And the relation between the anti-PT symmetrical system and the PT symmetrical system is Hamilton quantity H APT ＝±iH PT Therefore, it is a feasible approach to design a high-order EP to improve sensor sensitivity.
Disclosure of Invention
The invention aims to design a sensor, namely a high-sensitivity circuit by utilizing the characteristics near EP3 (third-order exception), and mainly comprises the following steps: firstly, a circuit system model with anti-PT symmetry is built, then an equation of the circuit model is built by utilizing a kirchhoff current-voltage law, and a characteristic value equation is solved by utilizing a metal containing formula based on three-order example outliers to obtain parameters of the circuit.
The technical scheme of the invention is as follows:
a highly sensitive circuit based on three-order exception points is shown in FIG. 1, and comprises a first unit and a second unitElement and third unit, wherein the first unit is composed of parallel first inductor L 1 A first resistor R 1 A first capacitor C 1 The second unit is composed of a second inductor L connected in parallel 2 A second resistor R 2 A second capacitor C 2 The third unit is composed of a third inductor L connected in parallel 3 A third resistor R 3 And a third capacitance C 3 Forming; one end of the first unit passes through a fourth resistor R 4 One end of the second unit is connected with one end of the second unit through a fifth resistor R 5 The other end of the first unit, the other end of the second unit and the other end of the third unit are all grounded; defining the voltage at one end of the first unit as V 1 The voltage at one end of the second unit is V 2 The voltage at one end of the third unit is V 3 The design method of the element parameters in the circuit comprises the following steps:
establishing a circuit equation:
Figure BDA0003653610590000021
definition R ═ R 1 ＝R 3 ＝R 4 ＝R 5 ＝2R 2 ，C＝C 1 ＝C 2 ＝C 3 ，
Figure BDA0003653610590000022
ω n ＝(L n C) -0.5 Where Vn is Vn x exp (-i ω t), n is 1, 2, 3, we can obtain:
Figure BDA0003653610590000023
due to the fact that
Figure BDA0003653610590000024
The determinant of (a) is zero, and the following result is obtained:
aω 6 +bω 4 +cω 2 +d＝0
wherein a is-1, b is omega 1 2 +ω 2 2 +ω 3 2 -2α 2 ，c＝α 2 ω 1 2 +α 2 ω 3 2 -ω 1 2 ω 2 2 -ω 1 2 ω 3 2 -ω 2 2 ω 3 2 ，d＝ω 1 2 ω 2 2 ω 3 2 (ii) a Let omega become omega 2 And the condition ω is set 1 2 +ω 3 2 ＝2ω 2 2 The substitution equation is simplified to obtain:
aω 3 +bω 2 +cω+d＝0
wherein a is-1, b is 3 omega 2 2 -2α 2 ，c＝2α 2 ω 2 2 -2ω 2 4 -2ω 2 2 ω 3 2 +ω 3 4 ，d＝2ω 2 4 ω 3 2 -ω 2 2 ω 3 4 ；
Solving an equation based on the third-order exception point pairs, specifically: the third-order example exterior point means that the cubic equation has triple roots, which indicates that three characteristic frequencies are coincided, firstly R, C, L is determined 2 Then solving a one-dimensional cubic equation by using a heyday formula, and using a multiple root discriminant formula A ═ B ═ 0, wherein A ═ B 2 -3ac, B ═ bc-9ad, giving L 3 Parameter, passing condition ω 1 2 +ω 3 2 ＝2ω 2 2 Obtaining L in the circuit 1 The parameters of (1) are obtained, and all the element parameters under the third-order exception point are obtained at the moment.
The invention has the advantages that through different coupling modes among the three units, both the wired sensor and the wireless sensor can be designed, the ultra-sensitive response and the ultra-high resolution are shown, and the non-linear response to external disturbance can be generated according to the non-Hermite degeneracy on an abnormal point, so that the sensitivity is improved.
Drawings
Fig. 1 is a schematic diagram of the circuit structure of the present invention.
FIG. 2 is an evolution diagram of eigenvalues in the example.
FIG. 3 is a schematic diagram of a fitted straight line in the example.
FIG. 4 is an evolution diagram of the real part of the eigenfrequency in the embodiment.
FIG. 5 is a graph showing the trend of relative error with resistance in the examples.
Detailed Description
The invention is described in detail below with reference to the figures and examples.
Examples
This example is used to verify the scheme of the present invention, where R is 20000 Ω, C is 47nF, and L is 2 1mH, by the condition ω 1 2 +ω 3 2 ＝2ω 2 2 Change of L 1 And L 3 An evolution diagram of eigenvalues can be obtained as in fig. 2, where the solid line is the real part evolution of the eigenvalues, the dashed line is the imaginary part evolution of the eigenvalues, and the point is EP 3. Taking the parameter L at point EP3 1 ≈989.913uH，L 2 ＝1mH，L 3 1.01mH, R20000 Ω, C47 nF, at which the circuit system is at an abnormal point, at R 2 Applying a perturbation to the resistor, to
Figure BDA0003653610590000031
Wherein
Figure BDA0003653610590000032
Calculate Δ R increases from 0 to 50 ohms, Δ ω ═ ω (ω ═ ω) 1 -ω 2 ) The change in (d) is obtained by fitting theoretical data to obtain a fitted straight line of lg Δ ω ═ 0.3326lg- δ +2.862, and Δ ω ∈ δ + δ can be obtained as shown in fig. 3 1/3 And the evolution diagram 4 of the real part of the eigenfrequency under the disturbance. It can be seen that the third order EP implemented under this circuit enables the characteristic frequency to be split in 1/3 exponential form in the event of a perturbation at EP3, which is superior to the conventional second order EP circuit.
Considering EP3 under different resistance size systems, it is found by theory that the relative error at the EP3 point is smaller with the increase of the resistance, and the trend of the relative error with the resistance is as shown in fig. 5. But due to the condition omega 1 2 +ω 3 2 ＝2ω 2 2 The eigenvalues evolve at ω 2 2 Is centrosymmetric, so the imaginary part area of the characteristic root evolution becomes narrower as R increases. Therefore, in the case of a small relative error, EP3 can be implemented to enhance the sensitivity of the system by selecting an appropriate resistance value.

Claims (1)

1. A high-sensitivity circuit based on three-order exception points is characterized by comprising a first unit, a second unit and a third unit, wherein the first unit is composed of a first inductor L connected in parallel 1 A first resistor R 1 A first capacitor C 1 The second unit is composed of a second inductor L connected in parallel 2 A second resistor R 2 A second capacitor C 2 The third unit is composed of a third inductor L connected in parallel 3 A third resistor R 3 And a third capacitance C 3 Forming; one end of the first unit passes through a fourth resistor R 4 One end of the second unit is connected with one end of the second unit through a fifth resistor R 5 The other end of the first unit, the other end of the second unit and the other end of the third unit are all grounded; defining the voltage at one end of the first unit as V 1 The voltage at one end of the second unit is V 2 The voltage at one end of the third unit is V 3 The design method of the element parameters in the circuit comprises the following steps:
establishing a circuit equation:
Figure FDA0003653610580000011
definition of R ═ R 1 ＝R 3 ＝R 4 ＝R 5 ＝2R 2 ，C＝C 1 ＝C2＝C 3 ，
Figure FDA0003653610580000012
ω n ＝(L n C) -0.5 Where Vn is Vn x exp (-i ω t), n is 1, 2, 3, we can obtain:
Figure FDA0003653610580000013
due to the fact that
Figure FDA0003653610580000014
The determinant of (a) is zero, and the following result is obtained:
aω 6 +bω 4 +cω 2 +d＝0
wherein a is-1, b is omega 1 2 +ω 2 2 +ω 3 2 -2α 2 ，c＝α 2 ω 1 2 +α 2 ω 3 2 -ω 1 2 ω 2 2 -ω 1 2 ω 3 2 -ω 2 2 ω 3 2 ，d＝ω 1 2 ω 2 2 ω 3 2 (ii) a Let omega become omega 2 And the condition ω is set 1 2 +ω 3 2 ＝2ω 2 2 The substitution equation is simplified to obtain:
aω 3 +bω 2 +cω+d＝0
wherein a is-1, b is 3 omega 2 2 -2α 2 ，c＝2α 2 ω 2 2 -2ω 2 4 -2ω 2 2 ω 3 2 +ω 3 4 ，d＝2ω 2 4 ω 3 2 -ω 2 2 ω 3 4 ；
Solving an equation based on the third-order exception point pairs, specifically: the third-order example exterior point means that the cubic equation has triple roots, which indicates that three characteristic frequencies are coincided, firstly R, C, L is determined 2 The parameter(s) is obtained by solving a simple cubic equation through a prime equation and utilizing a multiple root discriminant formula of A ═ B ═ 0, wherein A ═ B 2 -3ac, B ═ bc-9ad, giving L 3 By the condition ω 1 2 +ω 3 2 ＝2ω 2 2 Obtaining L in the circuit 1 Is thereby obtained atAll component parameters at the third order exception point.
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Cited By (1)

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Publication number Priority date Publication date Assignee Title
CN117890682A (en) * 2023-12-27 2024-04-16 暨南大学 Method for improving EP sensitivity based on nonlinear effect

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CN110943694A (en) * 2019-10-30 2020-03-31 中山大学 Inverse-space-time symmetric circuit for Frokay modulation
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US3505477A (en) * 1966-03-21 1970-04-07 Int Standard Electric Corp Impedance network for resonant transfer multiplexing
CN103595284A (en) * 2013-11-27 2014-02-19 电子科技大学 Modular multi-level current converter passivity modeling and control method
CN105871210A (en) * 2016-04-14 2016-08-17 上海电力学院 Finite time passive control method for Buck converter
US20190190464A1 (en) * 2017-12-20 2019-06-20 Nxp Usa, Inc. Rf power transistors with impedance matching circuits, and methods of manufacture thereof
CN110943694A (en) * 2019-10-30 2020-03-31 中山大学 Inverse-space-time symmetric circuit for Frokay modulation
CN113671247A (en) * 2021-09-03 2021-11-19 东南大学 Online microwave power sensor based on PT symmetrical circuit

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117890682A (en) * 2023-12-27 2024-04-16 暨南大学 Method for improving EP sensitivity based on nonlinear effect

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