CN106026966B - A kind of notch filter method and circuit for GMI Magnetic Sensors - Google Patents

A kind of notch filter method and circuit for GMI Magnetic Sensors Download PDF

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CN106026966B
CN106026966B CN201610313456.2A CN201610313456A CN106026966B CN 106026966 B CN106026966 B CN 106026966B CN 201610313456 A CN201610313456 A CN 201610313456A CN 106026966 B CN106026966 B CN 106026966B
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resistance
capacitance
operational amplifier
phase inversion
signal
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CN106026966A (en
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徐�明
周宗潭
胡德文
王志华
郭善磁
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National University of Defense Technology
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    • HELECTRICITY
    • H03ELECTRONIC CIRCUITRY
    • H03HIMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
    • H03H9/00Networks comprising electromechanical or electro-acoustic devices; Electromechanical resonators
    • H03H9/46Filters
    • H03H9/54Filters comprising resonators of piezoelectric or electrostrictive material
    • H03H9/547Notch filters, e.g. notch BAW or thin film resonator filters

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  • Investigating Or Analyzing Materials By The Use Of Magnetic Means (AREA)

Abstract

The invention discloses a kind of notch filter method and circuit for GMI Magnetic Sensors, notch filter method and step includes input signal being carried out width phase inversion, and only keep waiting for that filtering interference signals amplitude is constant, phase invariant;It is exported after signal after width phase inversion is synthesized with both original input signal progress difference;Notch filter circuit includes width phase inversion module and difference synthesis module, width phase inversion module only keeps waiting for that filtering interference signals amplitude is constant, phase invariant, and both signal and the original input signal after width phase inversion export after difference synthesizes by the difference synthesis module.The present invention by the width phase inversion and difference of signal synthesize in the way of effectively power frequency electromagnet interference signal in biological light current, Magnetic testi field can be filtered out, it can be widely applied to the engineering application scenario that the requirement of trap attenuation multiple is high, resistor- capacitor matching degree used is not high in practice, with attenuation multiple height, and allow capacitance-type resistor slightly unmatched advantage.

Description

A kind of notch filter method and circuit for GMI Magnetic Sensors
Technical field
The present invention relates to the signal detection techniques of GMI Magnetic Sensors, and in particular to a kind of trap for GMI Magnetic Sensors Filtering method and circuit.
Background technology
GMI effects, i.e., when the silk or band of soft magnetic material (being mostly Co bases amorphous and Fe base nanometer crystals) pass to alternating current Flow IacWhen, the alternating voltage U at material both endswWith the external magnetic field H added by silk longitudinal directionexVariation and the phenomenon that sensitive variation, Essence is the impedance of amorphous wire itself with the sensitive variation of externally-applied magnetic field.
GMI Magnetic Sensors based on the design of GMI effects include soft magnetic material (being mostly Co bases amorphous and Fe base nanometer crystals) Silk or band constitute induction coil the impedance variations value of soft magnetic material can be converted by material by induction coil The alternating voltage U at both endsw, to realize external magnetic field HexMeasurement.Sensor based on the design of GMI effects has weak well Magnetic detection performance, detectivity can be used for the extremely detection in weak biological magnetic field under unshielded environments up to 1pT, than Such as core field, lung magnetic field, brain magnetic field.But extremely serious, the common city of electromagnetic pollution in our environment lived at present Electromagnetic noise all reaches nT ranks, and this partial noise is mainly the disturbance of power frequency and its each harmonic that power device generates Magnetic field, therefore when GMI Magnetic Sensors are for pT detection of magnetic field under unshielded environments, it is necessary to city noise is effectively filtered It removes, i.e., mainly Hz noise is filtered out.
It is filtered out for Hz noise, traditional method is using double-T shaped topological structure notch filter to specific The signal of frequency is filtered out, but double-T shaped topological structure notch filter have to the matching degree of resistor it is extremely stringent It is required that more slightly mismatching for resistor- capacitor will make notch depth rapid decrease, even if using accurate capacitance resistance Device, it is also difficult to reach ideal filter effect, therefore be normally used for attenuation multiple occasion of less demanding.But GMI magnetic passes It is very stringent to the attenuation requirement of set specific frequency signal, it is desirable that decline when sensor is used to carry out pT magnetic field detections under unshielded environments Double-diminished number need to reach 1000 times (- 60dB), it is contemplated that engineer application environment needs that resistor- capacitor is allowed slightly to mismatch, accurate Capacitance-type resistor can be met the requirements, and double T topological structures notch filters traditional in this way are extremely difficult to require.
Invention content
The technical problem to be solved in the present invention:For ambient enviroment electromagnetic pollution it is extremely serious in the case of, when using GMI Magnetic Sensor power frequency and its each harmonic signal interference in the biological magnetic field detection of unshielded environments hypodermis tesla are particularly acute The technical issues of, provide it is a kind of by two paths of differential signals synthesized in the way of power frequency electromagnet interference signal balanced out, can It is widely used in the engineering applied field that the requirement of trap circuit attenuation multiple is high, resistor- capacitor matching degree used is not high in practice It closes, attenuation multiple is high, and allows the slight unmatched notch filter method and electricity for GMI Magnetic Sensors of capacitance-type resistor Road.
In order to solve the above-mentioned technical problem, the technical solution adopted by the present invention is:
A kind of notch filter method for GMI Magnetic Sensors, step include:
1) input signal is subjected to width phase inversion, and only keeps waiting for that filtering interference signals amplitude is constant, phase invariant;
2) it is exported after synthesizing the signal after width phase inversion with both original input signal progress difference.
Preferably, the step 1) specifically refers to carry out input signal by Two-orders Butterworth bandpass filter Width phase inversion, the centre frequency of the Two-orders Butterworth bandpass filter are to wait for the frequency of filtering interference signals, gain It is 1.
Preferably, the Two-orders Butterworth bandpass filter includes the two-stage circuit of cascade arrangement, two-stage circuit Middle first order circuit includes resistance R1, resistance R2, resistance R3, capacitance C1, capacitance C2 and operational amplifier U1, operational amplifier U1 Negative input connect reference voltage, electrode input end passes sequentially through capacitance C1, resistance R1 is connected with signal to be filtered, resistance R2 One end is connected between capacitance C1 and resistance R1, another termination reference voltage, and resistance R3 concatenations are arranged in operational amplifier U1's Between electrode input end and output end, the one end capacitance C2 is connected between capacitance C1 and resistance R1, the other end and operational amplifier The output end of U1 is connected;Second level circuit includes resistance R4, resistance R5, resistance R6, capacitance C3, capacitance C4 and fortune in two-stage circuit Amplifier U2 is calculated, the negative input of operational amplifier U2 connects reference voltage, electrode input end passes sequentially through capacitance C3, resistance R4 It is connected with the output end of operational amplifier U1, the one end resistance R5 is connected between capacitance C3 and resistance R4, another termination is with reference to electricity Pressure, resistance R6 concatenations are arranged between the electrode input end and output end of operational amplifier U2, and the one end capacitance C4 is connected to capacitance Between C3 and resistance R4, the other end is connected with the output end of operational amplifier U2.
Preferably, the step 2) specifically refer to by scaling circuit by after width phase inversion signal be originally inputted Both signals export after carrying out difference synthesis.
Preferably, the scaling circuit includes that resistance R7, resistance R8, resistance R9 and operational amplifier U3, operation are put The negative input of big device U3 is connected by resistance R7 with the signal after width phase inversion, electrode input end and original input signal phase Even, resistance R9 concatenations are arranged between the electrode input end and output end of operational amplifier U3.
A kind of notch filter circuit for GMI Magnetic Sensors, including width phase inversion module and difference synthesis module, input Signal is divided into two-way, and input signal exports after carrying out width phase inversion by width phase inversion module to difference synthesis module all the way One input terminal, another way input signal are directly output to another input terminal of difference synthesis module, the width phase transformation mold changing Block only keeps waiting for that filtering interference signals amplitude is constant, phase invariant, the difference synthesis module by after width phase inversion signal with Both original input signals export after carrying out difference synthesis.
Preferably, the width phase inversion module is Two-orders Butterworth bandpass filter, the Two-orders Bart The centre frequency of Butterworth bandpass filter is to wait for the frequency of filtering interference signals, gain 1.
Preferably, the Two-orders Butterworth bandpass filter includes the two-stage circuit of cascade arrangement, two-stage circuit Middle first order circuit includes resistance R1, resistance R2, resistance R3, capacitance C1, capacitance C2 and operational amplifier U1, operational amplifier U1 Negative input connect reference voltage, electrode input end passes sequentially through capacitance C1, resistance R1 is connected with signal to be filtered, resistance R2 One end is connected between capacitance C1 and resistance R1, the other end is grounded, and the anode that resistance R3 concatenations are arranged in operational amplifier U1 is defeated Enter between end and output end, the one end capacitance C2 is connected between capacitance C1 and resistance R1, the other end and operational amplifier U1 it is defeated Outlet is connected;Second level circuit includes resistance R4, resistance R5, resistance R6, capacitance C3, capacitance C4 and operation amplifier in two-stage circuit The negative input of device U2, operational amplifier U2 connect reference voltage, electrode input end passes sequentially through capacitance C3, resistance R4 and operation The output end of amplifier U1 is connected, and the one end resistance R5 is connected between capacitance C3 and resistance R4, another termination reference voltage, resistance R6 concatenations are arranged between the electrode input end and output end of operational amplifier U2, and the one end capacitance C4 is connected to capacitance C3 and resistance Between R4, the other end is connected with the output end of operational amplifier U2.
Preferably, the difference synthesis module is scaling circuit.
Preferably, the scaling circuit includes that resistance R7, resistance R8, resistance R9 and operational amplifier U3, operation are put The negative input of big device U3 is connected by resistance R7 with the signal after width phase inversion, electrode input end and original input signal phase Even, resistance R9 concatenations are arranged between the electrode input end and output end of operational amplifier U3.
Notch filter method tool of the present invention for GMI Magnetic Sensors has the advantage that:The present invention is first by input signal Carry out width phase inversion, and only keep waiting for that filtering interference signals amplitude is constant, phase invariant, by after width phase inversion signal with it is original Both input signals export after carrying out difference synthesis, so that amplitude is not in the signal and original input signal after width phase inversion Become, phase invariant waits for that filtering interference signals are eliminated during difference synthesizes, power frequency electromagnet interference signal can be supported Disappear, can be widely applied to engineering, the requirement of trap circuit attenuation multiple is high in practice, resistor- capacitor matching degree used is not high Application scenario has attenuation multiple height, and allows capacitance-type resistor slightly unmatched advantage.
The present invention is for the notch filter that the notch filter circuit of GMI Magnetic Sensors is that the present invention is used for GMI Magnetic Sensors The corresponding circuit structure of method, therefore equally also have the advantages that above-mentioned, details are not described herein.
Description of the drawings
Fig. 1 is the electrical block diagram of notch filter circuit of the embodiment of the present invention.
Fig. 2 is width phase inversion module amplitude characteristic analog result in the embodiment of the present invention.
Fig. 3 is width phase inversion module phase characteristic analog result in the embodiment of the present invention.
Specific implementation mode
The present embodiment be used for GMI Magnetic Sensors notch filter method the step of include:
1) input signal is subjected to width phase inversion, and only keeps waiting for that filtering interference signals amplitude is constant, phase invariant;
2) it is exported after synthesizing the signal after width phase inversion with both original input signal progress difference.
In the present embodiment, step 1) specifically refers to carry out input signal by Two-orders Butterworth bandpass filter Width phase inversion, the centre frequency of Two-orders Butterworth bandpass filter are to wait for the frequency of filtering interference signals, gain 1, It in this way can be by 360 ° of the Phase advance of centre frequency (waiting for filtering interference signals).Two-orders Butterworth bandpass filter Quality factor preferably uses 2 or 5 or 10.
In the present embodiment, step 2) specifically refer to by scaling circuit by after width phase inversion signal be originally inputted Both signals export after carrying out difference synthesis.
As shown in Figure 1, notch filter circuit of the present embodiment for GMI Magnetic Sensors includes width phase inversion module and difference Synthesis module, input signal are divided into two-way, all the way input signal by width phase inversion module carry out width phase inversion after export to One input terminal of difference synthesis module, another way input signal are directly output to another input terminal of difference synthesis module, The width phase inversion module only keeps waiting for that filtering interference signals amplitude is constant, phase invariant, and the difference synthesis module is by width phase Signal after transformation exports after being synthesized with both original input signal progress difference.
In the present embodiment, width phase inversion module is Two-orders Butterworth bandpass filter, the Two-orders Bart The centre frequency of Butterworth bandpass filter is to wait for the frequency of filtering interference signals, gain 1, in this way (can wait for centre frequency Filtering interference signals) 360 ° of Phase advance.In addition, width phase inversion module can also use other kinds of width phase as needed Translation circuit can realize the signal after width phase inversion as long as only keeping waiting for that filtering interference signals amplitude is constant, phase invariant With original input signal between the two wait for that filtering interference signals amplitude is constant, phase invariant, to by the letter after width phase inversion Number with both original input signals can filter out when difference synthesizes and therein waits for filtering interference signals.As shown in Figure 1, second order Cascade Butterworth bandpass filter includes the two-stage circuit of cascade arrangement, in two-stage circuit first order circuit include resistance R1, Resistance R2, resistance R3, capacitance C1, capacitance C2 and operational amplifier U1, the negative input of operational amplifier U1 connect reference voltage, Electrode input end passes sequentially through capacitance C1, resistance R1 is connected with signal to be filtered, and the one end resistance R2 is connected to capacitance C1 and resistance Between R1, other end ground connection, resistance R3 concatenation is arranged between the electrode input end and output end of operational amplifier U1, capacitance C2 One end is connected between capacitance C1 and resistance R1, the other end is connected with the output end of operational amplifier U1;Second in two-stage circuit Grade circuit includes resistance R4, resistance R5, resistance R6, capacitance C3, capacitance C4 and operational amplifier U2, the cathode of operational amplifier U2 Input termination reference voltage, electrode input end passes sequentially through capacitance C3, resistance R4 is connected with the output end of operational amplifier U1, electricity Resistance R5 one end is connected between capacitance C3 and resistance R4, another termination reference voltage, and resistance R6 concatenations are arranged in operational amplifier Between the electrode input end and output end of U2, the one end capacitance C4 is connected between capacitance C3 and resistance R4, the other end and operation are put The output end of big device U2 is connected.It should be noted that the reference voltage of Two-orders Butterworth bandpass filter can be grounded (being equivalent to 0V) can also use other reference voltages (such as 2.5V etc.) as needed.
In the present embodiment, identical capacitance C1, capacitance C2, capacitance C3, capacitance C4 values (are all Cf), according to cascade connection type Butterworth filter normalizes table, it may be determined that Two-orders Butterworth bandpass filter parameters at different levels are as follows:
In two-stage circuit shown in transmission function and the centre frequency such as formula (1) of first order circuit;
In formula (1), A1(s) transmission function of first order circuit in two-stage circuit, f are indicated0For Two-orders Butterworth band The centre frequency of bandpass filter, S are Laplace operator, C1Indicate the capacitance of capacitance C1, C2Indicate the capacitance of capacitance C2, R1Indicate the resistance value of resistance R1, R2Indicate the resistance value of resistance R2, R3Indicate the resistance value of resistance R3.
If Cf=C1=C2, then have formula (2);
In formula (2), R1Indicate the resistance value of resistance R1, R2Indicate the resistance value of resistance R2, R3Indicate the resistance of resistance R3 Value, Q are the quality factor (generally taking 2 or 5 or 10) of Two-orders Butterworth bandpass filter, f0It is fertile for Two-orders Bart The centre frequency (frequencies of power frequency interference signals to be filtered) of this bandpass filter, A1For the increasing of first order circuit in two-stage circuit Beneficial (amplification factor), CfFor the capacitance of capacitance C1 and capacitance C2.
In two-stage circuit shown in transmission function and the centre frequency such as formula (3) of first order circuit;
In formula (3), A2(s) transmission function of second level circuit in two-stage circuit, f are indicated0For Two-orders Butterworth band The centre frequency of bandpass filter, S are Laplace operator, C3Indicate the capacitance of capacitance C3, C4Indicate the capacitance of capacitance C4, R4Indicate the resistance value of resistance R4, R5Indicate the resistance value of resistance R5, R6Indicate the resistance value of resistance R6.
If Cf=C3=C4, then have formula (4);
In formula (4), R4Indicate the resistance value of resistance R4, R5Indicate the resistance value of resistance R5, R6Indicate the resistance value of resistance R6 Q is the quality factor of Two-orders Butterworth bandpass filter, f0For the center of Two-orders Butterworth bandpass filter Frequency, A2For the gain (amplification factor) of second level circuit in two-stage circuit, CfFor the capacitance of capacitance C3 and capacitance C4.Due to Two-orders Butterworth bandpass filter gain is 1, then understands the gain A of first order circuit in two-stage circuit1With two-stage electricity The gain A of second level circuit in road2Meet following relationships:A1·A2=1.Two-orders Butterworth band logical can be filtered in this way Another input terminal of an input terminal of the output of wave device as difference synthesis module, difference synthesis module is original signal Input terminal.In this way, the ends resistance R7 input signal is constant for the power frequency interference signals of original signal, other signals have to decline to a certain degree The signal subtracted, when making difference with original signal, power frequency interference signals can be cancelled.
The amplitude characteristic analog result of the present embodiment Two-orders Butterworth bandpass filter shown in Figure 2, passes through After Two-orders Butterworth bandpass filter carries out width phase inversion, the centre frequency of Two-orders Butterworth bandpass filter f0(frequency for waiting for filtering interference signals) corresponding gain G is 1.The present embodiment Two-orders Butterworth band shown in Figure 3 The phase characteristic analog result of bandpass filter, after carrying out width phase inversion by Two-orders Butterworth bandpass filter, input The phase of signal is switched between -180 °~180 °, and the centre frequency of wherein Two-orders Butterworth bandpass filter f0(frequency for waiting for filtering interference signals) corresponding phase is 0.Therefore, according to above-mentioned analog result as it can be seen that Two-orders Bart Input signal can be carried out width phase inversion by Butterworth bandpass filter, and only keep waiting for that filtering interference signals amplitude is constant, phase It is constant.
In the present embodiment, difference synthesis module is scaling circuit.As shown in Figure 1, scaling circuit includes resistance R7, resistance R8, resistance R9 and operational amplifier U3, after the negative input of operational amplifier U3 is by resistance R7 and width phase inversion Signal be connected, electrode input end is connected with original input signal, resistance R9 concatenation is arranged in the positive defeated of operational amplifier U3 Enter between end and output end.In scaling circuit shown in Fig. 1, the resistance sizes of resistance R7 will be determined by resistance R8 and resistance R9 Fixed, formula R7=R8//R9, amplification factor G is determined by R8 and R9, formula G=1+R9/R8.In addition, difference synthesis module Other kinds of difference combiner circuit can also be used as needed.
The above is only a preferred embodiment of the present invention, protection scope of the present invention is not limited merely to above-mentioned implementation Example, all technical solutions belonged under thinking of the present invention all belong to the scope of protection of the present invention.It should be pointed out that for the art Those of ordinary skill for, several improvements and modifications without departing from the principles of the present invention, these improvements and modifications It should be regarded as protection scope of the present invention.

Claims (6)

1. a kind of notch filter method for GMI Magnetic Sensors, it is characterised in that step includes:
1)Input signal is subjected to width phase inversion by Two-orders Butterworth band, and only keeps waiting for filtering interference signals amplitude Constant, phase invariant;
2)It is exported after signal after width phase inversion is synthesized with both original input signal progress difference;
The centre frequency of the Two-orders Butterworth bandpass filter is to wait for the frequency of filtering interference signals, gain 1;Institute The two-stage circuit that Two-orders Butterworth bandpass filter includes cascade arrangement is stated, first order circuit includes electricity in two-stage circuit Resistance R1, resistance R2, resistance R3, capacitance C1, capacitance C2 and operational amplifier U1, the negative input of operational amplifier U1 connect reference Voltage, electrode input end pass sequentially through capacitance C1, resistance R1 is connected with signal to be filtered, the one end resistance R2 be connected to capacitance C1 and Between resistance R1, another termination reference voltage, resistance R3 concatenation is arranged in the electrode input end and output end of operational amplifier U1 Between, the one end capacitance C2 is connected between capacitance C1 and resistance R1, the other end is connected with the output end of operational amplifier U1;Two-stage Second level circuit includes resistance R4, resistance R5, resistance R6, capacitance C3, capacitance C4 and operational amplifier U2, operation amplifier in circuit The negative input of device U2 connects reference voltage, electrode input end passes sequentially through capacitance C3, resistance R4 and operational amplifier U1 it is defeated Outlet is connected, and the one end resistance R5 is connected between capacitance C3 and resistance R4, another termination reference voltage, and resistance R6 concatenations are arranged in Between the electrode input end and output end of operational amplifier U2, the one end capacitance C4 is connected between capacitance C3 and resistance R4, is another End is connected with the output end of operational amplifier U2.
2. the notch filter method according to claim 1 for GMI Magnetic Sensors, which is characterized in that the step 2) It specifically refers to defeated after being synthesized the signal after width phase inversion with both original input signal progress difference by scaling circuit Go out.
3. the notch filter method according to claim 2 for GMI Magnetic Sensors, it is characterised in that:The ratio fortune It includes resistance R7, resistance R8, resistance R9 and operational amplifier U3 to calculate circuit, and the negative input of operational amplifier U3 passes through resistance R7 is connected with the signal after width phase inversion, electrode input end is connected with original input signal, and resistance R9 concatenations are arranged in operation and put Between the electrode input end and output end of big device U3.
4. a kind of notch filter circuit for GMI Magnetic Sensors, it is characterised in that:It is synthesized including width phase inversion module and difference Module, input signal are divided into two-way, and input signal exports after carrying out width phase inversion by width phase inversion module to difference all the way One input terminal of synthesis module, another way input signal are directly output to another input terminal of difference synthesis module, described Width phase inversion module only keeps waiting for that filtering interference signals amplitude is constant, phase invariant, and the difference synthesis module is by width phase inversion Signal afterwards exports after being synthesized with both original input signal progress difference;The width phase inversion module is fertile for Two-orders Bart This bandpass filter, the centre frequency of the Two-orders Butterworth bandpass filter be wait for the frequency of filtering interference signals, Gain is 1;The Two-orders Butterworth bandpass filter includes the two-stage circuit of cascade arrangement, the first order in two-stage circuit Circuit includes resistance R1, resistance R2, resistance R3, capacitance C1, capacitance C2 and operational amplifier U1, and the cathode of operational amplifier U1 is defeated Enter to terminate reference voltage, electrode input end passes sequentially through capacitance C1, resistance R1 is connected with signal to be filtered, the connection of the one end resistance R2 Between capacitance C1 and resistance R1, other end ground connection, resistance R3 concatenation is arranged in the electrode input end of operational amplifier U1 and defeated Between outlet, the one end capacitance C2 is connected between capacitance C1 and resistance R1, the other end is connected with the output end of operational amplifier U1; Second level circuit includes resistance R4, resistance R5, resistance R6, capacitance C3, capacitance C4 and operational amplifier U2, operation in two-stage circuit The negative input of amplifier U2 connects reference voltage, electrode input end passes sequentially through capacitance C3, resistance R4 and operational amplifier U1 Output end be connected, the one end resistance R5 is connected between capacitance C3 and resistance R4, another termination reference voltage, and resistance R6 concatenates cloth It is placed between the electrode input end and output end of operational amplifier U2, the one end capacitance C4 is connected between capacitance C3 and resistance R4, The other end is connected with the output end of operational amplifier U2.
5. the notch filter circuit according to claim 4 for GMI Magnetic Sensors, it is characterised in that:The difference is closed It is scaling circuit at module.
6. the notch filter circuit according to claim 5 for GMI Magnetic Sensors, it is characterised in that:The ratio fortune It includes resistance R7, resistance R8, resistance R9 and operational amplifier U3 to calculate circuit, and the negative input of operational amplifier U3 passes through resistance R7 is connected with the signal after width phase inversion, electrode input end is connected with original input signal, and resistance R9 concatenations are arranged in operation and put Between the electrode input end and output end of big device U3.
CN201610313456.2A 2016-05-12 2016-05-12 A kind of notch filter method and circuit for GMI Magnetic Sensors Active CN106026966B (en)

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CN108008205B (en) * 2017-12-07 2021-02-19 中国电子科技集团公司第四十一研究所 Self-adaptive signal conditioning circuit and method for electromagnetic field detection
CN109407157B (en) * 2018-12-05 2021-04-20 中国科学院地质与地球物理研究所 Induction type magnetic sensor and electromagnetic exploration equipment
CN109709500A (en) * 2019-02-28 2019-05-03 青岛海月辉科技有限公司 Low-intensity magnetic field signal acquisition circuit

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