CN103512592A - Wireless passive LC resonance sensor detecting circuit and corresponding information acquiring method - Google Patents

Abstract

The invention discloses a wireless passive LC resonance sensor detecting circuit which comprises a main controller, a direct digital frequency synthesizer, a high-speed analog-digital converter and a difference driving symmetrical detecting circuit. The main controller controls a signal source to output sweep-frequency signals, after the sweep-frequency signals pass through the difference driving symmetrical detecting circuit, the sweep-frequency signals are subjected to sampling controlled by the main controller, the main controller computes a phase spectrum of a network through DFT, and finally the main controller completes phase spectrum calibration and resonant frequency detecting. The invention further discloses a wireless passive LC resonance sensor information acquiring method. According to the method, the phase spectrum of a system without a sensor is obtained first, phase spectrums obtained each time are calibrated by subtracting the phase spectrum of the system, and the harmonic peak frequency of an LC resonance sensor is detected after the calibrated phase spectrums are subjected to filtering. Detecting sensitivity is effectively improved, influence of the system and coil phase spectrum reading is removed, and meanwhile the stability of detecting and the portability of the system are improved.

Description

Wireless and passive LC resonant transducer testing circuit and corresponding information getting method

Technical field

The present invention relates to sensor detection field, relate in particular to a kind of wireless and passive LC resonant transducer testing circuit and corresponding information getting method.

Background technology

The sensing system that wireless and passive LC resonant transducer is comprised of read coil and inductance, capacitor resonance loop, Fig. 1 (a) is the structural representation of wireless and passive LC resonant transducer conventional in prior art, wherein variable inductance or variable capacitance for example, as sensing unit impression measured (: pressure, temperature, chemical quantity), and resonant tank is by the measured resonance frequency that is converted to resonant tank; Fig. 1 (b) is the simplified model of described wireless and passive LC resonant transducer, wherein to obtain the principle of resonant tank resonance frequency be the coupling due to inductance in read coil and resonant tank to read coil, cause read coil impedance phase spectrum to occur little depression at resonant tank resonance frequency place, move along with the change of resonance frequency the position of depression, by detecting recessed position, obtain the resonance frequency of resonant tank, thereby realize measured detection.

Sensing unit employing passive device due to wireless and passive LC resonant transducer--inductance and electric capacity composition, make its have advantages of simple in structure, be easy to miniaturization, manufacturing cost is lower, because making it, sourceless characteristic is particularly suitable for For Long-term Monitoring Systems, such as the monitoring under inside of human body pressure monitoring, industrial high temperature environment and the detection of closed system etc. simultaneously.

According to the principle of work of wireless and passive LC resonant transducer, in experiment, usually use high-precision network analyzer to measure the impedance phase spectrum of read coil, from impedance phase spectrum, detect the position of resonance frequency, but the volume of network analyzer is large, equipment is heavy, cost is high, due to network analyzer, exist the restriction of the aspects such as above-mentioned volume, cost to make it be difficult to be applied in actual detection.The people such as Michel Nowak propose to use closed loop circuit to detect resonance frequency, and the mode of its closed loop circuit is phase method, by locking read coil impedance phase Wei Ling position, realize closed loop.Because the phase place of read coil own is 90 °, therefore need the coupling coefficient that read coil and inductance are stronger to make phase place back variation be greater than 90 °, thereby limited the detection distance of this circuit.The people such as J.Coosemans adopt read coil to construct voltage controlled oscillator device (VCO), by Control of Voltage VCO frequency sweep, export, in this process, the voltage at read coil two ends is because the existence of LC resonant transducer changes, the position of change in voltage maximum is the resonance frequency of LC resonant transducer, same this testing circuit needs stronger coupling coefficient, and the people such as J.Coosemans adopt this circuit only to realize the detection of the wireless and passive LC resonant transducer that coupling distance is 7.5mm.

For low coupling coefficient, remote wireless and passive LC resonance sensor systems, because read coil phase place changes the little detection difficult that causes, the present invention proposes a kind of information getting method and testing circuit of wireless and passive LC resonant transducer, improved sensitivity and convenience that wireless and passive LC resonant transducer detects.

Summary of the invention

In order to solve above-mentioned problems of the prior art, the present invention proposes a kind of wireless and passive LC resonant transducer testing circuit and corresponding information getting method, object is to provide the effective information detection of wireless and passive LC resonant transducer and acquisition methods in lower coupling coefficient situation, and described information detection and acquisition methods are equally applicable to the detection of wireless and passive LC resonant transducer under high coupling coefficient.

According to an aspect of the present invention, propose a kind of information detection of wireless and passive LC resonant transducer, this circuit comprises: the symmetrical testing circuit of master controller, Direct Digital Frequency Synthesizers DDS, high-speed AD converter ADC, differential driving wherein:

Described DDS is connected with the symmetrical testing circuit of described master controller and differential driving, for receiving the control signal of described master controller and producing the swept-frequency signal being determined by described control signal, the swept-frequency signal that described DDS produces exports the symmetrical testing circuit of described differential driving to;

The symmetrical testing circuit of described differential driving is connected with ADC with described DDS, and the phase place variation of its read coil impedance is extracted and amplified to the swept-frequency signal of exporting for receiving described DDS, and phase place is changed to feedback signal exports described ADC to;

Described ADC is connected with described master controller with the symmetrical testing circuit of described differential driving, for the phase place for the symmetrical testing circuit output of described differential driving, change feedback signal and carry out analog-to-digital conversion process, and export the feedback signal obtaining after processing to described master controller;

Described master controller is connected with described DDS, high-speed AD converter ADC, for described DDS and ADC are controlled to the harmonic peak frequency of also processing to the received signal to determine current LC resonant transducer.

According to a further aspect in the invention, propose a kind of information getting method of wireless and passive LC resonant transducer, the method comprises the following steps:

Step 1, main controller controls Direct Digital Frequency Synthesizers DDS completes a frequency sweep output, the symmetrical testing circuit of differential driving extracts and amplifies the phase place variation of its read coil impedance, described main controller controls high-speed AD converter ADC changes feedback signal sampling to phase place, and reads the phase place variation feedback signal of processing through ADC;

Step 2, the DSP in master controller processes according to described step 1 the phase place variation feedback signal obtaining and according to DFT algorithm, obtains the phase spectrum of this frequency sweep;

Step 3, utilizes the phase spectrum that described step 2 obtains to upgrade system phase spectrum;

Step 4, is positioned over LC resonant transducer to be detected in read coil in the symmetrical testing circuit of differential driving, and repeating said steps 1-2;

Step 5, the system phase spectrum of utilizing phase spectrum that described step 4 obtains and described step 3 to obtain is carried out phase spectrum calibration;

Step 6, carries out filtering for the phase spectrum after described step 5 calibration;

Step 7, based on filtered phase spectrum, adopts peak detection algorithm to obtain the harmonic peak frequency of described LC resonant transducer.

Information getting method and the testing circuit of above-mentioned a kind of wireless and passive LC resonant transducer disclosed in this invention have the following advantages:

A, the symmetrical Sampling network of differential driving have the function of the phase place variation of amplifying read coil impedance, have effectively improved the sensitivity detecting;

The impact of system and the phase spectrum of read coil own has been eliminated in the calibration of b, system phase spectrum;

C, there is limit for length's unit impulse response (FIR) digital filter to eliminate the noise in phase spectrum, improved the stability detecting;

The embedded system that d, DSP and FPGA realize has improved the portability of system.

Accompanying drawing explanation

Fig. 1 is the structural representation of wireless and passive LC resonant transducer of the prior art;

Fig. 2 is the structural representation of the wireless and passive LC resonant transducer testing circuit that proposes of the present invention;

Fig. 3 is the symmetrical testing circuit network topology structure of differential driving of the present invention figure;

Fig. 4 is the wireless and passive LC resonant transducer information getting method process flow diagram that the present invention proposes;

Fig. 5 is the frequency sweep phase spectrum comparison diagram of frequency sweep phase spectrum of the present invention (before comprising FIR filtering and after filtering) and Agilent E5061B network analyzer.

Embodiment

For making the object, technical solutions and advantages of the present invention clearer, below in conjunction with specific embodiment, and with reference to accompanying drawing, the present invention is described in more detail.

The present invention proposes a kind of information getting method and testing circuit of wireless and passive LC resonant transducer, object is to provide the effective information getting method of wireless and passive LC resonant transducer and testing circuit in lower coupling coefficient situation, and described information getting method and testing circuit are equally applicable to the detection of wireless and passive LC resonant transducer under high coupling coefficient.

From the principle of work of wireless and passive LC resonant transducer, can detect by measuring the variation of read coil impedance phase the frequency of harmonic peak.Therefore, the present invention realizes with the symmetrical Sampling network of differential driving the amplification that read coil impedance phase changes.

Fig. 2 is the structural representation of the wireless and passive LC resonant transducer testing circuit that proposes of the present invention, as shown in Figure 2, described testing circuit comprises: master controller, Direct Digital Frequency Synthesizers (DDS), high-speed AD converter (ADC), the symmetrical testing circuit of differential driving and display, wherein:

Described Direct Digital Frequency Synthesizers (DDS) is connected with the symmetrical testing circuit of described master controller and differential driving, for receiving the control signal of described master controller and producing the swept-frequency signal being determined by described control signal, the swept-frequency signal that described DDS produces exports the symmetrical testing circuit of described differential driving to, wherein, described swept-frequency signal is two paths of differential signals, be expressed as A (W) and-A (W), the frequency range of described swept-frequency signal is 10kHz～20MHz;

The symmetrical testing circuit of described differential driving is connected with high-speed AD converter (ADC) with described Direct Digital Frequency Synthesizers (DDS), and the swept-frequency signal of exporting for receiving described Direct Digital Frequency Synthesizers (DDS) is extracted and amplifies its read coil L _readthe phase place of impedance changes, and phase place is changed to feedback signal exports described high-speed AD converter (ADC) to;

The symmetrical testing circuit of described differential driving adopts the symmetrical Sampling network topological structure of differential driving as shown in Figure 3, the symmetrical Sampling network of described differential driving is by the symmetrical structure forming with reference to inductance and read coil, by differential signal, driven, the output terminal that is Sampling network with reference to the tie point of inductance and read coil, particularly, the symmetrical testing circuit of described differential driving further comprises with reference to inductance L _ref, read coil L _read, the first circuit for amplifying differential signal A1, the second circuit for amplifying differential signal A2, output signal amplification circuit A3, wherein:

The input end of described the first circuit for amplifying differential signal A1, the second circuit for amplifying differential signal A2 connects respectively two-way swept-frequency signal A (W) ,-A (W) being exported by described DDS, and its output terminal connects respectively described with reference to inductance L _ref, read coil L _readone end; Described with reference to inductance L _ref, read coil L _readthe other end interconnect, tie point is as the input end of described output signal amplification circuit A3, the output terminal of described output signal amplification circuit A3 is connected to the input end of described ADC, so that output signal B (W) is sent to described ADC.

In this structure, when the frequency of operation of this network is the resonance frequency of LC resonant transducer: with reference to inductance L<sub TranNum="102">ref</sub>impedance be Z<sub TranNum="103">ref</sub>=R<sub TranNum="104">ref</sub>+ jwL<sub TranNum="105">ref</sub>, wL wherein<sub TranNum="106">ref</sub>>>R<sub TranNum="107">ref</sub>, R<sub TranNum="108">ref</sub>for described with reference to inductance L<sub TranNum="109">ref</sub>dead resistance, w is the resonance frequency of LC resonant transducer; Read coil L<sub TranNum="110">read</sub>in while there is no LC resonant transducer, read coil L<sub TranNum="111">read</sub>impedance be Z<sub TranNum="112">read</sub>=R<sub TranNum="113">read</sub>+ jwL<sub TranNum="114">read</sub>, wL wherein<sub TranNum="115">read</sub>>>R<sub TranNum="116">read</sub>, R<sub TranNum="117">read</sub>for described read coil L<sub TranNum="118">read</sub>dead resistance; Read coil L<sub TranNum="119">read</sub>in while there is LC resonant transducer, read coil L<sub TranNum="120">read</sub>impedance be Z<sub TranNum="121">read</sub>'=R<sub TranNum="122">read</sub>+ Δ R+jwL<sub TranNum="123">read</sub>, wherein Δ R WeiLC loop equivalence is to the equivalent resistance in read coil.Owing to thering is similarity with reference to inductance and read coil, therefore can suppose Z<sub TranNum="124">ref</sub>=α Z<sub TranNum="125">read</sub>, α is the inductance value ratio with reference to inductance and read coil, 0.4<α<2.5.

The system function of the symmetrical Sampling network of described differential driving is:

$F\left(w\right)=2\frac{Z_{\mathrm{read}}}{Z_{\mathrm{read}}+Z_{\mathrm{ref}}}-1---\left(1\right)$

After LC resonant transducer adds in read coil, the phase differential of this network is:

$\mathrm{\&Delta;\&theta;}\left(w\right)=\arctan \left(\frac{(1-\mathrm{\&alpha;})w{L}_{\mathrm{read}}}{(1-\mathrm{\&alpha;})R_{\mathrm{read}}+\mathrm{\&Delta;R}}\right)-\arctan \left(\frac{(1+\mathrm{\&alpha;})w{L}_{\mathrm{read}}}{(1+\mathrm{\&alpha;})R_{\mathrm{read}}+\mathrm{\&Delta;R}}\right)---\left(2\right)$

The phase differential of read coil self is:

$\mathrm{\&Delta;}{\mathrm{\&theta;}}_0\left(w\right)=\arctan \left(\frac{w{L}_{\mathrm{read}}}{R_{\mathrm{read}}+\mathrm{\&Delta;R}}\right)-\arctan \left(\frac{w{L}_{\mathrm{read}}}{R_{\mathrm{read}}}\right)---\left(3\right)$

When ratio cc ≈ 1 with reference to inductance and read coil impedance, there is following relation:

$\arctan \left(\frac{(1-\mathrm{\&alpha;})w{L}_{\mathrm{read}}}{(1-\mathrm{\&alpha;})R_{\mathrm{read}}+\mathrm{\&Delta;R}}\right)<<\arctan \left(\frac{w{L}_{\mathrm{read}}}{R_{\mathrm{read}}+\mathrm{\&Delta;R}}\right)<\arctan \left(\frac{(1+\mathrm{\&alpha;})w{L}_{\mathrm{read}}}{(1+\mathrm{\&alpha;})R_{\mathrm{read}}+\mathrm{\&Delta;R}}\right)<\arctan \left(\frac{w{L}_{\mathrm{read}}}{R_{\mathrm{read}}}\right)$

（4）

$\arctan \left(\frac{w{L}_{\mathrm{read}}}{R_{\mathrm{read}}+\mathrm{\&Delta;R}}\right)\&ap;\arctan \left(\frac{(1+\mathrm{\&alpha;})w{L}_{\mathrm{read}}}{(1+\mathrm{\&alpha;})R_{\mathrm{read}}+\mathrm{\&Delta;R}}\right)\&ap;\arctan \left(\frac{w{L}_{\mathrm{read}}}{R_{\mathrm{read}}}\right)---\left(5\right)$

According to formula (4), (5), can obtain Δ θ (w)>Δ θ ₀(w), the phase differential of the symmetrical Sampling network of this explanation differential driving is greater than the phase differential of read coil self, adopts in addition numerical analysis method to verify when described Sampling network symmetry is higher, and the poor enlargement factor of this system phase is higher.

Described high-speed AD converter (ADC) is connected with described master controller with the symmetrical testing circuit of described differential driving, for the phase place for the symmetrical testing circuit output of described differential driving, change feedback signal and carry out analog-to-digital conversion process, and export the feedback signal obtaining after processing to described master controller;

Described master controller is connected with described Direct Digital Frequency Synthesizers (DDS), high-speed AD converter (ADC) and display, for described DDS and ADC are controlled to the harmonic peak frequency of also processing to the received signal to determine current LC resonant transducer, it further comprises digital signal processor (DSP) and field programmable device (FPGA), wherein, described FPGA controls respectively described DDS and ADC by control signal, to realize the synchronized sampling of swept-frequency signal and feedback signal; The phase place of described DSP based on described ADC output changes the harmonic peak frequency that feedback signal is determined current LC resonant transducer, is specially: the phase place of first described DSP based on described ADC output changes feedback signal and by DFT algorithm, calculate the phase spectrum of the symmetrical testing circuit of described differential driving; System phase spectrum subtraction during then by the phase spectrum calculating and without LC resonant transducer is realized the calibration of phase spectrum; Then adopt the Serial No. of FIR design of filter and the phase spectrum convolution after calibration to complete digital filtering; Finally by peak detection algorithm, search the harmonic peak frequency that value in filtered phase spectrum is determined current LC resonant transducer.

Described display is connected with described master controller, for the control signal that receives described master controller, show related data, such as the resonance frequency change curve of the running status of described master controller, the resonance frequency of current LC resonant transducer and LC resonant transducer etc.

Fig. 4 is the process flow diagram of the wireless and passive LC resonant transducer information getting method that proposes of the present invention, as shown in Figure 4, said method comprising the steps of:

Step 1, main controller controls DDS completes the output of frequency sweep, and the symmetrical testing circuit of differential driving extracts and amplifies its read coil L _readthe phase place of impedance changes, and described main controller controls ADC changes feedback signal sampling to phase place, and reads the phase place variation feedback signal of processing through ADC;

Step 2, the DSP in master controller processes according to described step 1 the phase place variation feedback signal obtaining and according to DFT algorithm, obtains the phase spectrum of this frequency sweep;

Step 3, utilizes the phase spectrum that described step 2 obtains to upgrade system phase spectrum;

Step 4, is positioned over LC resonant transducer to be detected in read coil in the symmetrical testing circuit of differential driving, and repeating said steps 1-2;

Step 5, the system phase spectrum of utilizing phase spectrum that described step 4 obtains and described step 3 to obtain is carried out phase spectrum calibration, and described calibration adopts described step 4 phase spectrum obtaining and the system phase that described step 3 obtains to compose the mode of subtracting each other;

Step 6, carries out filtering for the phase spectrum after described step 5 calibration, to eliminate the impact of high frequency noise, in an embodiment of the present invention, adopts Finite Impulse Response filter to carry out filtering;

Step 7, based on filtered phase spectrum, adopts peak detection algorithm to obtain the harmonic peak frequency of described LC resonant transducer, and the position of the harmonic peak of described LC resonant transducer is peaked position in filtered phase spectrum.

Described step 1-3 belongs to system calibration part, described step 4-7 belongs to sensor measurement part, the object of system calibration is the phase spectrum of system while obtaining without sensor itself, when sensor is measured, the phase spectrum that described information getting method obtains at every turn is all used the phase spectrum of system itself to calibrate, phase spectrum after calibration adopts Finite Impulse Response filter to eliminate high frequency noise, adopt peak detection algorithm to find out the harmonic peak frequency of LC resonant transducer, thereby realize the function that reads heat transfer agent.

Information getting method and the testing circuit of above-mentioned a kind of wireless and passive LC resonant transducer disclosed in this invention have the following advantages:

A, the symmetrical Sampling network of differential driving have the function of the phase place variation of amplifying read coil impedance, have effectively improved the sensitivity detecting.

The impact of system and the phase spectrum of read coil own has been eliminated in the calibration of b, system phase spectrum.

C, there is limit for length's unit impulse response (FIR) digital filter to eliminate the noise in phase spectrum, improved the stability detecting.

The embedded system that d, DSP and FPGA realize has improved the portability of system.

Fig. 5 is for same wireless and passive stomach pressure sensor, adopts respectively phase spectrum curve after the calibration that Agilent E5061B network analyzer and described information getting method and testing circuit record, and phase spectrum curve after FIR filtering.In figure, can very clearly find out, adopt described information getting method and testing circuit can obviously improve detection sensitivity, can effectively reduce the noise in phase spectrum, improve the combination property detecting.

Above-described specific embodiment; object of the present invention, technical scheme and beneficial effect are further described; institute is understood that; the foregoing is only specific embodiments of the invention; be not limited to the present invention; within the spirit and principles in the present invention all, any modification of making, be equal to replacement, improvement etc., within all should being included in protection scope of the present invention.

Claims (10)

1. an information detection for wireless and passive LC resonant transducer, is characterized in that, this circuit comprises: the symmetrical testing circuit of master controller, Direct Digital Frequency Synthesizers DDS, high-speed AD converter ADC and differential driving, wherein:

Described DDS is connected with the symmetrical testing circuit of described master controller and differential driving, for receiving the control signal of described master controller and producing the swept-frequency signal being determined by described control signal, the swept-frequency signal that described DDS produces exports the symmetrical testing circuit of described differential driving to;

The symmetrical testing circuit of described differential driving is connected with ADC with described DDS, and the phase place variation of its read coil impedance is extracted and amplified to the swept-frequency signal of exporting for receiving described DDS, and phase place is changed to feedback signal exports described ADC to;

Described ADC is connected with described master controller with the symmetrical testing circuit of described differential driving, for the phase place for the symmetrical testing circuit output of described differential driving, change feedback signal and carry out analog-to-digital conversion process, and export the feedback signal obtaining after processing to described master controller;

Described master controller is connected with described DDS, high-speed AD converter ADC, for described DDS and ADC are controlled to the harmonic peak frequency of also processing to the received signal to determine current LC resonant transducer.

2. circuit according to claim 1, is characterized in that, described swept-frequency signal is two paths of differential signals.

3. circuit according to claim 1, is characterized in that, the symmetrical testing circuit of described differential driving adopts the symmetrical Sampling network topological structure of differential driving.

4. circuit according to claim 1, is characterized in that, the symmetrical testing circuit of described differential driving comprises with reference to inductance L _ref, read coil L _read, the first circuit for amplifying differential signal A1, the second circuit for amplifying differential signal A2, output signal amplification circuit A3, wherein:

The input end of described the first circuit for amplifying differential signal A1, the second circuit for amplifying differential signal A2 connects respectively two-way swept-frequency signal A (W) ,-A (W) being exported by described DDS, and its output terminal connects respectively described with reference to inductance L _ref, read coil L _readone end;

Described with reference to inductance L _ref, read coil L _readthe other end interconnect, tie point is as the input end of described output signal amplification circuit A3, the output terminal of described output signal amplification circuit A3 is connected to the input end of described ADC, so that output signal B (W) is sent to described ADC.

5. circuit according to claim 1, is characterized in that, described master controller comprises digital signal processor DSP and on-site programmable device FPGA, wherein:

Described FPGA controls respectively described DDS and ADC by control signal, to realize the synchronized sampling of swept-frequency signal and feedback signal;

The phase place of described DSP based on described ADC output changes the harmonic peak frequency that feedback signal is determined current LC resonant transducer.

6. circuit according to claim 5, it is characterized in that, when described DSP determines the harmonic peak frequency of current LC resonant transducer, first the phase place variation feedback signal based on described ADC output calculates the phase spectrum of the symmetrical testing circuit of described differential driving by DFT algorithm; System phase spectrum subtraction during then by the phase spectrum calculating and without LC resonant transducer is realized the calibration of phase spectrum; Then adopt the Serial No. of FIR design of filter and the phase spectrum convolution after calibration to complete digital filtering; Finally by peak detection algorithm, search the harmonic peak frequency that value in filtered phase spectrum is determined current LC resonant transducer.

7. circuit according to claim 1, is characterized in that, also comprises display, and described display is connected with described master controller, for receiving the control signal of described master controller, shows related data.

8. circuit according to claim 7, is characterized in that, described data comprise the resonance frequency change curve of the running status of described master controller, the resonance frequency of current LC resonant transducer and LC resonant transducer.

9. an information getting method for wireless and passive LC resonant transducer, is characterized in that, the method comprises:

Step 1, main controller controls Direct Digital Frequency Synthesizers DDS completes a frequency sweep output, the symmetrical testing circuit of differential driving extracts and amplifies the phase place variation of its read coil impedance, described main controller controls high-speed AD converter ADC changes feedback signal sampling to phase place, and reads the phase place variation feedback signal of processing through ADC;

Step 2, the DSP in master controller processes according to described step 1 the phase place variation feedback signal obtaining and according to DFT algorithm, obtains the phase spectrum of this frequency sweep;

Step 3, utilizes the phase spectrum that described step 2 obtains to upgrade system phase spectrum;

Step 4, is positioned over LC resonant transducer to be detected in read coil in the symmetrical testing circuit of differential driving, and repeating said steps 1-2;

Step 5, the system phase spectrum of utilizing phase spectrum that described step 4 obtains and described step 3 to obtain is carried out phase spectrum calibration;

Step 6, carries out filtering for the phase spectrum after described step 5 calibration;

Step 7, based on filtered phase spectrum, adopts peak detection algorithm to obtain the harmonic peak frequency of described LC resonant transducer.

10. method according to claim 9, is characterized in that, the mode that the system phase spectrum that the phase spectrum that the described step 4 of phase spectrum calibration employing in described step 5 obtains and described step 3 obtain is subtracted each other.

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