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CN107643438A - Optical current sensor and its current measuring method based on Faraday magnetooptical effect - Google Patents

Optical current sensor and its current measuring method based on Faraday magnetooptical effect Download PDF

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CN107643438A
CN107643438A CN201710828444.8A CN201710828444A CN107643438A CN 107643438 A CN107643438 A CN 107643438A CN 201710828444 A CN201710828444 A CN 201710828444A CN 107643438 A CN107643438 A CN 107643438A
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杨鸣
司马文霞
孙魄韬
袁涛
郑荣锋
张涵
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Chongqing University
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Chongqing University
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Abstract

The invention discloses a kind of optical current sensor based on Faraday magnetooptical effect, including:Laser generator, for producing the polarization laser of setting wavelength;Integration probe, including magnet-optical medium, the both ends of the magnet-optical medium are respectively equipped with the polarizer and analyzer, and the polarizer and analyzer distinguish insulation-encapsulated at the both ends of the magnet-optical medium;Photodetector, for converting optical signals to electric signal;Data analysis and processing unit, noise is filtered out by the way of software filtering is combined using hardware filtering, obtains good response effect;Between the laser generator and the polarizer and optic fibre light path is respectively adopted between the photodetector and the analyzer to be connected.The invention also discloses a kind of current measuring method of the optical current sensor based on Faraday magnetooptical effect.

Description

基于法拉第磁光效应的光学电流传感器及其电流测量方法Optical current sensor and current measurement method based on Faraday magneto-optic effect

技术领域technical field

本发明属于非接触式的光学电流传感器测量技术领域,具体的为一种基于法拉第磁光效应的光学电流传感器及其电流测量方法。The invention belongs to the technical field of non-contact optical current sensor measurement, in particular to an optical current sensor based on the Faraday magneto-optic effect and a current measurement method thereof.

背景技术Background technique

随着电力系统的发展,系统对安全及稳定性的要求也越来越高。电流传感器作为电力系统中进行电能计量和继电保护的重要设备,其准确度及可靠性与电力系统的安全、可靠和经济运行密切相关。传统的电磁式电流传感器存在着诸多缺点,例如:绝缘结构复杂、体积大、易产生磁饱和铁磁谐振、存在磁滞等,越来越难适应电力系统发展的需求。虽然传统的电磁式电流传感器也在不断的改进,但这并不能从根本上改变其存在的缺点。与传统的电磁式电流传感器相比,光学电流传感器在以下几个方面都存在优势,例如:无铁心、高低压隔离、体积小、频率响应宽、适合数字化变电站的要求等。因此,人们将目光转向新型电流传感器的研究,光学电流传感器在此背景下产生。With the development of the power system, the system has higher and higher requirements for safety and stability. As an important device for energy measurement and relay protection in the power system, the current sensor's accuracy and reliability are closely related to the safe, reliable and economical operation of the power system. Traditional electromagnetic current sensors have many disadvantages, such as: complex insulation structure, large volume, easy to generate magnetic saturation ferromagnetic resonance, and hysteresis, etc. It is increasingly difficult to adapt to the needs of power system development. Although the traditional electromagnetic current sensor is also being continuously improved, this does not fundamentally change its existing shortcomings. Compared with traditional electromagnetic current sensors, optical current sensors have advantages in the following aspects, such as: no iron core, high and low voltage isolation, small size, wide frequency response, suitable for digital substation requirements, etc. Therefore, people turn their attention to the research of new current sensors, and optical current sensors are produced under this background.

发明内容Contents of the invention

有鉴于此,本发明的目的在于提供一种基于法拉第磁光效应的光学电流传感器及其电流测量方法,能够满足电流测量的要求。In view of this, the object of the present invention is to provide an optical current sensor based on the Faraday magneto-optical effect and a current measurement method thereof, which can meet the requirements of current measurement.

为达到上述目的,本发明提供如下技术方案:To achieve the above object, the present invention provides the following technical solutions:

本发明首先提出了一种基于法拉第磁光效应的光学电流传感器,包括:The present invention first proposes an optical current sensor based on the Faraday magneto-optical effect, including:

激光发生器,用于产生设定波长的偏振激光;A laser generator for generating polarized laser light with a set wavelength;

集成探头,包括磁光介质,所述磁光介质的两端分别设有起偏器和检偏器,所述起偏器和检偏器分别绝缘封装在所述磁光介质的两端;The integrated probe includes a magneto-optical medium, polarizers and analyzers are respectively provided at both ends of the magneto-optical medium, and the polarizer and analyzer are respectively insulated and packaged at both ends of the magneto-optical medium;

光电探测器,用于将光信号转换为电信号;Photodetectors for converting optical signals into electrical signals;

数据分析与处理装置,采用硬件滤波与软件滤波相结合的方式滤除噪声,得到良好的响应效果;The data analysis and processing device uses a combination of hardware filtering and software filtering to filter out noise and obtain a good response effect;

所述激光发生器与所述起偏器之间、以及所述光电探测器与所述检偏器之间分别采用光纤光路相连。The laser generator and the polarizer, and the photodetector and the polarizer are respectively connected by optical fiber paths.

进一步,所述磁光介质采用磁光玻璃。Further, the magneto-optical medium adopts magneto-optical glass.

进一步,所述磁光玻璃为用于测量螺旋管线电流的圆柱形或用于测量长直导线电流的长方体形。Further, the magneto-optic glass is cylindrical for measuring the current of a spiral pipeline or a cuboid for measuring the current of a long straight wire.

本发明还提出了一种如上所述的基于法拉第磁光效应的光学电流传感器的电流测量方法,令所述起偏器和所述检偏器之间成45°或135°角时,利用激光发生器输入光强I1,经过起偏器、磁光玻璃、检偏器后输出光强I2为:The present invention also proposes a current measurement method of an optical current sensor based on the Faraday magneto-optic effect as described above, when the angle between the polarizer and the analyzer is 45° or 135°, the laser The input light intensity I 1 of the generator, and the output light intensity I 2 after passing through the polarizer, magneto-optical glass, and analyzer are:

其中,β为法拉第旋转角,由于β极小,可将sinβ近似为β,则有:Among them, β is the Faraday rotation angle. Since β is extremely small, sin β can be approximated as β, then:

其中,β=VBLAmong them, β=VBL

式中,V为磁光材料的费尔德(Verder)常数,单位为rad/(T·m);B是电流引起的磁场;L是偏振光透射磁光介质的光程,即磁光介质的厚度;In the formula, V is the Verder constant of the magneto-optical material, and the unit is rad/(T m); B is the magnetic field caused by the current; L is the optical path of the polarized light transmitted through the magneto-optic medium, that is, the magneto-optic medium thickness of;

则:but:

当被测导线为长直导线时,最终输出电压与被测电流之间的关系为:When the measured wire is a long straight wire, the relationship between the final output voltage and the measured current is:

其中,则,in, but,

其中,I为长直导线内的被测电流;r为测量点距离长直导线的距离;μ0为磁光介质的磁导率;Wherein, I is the measured current in the long straight wire; r is the distance between the measuring point and the long straight wire; μ 0 is the magnetic permeability of the magneto-optical medium;

当I1和r为定值时,k2和k3为常数;When I 1 and r are fixed values, k 2 and k 3 are constants;

当被测导向为螺旋管线时,最终输出电压与被测电流之间的关系为:When the measured guide is a spiral pipeline, the relationship between the final output voltage and the measured current is:

其中,B=nμ0I,则,Among them, B=nμ 0 I, then,

其中,I为螺旋管线内的被测电流,n为螺旋管线单位长度匝数,μ0为磁光介质的磁导率;当I1为定值时,则,k2和k4均为常数。Among them, I is the measured current in the helical pipeline, n is the number of turns per unit length of the helical pipeline, μ 0 is the magnetic permeability of the magneto-optical medium; when I 1 is a fixed value, then k 2 and k 4 are constants .

本发明的有益效果在于:The beneficial effects of the present invention are:

本发明基于法拉第磁光效应的光学电流传感器相对于现有的电流传感器具有以下优点:Compared with the existing current sensor, the optical current sensor based on the Faraday magneto-optic effect of the present invention has the following advantages:

1)安全可靠,对线路设备的绝缘性能不产生影响;1) It is safe and reliable, and does not affect the insulation performance of line equipment;

2)灵敏度高,量程大;2) High sensitivity and large measuring range;

3)可测量多种类型的电流,包括直流电流、交流电流以及电网故障时的冲击大电流;3) It can measure various types of current, including DC current, AC current and the impact of large current when the power grid fails;

4)集成化设计,安装方便可靠;4) Integrated design, easy and reliable installation;

5)频率响应宽,暂态性能好;体积小,无铁心,高低压隔离,适合数字化变电站要求。5) Wide frequency response, good transient performance; small size, no iron core, high and low voltage isolation, suitable for digital substation requirements.

附图说明Description of drawings

为了使本发明的目的、技术方案和有益效果更加清楚,本发明提供如下附图进行说明:In order to make the purpose, technical scheme and beneficial effect of the present invention clearer, the present invention provides the following drawings for illustration:

图1为本发明基于法拉第磁光效应的光学电流传感器结构示意图;Fig. 1 is the structural representation of the optical current sensor based on the Faraday magneto-optic effect of the present invention;

图2为本实施例1的集成探头的结构示意图;Fig. 2 is the structural representation of the integrated probe of present embodiment 1;

图3为本发明基于法拉第磁光效应的光学电流传感器实施例2的集成探头的结构示意图;3 is a schematic structural view of the integrated probe of Embodiment 2 of the optical current sensor based on the Faraday magneto-optic effect of the present invention;

图4为采用本实施例2的光学电流传感器测量长直导线内电流值时的使用状态参考图。FIG. 4 is a reference diagram of the use state when the optical current sensor of the second embodiment is used to measure the current value in a long straight wire.

具体实施方式detailed description

下面结合附图和具体实施例对本发明作进一步说明,以使本领域的技术人员可以更好的理解本发明并能予以实施,但所举实施例不作为对本发明的限定。The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments, so that those skilled in the art can better understand the present invention and implement it, but the examples given are not intended to limit the present invention.

实施例1Example 1

如图1和图2所示,为本发明基于法拉第磁光效应的光学电流传感器实施例1的结构示意图。本实施例基于法拉第磁光效应的光学电流传感器,包括:As shown in FIG. 1 and FIG. 2 , it is a schematic structural diagram of Embodiment 1 of the optical current sensor based on the Faraday magneto-optic effect of the present invention. This embodiment is based on the optical current sensor of the Faraday magneto-optical effect, including:

激光发生器1,用于产生设定波长的偏振激光,本实施例的激光发生器1产生波长为632.8nm的偏振激光,在该波长下,所选用磁光玻璃的维尔德常数最大;The laser generator 1 is used to generate polarized laser light with a predetermined wavelength. The laser generator 1 in this embodiment generates polarized laser light with a wavelength of 632.8nm. At this wavelength, the Verdet constant of the selected magneto-optical glass is the largest;

集成探头8,包括磁光介质2,磁光介质2的两端分别设有起偏器3和检偏器4,起偏器3和检偏器4分别绝缘封装在磁光介质2的两端;另外,集成探头还包括固定支架和封装等;本实施例的磁光介质2采用磁光玻璃,磁光玻璃为用于测量螺旋管线电流的圆柱形;The integrated probe 8 includes a magneto-optical medium 2, and the two ends of the magneto-optical medium 2 are respectively provided with a polarizer 3 and an analyzer 4, and the polarizer 3 and the analyzer 4 are respectively insulated and packaged at both ends of the magneto-optical medium 2 ; In addition, the integrated probe also includes a fixed bracket and packaging, etc.; the magneto-optical medium 2 of the present embodiment adopts magneto-optic glass, and the magneto-optic glass is cylindrical for measuring the current of the spiral pipeline;

光电探测器5,用于将光信号转换为电信号;Photodetector 5, for converting optical signal into electrical signal;

数据分析与处理装置6,采用硬件滤波与软件滤波相结合的方式滤除噪声,得到良好的响应效果。The data analysis and processing device 6 uses a combination of hardware filtering and software filtering to filter out noise and obtain a good response effect.

本实施例的激光发生器1与起偏器3之间、以及光电探测器5与检偏器4之间分别采用光纤光路7相连。In this embodiment, the laser generator 1 and the polarizer 3 , and the photodetector 5 and the polarizer 4 are respectively connected by fiber optical paths 7 .

本实施例基于法拉第磁光效应的光学电流传感器的电流测量方法为,令起偏器3和检偏器4之间成45°或135°角,利用激光发生器输入光强I1,经过起偏器、磁光玻璃、检偏器后输出光强I2为:The current measurement method of the optical current sensor based on the Faraday magneto-optical effect in this embodiment is to make the polarizer 3 and the polarizer 4 form an angle of 45° or 135°, and use the laser generator to input the light intensity I 1 , after starting The output light intensity I after the polarizer, magneto - optical glass and analyzer is:

其中,β为法拉第旋转角,由于β极小,可将sinβ近似为β,则有:Among them, β is the Faraday rotation angle. Since β is extremely small, sin β can be approximated as β, then:

其中,β=VBLAmong them, β=VBL

式中,V为磁光材料的费尔德(Verder)常数,单位为rad/(T·m);B是电流引起的磁场;L是偏振光透射磁光介质2的光程,即磁光介质2的厚度;In the formula, V is the Verder constant of the magneto-optical material, and the unit is rad/(T m); B is the magnetic field caused by the current; L is the optical path of the polarized light transmitted through the magneto-optic medium 2, that is, the magneto-optic the thickness of medium 2;

则:but:

被测导线为螺旋管线,最终输出电压与被测电流之间的关系为:The measured wire is a spiral pipeline, and the relationship between the final output voltage and the measured current is:

其中,B=nμ0I,则,Among them, B=nμ 0 I, then,

其中,I为螺旋管线内的被测电流,n为螺旋管线单位长度匝数,μ0为磁光介质的磁导率;当I1为定值时,则,k2和k4均为常数。Among them, I is the measured current in the helical pipeline, n is the number of turns per unit length of the helical pipeline, μ 0 is the magnetic permeability of the magneto-optical medium; when I 1 is a fixed value, then k 2 and k 4 are constants .

测量前,先在本实施例基于法拉第磁光效应的光学电流传感器的安装处实地测量多组确定的电流值,数据分析处理装置输出多组对应的电压值,计算得到传感器的相关参数k2和k4,而后则可以根据公式以及输出的电压值,反算得到被测电流的精确值。Before the measurement, multiple sets of determined current values are measured at the installation place of the optical current sensor based on the Faraday magneto-optical effect in this embodiment, and the data analysis and processing device outputs multiple sets of corresponding voltage values, and the related parameters k2 and k4 of the sensor are calculated. , and then the exact value of the measured current can be obtained by inverse calculation according to the formula and the output voltage value.

实施例2Example 2

如图3所示,为本发明基于法拉第磁光效应的光学电流传感器实施例2的集成探头的结构示意图。本实施例基于法拉第磁光效应的光学电流传感器,包括:As shown in FIG. 3 , it is a schematic structural diagram of the integrated probe of Embodiment 2 of the optical current sensor based on the Faraday magneto-optical effect of the present invention. This embodiment is based on the optical current sensor of the Faraday magneto-optical effect, including:

激光发生器1,用于产生设定波长的偏振激光,本实施例的激光发生器1产生波长为632.8nm的偏振激光,在该波长下,所选用磁光玻璃的维尔德常数最大;The laser generator 1 is used to generate polarized laser light with a predetermined wavelength. The laser generator 1 in this embodiment generates polarized laser light with a wavelength of 632.8nm. At this wavelength, the Verdet constant of the selected magneto-optical glass is the largest;

集成探头,包括磁光介质2,磁光介质2的两端分别设有起偏器3和检偏器4,起偏器3和检偏器4分别绝缘封装在磁光介质2的两端;另外,集成探头还包括固定支架和封装等;本实施例的磁光介质2采用磁光玻璃,磁光玻璃为测量长直导线电流的长方体形;The integrated probe includes a magneto-optical medium 2, and the two ends of the magneto-optical medium 2 are respectively provided with a polarizer 3 and an analyzer 4, and the polarizer 3 and the analyzer 4 are respectively insulated and packaged at both ends of the magneto-optical medium 2; In addition, the integrated probe also includes a fixed bracket and packaging, etc.; the magneto-optical medium 2 of the present embodiment adopts magneto-optic glass, and the magneto-optic glass is a rectangular parallelepiped for measuring the current of a long straight wire;

光电探测器5,用于将光信号转换为电信号;Photodetector 5, for converting optical signal into electrical signal;

数据分析与处理装置6,采用硬件滤波与软件滤波相结合的方式滤除噪声,得到良好的响应效果。The data analysis and processing device 6 uses a combination of hardware filtering and software filtering to filter out noise and obtain a good response effect.

本实施例的激光发生器1与起偏器3之间、以及光电探测器5与检偏器4之间分别采用光纤光路7相连。In this embodiment, the laser generator 1 and the polarizer 3 , and the photodetector 5 and the polarizer 4 are respectively connected by fiber optical paths 7 .

本实施例基于法拉第磁光效应的光学电流传感器的电流测量方法为,令起偏器3和检偏器4之间成45°或135°角,利用激光发生器输入光强I1,经过起偏器、磁光玻璃、检偏器后输出光强I2为:The current measurement method of the optical current sensor based on the Faraday magneto-optical effect in this embodiment is to make the polarizer 3 and the polarizer 4 form an angle of 45° or 135°, and use the laser generator to input the light intensity I 1 , after starting The output light intensity I after the polarizer, magneto - optical glass and analyzer is:

其中,β为法拉第旋转角,由于β极小,可将sinβ近似为β,则有:Among them, β is the Faraday rotation angle. Since β is extremely small, sin β can be approximated as β, then:

其中,β=VBLAmong them, β=VBL

式中,V为磁光材料的费尔德(Verder)常数,单位为rad/(T·m);B是电流引起的磁场;L是偏振光透射磁光介质2的光程,即磁光介质2的厚度;In the formula, V is the Verder constant of the magneto-optical material, and the unit is rad/(T m); B is the magnetic field caused by the current; L is the optical path of the polarized light transmitted through the magneto-optic medium 2, that is, the magneto-optic the thickness of medium 2;

则:but:

被测导线为长直导线,最终输出电压与被测电流之间的关系为:The measured wire is a long straight wire, and the relationship between the final output voltage and the measured current is:

其中,则,in, but,

其中,I为长直导线内的被测电流;r为测量点距离长直导线的距离;μ0为磁光介质的磁导率;Wherein, I is the measured current in the long straight wire; r is the distance between the measuring point and the long straight wire; μ 0 is the magnetic permeability of the magneto-optical medium;

当I1和r为定值时,k2和k3为常数;When I 1 and r are fixed values, k 2 and k 3 are constants;

测量前,将本实施例基于法拉第磁光效应的光学电流传感器放置于距离被测长直导线较近的位置处,得到更高的灵敏度;集成探头的安装须与被测导线平行,若是测量三相导线中的一相,可以设置两个或多个集成探头,最后利用数学解耦的方法求解单根导线的电流大小与波形。Before the measurement, the optical current sensor based on the Faraday magneto-optic effect in this embodiment is placed at a position closer to the measured long straight wire to obtain higher sensitivity; the installation of the integrated probe must be parallel to the measured wire. For one phase of the phase wire, two or more integrated probes can be set, and finally the current magnitude and waveform of a single wire can be solved by using the method of mathematical decoupling.

以上所述实施例仅是为充分说明本发明而所举的较佳的实施例,本发明的保护范围不限于此。本技术领域的技术人员在本发明基础上所作的等同替代或变换,均在本发明的保护范围之内。本发明的保护范围以权利要求书为准。The above-mentioned embodiments are only preferred embodiments for fully illustrating the present invention, and the protection scope of the present invention is not limited thereto. Equivalent substitutions or transformations made by those skilled in the art on the basis of the present invention are all within the protection scope of the present invention. The protection scope of the present invention shall be determined by the claims.

Claims (4)

1.一种基于法拉第磁光效应的光学电流传感器,其特征在于:包括:1. An optical current sensor based on the Faraday magneto-optical effect, characterized in that: comprising: 激光发生器,用于产生设定波长的偏振激光;A laser generator for generating polarized laser light with a set wavelength; 集成探头,包括磁光介质,所述磁光介质的两端分别设有起偏器和检偏器,所述起偏器和检偏器分别绝缘封装在所述磁光介质的两端;The integrated probe includes a magneto-optical medium, polarizers and analyzers are respectively provided at both ends of the magneto-optical medium, and the polarizer and analyzer are respectively insulated and packaged at both ends of the magneto-optical medium; 光电探测器,用于将光信号转换为电信号;Photodetectors for converting optical signals into electrical signals; 数据分析与处理装置,采用硬件滤波与软件滤波相结合的方式滤除噪声,得到良好的响应效果;The data analysis and processing device uses a combination of hardware filtering and software filtering to filter out noise and obtain a good response effect; 所述激光发生器与所述起偏器之间、以及所述光电探测器与所述检偏器之间分别采用光纤光路相连。The laser generator and the polarizer, and the photodetector and the polarizer are respectively connected by optical fiber paths. 2.根据权利要求1所述的基于法拉第磁光效应的光学电流传感器,其特征在于:所述磁光介质采用磁光玻璃。2 . The optical current sensor based on the Faraday magneto-optic effect according to claim 1 , wherein the magneto-optic medium is magneto-optic glass. 3.根据权利要求2所述的基于法拉第磁光效应的光学电流传感器,其特征在于:所述磁光玻璃为用于测量螺旋管线电流的圆柱形或用于测量长直导线电流的长方体形。3. The optical current sensor based on the Faraday magneto-optical effect according to claim 2, wherein the magneto-optic glass is cylindrical for measuring the current of a spiral pipeline or a cuboid for measuring the current of a long straight wire. 4.一种如权利要求1-3任一项所述的基于法拉第磁光效应的光学电流传感器的电流测量方法,其特征在于:令所述起偏器和所述检偏器之间成45°或135°角时,利用激光发生器输入光强I1,经过起偏器、磁光玻璃、检偏器后输出光强I2为:4. A current measurement method of an optical current sensor based on the Faraday magneto-optical effect as claimed in any one of claims 1-3, characterized in that: make 45° between the polarizer and the analyzer ° or 135° angle, the laser generator is used to input the light intensity I 1 , and the output light intensity I 2 after passing through the polarizer, magneto-optic glass, and analyzer is: <mrow> <msub> <mi>I</mi> <mn>2</mn> </msub> <mo>=</mo> <msub> <mi>I</mi> <mn>1</mn> </msub> <mo>&amp;CenterDot;</mo> <mfrac> <mrow> <mn>1</mn> <mo>&amp;PlusMinus;</mo> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mn>2</mn> <mi>&amp;beta;</mi> </mrow> <mn>2</mn> </mfrac> </mrow> <mrow><msub><mi>I</mi><mn>2</mn></msub><mo>=</mo><msub><mi>I</mi><mn>1</mn></msub><mo>&amp;CenterDot;</mo><mfrac><mrow><mn>1</mn><mo>&amp;PlusMinus;</mo><mi>s</mi><mi>i</mi><mi>n</mi><mn>2</mn><mi>&amp;beta;</mi></mrow><mn>2</mn></mfrac></mrow> 其中,β为法拉第旋转角,由于β极小,可将sinβ近似为β,则有:Among them, β is the Faraday rotation angle. Since β is extremely small, sin β can be approximated as β, then: <mrow> <msub> <mi>I</mi> <mn>2</mn> </msub> <mo>=</mo> <msub> <mi>I</mi> <mn>1</mn> </msub> <mo>&amp;CenterDot;</mo> <mfrac> <mrow> <mn>1</mn> <mo>&amp;PlusMinus;</mo> <mn>2</mn> <mi>&amp;beta;</mi> </mrow> <mn>2</mn> </mfrac> </mrow> <mrow><msub><mi>I</mi><mn>2</mn></msub><mo>=</mo><msub><mi>I</mi><mn>1</mn></msub><mo>&amp;CenterDot;</mo><mfrac><mrow><mn>1</mn><mo>&amp;PlusMinus;</mo><mn>2</mn><mi>&amp;beta;</mi></mrow><mn>2</mn></mfrac></mrow> 其中,β=VBLAmong them, β=VBL 式中,V为磁光材料的费尔德(Verder)常数,单位为rad/(T·m);B是电流引起的磁场;L是偏振光透射磁光介质的光程,即磁光介质的厚度;In the formula, V is the Verder constant of the magneto-optical material, and the unit is rad/(T m); B is the magnetic field caused by the current; L is the optical path of the polarized light transmitted through the magneto-optic medium, that is, the magneto-optic medium thickness of; 则:but: <mrow> <msub> <mi>I</mi> <mn>2</mn> </msub> <mo>=</mo> <msub> <mi>I</mi> <mn>1</mn> </msub> <mo>&amp;CenterDot;</mo> <mfrac> <mrow> <mn>1</mn> <mo>&amp;PlusMinus;</mo> <mn>2</mn> <mi>V</mi> <mi>B</mi> <mi>L</mi> </mrow> <mn>2</mn> </mfrac> </mrow> <mrow><msub><mi>I</mi><mn>2</mn></msub><mo>=</mo><msub><mi>I</mi><mn>1</mn></msub><mo>&amp;CenterDot;</mo><mfrac><mrow><mn>1</mn><mo>&amp;PlusMinus;</mo><mn>2</mn><mi>V</mi><mi>B</mi><mi>L</mi></mrow><mn>2</mn></mfrac></mrow> 当被测导线为长直导线时,最终输出电压与被测电流之间的关系为:When the measured wire is a long straight wire, the relationship between the final output voltage and the measured current is: <mrow> <mi>U</mi> <mo>=</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <mo>&amp;CenterDot;</mo> <msub> <mi>I</mi> <mn>2</mn> </msub> <mo>=</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <mo>&amp;CenterDot;</mo> <msub> <mi>I</mi> <mn>1</mn> </msub> <mo>&amp;CenterDot;</mo> <mfrac> <mrow> <mn>1</mn> <mo>-</mo> <mn>2</mn> <mi>V</mi> <mi>B</mi> <mi>L</mi> </mrow> <mn>2</mn> </mfrac> </mrow> <mrow><mi>U</mi><mo>=</mo><msub><mi>k</mi><mn>1</mn></msub><mo>&amp;CenterDot;</mo><msub><mi>I</mi><mn>2</mn></msub><mo>=</mo><msub><mi>k</mi><mn>1</mn></msub><mo>&amp;CenterDot;</mo><msub><mi>I</mi><mn>1</mn></msub><mo>&amp;CenterDot;</mo>mo><mfrac><mrow><mn>1</mn><mo>-</mo><mn>2</mn><mi>V</mi><mi>B</mi><mi>L</mi></mrow><mn>2</mn></mfrac></mrow> 其中,则,in, but, <mrow> <mi>U</mi> <mo>=</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <mo>&amp;CenterDot;</mo> <msub> <mi>I</mi> <mn>1</mn> </msub> <mo>&amp;CenterDot;</mo> <mfrac> <mrow> <mn>1</mn> <mo>-</mo> <mfrac> <mrow> <msub> <mi>V&amp;mu;</mi> <mn>0</mn> </msub> <mi>I</mi> <mi>L</mi> </mrow> <mrow> <mi>&amp;pi;</mi> <mi>r</mi> </mrow> </mfrac> </mrow> <mn>2</mn> </mfrac> <mo>=</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <mo>&amp;CenterDot;</mo> <mfrac> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>k</mi> <mn>3</mn> </msub> <mo>&amp;CenterDot;</mo> <mi>I</mi> </mrow> <mn>2</mn> </mfrac> </mrow> <mrow><mi>U</mi><mo>=</mo><msub><mi>k</mi><mn>1</mn></msub><mo>&amp;CenterDot;</mo><msub><mi>I</mi><mn>1</mn></msub><mo>&amp;CenterDot;</mo><mfrac><mrow><mn>1</mn><mo>-</mo><mfrac><mrow><msub><mi>V&amp;mu;</mi><mn>0</mn></msub><mi>I</mi><mi>L</mi></mrow><mrow><mi>&amp;pi;</mi><mi>r</mi></mrow></mfrac></mrow><mn>2</mn></mfrac><mo>=</mo><msub><mi>k</mi><mn>2</mn></msub><mo>&amp;CenterDot;</mo><mfrac><mrow><mn>1</mn><mo>-</mo><msub><mi>k</mi><mn>3</mn></msub><mo>&amp;CenterDot;</mo><mi>I</mi></mrow><mn>2</mn></mfrac></mrow> 其中,I为长直导线内的被测电流;r为测量点距离长直导线的距离;μ0为磁光介质的磁导率;Wherein, I is the measured current in the long straight wire; r is the distance between the measuring point and the long straight wire; μ 0 is the magnetic permeability of the magneto-optical medium; 当I1和r为定值时,k2和k3为常数;When I 1 and r are fixed values, k 2 and k 3 are constants; 当被测导向为螺旋管线时,最终输出电压与被测电流之间的关系为:When the measured guide is a spiral pipeline, the relationship between the final output voltage and the measured current is: <mrow> <mi>U</mi> <mo>=</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <mo>&amp;CenterDot;</mo> <msub> <mi>I</mi> <mn>2</mn> </msub> <mo>=</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <mo>&amp;CenterDot;</mo> <msub> <mi>I</mi> <mn>1</mn> </msub> <mo>&amp;CenterDot;</mo> <mfrac> <mrow> <mn>1</mn> <mo>-</mo> <mn>2</mn> <mi>V</mi> <mi>B</mi> <mi>L</mi> </mrow> <mn>2</mn> </mfrac> </mrow> <mrow><mi>U</mi><mo>=</mo><msub><mi>k</mi><mn>1</mn></msub><mo>&amp;CenterDot;</mo><msub><mi>I</mi><mn>2</mn></msub><mo>=</mo><msub><mi>k</mi><mn>1</mn></msub><mo>&amp;CenterDot;</mo><msub><mi>I</mi><mn>1</mn></msub><mo>&amp;CenterDot;</mo>mo><mfrac><mrow><mn>1</mn><mo>-</mo><mn>2</mn><mi>V</mi><mi>B</mi><mi>L</mi></mrow><mn>2</mn></mfrac></mrow> 其中,B=nμ0I,则,Among them, B=nμ 0 I, then, <mrow> <mi>U</mi> <mo>=</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <mo>&amp;CenterDot;</mo> <msub> <mi>I</mi> <mn>1</mn> </msub> <mo>&amp;CenterDot;</mo> <mfrac> <mrow> <mn>1</mn> <mo>-</mo> <mn>2</mn> <msub> <mi>Vn&amp;mu;</mi> <mn>0</mn> </msub> <mi>I</mi> <mi>L</mi> </mrow> <mn>2</mn> </mfrac> <mo>=</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <mo>&amp;CenterDot;</mo> <mfrac> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>k</mi> <mn>4</mn> </msub> <mo>&amp;CenterDot;</mo> <mi>I</mi> </mrow> <mn>2</mn> </mfrac> </mrow> <mrow><mi>U</mi><mo>=</mo><msub><mi>k</mi><mn>1</mn></msub><mo>&amp;CenterDot;</mo><msub><mi>I</mi><mn>1</mn></msub><mo>&amp;CenterDot;</mo><mfrac><mrow><mn>1</mn><mo>-</mo><mn>2</mn><msub><mi>Vn&amp;mu;</mi><mn>0</mn></msub><mi>I</mi><mi>L</mi></mrow><mn>2</mn></mfrac><mo>=</mo><msub><mi>k</mi><mn>2</mn></msub><mo>&amp;CenterDot;</mo><mfrac><mrow><mn>1</mn><mo>-</mo><msub><mi>k</mi><mn>4</mn></msub><mo>&amp;CenterDot;</mo><mi>I</mi></mrow><mn>2</mn></mfrac></mrow> 其中,I为螺旋管线内的被测电流,n为螺旋管线单位长度匝数,μ0为磁光介质的磁导率;当I1为定值时,则,k2和k4均为常数。Among them, I is the measured current in the helical pipeline, n is the number of turns per unit length of the helical pipeline, μ 0 is the magnetic permeability of the magneto-optical medium; when I 1 is a fixed value, then k 2 and k 4 are constants .
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