CN109839610B - Helmholtz coil constant alternating current calibration system and method based on orthogonality principle - Google Patents
Helmholtz coil constant alternating current calibration system and method based on orthogonality principle Download PDFInfo
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Abstract
一种基于正交原理的亥姆霍兹线圈常数交流校准系统及方法，该方法包括：采用任意波形发生器产生不同频率正弦波交流信号；功率放大器将正弦波交流信号放大并发送至亥姆霍兹线圈，使其产生交流励磁信号；数字功率表采集已知匝面积小线圈的感应电压和通过亥姆霍兹线圈的励磁电流；根据第一计算规则对感应电压和励磁电流计算得到感应电压与励磁电流的乘积P'，以及根据第二计算规则对感应电压和励磁电流计算得到感应电压与励磁电流的乘积Q'；并采用正交原理计算得到感应电压有效值Urms；基于感应电压有效值Urms和励磁电流有效值Irms，计算亥姆霍兹线圈常数。从而能够去掉感应电压中的杂散信号，准确确定感应电压有效值，提高测量的准确度。
A Helmholtz coil constant AC calibration system and method based on the quadrature principle, the method comprising: using an arbitrary waveform generator to generate sine wave AC signals of different frequencies; a power amplifier amplifying the sine wave AC signal and sending it to the Helmholtz the coil to generate an AC excitation signal; the digital power meter collects the induced voltage of the coil with a known small turn area and the excitation current through the Helmholtz coil; according to the first calculation rule, the induced voltage and the excitation current are calculated to obtain the difference between the induced voltage and the excitation current. The product P' of the excitation current, and the product Q' of the induced voltage and the excitation current obtained by calculating the induced voltage and the excitation current according to the second calculation rule; and using the quadrature principle to calculate the effective value of the induced voltage U rms ; based on the effective value of the induced voltage U rms and excitation current rms I rms , calculate the Helmholtz coil constant. Therefore, the stray signal in the induced voltage can be removed, the effective value of the induced voltage can be accurately determined, and the measurement accuracy can be improved.
Description
Technical Field
The invention belongs to the field of accurate measurement of magnetic moment, and particularly relates to an alternating current calibration system and method for a Helmholtz coil constant.
Background
Helmholtz in 1849, german scientist designed helmholtz coils. The helmholtz coil is generally formed by a pair of circular coils connected in series in the same direction to generate a uniform magnetic field with low intensity and a large range. Connecting the calibrated helmholtz coil to a calibrated flux integrator can be used for accurate measurement of magnetic moment.
Fig. 1 shows an open-circuit measuring device for a helmholtz coil. The entire set of devices is placed in a non-ferromagnetic environment, preferably on a wooden table. As shown, the magnet is placed in the center position (homogeneous region) of the coil during measurement, and the magnetization of the magnet is in the x-axis direction, i.e., parallel to the axial direction of the coil. The two coil signals from the series connection are sent directly to the fluxmeter. After adjusting the zero point of the fluxmeter, the magnet is moved out of the coil so that it is parallel to the coil axis. The distance removed is typically 75-100 cm, which allows the sample to have no effect on the reading. By integrating the voltage with time (magnetic flux), the open magnetic moment of the sample can be obtained. Another measurement is to rotate the sample 180 degrees without taking the sample out, so the voltage generated would be 2 times the original and the coil constant would be 1/2 as original. Both methods are mentioned in the IEC60404-14 standard. When a magnetized sample is pulled from a Helmholtz coil, the magnetic dipole moment of the sample can be determined by:
j＝Δφ/kh (1.1)
in the formula: j is the magnetic dipole moment, in Webber meters (Wb m); k is a radical ofhIs the Helmholtz coil constant, the ratio of the magnetic field strength to the current, khH/I in units of amps per meter per amp (a/m/a); delta phi is the flux variation when the sample rotates or is drawn out of the detection coil, and the unit is Weber (Wb); h is the magnetic field intensity, and the unit is ampere per meter (A/m); i is the current intensity in amperes (A).
When the sample is rotated 180 ° at the center of the search coil, equation (1.1) evolves:
J＝ΔΦ/2kh (1.2)
the magnetic flux integrator measures the magnetic flux by measuring the induced voltage change generated during the rotation or drawing of the sample from the detection coil. The flux integrator may be calibrated using standard mutual inductance or volt-second generators.
The helmholtz coil needs to be calibrated before use. The Helmholtz coil should ensure that its homogeneous region covers the shape and volume of the sample to be measured. Coil constant (magnetic field strength to current strength ratio) k of Helmholtz coilhThis can be obtained by measuring the current through the coil and measuring the magnetic field strength in the centre of the coil with a magnetic field detecting device. Because the current intensity is easy to realize high-precision measurement, the technical difficulty of the conventional Helmholtz coil calibration method is mainly concentrated on the accurate measurement of the magnetic field intensity at the center of the coil.
At present, most of space magnetic field measurement is instruments utilizing Hall effect, and the method is also suggested by IEC 60404-14. In industrial applications, the calibration of the helmholtz coil can be completely achieved using a hall effect magnetometer with reliable performance, however, for establishing national measurement standards, it is obvious that the traceability of the gauss meter of the helmholtz coil in the required magnetic field range cannot meet the requirements.
The nuclear magnetic resonance magnetometer does not have the sensitive directionality of the Hall probe, the accuracy of the nuclear magnetic resonance magnetometer can reach 5ppm, and the nuclear magnetic resonance magnetometer is a standard accepted by magnetic field measurement, but a common nuclear magnetic resonance magnetometer has requirements on the range of a measured magnetic field, the minimum measured magnetic field is about 500Oe generally, and a Helmholtz coil cannot generate the magnetic field with the maximum value generally.
In the first prior art, a helmholtz coil is calibrated by an optical pumping magnetometer and a zero magnetic field space environment, and the optical pumping magnetometer utilizes the zeeman effect of atoms to realize accurate measurement of a magnetic field. When the optical pump magnetometer is used for calibrating the Helmholtz coil, the maximum magnetic field measurement range is 1Gs, so that the geomagnetic field and other space stray fields can influence the measurement precision to a great extent. To solve this problem, a zero magnetic field space (as shown in fig. 2) needs to be created, and the current method is implemented by a large three-dimensional combined helmholtz coil, so that the amplitude of the environmental field in each direction can be reduced to below 3 nT. Because the magnetic field generated by the Helmholtz coil is very small, the magnetic field is generally about (10-100) Gs under the allowable current, the geomagnetic field, the stray field and the zero point of the measuring instrument all bring great influence on the calibration, the uncertainty of the calibration is generally about 0.3%, and the uncertainty is high.
In the second prior art, a low-field magnetic resonance instrument is used to calibrate the helmholtz coil, and the low-field magnetic resonance instrument can provide accurate measurement of a magnetic field of about several oersteds to 150 oersteds, has an uncertainty of 5-10ppm, and is particularly suitable for calibrating the helmholtz coil. The low-field magnetic resonance instrument comprises a flow type nuclear magnetic resonance magnetometer and an electronic optional resonance magnetometer, in the past, the flow type nuclear magnetic resonance instrument manufactured by GMW company in America is FW101, but as the core technology is not inherited, the instrument is stopped selling at present GMW, and no product is available in other countries in the world. An electronic self-selection resonance probe is sold on a Metrolab website, and a nuclear magnetic resonance measuring instrument matched with the probe Metrolab can accurately measure a low-field magnetic field. In practice, however, the probe is not currently available internationally, again due to technical and material problems. The instrument suitable for direct current method calibration, such as a running water type nuclear magnetic resonance magnetometer and an electron spin resonance magnetometer, cannot be purchased in the market.
There are problems in the prior art that,
1. at present, an optical pump magnetometer and a zero magnetic field space environment calibration method are adopted, the influence of interference signals on a measurement result is large, and the accuracy rate of the measurement result is low.
2. At present, flowing water type nuclear magnetic resonance magnetometers, electron spin resonance magnetometers and other instruments suitable for direct current method calibration cannot be purchased in the market, and accurate measurement is difficult to achieve.
Disclosure of Invention
Objects of the invention
The invention aims to provide a Helmholtz coil constant alternating-current calibration method, device and system. On one hand, the influence of interference signals is avoided, and the accuracy of the measurement result is improved. On the other hand, the adopted calibration device is simple and convenient in design, and accurate measurement is easy to realize.
(II) technical scheme
In order to solve the above problem, a first aspect of the embodiments of the present invention provides a method for ac calibrating a helmholtz coil constant based on a quadrature principle, which uses a calibration apparatus, where the calibration apparatus includes: connected in seriesAn arbitrary waveform generator, a power amplifier, a Helmholtz coil and a digital power meter; the power amplifier is also connected with the digital power meter, and the Helmholtz coil comprises a pair of concentric circles coils which are connected in series in the same direction; a small coil is placed in the central uniform area of the Helmholtz coil; the calibration method comprises the following steps: generating sine wave alternating current signals with different frequencies by adopting an arbitrary waveform generator; the power amplifier amplifies the sine wave alternating current signal and sends the sine wave alternating current signal to the Helmholtz coil, so that the Helmholtz coil generates an alternating current excitation signal; under the action of the alternating current excitation signal, a digital power meter acquires the induction voltage U of a small coil with a known turn area and the excitation current I passing through the Helmholtz coil; calculating the induced voltage and the excitation current according to a first calculation rule to obtain a product P 'of the induced voltage and the excitation current, calculating the induced voltage and the excitation current according to a second calculation rule to obtain a product Q' of the induced voltage and the excitation current, and calculating by adopting an orthogonal principle based on the product P 'and the product Q' of the induced voltage and the excitation current to obtain an effective value U of the induced voltagerms(ii) a Based on the product P 'and Q' of the induced voltage and the exciting current, the effective value U of the induced voltage is obtained by calculation by adopting the orthogonal principlerms(ii) a Based on the effective value U of the induced voltagermsAnd the effective value of the exciting current IrmsAnd calculating to obtain the Helmholtz coil constant.
Further, the calculating the induced voltage and the excitation current according to the first calculation rule to obtain a product P' of the induced voltage and the excitation current includes: acquiring an induced voltage curve and an exciting current curve by adopting a digital power meter; collecting induced voltage data points from the voltage curve; shifting the current curve to the right along a horizontal axis by a first number of excitation current data points so that a first phase difference exists between the shifted current curve and the original current curve; and multiplying and calculating point by point to obtain a product P' based on the induction voltage data point on the voltage curve and the corresponding excitation current data point on the moved current curve.
Further, based on the sense on the voltage curveMultiplying the voltage data point and the corresponding excitation current data point on the shifted current curve point by point to obtain a product P ', wherein the product P' comprises the following steps:
wherein i represents the number of voltage data points on the induced voltage curve, i + x represents the number of voltage data points on the induced voltage curve after the voltage data points move to the right by x number points, n is the total number of voltage data points on the voltage curve, UiIs the induced voltage of a small coil of known turn area, IiIs the exciting current passing through the Helmholtz coil, and phi is the effective value U of the induced voltagermsAnd an excitation current IrmsThe phase angle of (c).
Further, the calculating the induced voltage and the excitation current according to the second calculation rule to obtain a product Q' of the induced voltage and the excitation current includes: acquiring an induction voltage curve and an exciting current curve by adopting a digital power meter; collecting induced voltage data points from the voltage curve; shifting the current curve by a second numerical point excitation current data point along a horizontal axis so that a second phase difference exists between the shifted current curve and an original current curve, wherein the difference between the second phase difference and the first phase difference is less than or equal to one period; and multiplying the induction voltage data point on the voltage curve and the corresponding excitation current data point on the moved current curve point by point to obtain a product Q'.
Further, based on the induced voltage data point on the voltage curve and the corresponding excitation current data point on the shifted current curve, performing point-by-point multiplication to obtain a product Q', including:
wherein i represents the number of voltage data points on the induced voltage curve, i + y represents the number of voltage data points on the induced voltage curve after the voltage data points move rightwards by y number of value points, y-x is less than or equal to one period, n is the total number of the voltage data points on the voltage curve, UiIs the induced voltage of a small coil of known turn area, IiIs the exciting current passing through the Helmholtz coil, and phi is the effective value U of the induced voltagermsAnd an excitation current IrmsThe phase angle of (c).
Further, based on the product P 'and the product Q' of the induced voltage and the exciting current, the orthogonal principle is adopted to calculate to obtain an effective value U of the induced voltagermsSpecifically, the method is calculated according to the following method:
in the formula IrmsEffective value of exciting current, UrmsIs the effective value of the induced voltage, phi is the phase difference between the product P 'and the product Q', sin phiy-xAnd cos phiy-xAre all constants.
Further, the excitation current effective value IrmsThe calculation method of (c) is as follows:
wherein j represents the number of current data points on the current curve, and m is the total number of current data points on the current curve.
Further, the effective value U based on the induced voltagermsAnd the exciting current I, calculating to obtain a Helmholtz coil constant, and specifically calculating according to the following method:
in the formula: u shapermsIs effective value of the induced voltage of the small coil, f is signal source frequency, NS is known turn area of the small coil, mu0Is a magnetic constant, khIs the Helmholtz coil constant, IrmsIs the effective value of the current through the helmholtz coil.
According to another aspect of the embodiments of the present invention, there is provided a helmholtz coil constant ac calibration system based on the quadrature principle, including: the sine wave alternating current signal generating device is used for generating sine wave alternating current signals with different frequencies; the power amplifier is used for amplifying the sine wave alternating current signal and sending the sine wave alternating current signal to the Helmholtz coil to enable the Helmholtz coil to generate alternating current excitationA magnetic signal; the digital power meter is used for acquiring the induced voltage generated by a small coil with a known turn area and the exciting current passing through the Helmholtz coil under the action of the alternating current exciting signal; the induction voltage effective value calculation module is used for calculating the induction voltage and the excitation current according to a first calculation rule to obtain a product P 'of the induction voltage and the excitation current, calculating the induction voltage and the excitation current according to a second calculation rule to obtain a product Q' of the induction voltage and the excitation current, and calculating by adopting an orthogonal principle based on the product P 'and the product Q' of the induction voltage and the excitation current to obtain an induction voltage effective value Urms(ii) a A coil constant calculation module for calculating an effective value U based on the induced voltagermsAnd the effective value of the exciting current IrmsAnd calculating to obtain the Helmholtz coil constant.
Further, the induced voltage effective value calculation module includes: the acquisition submodule is used for acquiring an induction voltage curve and an excitation current curve; the induced voltage data point acquisition submodule is used for acquiring induced voltage data points from the voltage curve; the first moving submodule is used for moving the current curve to the right along a horizontal axis by a first number of excitation current data points so that a first phase difference exists between the moved current curve and an original current curve; and the first calculation submodule is used for multiplying and calculating point by point to obtain a product P' based on the induction voltage data point on the voltage curve and the corresponding excitation current data point on the moved current curve.
Further, the product P' of the induced voltage and the excitation current is calculated according to the following formula, including:
wherein i represents the number of voltage data points on the induced voltage curve, i + x represents the number of voltage data points on the induced voltage curve after the voltage data points move to the right by x number points, n is the total number of voltage data points on the voltage curve, UiIs the induced voltage of a small coil of known turn area, IiIs the exciting current passing through the Helmholtz coil, and phi is the effective value of the induced voltageUrmsAnd an excitation current IrmsThe phase angle of (c).
Further, the induced voltage effective value calculation module includes: the acquisition submodule is used for acquiring an induction voltage curve and an excitation current curve; the induced voltage data point acquisition submodule is used for acquiring induced voltage data points from the voltage curve; the second moving submodule is used for moving the current curve by a second numerical value point excitation current data point along a horizontal axis, so that a second phase difference exists between the moved current curve and an original current curve, and the difference value between the second phase difference and the first phase difference is smaller than or equal to one period; and the second calculation submodule is used for calculating to obtain a product Q' based on the induction voltage data point on the voltage curve and the corresponding excitation current data point on the shifted current curve.
Further, calculating a product Q' of the induced voltage and the excitation current according to the following formula, including:
wherein i represents the number of voltage data points on the induced voltage curve, i + y represents the number of voltage data points on the induced voltage curve after the voltage data points move rightwards by y number points, y-x is less than or equal to one period, n is the total number of the voltage data points on the voltage curve, UiIs the induced voltage of a small coil of known turn area, IiIs the exciting current passing through the Helmholtz coil, and phi is the effective value U of the induced voltagermsAnd an excitation current IrmsThe phase angle of (c).
Further, based on the product P 'and the product Q' of the induced voltage and the exciting current, the orthogonal principle is adopted to calculate to obtain an effective value U of the induced voltagermsThe method comprises the following steps:
in the formula IrmsEffective value of exciting current, UrmsIs an effective value of the induced voltage, phi is the phase difference between the product P 'and the product Q', sin phiy-xAnd cos phiy-xAre all constants.
Further, the excitation current effective value IrmsThe calculation method of (c) is as follows:
wherein j represents the number of current data points on the current curve, and m is the total number of current data points on the current curve.
Further, the coil constant calculation module calculates the Helmholtz coil constant according to the following method:
in the formula: u shapermsIs effective value of the induced voltage of the small coil, f is signal source frequency, NS is known turn area of the small coil, mu0Is a magnetic constant, khIs the Helmholtz coil constant, IrmsIs the effective value of the current through the helmholtz coil.
(III) advantageous effects
The technical scheme of the invention has the following beneficial technical effects:
firstly, by using the calibration device and the calibration method of the present invention, the product P 'and the product Q' of the induced voltage and the excitation current are calculated respectively based on the induced voltage and the excitation current, and the effective value U of the induced voltage is calculated by using the orthogonality principlerms. Stray signals in the induction voltage can be effectively removed, so that the effective value of the induction voltage can be accurately determined, and the measurement accuracy is improved.
Secondly, the calibration device provided by the invention adopts an arbitrary waveform generator, a power amplifier, a Helmholtz coil, a digital power meter and a small coil, and the above instruments can be purchased from the market, and the calibration device is simple in design, convenient to operate and capable of measuring the voltage effective value more accurately.
Drawings
FIG. 1 is a schematic diagram of a prior art method for measuring the permanent magnetic moment of a magnetic flux integrator and a Helmholtz coil;
FIG. 2 is a schematic view of a zero magnetic field space created by a large three-dimensional combined Helmholtz coil in the prior art;
FIG. 3 is a schematic structural diagram of an apparatus for calibrating Helmholtz coil constants by AC based on the quadrature principle according to an embodiment of the present invention;
FIG. 4 is a flow chart of a calibration method in an embodiment of the invention;
FIG. 5 is a schematic diagram of a calibration system in an embodiment of the invention;
fig. 6 is a schematic structural diagram of an induced voltage effective value calculation module in an embodiment of the present invention;
fig. 7 is a schematic structural diagram of an induced voltage effective value calculation module in an embodiment of the present invention.
Reference numerals:
the method comprises the following steps of 1-an arbitrary waveform generator, 2-a power amplifier, 3-a Helmholtz coil, 4-a digital power meter, 5-a small coil, 6-a sine wave alternating current signal generating device, 7-an induced voltage effective value calculating module, 71-an obtaining submodule, 72-an induced voltage data point collecting submodule, 73-a first moving submodule, 74-a first calculating submodule, 75-a second moving submodule, 76-a second calculating submodule and 8-a coil constant calculating module.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail with reference to the accompanying drawings in conjunction with the following detailed description. It should be understood that the description is intended to be exemplary only, and is not intended to limit the scope of the present invention. Moreover, in the following description, descriptions of well-known structures and techniques are omitted so as to not unnecessarily obscure the concepts of the present invention.
Example one
Fig. 3 is a helmholtz coil constant ac calibration apparatus based on the quadrature principle in this embodiment.
As shown in fig. 3, in this embodiment, the calibration apparatus includes: the device comprises an arbitrary waveform generator 1, a power amplifier 2, a Helmholtz coil 3 and a digital power meter 4 which are connected in sequence. The power amplifier 2 is also connected with the digital power meter 4, and the helmholtz coil 3 comprises a pair of concentric circles which are connected in series in the same direction. A small coil 5 is placed in the central uniform area of the helmholtz coil 3. Specifically, the power amplifier 2 adopts an AE Techron 7548P high-stability power amplifier 2 to provide a stable current for calibrating the helmholtz coil 3. Maximum output power: 3300w rms, output frequency: DC-200 kHz, DC Drift: + -200 μ V. The arbitrary waveform generator 1 adopts an Agilent 33500B arbitrary waveform generator 1 to provide a signal source for the high-stability power amplifier 2, and the total harmonic distortion is 0.04%. The instruments adopted by the device can be purchased in the market, and the operation is simple and easy to realize. The digital power meter 4 adopts an LMG610 power meter to accurately measure the induction voltage and the exciting current of the small coil 5. Specifically, the digital power meter 4 is provided with a sensor capable of directly measuring the induced voltage of the small coil 5. Input voltage range of the sensor: 0-4V. Maximum allowable error: + (0.01% measurement + 0.02% full scale).
Preferably, the plane of the small coil 5 and the plane of the helmholtz coil 3 form a preset angle, and the angle is adjustable. Specifically, the angle value range is as follows: 0-90 degrees. The Helmholtz coil 3 is calibrated by the small coil 5, the parallelism of the plane of the small coil 5 and the Helmholtz coil 3 is considered, and the maximum induction voltage signal needs to be found by fine adjustment on the basis of ensuring the parallelism of mechanical design so as to realize the lowest calibration uncertainty. This embodiment has designed the 5 angle modulation functions of little coil, can universal regulation 5 planar and 3 planar angles of helmholtz coil of little coil, finds the biggest induced voltage signal after, can lock the angle to improve the accuracy of calibration. Test data show that the method can reduce the background noise deduction rate to about 99%, and the influence of the background noise on the voltage measurement after orthogonal calculation is reduced to a level lower than 0.005%.
FIG. 4 is a flow chart of a calibration method in an embodiment of the invention.
As shown in fig. 4, the calibration method includes: s1: an arbitrary waveform generator 1 is adopted to generate sine wave alternating current signals with different frequencies; s2: the power amplifier 2 amplifies the sine wave alternating current signal and sends the sine wave alternating current signal to the Helmholtz coil 3, so that the Helmholtz coil 3 generates an alternating current excitation signal; s3: under the action of the AC excitation signal, the digital power meter 4Acquiring the induced voltage U of a small coil 5 with a known turn area and the exciting current I passing through the Helmholtz coil 3; s4: calculating the induced voltage and the excitation current according to a first calculation rule to obtain a product P 'of the induced voltage and the excitation current, and calculating the induced voltage and the excitation current according to a second calculation rule to obtain a product Q' of the induced voltage and the excitation current; s5: based on the product P 'and the product Q' of the induced voltage and the exciting current, the orthogonal principle is adopted to calculate to obtain an effective value U of the induced voltagerms(ii) a S6: based on the effective value U of the induced voltagermsAnd the effective value of the exciting current IrmsAnd calculating to obtain the Helmholtz coil constant.
In this embodiment, the induced voltage of the small coil 5 contains useful signals and stray field signals, and measuring its effective value directly leads to a large uncertainty. Because the current signal only contains a specified frequency signal, the product P 'and the product Q' of the induced voltage and the current are respectively calculated by using the digital power meter 4, and according to the positive crossing principle, stray signals in the induced voltage can be removed, so that the effective value of the induced voltage can be accurately determined, and the measurement accuracy is improved, see the formula (1.3) (1.4) (1.5).
The Helmholtz coil 3 is electrified with constant sine wave current, a small coil 5 with known turn area is placed in the center of the Helmholtz coil 3, the induced voltage of the small coil 5 is accurately measured, and therefore the coil constant is calculated, and the formula (2.1) is shown. As can be seen from the formula, khInduced voltage from the small coil 5, exciting current and frequency generated by the Helmholtz coil 3And a small coil 5 turn area, where current and frequency can be accurately determined. Therefore, the key factor of the ac calibration is the uncertainty of the 5-turn area NS of the small coil and whether the voltage effective value signal under the influence of the spatial stray field can be accurately determined.
Urms＝2πf·NS·μ0·kh·Irms (2.1)
Wherein: u shapermsIs effective value of the induced voltage of the small coil, f is signal source frequency, NS is known turn area of the small coil, mu0Is a magnetic constant, khIs the Helmholtz coil constant, IrmsIs the effective value of the current through the helmholtz coil.
The random waveform generator 1 provides sine wave alternating current signals with different frequencies, the power amplifier 2 amplifies the sine wave alternating current signals to proper strength to carry out alternating current excitation on the Helmholtz coil 3, under the excitation of an alternating magnetic field, the small coil 5 placed in a uniform region in the center of the Helmholtz coil 3 generates an induced voltage signal, and the induced voltage signal is sent to a voltage sensor end of the digital power meter 4 to accurately measure voltage.
Wherein, calculating the induced voltage and the excitation current according to a first calculation rule to obtain a product P' of the induced voltage and the excitation current comprises: acquiring an induction voltage curve and an exciting current curve by adopting a digital power meter; collecting induced voltage data points from the voltage curve; shifting the current curve to the right along the horizontal axis by a first number of excitation current data points (for example, shifting the excitation current data points to the right by 100) so that a first phase difference exists between the shifted current curve and the original current curve; and multiplying and calculating point by point to obtain a product P' based on the induction voltage data point on the voltage curve and the corresponding excitation current data point on the moved current curve. Specifically, the product P' of the induced voltage and the excitation current is calculated according to the following formula, including:
wherein i represents the number of voltage data points on the induced voltage curve, i + x represents the number of voltage data points on the induced voltage curve after the voltage data points move to x number points in the right direction, n is the total number of voltage data points on the voltage curve, UiIs the induced voltage, I, of a small coil 5 of known turn areaiIs the exciting current passing through the Helmholtz coil 3, phi is the effective value U of the induced voltagermsAnd an excitation current IrmsThe phase angle of (c).
Wherein calculating the induced voltage and the excitation current according to a second calculation rule to obtain a product Q' of the induced voltage and the excitation current comprises: acquiring an induction voltage curve and an exciting current curve by adopting a digital power meter 4; collecting induced voltage data points from the voltage curve; shifting the current curve by a second number of excitation current data points along the horizontal axis (e.g., shifting the excitation current data points by 300) such that a second phase difference exists between the shifted current curve and the original current curve, wherein the difference between the second phase difference and the first phase difference is less than or equal to one period; and multiplying the induction voltage data point on the voltage curve and the corresponding excitation current data point on the moved current curve point by point to obtain a product Q'. Specifically, the product Q' of the induced voltage and the excitation current is calculated according to the following formula, including:
wherein i represents the number of voltage data points on the induced voltage curve, i + y represents the number of voltage data points on the induced voltage curve after the voltage data points move rightwards by y number of value points, y-x is less than or equal to one period, n is the total number of the voltage data points on the voltage curve, U is the total number of the voltage data points on the voltage curveiIs the induced voltage, I, of a small coil 5 of known turn areaiIs the exciting current passing through the Helmholtz coil 3, phi is the effective value U of the induced voltagermsAnd an excitation current IrmsThe phase angle of (c).
Wherein, based on the product P 'and Q' of the induced voltage and the exciting current, the orthogonal principle is adopted to calculate to obtain the effective value U of the induced voltagermsSpecifically, the method is calculated according to the following method:
in the formula IrmsEffective value of exciting current, UrmsFor the effective value of the induced voltage, phi is the phase difference between the product P 'and the product Q', sin phiy-xAnd cos phiy-xAre all constants.
Wherein, the effective value of the exciting current IrmsThe calculation method of (c) is as follows:
where j represents the number of current data points on the current curve and m is the total number of current data points on the current curve.
Wherein the effective value U is based on the induced voltagermsAnd the exciting current I, calculating to obtain a Helmholtz coil constant, and specifically calculating according to the following method:
in the formula: u shapermsIs effective value of the induced voltage of the small coil, f is signal source frequency, NS is known turn area of the small coil, mu0Is a magnetic constant, khIs the Helmholtz coil constant, IrmsIs the effective value of the current through the helmholtz coil.
In this embodiment, the processing manner of moving the current to different phases twice obtains P 'and Q'. P 'and Q' have a fixed phase difference, still can realize the quadrature computation as before, realize the accurate measurement of low-voltage signal, the induced voltage that obtains of measurement is the part that only becomes consistent with the frequency of excitation current signal, and the interference magnetic field of external different frequencies, especially various wireless signals, and power frequency power supply signal will be filtered out, can promote the measurement accuracy of induced voltage signal by a wide margin.
Taking a sampling rate of 50hz, 50.505kS/s as an example, the measurement principle is derived as follows: multiplying the collected current data points by the voltage points one by moving 100 points to obtain P'; and in the second step, the collected current data points are moved to 300 points and multiplied by the voltage points point by point to obtain Q'. So that there is a phase difference of 200 points between the two. The phase difference can be set freely as long as the phase difference is within a reasonable range. If the rationality and the correctness of the method need to be verified, the method can be realized by setting different phase differences and checking whether the measurement results are completely consistent. The above formula can be transformed in this example to the following formula:
expanding the above formula according to a trigonometric function sum and difference formula
Q'＝UrmsIrmscos(φ+φ200)＝UrmsIrmscosφcosφ200-UrmsIrmssinφsinφ200
(3.3)
sinφ200And cos phi200Are all constants, and have the following formula:
and respectively squaring the formula and two sides of the formula, and then adding to obtain:
the calibration method in the embodiment can accurately obtain the effective value of the induction voltage, and offset the external interference signal to the greatest extent. If the method is accurate and effective, the measurements should be consistent at different phase angles. To verify the method, different phase angles, even different initial phases, are transformed in the same measurement result, and the measurement results are shown in the following table 1-1, and it can be seen that the calculation results under different phase angles are consistent, and the deviation is ± 0.001%, which illustrates the correctness and effectiveness of the subject algorithm.
TABLE 1-1
In the second embodiment, the first embodiment of the method,
fig. 5 is a structural schematic diagram of a helmholtz coil constant ac calibration system based on the quadrature principle.
As shown in fig. 5, a helmholtz coil constant ac calibration system based on the quadrature principle includes: sine wave alternating current signal generating means 6 for generating sine wave alternating current signals of different frequencies; the power amplifier 2 is used for amplifying the sine wave alternating current signal and sending the sine wave alternating current signal to the Helmholtz coil 3, so that the Helmholtz coil 3 generates an alternating current excitation signal; the digital power meter 4 is used for acquiring the induced voltage U generated by the small coil 5 with a known turn area and the exciting current I passing through the Helmholtz coil 3 under the action of the alternating current exciting signal; an induced voltage effective value calculation module 7, configured to calculate, according to a first calculation rule, the induced voltage and the excitation current to obtain a product P' of the induced voltage and the excitation current, and calculate, according to a second calculation rule, the induced voltage and the excitation currentThe exciting current is calculated to obtain a product Q ' of the induced voltage and the exciting current, and the product P ' and the product Q ' of the induced voltage and the exciting current are calculated by adopting an orthogonal principle to obtain an effective value U of the induced voltagerms(ii) a A coil constant calculation module 8 for calculating an effective value U based on the induced voltagermsAnd calculating the Helmholtz coil constant number according to the excitation current I.
As shown in fig. 6, the induced voltage effective value calculating module 7 includes: the obtaining submodule 71 is used for obtaining an induction voltage curve and an excitation current curve; an induced voltage data point acquisition submodule 72 for acquiring an induced voltage data point from the voltage curve; the first moving submodule 73 is used for moving the current curve to the right along the horizontal axis by a first number of excitation current data points, so that a first phase difference exists between the moved current curve and the original current curve; and the first calculating submodule 74 is configured to multiply, point by point, the induced voltage data point on the voltage curve and the excitation current data point on the shifted current curve to obtain a product P'. Specifically, the product P' of the induced voltage and the excitation current is calculated according to the following formula, including:
wherein i represents the number of voltage data points on the induced voltage curve, i + x represents the number of voltage data points on the induced voltage curve after the voltage data points move to x number points in the right direction, n is the total number of voltage data points on the voltage curve, UiIs the induced voltage, I, of a small coil 5 of known turn areaiIs the exciting current passing through the Helmholtz coil 3, phi is the effective value U of the induced voltagermsAnd an excitation current IrmsThe phase angle of (c).
As shown in fig. 7, the induced voltage effective value calculating module 7 includes: the obtaining submodule 71 is configured to obtain an induction voltage curve and an excitation current curve; the induced voltage data point acquisition submodule 72 is used for acquiring induced voltage data points from the voltage curve; a second shift submodule 75, configured to shift the current curve by a second number of excitation current data points along a horizontal axis, so that a second phase difference exists between the shifted current curve and the original current curve, where a difference between the second phase difference and the first phase difference is less than or equal to one period; and a second calculating submodule 76, configured to calculate a product Q' based on the induced voltage data point on the voltage curve and the shifted excitation current data point corresponding to the current curve. Specifically, the product Q' of the induced voltage and the excitation current is calculated according to the following formula, including:
wherein i represents the number of voltage data points on the induced voltage curve, i + y represents the number of voltage data points on the induced voltage curve after the voltage data points move rightwards by y number of value points, y-x is less than or equal to one period, n is the total number of the voltage data points on the voltage curve, U is the total number of the voltage data points on the voltage curveiIs the induced voltage, I, of a small coil 5 of known turn areaiIs the exciting current passing through the Helmholtz coil 3, phi is the effective value U of the induced voltagermsAnd an excitation current IrmsThe phase angle of (c).
Specifically, the induced voltage effective value calculation module 7 calculates the induced voltage effective value according to the following method:
in the formula IrmsEffective value of exciting current, UrmsFor the effective value of the induced voltage, phi is the phase difference between the product P 'and the product Q', sin phiy-xAnd cos phiy-xAre all constants.
Specifically, the effective value of the exciting current IrmsThe calculation method of (c) is as follows:
where j represents the number of current data points on the current curve and m is the total number of current data points on the current curve.
Specifically, the coil constant calculation module 8 calculates the helmholtz coil constant according to the following method:
in the formula: u shapermsIs effective value of the induced voltage of the small coil, f is signal source frequency, NS is known turn area of the small coil, mu0Is a magnetic constant, khIs the Helmholtz coil constant, IrmsIs the effective value of the current through the helmholtz coil.
In practical use, it is found that the product P ' provided by the digital power meter 4 is calculated for each point on the real curve, and the product Q ' is not calculated point by point according to the definition, but calculated by the apparent power and the product P ', so that the quadrature calculation cannot be realized according to the products P ' and Q ' given by directly applying the instrument.
In order to realize accurate measurement of the effective value of the voltage, the embodiment of the invention designs an effective value calculation module 7 of the induced voltage, which is used for collecting and recording data points of a measurement curve of the digital power meter 4, and aims to extract data automatically, perform data processing automatically from the principle, realize real measurement of Q', further realize orthogonal calculation and obtain an accurate induced voltage value.
However, in practice, another problem is encountered in doing so — because the digital power meter 4 can sample the number of points only with fixed values such as 50.505kS/s,151.515kS/s,303.03kS/s,606.061kS/s, 1212.12kS/s, as shown in the following table, the number of points in one cycle cannot be exactly divided by 4, so that the 90-degree phase cannot be accurately controlled, and thus the calculation cannot be directly performed according to the conventional method for active power and reactive power.
Tables 1 to 2
To overcome the above problem, in this embodiment, the processing method of moving the current to different phases twice obtains P 'and Q'. P 'and Q' have a fixed phase difference, still can realize the quadrature computation as before, realize the accurate measurement of low-voltage signal, the induced voltage that obtains of measurement is the part that only is unanimous with the frequency of excitation current signal, and the interference magnetic field of external different frequencies, especially various wireless signals, and power frequency power supply signal will be filtered out, can promote the measurement accuracy of induced voltage signal by a wide margin.
In the third embodiment, the first step is that,
in order to verify the effectiveness of the device, the method and the system for calibrating the helmholtz coil constant by alternating current based on the orthogonality principle provided by the embodiment of the invention, the calibration device and the quadrature voltage measurement method provided by the embodiment of the invention are used for measuring the background noise of the voltage signal under different frequencies, namely, the small coil 5 is removed from the helmholtz coil 3 and is far away from the helmholtz coil 3 while the helmholtz coil 3 is excited, and the induced voltage signal at the moment is measured by the positive intersection method. The measurement results are shown in tables 1 to 3 below, and it can be seen in the tables that under the selected frequency, the voltage background noise after the orthogonal calculation is greatly reduced compared with the unprocessed background noise, that is, most of useless interference signals are effectively processed, and the influence of the background noise after the orthogonal calculation on the voltage measurement is reduced to within 0.005%, which indicates that when the helmholtz coil 3 is calibrated by using the method provided by the embodiment of the present invention, the background noise can be controlled to a level which can be ignored with respect to the measured signal, and at the same time, the measurement method provided by the embodiment of the present invention can effectively resist interference, and improve the measurement accuracy of the induced voltage.
Tables 1-360 Hz are the frequencies selected by embodiments of the present invention to calibrate the helmholtz coil 3, and the background noise of the voltage signal is measured multiple times at 60Hz using the quadrature voltage measurement method established by embodiments of the present invention. The results of 6 measurements are shown in the following table, and it can be seen that the voltage background noise after orthogonal calculation at 60Hz is 0.003-0.004mV, which is not only weak but also consistent, indicating that the uncertainty component of measurement caused by the background noise (or interference signal) is 0.005% by using the measurement method provided by the embodiment of the present invention.
Tables 1 to 4
The invention has the following beneficial effects:
1. by adopting the calibration method, products P 'and Q' are respectively calculated based on the induction voltage and the excitation current, and the effective value U of the induction voltage is obtained by adopting the orthogonal principle to calculaterms. Stray signals in the induction voltage can be effectively removed, so that the effective value of the induction voltage can be accurately determined, and the accuracy of measurement is improved.
2. The calibration device provided by the invention adopts the arbitrary waveform generator 1, the power amplifier 2, the Helmholtz coil 3, the digital power meter 4 and the small coil 5, all the instruments can be purchased from the market, the design is simple, the operation is convenient, and the voltage effective value is measured more accurately.
It is to be understood that the above-described embodiments of the present invention are merely illustrative of or explaining the principles of the invention and are not to be construed as limiting the invention. Therefore, any modification, equivalent replacement, improvement and the like made without departing from the spirit and scope of the present invention shall be included in the protection scope of the present invention. Further, it is intended that the appended claims cover all such variations and modifications as fall within the scope and boundaries of the appended claims or the equivalents of such scope and boundaries.
Claims (12)
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