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Standard of Magnetic Flux

Name: National standard of magnetic flux

Code designation: ECM 260-1/01-011

Year of publication: 2001

Department: dpt. 8017 CMI Laboratory for Fundamental Metrology Prague

Guarantor: Ing. Michal Ulvr, Ph.D.

Related KCDB CMC lines: 5

Realized unit

Range (nominal value)

Expanded uncertainty (k=2)


miliweber per amper

10 mWb.A-1

0,0006 mWb.A-1

group standard

Magnetic flux is one of the main quantities describing the magnetic field. The magnetic flux Φ is the surface integral of magnetic flux density. The unit of magnetic flux is weber (Wb). One weber equals one tesla times one square meter. The relationship of the unit of magnetic flux to the units of electrical quantities is evident from the following older definition. One weber is a magnetic flux that induces an electromotive voltage of one volt in a thread encircling it, if this flux decreases uniformly so that it disappears in one second.

Magnetic flux standards together with magnetic flux desnity standards and magnetic moment standards (area turns standards) form an interconnected unit of metrological security for the measurement of magnetic field quantities. Very simply, for the magnetic flux Φ (Wb):

where B is the magnetic flux density (T) and S is the magnetic moment constant or area turns (Wb×T-1 or m2). From two of these quantities, the remaining third can be derived or linked. Coils with dual windings are most often used as magnetic flux standards – suitable standards of mutual inductance, most with a nominal value of 10 mWb×A-1. After more than ten years of research, a number of seemingly high-quality types of coils (Sullivan, Tinsley, RFT) that we had at our disposal were discarded and two coils of our own production and two coils of production of Točelektropribor were selected, all with separate primary and secondary windings of cylindrical shape. The set of these four coils was declared the Czechoslovak national standard in 1980.  After continuous monitoring and research and a new multiple international linkage, this group standard was approved and declared the Czech national standard in 2001. In 2004, one of the Točelektropribor standards was removed from the state standard and was replaced by another standard of our own production from 1977, which has the designation No. 7706. The uncertainty of the national standard was also changed (halved) and approved. This also adjusted the value of the national standard. Standards – members of the naional group standard are compared with each other for many years at least once a year, while we maintain and maintain the arithmetic mean of their values.

The value of the national magnetic flux standard is the arithmetic mean of the values of the standards – members of this group standard:

                                      9.99080 mWb×A-1  with expanded uncetainty (k = 2) 0.0006 mWb×A-1 

Magnetic flux standards are used, among other things, for calibration of webermeters (fluxmeters), which measure the voltage pulse corresponding to the change in magnetic flux in an integrative way. These devices are also used to compare magnetic flux standards. The difference of induced pulses in the secondary windings in the step change of current (off or on) in the primary windings is measured. These sensitive webermeters are an important part of the standard equipment for the national standard of magnetic flux. We use two microwebermeters F191 (Etalon, St. Petersburg) equipped with photoelectric amplifiers, microwebermeter 702P (LDJ, USA) or digital webermeter DFM-R (Eckel, Germany). Other necessary components of the standard equipment are standard resistors (Guildline) together with voltmeters (HP 34401A, 3458A) and resistance decades.

The second possibility of tracebility of magnetic flux standards is the traceability to electrical impedance standards at low frequency. Coil standards of magnetic flux are identical to mutual inductance standards M (unit Henry, H), which are designed for periodically variable electric current.  Their values do not differ within the uncertainties stated here and the types of standards we use for frequencies up to about 30 Hz. For higher frequencies, parasitic capacities are applied and the differences in values with frequency increase. By means of special bridges, mutual inductance can be linked to the standards of electrical capacity and resistance, respectively electric voltage, which are today the most accurate among electrical quantities in their realizations by quantum phenomena. This sequence (calibration of our standard) was carried out at 20 Hz in February 1996 at NPL in Teddington near London and repeated in May 1998. The reported uncertainty of 0.0015 mH (equivalent to 0.0015 mWb×A-1) was greater than for our other options, so we have abandoned this path for the time being.

In 2019, an analysis of the possibility of ensuring the tracebility of individual members of the magnetic flux standard to primary standards of electrical quantities was prepared. A method of measuring mutual inductance from the voltage induced on the secondary winding of the standard at the current passing through the primary winding measured on the resistance standard at low frequency (16 Hz or 32 Hz), which is connected in series with the primary winding of the standard of flux, was implemented. Two 3458A multimeters were used to measure secondary voltage and primary current. To increase the accuracy of voltage measurement at these frequencies, Swerlein's algorithm was also applied in the software. Using the given method and equipment, it is possible to achieve an extended uncertainty of 182 ppm (when using SW without Swerlein's algorithm) or an extended uncertainty of 50 ppm (when using SW with Swerlein's algorithm). The differences from the DC value found by the internal comparison were 25 ppm (without Swerlein's algorithm) and 109 ppm (with Swerlein's algorithm). It was thus proved that the tested method is suitable for calibration of members of the national magnetic flux standard.

Our laboratory has been dealing with magnetic flux measurement and comparison of magnetic flux standards since 1964. Until 1990, the standard was compared with the VNIIM standard in St. Petersburg, it was the absolute standard of the so-called Campbell coils, where the value of the magnetic flux or the constant of the standard was calculated on the basis of a very precise and complicated measurement of dimensions. The last comparison with this standard was in 1988. In 1996 and 1998, the benchmark was established at the NPL in London. In 2001, at the suggestion of CMI, the Euromet Project No. 597- was redesignated EUROMET. EM. M-S1 "Intercomparison of magnetic flux by means of coil tranfer standard". The pilot laboratory was CMI and participated in addition to CMI: NPL (Teddington), PTB (Braunschweig), IEN (Torino) and VNIIM (St. Petersburg). The task ended successfully in 2003. As a transfer of the standard served one of the standards - members of the state standard marked No. 7704. Apart from the key magnetic flux comparison (2001), the previous magnetic flux comparison (1998), this magnetic flux comparison (2003) and the bilateral comparison with VNIIM, Russia (2017-2018), there was no pan-European or worldwide comparison of magnetic quantities.

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