AC calibration methods of magnetic flux density coil standard up to 100 kHz Michal Ulvr* *
Czech Metrology Institute, Brno, Czech Republic
[email protected]
Abstract — The frequency dependence of the constant of the coil magnetic flux density standard is needed in order to generate the AC magnetic flux density with precision. This paper presents an analysis of methods that can be used for calibration of the frequency dependence of the coil magnetic flux density standard up to 100 kHz. In addition, experimental results with expanded uncertainty up to 0.25 % in the whole frequency range are compared with the simulated and calculated frequency dependence. Index Terms — Calibration, coil standard, current shunt, magnetic flux density, search coil.
I. INTRODUCTION AC calibration of the coil standard involves determining the frequency dependence of the coil standard constant. Methods that are applied involve using a search coil in quite different ways - calibration methods up to 20-30 kHz are described in [1], [2]. The frequency range is mostly limited by the frequency dependence of the constant of the search coil. An analysis of methods that can be used for calibration of the coil standard up to 100 kHz will be presented here. II. THEORY Fig. 1 presents a method using two search coils, S1 and S2, with nominally the same values. One search coil is placed in calibrated coil standard X, and the other is placed in coil standard E, the frequency dependence of the constant KE is well known. The two coil standards are positioned three power source
3458A
U2
S2 I
UR
3458A
X E
3458A
X
U1
Fig. 1. Schematic diagram of the method using two search coils with nominally the same values.
meters apart, and they are connected in series, so that they carry the same current during the measurements. Voltages U1
UX S
3458A
I UR 3458A
R
FIG. 2. Schematic diagram of the method using a precise AC current shunt.
and U2, which are induced in the two search coils are measured by means of a 3458A digital multimeter. This procedure is repeated after transposing the search coils to eliminate their coil factors from the result. The current I through the two coil standards is measured as the voltage drop UR on the AC current shunt R, using an 3458A digital multimeter. Current I is measured for information only. The constant of the calibrated coil standard is calculated from the equation
U 2 S1 K E . U1S 2
KX =
(1)
The method presented in Fig. 2 involves measuring the voltage UX induced in search coil S placed inside calibrated coil standard X, and measuring the current I through the coil standard as the voltage drop UR across the AC current shunt R. A precise AC current shunt with a known AC-DC difference and a search coil with the flat frequency characteristic in a given frequency range is needed. The constant of the calibrated coil standard is calculated from the equation
KX =
S1 R
power source
UXR 4 2U R Sf
.
(2)
Influence of parasitic capacitance of connecting cable is negligible. A method using a precise AC current shunt is much simpler, and a lower uncertainty value can be achieved than by the method using two search coils with nominally the same values. Another option is to use an approximate formula [3]
K bAC
978-1-5386-0974-3/18/$31.00 ©2018 IEEE
f 2 , = K bDC 1 + f r
(3)
Fig. 3. Frequency dependence of the coil standard constant. Search coils KII and EP02/00 were used for the measurements.
Fig. 4. Frequency dependence of the coil standard constant. Search coils KII, EP02/00 and KII with an I/U converter were used for the measurements.
where KbDC is the solenoid constant with a DC current value of 1 A (mT), f is the frequency of the generated AC MFD (Hz), and fr is the resonance frequency value (Hz). The change of KbAC from KbDC is 1% for f/fr = 0.1, and 4% for f/fr = 0.2. This formula is valid only in its approach for small changes of KbAC from KbDC. II. EXPERIMENTAL RESULTS A single-layer Helmholtz-type solenoid was calibrated by a method using a precise AC current shunt. The measured frequency dependence was also compared with the frequency dependence simulated in FLUX 3D, and with the calculated frequency dependence according formula (3). A precise cagetype AC current shunt with an AC-DC difference of up to 70 ppm was used. Two special search coils with a cylindrical frame and a suppressed octupole were used for the calibration of the solenoid. When a search coil is used far below its resonance frequency (which is given by a parasitic capacitance), it can be considered that the search coil is frequency independent in the described frequency range. A single-layer search coil No. EP 02/00 with the calibrated constant KS = (0.045394 ± 0.000036) m2 and resonance frequency value of 3.8 MHz was used from 2 kHz up to 100 kHz. A special multi-layer search coil No. KII with the calibrated constant KS = (1.3312 ± 0.0011) m2 and resonance
frequency value of 49.6 kHz was used for frequencies up to 3 kHz. The results are presented in Fig. 3. An early change in the search coil KII constant can be seen in the range of 23 kHz. However, the differences between the EP 02/00 results and the calculated and simulated frequency dependence in the range of 3-20 kHz were larger than expected. Differences of about 0.5 % were probably caused by interferences, and by the lower sensitivity of EP 02/00 in this frequency range. Search coil No. KII with I/U converter was therefore used in the range of 2-20 kHz. The I/U converter increased the frequency range of the KII coil up to 30 kHz. The disadvantages of the EP 02/00 coil were thus eliminated in this range (see the results in Fig. 4.). The relative difference of the measured values from the calculated values is up to 0.25% in the frequency range up to 50 kHz, up to 1.2% in the frequency range of 50-70 kHz and up to 3.2% in the frequency range of 70-100 kHz. It is evident that formula (3) can be used only up to 50 kHz in this case. The relative difference of the measured values from the simulated values is up to 0.15% in the frequency range up to 20 kHz, up to 0.35% in the frequency range of 20-50 kHz, and up to 0.5% in the frequency range of 50-100 kHz. The uncertainty depends mainly on the uncertainty of the search coil constant and on the uncertainty of the measured voltages. The repeatability was around 0.01%. Expanded uncertainty (k=2) from 0.12% to 0.25% up to 100 kHz can be achieved by this method using a precise AC current shunt. However, when search coil No. KII with the I/U converter is used, the expanded uncertainty value is 0.25% in the range of 2-20 kHz, due to the measurement uncertainty of the self inductance of the KII search coil. III. CONCLUSION Methods that can be used for calibration of coil standard up to 100 kHz have been presented. The frequency dependence of a single-layer Helmholtz-type solenoid has been calibrated up to 100 kHz by the method using a precise AC current shunt with expanded uncertainty from 0.12% up to 0.25%. The expanded uncertainty value is 0.25% in the range of 2-20 kHz when coil KII with an I/U converter is used. The measured frequency dependence has also been compared with the simulated and calculated frequency dependence, with very good results. REFERENCES [1] [2] [3]
K. Weyand, R. Ketzler, “Improved AC-Field CalibrationSetup”, in Proc. of CPEM 2004, London, 2004, pp 396-397. Po Gyu Park , Y. G. Kim, V. N. Kalabin, V. Ya. Shifrin, “AC magnetic flux density standards in the low frequency range”, in Proc. of CPEM 2008, USA, 2008. V. E. Czernyshev, “Rasczot czastotnoj pogreshnosti mier magnitnoj indukcii”, in Trudy Metrologiceskich Institutov SSSR, vol. 140. Moscow, Russia: Izd. standartov, 1972.
