Calibration of a reference field coil by means of the NMR magnetometer and induction coils

Transcription

1 Elektrotehniški vestnik 68(5): , 2001 Electrotechnical Review, Ljubljana, Slovenija Calibration of a reference field coil by means of the NMR magnetometer and induction coils Gregor Geršak, Janez Humar, Dušan Fefer University of Ljubljana, Faculty of Electrical Engineering Tržaška 25, 1000 Ljubljana, Slovenia gregorg@fe.uni-lj.si Abstract. Field coils are widely utilized in every precision measurement using stable reference magnetic fields. The basic property defined for any such coil is the coil-constant. It is a quotient of the generated magnetic flux density in the center of the coil and its energizing current. Field coils with a very accurately determined coil-constant are commonly used as a reference magnetic flux standard. By measuring the current energizing the coil the reference magnetic flux density is generated, providing the coil- constant is well know. The accuracy of the generated reference field thus depends mainly on the uncertainty of the coil-constant. In this paper, a calibration procedure for determining the coil-constant of a cylindrical field coil is described. Determination of coil properties in AC and DC conditions is shown. The coil DC constant is determined by employing a nuclear magnetic resonance (NMR) magnetometer used as a magnetic field standard. In AC conditions the frequency dependence of the DC constant is measured by using induction coils. Key words: calibration, field coil, proton magnetometer, NMR, induction coils Kalibracija referenčne tuljave s pomočjo NMR magnetometra in indukcijskih tuljavic Povzetek. Pri vsakem precizijskem merjenju, pri katerem uporabljamo stabilno referenčno magnetno polje, uporabljamo referenčne tuljave. Osnovni parameter, ki ga podajamo za vsako referenčno tuljavo, je konstanta tuljave. Konstanta tuljave je razmerje med gostoto magnetnega pretoka, generiranega v središču tuljave, in tokom, ki napaja tuljavo. Poljske tuljave s točno določeno konstanto tuljave so etaloni gostote magnetnega pretoka. Točnost magnetnega polja, ki ga tako generiramo, je v veliki meri odvisna od negotovosti konstante tuljave. V članku je opisana metoda določanja konstante tuljave v izmeničnih ali enosmernih pogojih. Enosmerna konstanta tuljave je bila določena s pomočjo protonskega magetometra, to je magnetometra, ki izkorišča jedrsko magnetno resonanco (NMR). Izmenična konstanta je bila določena z indukcijo, s pomočjo indukcijskih tuljavic. Ključne besede: kalibracija, tuljava, protonski magnetometer, NMR, indukcijska tuljavica 1 Introduction In the field of precision magnetic field measurements, field coils are widely used in most experiments and calibration procedures [5,6]. Field coils are used as working and also primary standards, depending on the level of accuracy of determining the generated magnetic field. Received 12 February 2001 Accepted 4 September 2001 Every standard should fulfill three basic properties. It should realize a physical quantity on a wide range and should be time and place independent as well. In the area of magnetic field measurements, there are three types of standards used. Permanent magnets can be used in the range of some 50 mt to 500 mt, with an accuracy of 10 2 to Although place independent, they can be used for a single value of the magnetic field only, are very time dependent and thus need short recalibration intervals. Another type of standards is the field coil that can have various designs and forms (solenoids, Helmholtz coils, Braunbek coils, etc. [7]). Its range is typically under some 200 mt (for multi-layer coils) and the accuracy of 10 2 (multi-layer coils) to Coils are more time independent than permanent magnets. The third type of the magnetic field standard are magnetometers. Their measuring range is from some nt to tens of T and accuracyof10 2 (Hall, fluxgate or Faraday magnetometers) down to 10 6 (magnetic resonance magnetometers). On the other hand magnetometers do not realize a physical quantity. As they merely measure it, a magnetic field generator is always needed. Magnetic field is usually generated in field coils, especially in air core coils having enough space in the center for magnetometer probe positioning. Field coils are generally defined by their coil- con-

2 Calibration of a Reference Field Coil by Means of the NMR Magnetometer and Induction Coils 295 stant. The coil-constant K is a parameter defining the proportionality between the generated magnetic flux and the current energizing the coil. It represents the geometrical property of the coil (diameter, length of the windings, number of layers and windings, etc.) and defines the generated magnetic flux density B in the center of the coil when the coil is energized by the current I B = KI. (1) Thus by a common current measurement one can calculate the generated magnetic field. In AC conditions, when the coil is AC energized, the coil-constant changes when increasing the frequency of the energizing current. The coil properties change due to a faster increasing influence of parasitic capacities between the windings compared to the increasing impedance of the coil. The frequency dependence of the generated AC magnetic flux density is given by B = K(f)I, (2) where B is AC magnetic flux density generated in the coil, I alternating current energizing the coil and K(f) frequency dependant coil- constant. There are several methods to determine the coilconstant of a calibrated field coil. The most common ones are the direct method and the comparison method. The direct method involves measuring the generated magnetic flux density in the center of the coil along with measuring the current energizing the windings of the coil. The coil-constant is then calculated. On the other hand, the comparison method uses field compensation of a standard coil and the calibrated field coil with zeroing the zero indicator (commonly a fluxgate magnetometer) output and measuring of currents energizing both field coils. The ratio of both currents is the proportionality factor between the well-known constant of the standard coil and the unknown constant of the calibrated coil. In this paper, the direct method of determining the coil-constant is discussed. In order to gain the optimal accuracy with the direct method, the magnetic flux density of the generated field is determined by using a low uncertainty measuring method, such as magnetic resonance methods (NMR - Nuclear Magnetic Resonance magnetometer). The magnetic flux density generated in the calibrated coil was measured by means of a proton magnetometer with accuracy of some By measuring the energizing current the coil-constant can be calculated with a high accuracy. The frequency dependence of the coil-constant was determined by using an induction coil placed in the center of the calibrated coil and by observing the induced voltage versus the frequency of the alternated current energizing the calibrated coil. The calibration procedures were developed in cooperation with the Laboratory for Weak Magnetic Fields of the Physikalisch-Technische Bundesanstalt (PTB) from Braunschweig, Germany, where also our NMR magnetometer was developed and built. 2 DC coil-constant measurements Using a fluxgate magnetometer (MAG01H by Bartington Instruments) as a zero indicator, the earth magnetic field and other possible extraneous DC fields were compensated. Compensation was achieved by DC currents I x, I y and I z energizing cubic compensating coil (Figure 1). Three pairs of square coils ensure the compensation of the flux density in the center to less than 1 µt in a time period of an hour. The compensation currents energizing the compensation coil were noted and checked throughout the measurements. Afterwards the field in the center was verified. The extraneous fields having been compensated, a field of 2 mt was generated in the calibrated coil. This was due to the fact that we were limited to 1 Amp current as a result of using a 1 Amp measuring range of a digital multimeter (HP 3458A by Hewlett Packard). A field of 2 mt is on the border of the measuring range of the NMR magnetometer [1]. The NMR magnetometer is a marginal oscillator type magnetometer operating with water samples dopped with copper sulfate paramagnetic ions to gain an absorption linewidth of 2 µt. The volume of the sample used was 2,7 cm 3. The uncertainty of detecting the center of the absorption line was lower than 0,1 µt [4]. The NMR probe was fixed into a specially designed holder, which ensured the central position in the coil. The measuring time of the NMR magnetometer was set to 2,3 seconds. The signal to noise ratio of the low-frequency NMR signal was typically 2 to 3, whereas after phase detection in the Phase Sensitive Detector (PSD) with a 1 Hz filter was typically 20 to 30. To ensure an optimal compensation of extraneous fields in the y-axis direction, a custom designed current reverse switch has been implemented (Figure 1). Each measurement was then composed of two parts, measured in different current directions, to enable elimination of the extraneous fields in the y direction. The coil-constant was calculated using (1). 3 AC calibration Procedure The sine input signal energizing the calibrated coil was generated by the frequency generator and high speed power amplifier (type NF 4020, 300 V pp,2a rms,50 khz) to ensure a 1 Amp current amplitude of the energizing current. The signal wire was connected with its

3 296 Geršak, Humar, Fefer 3x power supply HP6205B A A A NMR magnetometer B NMR z y NMR probe calibrated coil current reverse switch I ampermeter HP 3458A S W E N x cubiccompensating coil current source HP6554A Figure 1. Measuring set-up for DC coil-constant determination. It is composed of a cubic compensation coil system for extraneous magnetic fields compensation, calibrated coil, NMR magnetometer for measuring the magnetic flux density and ampermeter for current measurements U i DVM HP 3456A induction coil calibrated coil i ampermeter HP 3458A S W E N +15 V -15 V LO HI power amplifier NF 4020 DC power supply HP 6205B f frequency generator HP33120A Figure 2. Measuring set-up for determining the frequency dependence of the coil. By changing the frequency of the AC energizing the calibrated coil, the induced voltage in the induction coil is observed shield by an operational amplifier (LF411CP) to prevent the parasitic current from leaking through the parasitic wire-shield capacitance (Figure 2) and consequently decreasing the amplitude of the measured energizing current and with it increasing the uncertainty of the current measurement. The frequency dependence of the coil AC characteristics was measured by using an induction coil. In such a multi-layer cylindrical coil, when put in the AC magnetic field, a voltage is induced. By observing this induced voltage one can determine changes in the coil properties due to the frequency variations. In the induction coil (NA = 0.07 windings m 2 and resonance frequency f 0 =450 khz) a voltage was induced. The amplitude of the induced voltage was measured by a digital voltmeter HP3456A. By using a specially designed holder the in-

4 Calibration of a Reference Field Coil by Means of the NMR Magnetometer and Induction Coils 297 duction coil was fixed in the central and axial position inside the calibrated coil. Thus a stationary position of the induction coil was ensured throughout the measurement. The frequency of the energizing AC currents was altered from 100 Hz to 30 khz. Induced voltage u i and amplitude (rms) of the energizing current i were measured at frequencies f. Using a parameter K AC from (3) the frequency dependence of the calibrated coil was determined: K AC = u i fi, (3) where u i is the induced voltage and i and f are the amplitude and frequency of the energizing current. Parameter K AC was defined with frequency in the denominator to compensate the linear frequency dependence of the induced voltage. Frequency dependence of the calibrated coil coil-constant was determined by observing K AC versus frequency. A polynomial function of the fourth order was fitted to the measured data for an easier representation of the coil-constants frequency dependence. 4 Discussion and Conclusions A calibrating procedure for calibration of field coils, which can be used as working, transfer or primary laboratory standards for magnetic flux density, is presented. In the AC calibration part, an influence of the calibrated coil own resonance at approximately 90 Hz was detected. Above 300 Hz its influence is not significant. Thus the coil- constant K(f) was observed from 400 Hz to 30 khz. The frequency dependence of K(f) below 400 Hz was set to zero, according to the theory that DC coilconstant is not frequency dependent. It was assumed that using a ferromagnetic coaxial cable for the induction coil output signal causes additional noise and error. For that reason a non-ferromagnetic coaxial cable was used. It was established that the presence of a metal object of any kind near the observed coil can have an influence on the measurement (deviations of magnetic flux lines, eddy currents, etc.). Thus the calibrated coil was placed on a wooden desk 1.5 m away from all ferromagnetic materials or other metals (aluminum plates). Usage of a 220 µf capacitor in series with the calibrated coil allowed us to apply a current of 1 A rms from 100 Hz to 1 khz since the ampermeter was calibrated in a 1 Amp range. Above 1 khz the measurements were performed with a decreasing current. Another important improvement in the measuring setup is equalizing the signal wire and shield potentials. To ensure an equal voltage potential of the grounds of all instruments, the common output of the amplifier was connected to the common terminal of the digital ampermeter HP3458A and to the ground of the DC power supply HP6205B in the same point (Figure 2). The voltage between the signal wire and its shield, when the operational amplifier was not applied, was approximately 2.5 V at 1 A, and only 2 mv when applied. Therefore the usage of the operational amplifier had to be determined, especially to prevent measuring by the parasitic currents decreased coil energizing current. The determination of measurement uncertainty, a very common metrological problem, was not an uneasy task. The error due to the influence of the DC extraneous fields on the measured field was evaluated. The extraneous field vector was divided into three Cartesian components (according to the coordinate system in Figure 1). The eastwest component of the earth magnetic field is far too small to influence the measurement, the influence of the northsouth direction is anulled by changing the current direction. The contribution of fields in z-axis (vertical component) thus represented the main contribution to uncertainty due to the extraneous fields. It was calculated that if z-axis fields were compensated to less than 1 µt, the influence of extraneous fields to the measured field of 2 mt would be 1,2 10 7, which is not significant for the total measurement uncertainty. When calculating the total uncertainty of the DC coilconstant, the following uncertainties should be considered in addition to the uncertainty due to the influence of the extraneous field. Apart from the uncertainty due to the current measurement by the digital multimeter HP3458A the NMR magnetometer measurement uncertainty adds an important contribution to the total uncertainty. The uncertainty of the NMR magnetometer is composed of several partial uncertainties; uncertainty due to the zero crossing detection, uncertainty resulting from the chemical shift caused by the added paramagnetic ions into the sample, sample susceptibility uncertainty due to the cylindrical shape of the sample rather than spherical sample, uncertainty of the magnetometers time-base calibration, uncertainty of the gyromagnetic ratio value and uncertainty of the magnetometers digital counter [8]-[10]. In our case, the total NMR magnetometer uncertainty was calculated to be u NMR = The total uncertainty of the AC coil-constant is on the other hand composed of four uncertainties; uncertainty of the AC current measurement with digital multimeter HP3458A, measuring uncertainty of the DVM HP3456A, which measures the induced voltage, uncertainty due to the scattering of the measurements performed for the checking of the repeatability of the measurements, and goodness of fit for the fitted function of frequency dependence of the coil-constant. The reported expanded uncertainty of the measurement is considered as the standard uncertainty of the measurement multiplied by the coverage factor k=2, which for a normal distribution corresponds to a coverage probability of approximately 95% [2]. As a conclusion, the reported extended result for the calibrated coil can be stated in two parts; a DC reported

5 298 Geršak, Humar, Fefer K(f) / K(0 Hz) - 1 0,019 0,017 K(f) = ( f f f f ) mt/a 0,015 0,013 0,011 0,009 0,007 0,005 0,003 0,001-0, f /Hz Figure 3. Fitted function of the frequency dependence of the relative change in the coil-constant K(f) from the DC value K(0Hz) Figure 4. Determination of the DC coil constant for the various European laboratories against the period when the measurements were carried out. Our result is indicated as SMIS (Figure by K. Weyand in [11]) result and AC reported result. The DC reported extended result is shown in (4): K = mT/A ± mT/A = (1 ± 1, )mt/a. (4) Based on the HP3458A multimeter calibration certificate [3], the coil-constant frequency dependence is defined. In the frequency range from DC up to 5 khz, the coil-constant can be calculated according to (5) with uncertainty of 0.16% and from 5 khz to 10 khz with 0.32%:

6 K(f) = =2.0236( f f f f )mt/a, (5) where f is in Hz. The frequency dependence of the coilconstant as a result of the measurements is shown in Figure 3. As a conclusion and a proof that the developing of our measurement method is proceeding in the right way, we can cite the Euromet project No. 446 Intercomparison of Low Frequency Magnetic Flux Density by Means of Transfer Standards official results. A comparison of our result to the results of eight European laboratories, which were involved in the project and employed different measuring methods, showed only a deviation from the reported mean value of the transfer standard (Figure 4). Acknowledgment The authors wish to thank Dr. Kurt Weyand of the Physikalisch-Techische Bundesanstalt (PTB), Braunschweig, Germany, for the valuable information on the proton magnetometer, his help in determining its measurement uncertainty and valuable comments on magnetic measurement methods. 5 References [1] K. Weyand, An NMR Marginal Oscillator for Measuring Magnetic Fields Below 50 mt, IEEE Trans. Instrum. Measur., vol. 38, pp , [2] European Cooperation for Accreditation of Laboratories, Expression of the Uncertainty of Measurement in Calibration, EAL-R2, April, [3] Slovenian Institute of Quality and Metrology, Calibration certificate for HP3458A, Nr. 99/00114, Ljubljana, Slovenia, [4] K. Weyand, Magnetometer Calibration Setup Controlled by Nuclear Magnetic Resonance, IEEE Trans. Instrum. Measur., vol. 48, pp , [5] H. Zijstra, Experimental Methods in Magnetism, Part 2, Amsterdam, North-Holland Publishing Company, [6] A. Loesche, Kerninduktion, Berlin, VEB Deutscher Verlag der Wissenschaften, [7] K. Weyand, Homogene Magnetfelder in einlagigen Solenoiden durch ungleichmaessigen Strombelag, Archiv fuer Elektrotechnik, vol. 69, pp , [8] J. H. Burgess, R. M. Brown, Modulation Effects in Nuclear Magnetic Resonance, Rev. Sci. Instr., vol. 23, p. 334, [9] W. C. Dickinson, The Time Average Magnetic Field at the Nucleus in Nuclear Magnetic Resonance Experiments, Phys. Rev., vol. 81, p. 717, [10] Z. Frait, D. Fraitova, Measurement of Magnetic Field Intensity by Means of Nuclear Magnetic Resonance - Accuracy of measurement, Czech. J. Phys., vol. B27, p. 1292, [11] K. Weyand, Intercomparison of magnetic flux density by means of field coil transfer standard, J. Hunter, L. Johnson, Conference on Precision Electromagnetic Measurements, Digest, Sydney, p. 246, Gregor Geršak was born in 1973 in Jesenice, Slovenia. He received his B.Sc. and M.Sc. degrees in Electrical Engineering from the Faculty of Electrical Engineering of the University of Ljubljana in 1996 and 1999, respectively. He is currently working towards his Ph.D. thesis at the Laboratory for Magnetic Measurements at the same faculty. His research interest includes measurements of magnetic field by means of nuclear magnetic resonance and precision magnetic measurements in the field of metrology. Janez Humar was born in 1971 in Jesenice, Slovenia. He received his B.Sc. and M.Sc. degrees in Electrical Engineering from the Faculty of Electrical Engineering of the University of Ljubljana in 1997 and 2000, respectively. His research interest includes precision magnetic measurements and digital signal processing of signals in magnetic measurements using nuclear magnetic resonance. Dušan Fefer was born in 1949 in St. Vrhnika, Slovenia. He received his B.Sc., M.Sc. and Ph.D. degrees in Electrical Engineering from the Faculty of Electrical Engineering of the University of Ljubljana in 1975, 1983 and 1986, respectively. He began his professional career in industry developing HF measuring systems for TV purposes. In 1976 he joined the same faculty, where he is currently a Professor. His professional interest includes electronic and electrical measurements, sensors, acoustics, magnetics and bioelectromagnetics.