Physica B 486 (2016) 34–39

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Physica B

http://d0921-45

n CorrE-m

alenka.m

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Electromagnetic characterization of current transformer with toroidalcore under sinusoidal conditions

Branko Koprivica n, Alenka MilovanovicFaculty of Technical Sciences Cacak, University of Kragujevac, Svetog Save 65, 32000 Cacak, Serbia

a r t i c l e i n f o

Article history:Received 18 May 2015Received in revised form5 October 2015Accepted 10 October 2015Available online 21 October 2015

Keywords:Measuring current transformerMathematical modelMagnetic hysteresisIterative procedure

x.doi.org/10.1016/j.physb.2015.10.01726/& 2015 Elsevier B.V. All rights reserved.

esponding author. Fax: þ381 32342101.ail addresses: branko.koprivica@ftn.kg.ac.rs (Bilovanovic@ftn.kg.ac.rs (A. Milovanovic).

a b s t r a c t

The aim of this paper is to present a new procedure for the electromagnetic analysis of a measuringcurrent transformer under sinusoidal conditions in its electrical and magnetic circuit. The influence ofthe magnetic hysteresis has been taken into account using the measured inverse magnetization curveand phase lag between the time waveforms of the magnetic field and the magnetic induction. Using theproposed analysis, ratio and phase errors of the current transformer have been calculated. The results ofthe calculation have been compared with experimental results and a good agreement has been found.

& 2015 Elsevier B.V. All rights reserved.

1. Introduction

Current transformers with a toroidal core are widely used inthe measurement of electric current amounting up to severalthousands of amperes. These transformers are usually made bywinding a strip of electrical steel. They introduce a measurementerror (in amplitude and phase) in the electric circuit with mea-surement instruments. The limits of these errors are specified bythe IEC standard [1] and such transformers need to fulfil theserequirements. In contrast to the protective current transformerwhich needs to represent an inrush current correctly during faultsin the electric network, current measuring transformers need toperform very accurately under normal conditions [2]. Recent re-search related to the current transformer is more devoted to itsprotective purposes. There are many papers dealing with the cal-culation of the current transformer inrush current, adequatetransformer modelling and compensation techniques [3–9].Proper modelling of the measuring current transformer seems tobe almost of no interest, while some specific cases of its perfor-mance have recently been analysed, such as, the influence of themagnetic core material, the influence of the primary currentshape, the influence of the permanent magnet and the influence ofthe current overload on the transformer errors [10–12]. Theseresearches present experimental results of interest to the electricalengineers, while physical explanations and interpretations were

. Koprivica),

omitted. Therefore, the subject of this paper is a comprehensiveanalysis of the measuring current transformer through the math-ematical model, with a focus on the magnetic hysteresis, andcalculation of its ratio and phase errors.

In this paper, the current transformer has been representedusing its standard mathematical model, taking into account themagnetic hysteresis [13]. In the normal working regime, themeasuring current transformer operates under low values of themagnetic inductions in the core, most often not higher than 0.6 Tat a frequency of 50 Hz, at rated load in the secondary circuit. Inthat case, all the quantities of interest (primary and secondarycurrent, secondary voltage, magnetic field and magnetic induc-tion) are sinusoidal in time. Under such conditions, the minorhysteresis loop, obtained from the magnetic field and inductionwaveforms, is elliptical. Such loop can be simply represented usingthe maximums of the magnetic field and the magnetic inductionand the phase lag between these two waveforms [14]. Such re-presentation of the magnetic hysteresis allows development of themathematical model of the current transformer to a series ofequations which can be easily solved using an iterative procedure,proposed in this paper. As a solution, the time waveform of thesecondary current and the ratio and phase errors can be obtainedafter a few iterations.

A PC based measurement setup has been used in the mea-surement of the magnetic hysteresis at low values of the magneticinduction to obtain the actual magnetic characteristics of the tor-oidal core used in the analysis presented in this paper. A largenumber of the minor hysteresis loops have been measured and theresults obtained have been used in the calculation of the phaselags between the magnetic field and induction and their

B. Koprivica, A. Milovanovic / Physica B 486 (2016) 34–39 35

maximums in each loop. These results have been used in thecalculation of the secondary current and the ratio and shift error ofthe current transformer under sinusoidal conditions using pro-posed iterative procedure. Also, another measurement setup hasbeen used in the measurement of the primary and secondarycurrent of the measuring current transformer at low values of themagnetic induction. From this measurement the actual ratio andshift errors of the transformer have been calculated.

The calculated secondary current, ratio and shift errors havebeen compared to those obtained by measurement and a verygood agreement has been obtained.

2. Transformer modelling, hysteresis representation anditerative procedure

The measuring current transformer with a toroidal core can bepresented with an equivalent circuit as shown in Fig. 1. The cor-responding equations for this circuit are [13]:

i N i N H l 11 1 2 2− = ( )

R R i L Lit

N SBt

dd

dd

0 22 2 22

2( + ) + ( + ) − = ( )

B f H 3= ( ) ( )

where:

1. R L,1 1 – are the resistance and inductance of the primarywinding,

2. R L,2 2 – are the resistance and inductance of the secondarywinding,

3. R L, – are the resistance and inductance of the load in thesecondary circuit,

4. i i,1 2 – are the currents in the primary and secondary circuits,5. u2 – is the voltage in the secondary circuit,6. N N,1 2 – are the number of turns in the primary and sec-

ondary circuits,7. l S, – are the effective length and cross section of the magnetic

core and8. B f H= ( ) – is the magnetic hysteresis of the core.

The main difficulty in solving Eqs. (1)–(3) is in the im-plementation of the magnetic hysteresis. Consequently, the properhysteresis model is required in these calculations.

Under normal working conditions in the circuit shown in Fig. 1the magnetic hysteresis loop in the core is elliptical in shape,Fig. 2a, and the corresponding magnetic field and induction aresinusoidal waveforms, Fig. 2b. This simple case of hysteretic be-haviour is characterized by the phase lag between these two wa-veforms in which the output is lagging the input [14].

From the waveforms of the magnetic field and induction acorresponding maximums of the magnetic field and induction canbe obtained and represented in inverse notation as B H,max max( )

1R

1iR

2R1L

L

2L

1N 2N

l 2iS

2u

Fig. 1. Model of measuring current transformer.

pairs (inverse to the usual B–H curve notation). Also, a corre-sponding phase lags φ and pairs B ,max φ( ) can be obtained fromthese waveforms. With a sufficient number of pairs B H,max max( )and B ,max φ( ), any value H Bmax max( ) and Bmaxφ( ) can be obtained bylinear interpolation. The family of minor loops, consequently timewaveforms of the magnetic field and induction, can be obtainedfrom measurement [15,16] (as in this paper) or by implementationof the hysteresis model that can reproduce minor loops [17–25].

With such simple representation of the magnetic hysteresisadequately simple solution of Eqs. (1)–(3) can be obtained using aproposed iterative procedure. At the beginning, assume that theprimary current is i I t2 sin1 1 ω= and that the magnetic field isequal to zero (H 01 =( ) ). From (1) can be obtained:

iNN

i42

1 1

21=

( )( )

or

INN

I52

1 1

21=

( )( )

where (1) indicates the first iteration.The induced voltage in the secondary winding can be calcu-

lated as:

u R R i L Lit

dd 62

12 2

12

21

= ( + ) + ( + ) ( )( ) ( )

( )

or

u Z I t2 sin 7s21

2 21

21ω φ φ= [ + + ] ( )( ) ( ) ( )

where Z R R L L2 22

22ω ω= ( + ) + ( + ) , L L R Rarctg /2 2 2φ ω= [ ( + ) ( + )],

f2ω π= , f is the frequency (in this case 50 Hz), I21( ) is the effective

value of the secondary current and s1φ( ) is the phase of the sec-

ondary current (in this case 0s1φ =( ) ).

On the other hand, this voltage can be calculated as:

u Nd

dtN S

dBdt 82

12

1

2

1Φ= − = − ( )( )

( ) ( )

After integration of Eq. (8), the magnetic induction in the firstiteration is:

⎡⎣⎢

⎤⎦⎥

BN S

u dt

N SZ I t

1

12 sin

2 9

t

s

1

2 021

22 2

12

1

∫

ωω π φ φ

= −

= − + +( )

( ) ( )

( ) ( )

Its maximum value can be calculated as:

BI Z

f S N2 10max1 2

12

2π=

( )( )

( )

This maximum value of the magnetic induction corresponds tothe maximum value of the magnetic field in the minor hysteresisloop, Fig. 2a. At low magnetic inductions the magnetic field is alsosinusoidal in time and the magnetic field is lagging the magneticinduction [14], Fig. 2b.

Consequently, the magnetic field in the second iteration can becalculated as:

H H B t Bsin2 11s

2max max

12

1max1ω π φ φ φ= ( ) [ − + + + ( )] ( )

( ) ( ) ( ) ( )

where H Bmax max( ) represents the inverse magnetization curve аndBmaxφ( ) is the phase lag between the magnetic field and induction.

Required values of H Bmax max1( )( ) and Bmax

1φ( )( ) at the first iteration ofthe proposed procedure can be obtained by linear interpolationfrom a series of pairs obtained from the minor loops (as previously

B

H0 60 120 180 240 300 360

-15

-10

-5

0

5

10

15 Hmax Bmax

θ [ ]

H [A/m]B [T]

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

ϕ

Fig. 2. (a) Family of minor hysteresis loops (b) waveforms of the magnetic field and induction of one minor loop.

B. Koprivica, A. Milovanovic / Physica B 486 (2016) 34–3936

described in this section).After calculation of the magnetic field in the second iteration, it

can be substituted into Eq. (1), which will give the secondarycurrent in the second iteration:

iNN

iH l

N 1222 1

21

2

2= −

( )( )

( )

The proposed iteration procedure should be performed untilconvergence of the results is obtained.

After calculation of the secondary current, the ratio error of thecurrent transformer, gi, can be expressed as [2]:

gK I I

I% 100

13in 2 1

1[ ] =

−( )

where I1 and I2 are the effective values of the primary and sec-ondary currents in the circuit from Fig. 1 and Kn is the rated ratio ofthe transformer. The phase error, δi, can be defined as phase lagbetween these two currents and it has a negative value if thesecondary current leads the primary current.

3. Experimental setup

An experimental setup presented in Fig. 3 has been built andused in the characterization of the measuring current transformerwith toroidal core wound from an electrical steel strip.

This setup is based on a PC with LabVIEW software [26]. It alsocontains an AC current source, two shunt resistors (R, R1) and atoroidal core with single-turn primary winding (N1¼1, Fig. 1) andtwo secondary windings (N21 with 20 and N22 with 40 turns).Winding N21 corresponds to winding N2 from Fig. 1. Consequently,a rated current ratio of the current transformer is 20 A/1 A.

NI cDAQ-9172

21N

1u 21u

1R

PC

AMPLIFIER

u

ITR

22N

22u

Fig. 3. Measurement setup.

Winding N22 is additional winding for measurement of the mag-netic induction B in the core in order to confirm its sinusoidalshape.

An amplifier in Fig. 3 provides a sinusoidal current amountingto up to 20 A (RMS value), at a frequency of 50 Hz. This current hasbeen used to magnetize the toroidal core over the single-turnprimary winding. In series with the primary winding, a shunt re-sistor R1 has been connected and used in the measurement of theprimary current. A secondary winding N21 has been closed withanother shunt resistor R, used in the measurement of the sec-ondary current. The electric circuit of the secondary winding N22

has been left open and induced voltage u22 has been integratedprogrammatically and used in the measurement of the magneticinduction in the core. According to the measured primary andsecondary current a ratio error and a phase error of this currenttransformer have been calculated for different values of the ex-citation current. Also, a maximum value of the magnetic inductionhas been recorded during these measurements. A LabVIEW ap-plication has been created and used to measure all of the quan-tities of interest of this experiment. Its front panel, showing someof the results obtained, is presented in Fig. 4.

Another experiment has been performed to measure themagnetic hysteresis in a toroidal core of the tested measuringcurrent transformer [25,26]. The core from Fig. 3 has been excitedover winding N22 while the induced voltage has been measured atthe open ends of the secondary winding N21. The measured ex-citation current and induced voltage have been used in the cal-culation of the magnetic field and the magnetic induction in thecore. Measurements have been taken at low values of the mag-netic inductions, amounting from 0.025 T to 0.65 T, at a frequencyof 50 Hz. It is observed that during such measurements, both themagnetic induction and the magnetic field are sinusoidal in time.A phase lag exists between these two waves due to the magnetichysteresis of the core material. This phase lag has been calculatedand represented as a function of the maximum of the magneticinduction, Bmaxφ( ). Also, these results have been used in the con-struction of the inverse magnetization curve B Hmax max( ).

The parameters of the toroidal core and electric circuit fromFig. 3 are: N1¼1, N21¼20, N22¼40, l¼0.1382 m, S¼4066 �10�5 m2,R2¼0.095Ω, L2¼105 μH and R1¼R¼0.00375Ω.

4. Experimental and numerical results and discussion

A number of hysteresis loops have been measured and themaximums of the magnetic field and induction and phase lagsbetween corresponding waveforms have been calculated. The

Fig. 4. LabVIEW application.

-20 -15 -10 -5 0 5 10 15 20

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6B [T]

H [A/m]

Fig. 5. Family of minor hysteresis loops.

Table 1Magnetic field and phase lag variation with induction.

B Tmax [ ] H A/mmax [ ] degφ [ ] B Tmax [ ] H A/mmax [ ] degφ [ ]

0.025 1.24 21.16 0.350 13.68 37.590.050 2.43 22.11 0.375 14.18 38.360.075 3.54 24.07 0.400 14.85 39.560.100 4.90 25.42 0.425 15.64 40.500.125 6.01 27.68 0.450 16.30 40.810.150 7.45 29.47 0.475 16.76 42.460.175 8.06 29.97 0.500 17.16 42.610.200 8.93 31.90 0.525 17.80 42.980.225 9.70 33.39 0.550 18.22 43.700.250 10.70 34.08 0.575 18.81 44.250.275 11.43 34.77 0.600 19.75 44.420.300 12.23 36.28 0.625 20.22 44.890.325 12.82 37.05 0.650 20.68 45.37

i1 [A]

t [s]0 0 .02 0 .04 0 .06 0 .08

-6

-4

-2

2

4

6

-0 .27

-0 .18

-0 .09

0 .09

0 .18

0 .27i2 [A]

Fig. 6. Comparison of the simulated secondary current and input primary current.

B. Koprivica, A. Milovanovic / Physica B 486 (2016) 34–39 37

results obtained are presented in Fig. 5 and Table 1. These resultshave been used in the calculation of the secondary current of thetransformer with the proposed iterative procedure. The result ofsuch a calculation is presented in Fig. 6, which shows a compar-ison of the input primary current and the calculated secondarycurrent.

Another set of results relates to the measured primary andsecondary current of the transformer. A comparison of the mea-sured primary and secondary current is presented in Fig. 7. Incomparison to Fig. 6, good agreement between the results can beobserved.

Furthermore, the ratio and phase errors and the amplitudes ofthe magnetic induction have been calculated for different values ofthe primary current. These results are presented in Table 2. Thistable also shows a comparison of the measured and calculatedratio errors, phase errors and induction maximums.

Good agreement between the measured and calculated valuesof the ratio and phase errors of the tested transformer, as well as

i1 [A]

t [s]0 0 .02 0 .04 0 .06 0 .08

-6

-4

-2

2

4

6

-0 .27

-0 .18

-0 .09

0 .09

0 .18

0 .27i2 [A]

Fig. 7. Comparison of the measured primary and secondary current.

Table 2Comparison of measured and calculated results.

I1 [A] gi [%]Measured

gi [%]Calculated

δi [deg]Measured

δi [deg]Calculated

Bmax [T]Measured

Bmax [T]Calculated

4.98 �6.358 �7.837 �4.433 �6.028 0.143 0.1327.11 �7.705 �7.831 �3.511 �5.236 0.204 0.1898.53 �8.137 �7.888 �3.083 �4.736 0.245 0.226

10.62 �8.417 �7.887 �3.058 �4.353 0.305 0.28214.13 �8.627 �7.681 �1.933 �3.651 0.406 0.37620.07 �8.653 �7.385 �1.113 �2.787 0.501 0.536

B. Koprivica, A. Milovanovic / Physica B 486 (2016) 34–3938

the maximum magnetic induction, can be observed.The values of the errors are large, but in accordance with the

values already known in engineering practice. The tested trans-former has been made in a simple way, just by winding windingsonto the previously prepared core, while no attention has beengiven to the quality of the core material (its magnetic properties).The values of the errors are as expected and the calculated errorsare close to the measured. Also, the measured and calculatedmaximum values of the magnetic induction agree well.

In this case, none of the well-known techniques of the mea-surement accuracy improvement of the current transformer wereimplemented in advance [2]. The idea was to maintain the originaldata, as they appear in the beginning of the manufacturing pro-cess. It is shown that the proposed analysis of the current trans-former can give a good overview of its characteristics even beforeproduction. Therefore, one can manipulate the input parameters inthe calculation until obtaining satisfactory accuracy of the currenttransformer. This manipulation can include changes in the coregeometry (in the effective length and cross section) or correctionof the numbers of turns in the secondary coil without changingthe rated ratio (usually it should be reduced because the ratioerror is negative). Also, changes can be made to the load in thesecondary circuit of the transformer to keep the induction max-imum in the desirable range. Moreover, one can manipulate themagnetic characteristics of the core and investigate how differentmaterials influence the transformer behaviour of the givengeometry.

5. Conclusion

Electromagnetic analysis of a measuring current transformerwith toroidal core, under sinusoidal conditions, has been pre-sented in this paper. A new iterative procedure has been proposedfor the development of the mathematical model of this transfor-mer. The procedure takes into account the magnetic hysteresis ofthe core by representing minor hysteresis loops over the inverse

magnetization curve and phase lag between the magnetic fieldand induction (both are sinusoidal waveforms).

In this paper, actual magnetic characteristics of the testedmeasuring current transformer have been obtained using PC basedmeasurement setup. A number of minor hysteresis loops havebeen measured and the corresponding maximums of the magneticfield and induction and the phase lags between their waveformshave been determined. The results obtained, along with the pro-posed procedure, have been successfully applied to the calculationof the secondary current and the ratio and phase error of such atransformer.

Measurement of the actual secondary current of the measuringcurrent transformer has been performed using another PC basedmeasurement setup. The results of this measurement are timewaveforms of the primary and secondary current of the measuringcurrent transformer and the actual ratio and shift error of thetransformer during the measurement. Additionally, a waveform ofthe magnetic induction has been obtained during the measure-ment and its sinusoidal shape has been obtained. This confirmsthe sinusoidal working regime of the measuring currenttransformer.

The measured and calculated values of the ratio and phaseerrors of the tested transformer, as well as the maximum magneticinduction, have been compared and good agreement betweenthese results has been observed.

The results obtained can be useful to the designer of thetransformer as a good indicator of the transformer′s characteristicsbefore its manufacture. If the magnetic characteristics of the ma-terial are known in advance (given by the manufacturer or mea-sured) for a given geometry of the toroidal core, a designer cancalculate all quantities of interest before the production of thecurrent transformer. Furthermore, the analysis allows the designerto manipulate the input data of the transformer in order to achievebetter accuracy. Therefore, the proposed electromagnetic analysiscan be used in the manufacturing process in characterizing thiskind of transformer.

Acknowledgements

This work was supported by the Ministry of Education, Scienceand Technological Development of the Republic of Serbia, Grantno. TR33016.

References

[1] IEC 61869-2 – Instrument Transformers – Part 2: Additional Requirements forCurrent Transformers, IEC, Geneva, Switzerland, 2012.

[2] C. Christopoulos, A. Wright, Electrical Power System Protection, Kluwer Aca-demic Publishers, Dordrecht, The Netherlands, 1999.

[3] F.C.F. Guerra, W.S. Mota, Current transformer model, IEEE Trans. Power Deliv.22 (1) (2007) 187–194.

[4] A. Rezaei-Zare, R. Iravani, M. Sanaye-Pasand, H. Mohseni, S. Farhangi, An ac-curate current transformer model based on Preisach theory for the analysis ofelectromagnetic transients, IEEE Trans. Power Deliv. 23 (1) (2008) 233–242.

[5] E. Cardelli, E. Della Torre, V. Esposito, A. Faba, Theoretical considerations ofmagnetic hysteresis and transformer inrush current, IEEE Trans. Magn. 45 (11)(2009) 5247–5250.

[6] G.B. Kumbhar, S.M. Mahajan, Analysis of short circuit and inrush transients ina current transformer using a field-circuit coupled FE formulation, Electr.Power Energy Syst. 33 (8) (2011) 1361–1367.

[7] R. Matussek, C. Dzienis, J. Blumschein, H. Schulte, Current transformer modelwith hysteresis for improving the protection response in electrical transmis-sion systems, J. Phys.: Conf. Ser. 570 (2014) 062001.

[8] D.Y. Shia, J. Buseb, Q.H. Wub, C.X. Guo, Current transformer saturation com-pensation based on a partial nonlinear model, Electric Power Syst. Res. 97(2013) 34–40.

[9] Y.C. Kang, T.Y. Zheng, Y.H. Kim, B.E. Lee, S.H. So, P.A. Crossley, Development of acompensation algorithm for a measurement current transformer, IET Gener.Transm. Distrib. 5 (5) (2011) 531–539.

B. Koprivica, A. Milovanovic / Physica B 486 (2016) 34–39 39

[10] M. Soinski, W. Pluta, S. Zurek, A. Kozlowski, Metrological attributes of currenttransformers in electrical energy meters, International Workshop on 1&2 Di-mensional Measurement and Testing, Vienna, Austria, 04-06 September, 2012,pp. 33–34.

[11] T.C. Batista, B.A. Luciano, R.C.S. Freire, W.B. Castro, E.M. Araujo, Influence ofmagnetic permeability in phase error of current transformers with nano-crystalline alloy cores, J. Alloy. Compd. 615 (S1) (2014) S228–S230.

[12] S. Puzovic, B. Koprivica, A. Milovanovic, M. Djekic, Analysis of measurementerror in direct and transformer-operated measurement systems for electricenergy and maximum power measurement, Facta Univ. – Ser.: Electron. Energ.27 (3) (2014) 389–398.

[13] V.A. Naumov, V.M. Shevtsov, Mathematical models of current transformers inalgorithms of differential protection, Power Technol. Eng. 37 (2) (2003)123–128.

[14] G. Bertotti, Hysteresis in Magnetism, Academic Press, New York, USA, 1998.[15] P. Kis, M. Kuczmann, J. Fuzi, A. Ivanyi, Hysteresis measurement in LabVIEW,

Phys. B: Condens. Matter 343 (1–4) (2004) 357–363.[16] B.M. Koprivica, A.M. Milovanovic, M.D. Djekic, Effects of wound toroidal core

dimensional and geometrical parameters on measured magnetic properties ofelectrical steel, Serbian J. Electr. Eng. 10 (3) (2013) 459–471.

[17] M. Dimian, P. Andrei, Noise-Driven Phenomena in Hysteretic Systems,Springer, New York, USA, 2014.

[18] I.D. Mayergoyz, Mathematical Models of Hysteresis and Their Applications,Academic Press-Elsevier, Oxford, UK, 2003.

[19] C. Ragusa, An analytical method for the identification of the Preisach dis-tribution function, J. Magn. Magn. Mater. 254–255 (2003) 259–261.

[20] M. Kuczmann, G. Kovacs, Improvement and application of the viscous-typefrequency-dependent Preisach model, IEEE Trans. Magn. 50 (2) (2014)7009404.

[21] D.C. Jiles, D. Atherton, Theory of ferromagnetic hysteresis, J. Magn. Magn.Mater. 61 (1–2) (1986) 48–60.

[22] M. Hamimid, S.M. Mimoune, M. Feliachi, Minor hysteresis loops model basedon exponential parameters scaling of the modified Jiles–Atherton model, Phys.B: Condens. Matter 407 (13) (2012) 2438–2441.

[23] M. Hamimid, S.M. Mimoune, M. Feliachi, Evaluation of minor hysteresis loopsusing Langevin transforms in modified inverse Jiles–Atherton model, Phys. B:Condens. Matter 429 (2013) 115–118.

[24] T. Matsuo, Y. Terada, M. Shimasaki, Representation of minor hysteresis loops ofa silicon steel sheet using stop and play models, Phys. B: Condens. Matter 372(1-2) (2006) 25–29.

[25] A.M. Milovanovic, B.M. Koprivica, Mathematical model of major hysteresisloop and transient magnetizations, Electromagnetics 35 (3) (2015) 155–166.

[26] ⟨http://www.ni.com/⟩.