A system for controllable magnetic measurements …stupak/4_IEEE2016.pdfSUBMITTED FOR PUBLICATION...

SUBMITTED FOR PUBLICATION TO: IEEE TRANS. ON INSTRUM. MEAS., SEPTEMBER 8, 2015 1

I2MTC 2015 paper identifier 1570029627

A system for controllable magneticmeasurements of hysteresis and Barkhausen

noiseAlexandr Stupakov, Oleksiy Perevertov and Vitalii Zablotskii

Abstract

A specially developed setup for precise measurement of the magnetic hysteresis and

Barkhausen noise is presented in this work. A novelty of the setup consists in a unique

combination of two main features: an accurate local determination of the magnetic field and

an improved feedback control of the magnetization process. Firstly, the magnetic field is

measured by two Hall sensors at different distances above the sample. The sample field is

determined by a linear extrapolation of these measured profiles of the tangential fields to

the sample surface. Secondly, a digital feedback loop for precise control of the ac magneti-

zation process is proposed. The feedback algorithm combines two methods of magnetizing

signal adjustment: linear corrections of the magnetizing voltage amplitude and phase. The

presented system is able to adjust the waveform of the magnetic induction or field to the pre-

scribed sinusoidal or triangular shape. This provides stable and physically accurate results,

which are independent of a specific experimental configuration.

Index Terms

Magnetic hysteresis, Barkhausen effect, Magnetic field measurement, Feedback circuits,

Magnetization processes, Silicon steel.

The authors are with Institute of Physics, Czech Academy of Sciences, Na Slovance 2, 18221 Prague, CzechRepublic. Phone: + 420–26605–2114, e-mail: [email protected], URL: www.fzu.cz/˜stupak

STUPAKOV et al.: A SYSTEM FOR CONTROLLABLE MAGNETIC MEASUREMENTS... 2

I. Introduction1

Despite a long history of magnetic investigations, there is still no widely-accepted “uni-2

versal” technique for precise measurement of the industrial ferromagnetic steels. The first3

principal problem is a precise determination of the sample magnetic field. The IEEE stan-4

dard measurements are performed in cumbersome quasi-closed configurations in order to5

approximate the conditions where the sample magnetic field is proportional to the magne-6

tizing current. Although the single sheet tester standard mentions a possibility of the direct7

field measurement with a flat air H-coil, it is not recommended because of technical complex-8

ity and higher measurement error [1], [2]. Recently we proposed a suitable technical solution9

of this classical problem: using modern field sensors and a specific magnetic shielding we can10

accurately measure the surface field of the magnetically open flat samples [3], [4]. This work11

presents our first successful attempt of the accurate feedback adjustment of this surface field12

waveform [5].13

The second fundamental issue is a control of the magnetization conditions, i.e. the wave-14

form of the magnetic induction (material magnetic response) or the magnetic field (driving15

force of the magnetization process). However, controlling the highly inductive magnetic cir-16

cuit is by no mean a trivial task. Even slight variations of the magnetic circuit parameters,17

e.g. the dimensions of the magnet and the sample or the air gap between them, can sig-18

nificantly alter the real magnetization rate and thereby the ac measurement results if the19

magnetizing signal is not adapted to compensate these variations.20

Previous researches mostly followed the trend given by the IEEE standards: adjustment21

of the magnetic induction B(t) or its time derivative to the sinusoidal shape, which corre-22

sponds to the operation conditions of transformers and motors [1], [2]. Different feedback23

methods were proposed over the last 30 years with gradual transition from the analogue loops24


to the digital or combined analogue-digital feedback circuits in the last two decades [6], [7],25

[8], [9]. Recent attempts to improve the B(t) adjustment accuracy and to adapt the stan-26

dard measurement systems to modern industrial needs led to more mathematically complex27

feedback algorithms [10], [11], [12]. Our concept of the feedback procedure development is28

trying to avoid too complex or physically baseless adjustment algorithms, e.g. with the direct29

and backward Fourier transforms. The feedback method should be as simple as possible for30

better stability and faster convergence but, on the other side, it should be complex enough31

to provide a sufficient accuracy. In the simplest case, only two signals can be considered:32

the adjusted magnetizing voltage/current and the controlled magnetic waveform (magnetic33

induction or field) [7], [11]. It is also obvious that for the inductive circuits, both amplitude34

and phase of the magnetizing signal should be adjusted [12].35

This work proposes using a linear combination of two feedback approaches of the linear36

amplitude correction and the direct phase shift [6], [7], [9], [12]. Despite its relative simplicity,37

this solution demonstrates an improved performance. Stabilization of the ac magnetization38

process together with the direct field measurement approach make the measurements of the39

magnetic hysteresis and Barkhausen noise (BN) repeatable and independent of a specific40

design of the magnetic circuit [4], [5]. This work is an extended version of the conference41

paper [13]. It describes the experimental system, the developed measurement software and42

important technical issues in more detail. The extended work presents additional results43

of the induction waveform adjustment in a wide range of the magnetizing frequencies for a44

non-oriented steel together with an experimental proof of the improved result repeatability.45

Advantages of the developed system and application limits of the proposed feedback loop46

are analysed in the added discussion section.47


II. Measurement system48

A. Hysteresis loop with direct field measurement49

The typical block schemes of the magnetizing-sensing unit and the measurement setup50

are shown in Fig. 1 [3], [4], [14]. Flat samples are usually magnetized by an U-shape trans-51

former yoke carrying the magnetizing winding. The magnetic induction B is measured by a52

sample-wrapping coil. Profiles of the tangential surface field Hτ at 1.5 and 4.5 mm above the53

sample are measured between the yoke poles by the Hall sensors, which propose a good al-54

ternative to the classical air H-coil and Rogowski-Chattock potentiometer. The modern Hall55

chips are miniature, easy-to-operate and more sensitive at low magnetizing frequencies [15],56

[16], [17], [18]. However, their sensitivity is still insufficient for the accurate measurements of57

the soft electrical steels with Hmax ∼ 100 A/m. The measurements of the transformer steels58

with ∼ 1 cm grains could be also influenced by a small sensitive area ∼ 0.1 mm of the Hall59

sensors [4], [19]. At present, the Hall chips A1301 from Allegro MicroSystems are used; they60

integrate a high-gain amplifier with special compensation circuits providing a 2.5 mV/G sen-61

sitivity. Compared with the A1321 chips with twice the sensitivity used previously [3], the62

A1301 sensors have a 10 times lower level of the output thermal noise, which is additionally63

suppressed by low-pass filters at 20 kHz.64

The measurements are performed using a modern 16-bit generation-acquisition board65

NI PCIe-6351. The input voltage range is strictly set to a default ±5 V to avoid distortions66

of the acquired signals by the integrated amplifiers. The magnetizing output voltage Vmag67

is generated in the ±10 V range with a sampling rate of 1 MSa/s and power amplified in a68

voltage control mode by a APEX MP39 module mounted on an EK59 evaluation kit. No69

noticeable signal distortion was found during the power amplification [12]. The measurement70

software is realized in a NI LabVIEW graphical environment using lower level subroutines71


Fig. 1. Block schemes of the magnetizing-sensing unit and the measurement setup.

to make the program faster and more stable [20]. The magnetizing output voltage Vmag is72

synchronized with the acquired signals by an internal digital trigger.73

For the magnetic hysteresis measurements, four signals are sampled with a 200 kSa/s74

rate: the magnetizing current Imag from a shunt resistor, the two Hall signals Hsur and the75

voltage ∼ dB/dt induced in the sample-wrapping coil. Before the sampling, the acquired76

signals are amplified by SRS SIM911 modules; the corresponding amplification coefficients77

are adjusted by a GPIB controller. Since the signals are recorded using an acquisition78

board multiplexor, a special subroutine is composed to compensate the introduced constant79

phase shift between the different channels. The analyzed magnetizing cycle is taken after80

the stabilization of the recorded inductive signals: for the magnetizing frequency fmag ≃81


1 − 10 Hz, the second/third cycle is usually taken; for fmag ≃ 50 Hz, the fifth/six cycle82

should be collected [3]. The final data are reduced to ∼ 1000 points per a magnetization83

cycle using an adjacent point averaging. A cycle averaging is used for further data smoothing.84

The noisier Hall signals usually need an additional smoothing, so a cubic spline fit is used85

for this purpose. The smoothing correctness is checked visually.86

The magnetic field is determined by three different methods: the common current field87

Hi ∼ Imag, which is proportional to the magnetizing current, the surface field Hsur measured88

by the closest Hall sensor and the field Hext obtained by a linear extrapolation of the two89

measured field profiles to the sample face. Validity of the field extrapolation method is90

confirmed experimentally. The finite element calculations and the direct field measurements91

show that the vertical profile of the tangential magnetic field between the yoke poles is of92

a roughly parabolic shape with a distinct linear region at the sample surface. The field93

extrapolation technique is proved to stabilize the magnetic measurements with respect to94

variations of an air gap between the magnetizing yoke and the tested sample; so the precise95

measurements can be performed in a magnetically open configuration [4], [5], [21], [22].96

Accuracy of the extrapolation procedure is primarily determined by the vertical gradient97

of the tangential surface field, which can be really high between the poles of the small98

yokes [16], [23]. Probably, this is the main reason of an insufficient reproducibility of the99

results obtained by the single sheet tester modifications with the air H-coils for the field100

determination [2], [19]. Therefore, a special shielding technique is used to suppress the field101

gradient: two magnetically soft sheets are placed around the Hall sensors to make the flux102

leakage between the yoke poles flow through the sample bulk [24]. The measurements of103

the thin samples can be simplified placing the Hall sensors and the BN coil on the opposite104

yoke-free side, where the vertical field profile is gently sloping and linear at higher distance105


from the sample (see Fig. 1). Under homogeneous magnetization, the extrapolated fields106

measured on both sample sides are identical, which additionally confirms the validity of the107

Hext method [4], [22].108

Before the extrapolation procedure, the chosen period of the acquired Hall signals is sep-109

arated from the measured data using the signal maxima and integrated in order to evaluate110

and correct the zero offset. Numerical trapezoidal integration of the voltage induced in the111

sample-wrapping coil and its similar processing (one-period separation, zero threshold cor-112

rection and symmetrization) gives the magnetic induction B [20]. Then all field waveforms113

are additionally symmetrized over the coercivity field values Hc of the ascending and the114

descending hysteresis branches. These methods of the curve symmetrization and the zero115

offset correction simplify and automatize the measurement procedure, but such a system can116

measure only the standard symmetrical hysteresis loops. Before each test, the sample de-117

magnetization can be performed. After the measurement, the classical hysteresis parameters118

and the hysteresis loops in the different field representations are calculated and recorded to119

the data files. The flowchart of the described measurement procedure and data processing120

is shown in Fig. 2(a). The total systematic error of the measurements evaluated from the121

device calibration certificates is about 0.5-1% depending on the setup configuration. It can122

be usually neglected because the random measurement error is on the acceptable level of a123

few percents [2], [4], [5], [17].124

B. Feedback circuit125

The feedback loop controls the three magnetic parameters simultaneously (see Fig. 2(b))126

[14]. The first parameter is the magnetic waveform amplitude Bmax or Hmax, which is ad-127

justed by changing the amplitude of the magnetizing voltage Vmax. The correction coeffi-128

cients kBmax = δVmax/δBmax and kHmax = δVmax/δHmax describing the rate of change of129


(a) (b)

Measurement

4 channels acquisition: Hi, 2´ H

sur, B

B: integration, zero offset corr., symmetrization

Fields symmetrization on Hc

values

1 channel generation of the magnetizing voltage

Optional demagnetization

Amplifier coefficient adjustment

Compensation of the multiplexor phase shift

Hsur

: smoothing, 1-cycle cut, zero offset correct.

Calculation of the extrapolated field Hext

Calculation of hysteresis parameters and loops

Data presentation and saving

trigger

GPIB

Fig. 2. Flowcharts of the measurement (a) and the feedback (b) algorithms.

the magnetizing voltage amplitude with respect to the amplitude of the controlled magnetic130

waveform is calculated for further amplitude corrections. The second parameter is the field131

amplitude asymmetry, which is defined as a half of difference between the field amplitudes132

at positive and negative saturations δHmax/2. It is corrected by introducing the magnetiz-133

ing voltage offset δVoff = kHmax · δHmax/2. The control of the Hmax symmetry becomes134

especially important for the soft magnetic materials, when the Earth’s magnetic field or the135

power amplifier offset can introduce a significant field shift in comparison with the material136


coercivity [4]. The third controlled parameter is the mentioned magnetic waveform B(t) or137

H(t). All these parameters are interrelated, i.e. change of Vmax for adjusting Bmax or Hmax138

can also alter the field symmetry and/or the magnetic waveform and vice versa. Therefore,139

these three parameters are controlled sequentially. Firstly, the amplitude Bmax or Hmax is140

controlled: if its value equals to the required amplitude with a feasible accuracy of∼ 0.5−1%,141

the δHmax/2 is similarly checked not to exceed the same accuracy limit. If the amplitude or142

the field symmetry parameters get over the prescribed accuracy limits, the kBmax and kHmax143

coefficients are used to correct Vmax or Voff value, e.g. for the Bmax correction144

Vmag(t)i+1 = [Vmag(t)

i − V ioff ] ·

[V imax + kBmax · δBi

max]

V imax

+ V ioff (1)

where δBimax = Breq

max − Bimax is a difference between the required and the real Bmax at the145

i-th iteration step. If both amplitude and field symmetry parameters are within the feasible146

accuracy limits, the Vmag(t) shape is corrected in order to adjust the magnetic waveform B(t)147

or H(t). According to the operator request, the magnetic waveform can be controlled for the148

specific field representation: the induction waveform B(t) can be controlled together with149

the field symmetry δHi/2, δHsur/2 or δHext/2 as well as the field waveform Hi(t), Hsur(t)150

or Hext(t) can be adjusted.151

The chosen magnetic waveform B(t) or H(t) is adjusted to the prescribed shape by cor-152

recting the magnetizing voltage signal Vmag(t). The common prescribed shapes are sinusoidal153

and triangular. The B(t) sine shape is usually selected for the IEEE standard tests of the154

soft magnetic materials [4]. The triangular shape corresponds to the constant magnetiza-155

tion rate, dB/dt or dH/dt = const, and is suitable for physical study of the magnetization156

dynamics. Because the sharp edges of the triangular signal are smoothed by the high circuit157

induction, the prescribed triangular signal is usually taken with the sinusoidally rounded158

edges at ∼ 10% of the amplitude level. The magnetic waveform can be also adjusted to an159


arbitrary function downloaded from the data file.160

The initial shape of the magnetizing voltage Vmag(t) is also sinusoidal or triangular161

depending of the prescribed shape of the adjusted magnetic waveform. The program works162

with one period of the Vmag(t) signal (∼ 1000 data points). The chosen magnetization163

cycle with the same number of the experimental points is cut from the measured data set164

{Hi, Hsur, Hext, B} using the maximum amplitude points of the controlled magnetic quantity165

H or B (there is usually a significant phase shift between H(t) and B(t), especially at high166

fmag). After the Vmag(t) correction, the magnetizing signal is resampled up to the selected167

1 MSa/s using the cubic spline interpolation.168

Two different methods of Vmag(t) correction are used. The first method of phase correc-169

tion shifts each sampled point j of the magnetizing signal to the position of a time lag φj170

between the required and the actual magnetic waveform, i.e. for the B(t) control171 Vph(tj)i+1 = V (tj + φj)

i

Breq(tj) = B(tj + φj)i

(2)

(see Fig. 3(a)) [3], [6], [7], [14]. The signal phase is corrected for the ascending and the de-172

scending branches separately. To get the final smooth Vmag(t) curve, the actual magnetizing173

amplitude Bmax or Hmax should not be lower than the required amplitude. So before the174

Vmag(t) correction, the adjusted magnetic waveform is normalized to the required amplitude175

level.176

The second method adjusts the amplitude of the magnetizing signal using the relative177

difference between the required and the actual magnetic waveform178

Vamp(tj)i+1 = Vmag(tj)

i + kBmax · [Breq(tj)−B(tj)i] (3)

(see Fig. 3(b)) [12]. To accelerate the feedback convergence, an additional derivative term179

d(δB(tj)i)/dt can be used [8], [11]. However, it could also result in worse feedback stability,180


(a) (b)

25 50 75

-2

-1

0

1

2

-1

-0.5

0

0.5

1B, TVmag , V

t, ms

Vmag(t) Bmax

B(t)

j

Vph(tj )

B(t) Bmax

B(t) sine

j

25 50 75

-3

-2

-1

0

1

2

3

-0.8

-0.4

0.0

0.4

0.8Hext , kA/mVmag , V

t, ms

Vmag(t) Hmax

H(t)

Vamp(tj ) H(tj )

Hext(t) Hmax

H(t) tri

j

Fig. 3. Magnetizing voltage signals Vmag(t) (left axes) and the corresponding magnetic waveforms (rightaxes) for the measurements performed with a partial amplitude-symmetry (Bmax/Hmax) and the full wave-form (B(t)/H(t)) controls. The feedback system efficiency is illustrated for the induction waveform B(t)adjusted to the sinusoidal shape (a) and for the extrapolation field waveform Hext(t) adjusted to the trian-gular shape (b). The dots show the ideal sinusoidal and triangular signals. Principles of the Vph (a) andVamp (b) correction methods are illustrated by arrows.

especially if the noisy waveform of the Hall fields Hsur(t)/Hext(t) is controlled [3], [4]. Sim-181

ple linear adjustment using the constant coefficients kBmax and kHmax demonstrated good182

efficiency, although the coefficient values should be sometimes corrected manually. Recal-183

culation of the kBmax and kHmax values at each iteration can lead to a mistake at the final184

adjustment stage, when the magnetic parameter changes δV , δB and δH are on the level of185

the measurement error.186

The final magnetizing signal is defined as a linear combination of these two corrected187

waveforms:188

Vmag(t) = kph · Vph(t) + (1− kph) · Vamp(t) (4)

The constant 0 ≤ kph ≤ 1 is responsible for the adjustment accuracy and is chosen manually189

for a certain experimental condition. Coincidence between the measured magnetic and the190

required standard waveforms is estimated analytically using a Pearson’s correlation coeffi-191

cient kcor, which equals to 1 at the perfect coincidence [3], [14]. If this coefficient exceeds the192


chosen critical value kcor ≃ 0.99999 and the two other controlled parameters, Bmax (or Hmax)193

and δHmax/2, are within the prescribed accuracy limits, the feedback loop stops and the final194

magnetic data are measured with the Vmag(t) of the last iteration step. The form factor value195

FF is also calculated for alternative standard estimation of the waveform coincidence [8].196

C. BN measurement197

The BN is measured separately by a surface-mounted bobbin coil positioned between198

the yoke pole in close vicinity to the Hall sensors. The weak BN signal is amplified by the199

low-noise SRS device SR560 and filtered by the SRS SIM965 modules. The cutoff frequencies200

of the filters are adjusted by the GPIB controller (see Fig. 1). Then the BN signal is sampled201

with a 1 MSa/s rate and digitally filtered in the same frequency bandwidth. The raw BN202

signal can be saved and is used for calculation of the BN frequency spectrum, the BN pulse203

distribution and the classical BN parameters as the rms value, BN pulse count, etc. The rms204

profile of BN (BN envelope) is sampled down to the same ∼ 1000 points for a magnetization205

cycle and superposed with the hysteresis data using the time scale. A principal advantage206

of the presented approach over the common techniques is that the surface BN signal (rms207

envelope) can be referred to a real descriptor of the sample surface magnetization: the surface208

magnetic fields Hsur and Hext, but not only to the indirect scales of time or Hi ∼ Imag [23],209

[25], [26]. The measurements with one Hall sensor (reference to Hsur) can also give the210

corrupted results because of a high vertical gradient of the surface magnetic field [16].211

Usually the BN envelope looks similar to the differential magnetic permeability. The212

time integration of the BN envelope gives a so-called BN loop, which provides an important213

magnetic information, e.g. a surface BN coercivity [5], [27]. However, in order to perform214

this integration, the descending branch of the positive rms envelope should be accurately215

reversed (made negative). For the measurements with low magnetizing frequencies, there is216


usually a stepwise transition between the branches; so they can be easily separated using217

the envelope derivative. However, for the ac measurements, the transition point between the218

branches is smoothed and there is a noticeable phase shift between the BN and the hysteresis219

signals. In this case, the branches are separated using the envelope minimums, which is less220

accurate due to the ac smoothing and a noisy profile of the BN envelope. The next source221

of the envelope integration error is a white background noise, which adds a nearly constant222

component shifting the envelopes up. The level of the background noise is mostly dependent223

on the filtering bandwidth. For the BN filtering from 1-2 kHz to 50-100 kHz, the rms noise224

level is negligibly small: about a few µm against the envelope peak of ∼ 100 µm. For the225

higher filtering frequencies, the signal-to-noise ratio decreases and the background noise level226

can reach a few tens of µm. So the constant rms component should be subtracted before the227

envelope integration.228

III. System performance229

A. Micro-alloyed steel230

Fig. 3 illustrates efficiency of the proposed feedback method: the corrected magnetiz-231

ing and the controlled magnetic signals at the initial (after amplitude-symmetry adjustment232

only) and the final (after full waveform control) stages. The measurements are performed for233

a soft micro-alloyed steel with dc Hc ≃ 220 A/m; the magnetizing frequency fmag = 10 Hz.234

The steel strip of 300 × 50 × 0.9 mm size is magnetized by a U-shaped Fe-Si yoke of the235

same length and width through a 3 mm air gap [27]. The induction waveform B(t) is236

adjusted to the sinusoidal shape of Bmax = 1.2 T amplitude with kph = 0.8 (Fig. 3(a)).237

The extrapolation field waveform Hext(t) is adjusted to the triangular shape of the com-238

parable Hmax = 0.8 kA/m amplitude with kph = 0 (Fig. 3(b)). With the combined feed-239

back algorithm, better adjustment accuracy was achieved as compared with our previous240


(a) (b) (c)

0 10 20 30 40 50 60

1.8

1.9

2.0

2.1

2.2

-30

-20

-10

0

10

20

30Vmax

, V

Iteration

Voff

, mV

0 10 20 30 40 50 60

1.18

1.19

1.20

1.21

1.22

1.23

Iteration

Bmax

, T

0 10 20 30 40 50 60

-15

-10

-5

0

5

10

15δH

max /2, A/m

Iteration

(d) (e) (f)

0 10 20 30 40 50 60

0.94

0.95

0.96

0.97

0.98

0.99

1.00 kcor

Iteration

final kcor = 0.999994

0 10 20 30 40 50 601.0

1.1

1.2

1.3

1.4

1.5FF

Iteration

B(t), FF = 1.11069 dB(t)/dt, FF = 1.10991

25 50 75

-80

-40

0

40

80 dB/dt, T/s

t, ms

dB/dt

sine

Fig. 4. Variation of the magnetic parameters with the feedback iterations: (a) magnetizing voltage ampli-tude Vmax (left axis) and offset Voff (right axis); (b) magnetic induction amplitude Bmax with the ±0.5%tolerance limits; (c) extrapolation field asymmetry δHmax/2 with the ±5 A/m limits; (d) Pearson’s correla-tion coefficient kcor; and (e) form factors FF of B(t) and dB/dt waveforms with the ±1% tolerance limitsdefined by the IEEE standards. (f) Final induced voltage waveform dB/dt together with the ideal sinusoid.

works, which use the phase correction method only [3], [4], [5]. For the sinusoidal B(t)241

control shown in Fig. 3(a), the achieved correlation coefficient kcor = 0.999994 and the form242

factor FF = 1.11069. For the Hext(t) control shown in Fig. 3(b), kcor = 0.999995 and243

FF = 1.15323. The form factors of the ideal sinusoidal and triangular waves are 1.11072244

and 1.1547, respectively; the acceptable FF deviation according to the IEEE standards is245

±1%. To the best of our knowledge, such an accurate adjustment of the magnetic field,246

especially the directly measured surface field, has not been reported before.247

Figs. 4(a)-(e) illustrate changes of the controlled magnetic parameters during the feed-248

back convergence for the sinusoidal B(t) adjustment presented in Fig. 3(a). About 40-60249

iterations or ∼ 5 s time interval are needed for the accurate adjustment of the magnetic250


(a) (b)

25 50 75

-2

-1

0

1

2

-1

-0.5

0

0.5

1

B, TVmag

, V

t, ms

⇐ Vmag

(t)

kph

=

1

0

0.8

B(t) ⇒

kph

=

1

0

0.8 0.2 0.4 0.6 0.8

-3

-2

-1

0

1

2

3

-1

-0.5

0

0.5

1

⇐ Vmag

(t)

Bmax

B(t)

B, TVmag

, V

t, s

B(t) ⇒

Bmax

B(t)

tri

Fig. 5. (a) Final magnetizing signals Vmag(t) (left axis) and the corresponding sinusoidally adjusted wave-forms B(t) (right axis) obtained by the phase, the amplitude and the combined correction methods, i.e. withkph = 1, 0 and 0.8, respectively. (b) Magnetizing voltage signals Vmag(t) (left axes) and the correspondingB(t) waveforms (right axes) for the measurements performed with the partial amplitude-symmetry Bmax

and the full triangular B(t) waveform controls. The dots show the ideal triangular signal; the measurementsare performed with the lower magnetizing frequency fmag = 1 Hz.

waveforms shown in Fig. 3. Fig. 4(f) shows the corresponding final dB/dt waveform, which251

should be controlled according to the IEEE standards. Its shape noticeably deviates from252

the ideal sine, although its FF value used by the standards deviates from the sine wave FF253

only by 0.1% (see Fig. 4(e)) [4], [8].254

Fig. 5(a) presents the results of the same sinusoidal B(t) control with varied kph value.255

The best B(t) adjustment is achieved with kph ≃ 0.7 − 0.8 (see Fig. 3(a)). The B(t) ad-256

justment with the phase and the amplitude correction methods, i.e. with kph = 1 and 0,257

gives worse results: kcor = 0.999787 and 0.999966; FF = 1.10791 and 1.11102, respectively.258

Moreover, the adjustment with the proposed combined algorithm is faster. Fig. 5(b) demon-259

strates the results of the similar triangular B(t) control. The best B(t) adjustment is again260

obtained with kph = 0.8 but at the lower magnetizing frequencies fmag ≃ 1 Hz. It takes261

∼ 1.5 s (13 iterations); the achieved kcor = 0.999997 and FF = 1.15404 for the data pre-262

sented in Fig. 5(b). For the tested micro-alloyed strip, the sinusoidal B(t) and the triangular263

Hext(t) waveforms can be adjusted up to fmag ≤ 30 Hz; the triangular B(t) – only up to264


(a) (b)

-0.4 0.4 0.8

-1

-0.5

0.5

1

B, T

Hext

, kA/m

sine Vmag

(t)

tri Vmag

(t)

sine B(t)

tri Hext

(t) -0.8 -0.4 0 0.4 0.8

0.1

0.2

0.3 Uenv

, mV

Hext

, kA/m

sine Vmag

(t)

tri Vmag

(t)

sine B(t)

tri Hext

(t)

Fig. 6. Hysteresis loops (a) and BN envelopes (b) measured with the different magnetizing signals: sinu-soidal and triangular Vmag(t) (partial amplitude-symmetry control) as well as sinusoidal B(t) and triangularHext(t). The measurements are performed at fmag = 10 Hz; the BN is filtered in the range of 2–70 kHz.

fmag ≤ 5 Hz [27]. Fig. 6(a) illustrates the influence of the magnetizing waveform on the265

magnetic hysteresis loops at fmag = 10 Hz [28]. Variations of the magnetizing waveform266

particularly alters the BN envelope as shown in Fig. 6(b) [23], [26].267

B. Non-oriented steel268

The next example of the system efficiency is presented for an industrial non-oriented269

steel strip of the standard size 300× 30× 0.5 mm and dc Hc ≃ 28 A/m. The non-oriented270

steel is similarly measured at Bmax = 1.2 T in the wide range of the magnetizing frequency271

0.25 ≤ fmag ≤ 125 Hz [4]. Fig. 7(a) illustrates the sinusoidally adjusted B(t) waveform at272

the standard frequency fmag = 50 Hz with the achieved kcor = 0.999997 and FF = 1.11051273

(0.02% error). The shape of the corresponding dB/dt dependence again noticeably deviates274

from the sine wave, but its FF = 1.10687 is within the acceptable tolerance limits: the error275

is 0.35%. The B(t) adjustment to the triangular shape also works better at lower magnetizing276

frequencies: at fmag = 5 Hz the achieved kcor = 1 and FF = 1.15078 (see Fig. 7(b)). Fig. 8277

outlines the range of the magnetizing frequency, where the system can effectively control278


(a) (b)

5 10 15

-1

-0.5

0

0.5

1

-400

-200

0

200

400dB/dt, T/s

B(t)

sine

t, ms

B, T

dB/dt 50 100 150

-1

-0.5

0

0.5

1

-30

-20

-10

0

10

20

30

t, ms

B(t) tri

B, T dB/dt, T/s

dB/dt

Fig. 7. The B(t) waveforms (left scales) adjusted to the sinusoidal shape at fmag = 50 Hz (a) and to thetriangular shape at fmag = 5 Hz (b) together with the corresponding dB/dt curves (right scales).

the magnetic induction waveform B(t). The sinusoidal magnetization can be adjusted up to279

fmag ≤ 125 Hz. The measurements without the B(t) control (with the sinusoidal magnetizing280

voltage Vmag(t)) keeps more sinusoidal magnetization with fmag increase: theB(t) form factor281

is already within the ±1% tolerance limits at fmag ≥ 100 Hz (see Fig. 8(b)). However, the282

triangular magnetization can be controlled only up to fmag ≤ 25 − 50 Hz. Fig. 8(a) also283

estimates the amount of time needed for theB(t) adjustment. The quasi-static measurements284

at fmag ≤ 1 Hz takes about 10-25 iterations or 20-30 s; the feedback loop at fmag ≃ 50 Hz285

converges after about 60 iterations taking ∼ 1.3 s. The directly measured field Hext or Hsur286

can not be accurately controlled for the soft electrical steels magnetized to Hmax ≃ 150 A/m287

because of an insufficient resolution of the Hall sensors [18].288

C. Contact problem289

Stability of the measurement method with respect to variations of the yoke-sample con-290

tact is checked on an industrial low-carbon steel S235JR. The flat sample of 110×20×4 mm291

size is magnetized similarly by a U-shaped Fe-Si yoke of the same length and width carrying292

the magnetizing and the induction coils. The Hall sensors and the BN coil are placed be-293


(a) (b)

0 25 50 75 100 125

0.99992

0.99994

0.99996

0.99998

1

0

10

20

30

τ, s

kcor

fmag

, Hz

sine B(t)

tri B(t)

0 25 50 75 100 125

1.07

1.08

1.09

1.10

1.11

1.12

1.12

1.13

1.14

1.15

1.16

FFFF

fmag

, Hz

sine

B(t)

dB/dt

Vmag

(t)

tri B(t) ⇒

Fig. 8. Dependence of the achieved Pearson’s correlation coefficients kcor (a, left scale) and the form factorsFF (b) on the magnetizing frequency fmag for the different shapes of the magnetizing waveforms. In (a)the dashed horizontal line at kcor = 0.99999 shows the typical sufficient level of the waveform adjustment.The right scale dependence in (a) estimates the convergence time of the corresponding B(t) adjustment,τ = (number of iterations)/fmag. In (b) the left and the right scales correspond to the sinusoidal and thetriangular waveforms, respectively. The solid horizontal line shows the FF values of the ideal sinusoidaland triangular signals. The dashed lines show the acceptable tolerance limits of ±1% defined by the IEEEstandards.

tween the yoke poles. The extrapolated field amplitude is adjusted to Hmax = 2 kA/m, the294

magnetizing frequency fmag = 0.5 Hz. The BN is filtered in the range of 2–70 kHz. An air295

gap between the attached yoke and the sample (yoke lift-off) is varied in the range of 0–1.5296

mm. Fig. 9 clearly demonstrates that the common method of the current field Hi cannot297

give the stable measurement results because the demagnetizing factor becomes substantial298

even at small frequently occurred lift-offs [23], [25], [26]. The direct field determination299

drastically improves the measurement stability to the yoke lift-off, which is especially true300

for the hysteresis data [16]. The small difference between the hysteresis measurements with301

and without the Hext(t) control is determined by the low fmag: the measurements are per-302

formed at a nearly quasi-static regime. The observed deviations of the field adjusted loops303

with the lift-off is caused by the positioning of the induction coil on the yoke pole: small304

uncontrollable part of the yoke-generated flux flows through the air. For the BN data, the305


0 1 2

20

40

60

80

100

-3 -2 -1 0 1 2 3

20

40

60

80

0 1 2

20

40

60

80

0 1 2

0.5

1

1.5

0 1 2

0.5

1

1.5

0 1 2 3 4 5

0.5

1

1.5

c) extrapolated fieldwith H(t) control

Uenv ,

mV

Hext , kA/m

Uenv , mV

Hi , kA/m

BN envelope

a) current fieldno H(t) control

b) extrapolated fieldwithout H(t) control

Hext , kA/m

Uenv ,

mV

b) extrapolated fieldwithout H(t) control

B, T

Hext , kA/m

B, T

Hext , kA/m

c) extrapolated fieldwith H(t) control

a) current fieldno H(t) control

BH loop

Hi , kA/m

B, T

Fig. 9. Three upper subfigures present the magnetic hysteresis loops B(H) obtained with increasing lift-offof the magnetizing yoke for the different measurement conditions: (a) the current field Hi method withoutthe field waveform control; (b) the extrapolated field Hext method without the Hext(t) control; (c) theextrapolated field Hext method with the Hext(t) control. Three bottom subfigures present the correspondingBN envelopes Uenv(H) obtained for the same measurement conditions. The yoke lift-off is set to 0, 0.1, 0.2,0.5, 0.75, 1.1 and 1.5 mm; the arrows indicate how the results are changed with the lift-off increase.

advantage of the triangular Hext(t) control is more pronounced: the BN envelopes measured306

with the different lift-offs are practically the same [5]. The corresponding largest drop of the307

BN energy parameter (BN loop amplitude) with the yoke lift-off is 4% (the standard error308

is 0.4%), whereas, the similar published experiments with the sinusoidally controlled B(t)309

gives a 10% drop of the BN energy [9].310


IV. Discussion311

The developed measurement system is conceived as a source of the repeatable and phys-312

ically accurate data needed for investigation of the magnetization dynamics and for devel-313

opment of the theoretical models [1], [27], [28]. It can be also useful for a non-destructive314

testing of the industrial steel samples, e.g. for the standard quality control of the mag-315

netically soft electrical steels, which are used as the cores of transformers, generators and316

motors [2], [19]. The accurate determination of the surface sample field allows the solution to317

the classical contact problem to be obtained and to correctly perform the measurements in318

the magnetically open configurations, which was considered to be a real technical challenge319

so far (see Fig. 9) [2], [3], [4]. It is also clear that the repeatable ac magnetic measurements320

should be made under a controlled magnetizing waveform (see Fig. 6) [7], [12]. So the pro-321

posed combination of the surface field measurement and the magnetizing waveform control322

can only guarantee the repeatable and accurate results.323

The presented system was successfully tested for a broad range of the industrial fer-324

romagnetic materials, from the magnetically soft ribbons and electrical/low-carbon steels325

to the much harder spring/TRIP steels [27]. Typical measurement results are presented326

in this work. Analysing the data obtained, we can generally discuss the efficiency and the327

limitations of the developed measurement system.328

The proposed feedback algorithm can efficiently adjust the magnetic induction waveform329

B(t) to the standard shapes. The achieved adjustment error is ∼ 0.1 − 0.3% (see Figs. 3,330

4, 7 and 8), which is well below the standard 1% threshold and on the level of the best331

published results [2], [8], [9], [10], [12]. The adjustment procedure takes about 50 iterations332

(see Figs. 4 and 8(a)), which is also comparable with the alternative feedback systems [10],333

[12]. In practice, the convergence time can be significantly reduced to 3-5 iterations only by334


adapting the initial magnetizing voltage, i.e. by setting Vmag(t)i=0 to be equal to the mean335

Vmag(t)i≈50 for the given measurement conditions.336

The known disadvantage of the proportional feedback controller (the amplitude cor-337

rection method, kph = 0) is parasitic mini-oscillations on the magnetizing signal profile338

Vamp(t). The oscillations can be suppressed by decreasing the proportional coefficient, kBmax339

or kHmax, however, this also increases the convergence time. The serious drawback of the340

phase correction method (kph = 1) is an exclusively monotonous Vph(t) profile [4], [14].341

The proposed combination of Vph and Vamp moderates the mentioned disadvantages of each342

method: the Vph transformation smooths the Vamp oscillations, whereas, the Vamp correction343

makes a non-monotonous contribution to the final Vmag(t). The higher contribution of the344

phase correction method (typical value of kph ≃ 0.75) is caused by a substantial phase shift345

between Vmag(t) and B(t) signals. Therefore, the proposed combined method demonstrates346

an improved performance in case of the induction waveform B(t) adjustment (see Fig. 5(a)).347

The main physical factor influencing the feedback adjustment is an inductance of the348

magnetizing circuit. The high inductance favours the sinusoidal magnetization [3], [4]. Even349

without the B(t) control, the open magnetic circuit with a 3 mm air gap between the yoke350

and the non-oriented steel strip maintains the sinusoidal B(t) shape at fmag ≥ 100 Hz351

(see Fig. 8(b)). Therefore, for the sinusoidal B(t) adjustment, the main limiting factor352

is the sample thickness. It seems that the inhomogeneous sample magnetization at high353

fmag influenced by the eddy currents (skin effect) leads to a generally uncontrollable and354

unrepeatable magnetization process [29]. Just that factor is responsible for the maximal355

working frequencies of fmag = 30 and 125 Hz for the micro-alloyed and the non-oriented356

steels, respectively. At slightly higher fmag than these maximal values, the tested samples357

cannot be magnetized to the chosen induction amplitude Bmax = 1.2 T at all due to a strong358


inductive feedback.359

The triangular magnetization (the constant magnetization rate dB/dt = const) is more360

suitable for a physical interpretation of the data. However, the triangular shape is not so361

natural: the inductance factor dominates over the size/skin effect; it tends to bend the362

triangular curve and smooth its edges. Therefore, the inductance of the magnetizing circuit363

is usually decreased by introducing a few mm air gap between the magnetizing yoke and the364

tested sample (see Fig. 9). This allows to adjust the B(t) waveform to the triangular shape365

up to fmag = 5 and 50 Hz for the micro-alloyed and the non-oriented steels, respectively (see366

Fig. 8).367

The physically accurate and repeatable BN results with the Hext(t) control is expected368

because the both signals, BN and Hext, are detected from the sample surface. The BN369

results can be really stabilized with respect to the yoke lift-off [23], [26]. Moreover, the BN370

envelopes obtained with the triangular Hext(t) demonstrate a traditional one-peak profile371

(see Figs. 6(b) and 9) [5], [27]. Therefore, the precise control of the surface magnetic field372

can offer a new opportunity for the BN technique development. The phase shift between373

Vmag(t) and H(t) signals is insignificant; so the dc measurements with the low magnetizing374

frequencies fmag < 5 − 10 Hz are usually performed with kph = 0. Small increase of the375

phase constant up to kph ≃ 0.1 at higher fmag can slightly improve the adjustment accuracy,376

probably due to an additional smoothing of the noisy Hall sensor signals (see Fig. 3(b)).377

Introducing the initial yoke lift-off can suppress the inductive component, but the eddy378

current factor similarly limits the field adjustment efficiency up to fmag ≤ 30 Hz for the379

the micro-alloyed steel. Unfortunately, it seems that the surface magnetic field cannot be380

controlled for the bulky samples because of a rising inductance of the magnetizing circuit381

as well as a higher influence of the eddy currents. The further improvement of the setup382


performance can be probably achieved only by a significant technical complication of the383

measurement system, e.g. by controlling the magnetizing current waveform Imag(t) instead384

of Vmag(t).385

V. Conclusion386

The system developed for the repeatable and physically accurate measurements of the387

bulk magnetic hysteresis and the surface Barkhausen noise is described in detail. The main388

features of the proposed setup are (i) the direct measurement of the surface magnetic field and389

(ii) the control of the magnetization process. The effective feedback algorithm based on the390

physically clear principle is developed for the precise control of the ac magnetizing waveforms391

(bulk magnetic induction or surface magnetic field). In particular, the actual field waveform392

measured directly by the Hall sensors can be adjusted with an acceptable accuracy in case393

of relatively hard and thin samples. The outcomes of this work are important for further394

development of the measurement standards and the industrial non-destructive techniques.395

Acknowledgment396

The work was supported by the Czech Science Foundation (GACR) under Project 13-397

18993S.398

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