BH Curve and Iron Loss Measurements for Magnetic Materials (Research Paper) - Personal Learning PDF Download

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Power Engineering Briefing Note Series 
http://www.eleceng.adelaide.edu.au/research/power/pebn/ 
pebn rv1.2.doc Page 3 24-Jul-08 
BH Curve and Iron Loss Measurements 
for Magnetic Materials              
PEBN  #5   (12 May 2008) 
W.L. Soong 
School of Electrical and Electronic Engineering 
University of Adelaide, Australia 
soong@ieee.org 
 
Abstract – This brief discusses the measurement of the BH curve 
and iron loss characteristics of magnetic materials based on tests 
on cores done at mains frequency. 
I. INTRODUCTION  
The BH loop of a magnetic material represents the 
relationship between its magnetic flux density B as a function 
of the magnetic field intensity H.  For an ideal lossless, linear 
magnetic material the curve would be a straight line whose 
slope is equal to the permeability µ of the material (see Fig. 
1a).  Practical effects include : magnetic saturation that limits 
the maximum achievable magnetic flux density in the material 
and so causes the BH curve to be non-linear (see Fig. 1b), and 
iron losses which cause the BH curve to become a loop whose 
area represents the energy losses due to effects such eddy-
current and hysteresis loss (see Fig. 1c). 
B
H
B
H
B
H
a) ideal BH loop b) with saturation c) with saturation and 
low iron loss
 
Fig. 1. The effect of saturation and iron loss on the shape of the BH loop. 
II. BH LOOP MEASUREMENT PRINCIPLES 
The magnetic properties and in particular the iron losses are 
sensitive to mechanical stress and the heat treatment used in 
the laminations. 
Standard BH curve and iron loss measurements are normally 
made using a square-shaped stack of laminations called an 
Epstein frame [1].  It is however possible to make 
measurements using other core shapes.  It is important that the 
core have a uniform cross-sectional area otherwise it is 
difficult to interpret the results because B and H are not 
uniform in the material.  In Fig. 2 the core has a circular 
shape. 
i
main
AC
N
main N
sense
+
-
v
sense
l
core
A
core 
Fig. 2. Test arrangement for measuring BH loops. 
The magnetic core has two windings.  The main winding is 
used to create the magnetic field intensity H.  The magnetic 
field intensity is given by :   
  
()
()
main main
core
Ni t
Ht
l
= (1) 
where N
main
 is the number of turns in the main winding, i
main
 is 
the current flowing in the main winding and l
core
 is the mean 
magnetic path length of core (shown as a dashed line in Fig. 
2).  In order to create high levels of magnetic field intensity to 
saturate the material (e.g. 10 kA/m) it is necessary that the 
main winding has many turns of relatively thick wire which 
can carry high levels of current.  
The required rms AC supply voltage V
s
 for the main 
winding is given by :  
 4.44
s main pk core
VNBAf = (2) 
where B
pk
 is the expected saturation flux density of the core, 
A
core
 is the magnetic cross-sectional area of the core (see Fig. 
2) and f is the supply frequency. 
The sense coil winding is used to measure the magnetic flux 
density B created by the main winding current.  The induced 
voltage in the sense coil winding v
sense
 is given by :  
 
() ()
()
sense sense sense core
dt dBt
vt N N A
dt dt
f
== (3) 
where N
sense
 is the number of turns in the sense winding.  Re-
arranging (3) to solve for the flux density produces :  
 
11
() ()
sense sense
core sense core sense
Bt v dt t
AN AN
? ==
?
 (4) 
where ?
sense
 is the instantaneous flux-linkage of the sense coil 
which is the integral of the sense coil voltage.  This integration 
can be approximated for a sampled waveform by : 
 [ ] [ ] [ ] 1
sense sense sense
kkvkt ?? +=+ ? (5) 
where ?t is the sampling time interval and k represents the 
sample number.  
Unlike what is shown in Fig. 2, both the main and sense coil 
windings are uniformly distributed around the magnetic core 
to produce a more uniform magnetic field distribution in the 
core and also to improve the magnetic coupling between the 
two windings. 
 
Fig. 3. Diagram showing the winding uniformly distributed around the test 
core (left) and photograph of actual coil (right). 
The average power loss P
loss
 in the core is given by :  
 
0
1
T
main
loss sense main
sense
N
Pvidt
NT
=
?
 (6) 
where T is the period of the supply waveform.  This 
expression can be approximated for sampled data as :  
 [] []
1
1
K
main
loss sense main
sense k
N
Pvkik
NK
=
=
?
 (7) 
where K is the number of samples in one period. 
Page 2


Power Engineering Briefing Note Series 
http://www.eleceng.adelaide.edu.au/research/power/pebn/ 
pebn rv1.2.doc Page 3 24-Jul-08 
BH Curve and Iron Loss Measurements 
for Magnetic Materials              
PEBN  #5   (12 May 2008) 
W.L. Soong 
School of Electrical and Electronic Engineering 
University of Adelaide, Australia 
soong@ieee.org 
 
Abstract – This brief discusses the measurement of the BH curve 
and iron loss characteristics of magnetic materials based on tests 
on cores done at mains frequency. 
I. INTRODUCTION  
The BH loop of a magnetic material represents the 
relationship between its magnetic flux density B as a function 
of the magnetic field intensity H.  For an ideal lossless, linear 
magnetic material the curve would be a straight line whose 
slope is equal to the permeability µ of the material (see Fig. 
1a).  Practical effects include : magnetic saturation that limits 
the maximum achievable magnetic flux density in the material 
and so causes the BH curve to be non-linear (see Fig. 1b), and 
iron losses which cause the BH curve to become a loop whose 
area represents the energy losses due to effects such eddy-
current and hysteresis loss (see Fig. 1c). 
B
H
B
H
B
H
a) ideal BH loop b) with saturation c) with saturation and 
low iron loss
 
Fig. 1. The effect of saturation and iron loss on the shape of the BH loop. 
II. BH LOOP MEASUREMENT PRINCIPLES 
The magnetic properties and in particular the iron losses are 
sensitive to mechanical stress and the heat treatment used in 
the laminations. 
Standard BH curve and iron loss measurements are normally 
made using a square-shaped stack of laminations called an 
Epstein frame [1].  It is however possible to make 
measurements using other core shapes.  It is important that the 
core have a uniform cross-sectional area otherwise it is 
difficult to interpret the results because B and H are not 
uniform in the material.  In Fig. 2 the core has a circular 
shape. 
i
main
AC
N
main N
sense
+
-
v
sense
l
core
A
core 
Fig. 2. Test arrangement for measuring BH loops. 
The magnetic core has two windings.  The main winding is 
used to create the magnetic field intensity H.  The magnetic 
field intensity is given by :   
  
()
()
main main
core
Ni t
Ht
l
= (1) 
where N
main
 is the number of turns in the main winding, i
main
 is 
the current flowing in the main winding and l
core
 is the mean 
magnetic path length of core (shown as a dashed line in Fig. 
2).  In order to create high levels of magnetic field intensity to 
saturate the material (e.g. 10 kA/m) it is necessary that the 
main winding has many turns of relatively thick wire which 
can carry high levels of current.  
The required rms AC supply voltage V
s
 for the main 
winding is given by :  
 4.44
s main pk core
VNBAf = (2) 
where B
pk
 is the expected saturation flux density of the core, 
A
core
 is the magnetic cross-sectional area of the core (see Fig. 
2) and f is the supply frequency. 
The sense coil winding is used to measure the magnetic flux 
density B created by the main winding current.  The induced 
voltage in the sense coil winding v
sense
 is given by :  
 
() ()
()
sense sense sense core
dt dBt
vt N N A
dt dt
f
== (3) 
where N
sense
 is the number of turns in the sense winding.  Re-
arranging (3) to solve for the flux density produces :  
 
11
() ()
sense sense
core sense core sense
Bt v dt t
AN AN
? ==
?
 (4) 
where ?
sense
 is the instantaneous flux-linkage of the sense coil 
which is the integral of the sense coil voltage.  This integration 
can be approximated for a sampled waveform by : 
 [ ] [ ] [ ] 1
sense sense sense
kkvkt ?? +=+ ? (5) 
where ?t is the sampling time interval and k represents the 
sample number.  
Unlike what is shown in Fig. 2, both the main and sense coil 
windings are uniformly distributed around the magnetic core 
to produce a more uniform magnetic field distribution in the 
core and also to improve the magnetic coupling between the 
two windings. 
 
Fig. 3. Diagram showing the winding uniformly distributed around the test 
core (left) and photograph of actual coil (right). 
The average power loss P
loss
 in the core is given by :  
 
0
1
T
main
loss sense main
sense
N
Pvidt
NT
=
?
 (6) 
where T is the period of the supply waveform.  This 
expression can be approximated for sampled data as :  
 [] []
1
1
K
main
loss sense main
sense k
N
Pvkik
NK
=
=
?
 (7) 
where K is the number of samples in one period. 
Power Engineering Briefing Note Series 
http://www.eleceng.adelaide.edu.au/research/power/pebn/ 
pebn rv1.2.doc Page 4 24-Jul-08 
-2
-1
0
1
2
Main Coil Current [A]
-2
-1
0
1
2
Sense Coil Voltage [V]
Imain
Vsense
 
Fig. 4.  Examples of measured main coil current and sense coil voltage. 
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1500 -1000 -500 0 500 1000 1500
Field Strength (A/m)
Flux Density (Tesla)
 
Fig. 5. Example of measured BH loop corresponding to data in Fig. 4. 
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1500 -1000 -500 0 500 1000 1500
Field Strength (A/m)
Flux Density (Tesla)
 
Fig. 6. Example of BH loops for other values of peak flux density. 
When the core is heavily saturated, the low power-factor of 
the waveforms means that the power loss calculation is very 
sensitive to small phase shift differences between the voltage 
and current sensors.  These errors can cause the power loss 
calculation result to become negative at high currents. 
An alternative and possibly more accurate power loss 
measurement method is to also feed v
sense
 and i
main
 signals to a 
power analyser and to record the power reading from this. 
III. TEST AND ANALYSIS PROCEDURE 
A. Test Method 
The test arrangement was shown in Fig. 2.  The main 
winding is connected to a variable-magnitude, low-voltage AC 
source which can be safely produced from the output of a step-
down transformer connected to an auto-transformer.   
The main winding current i
main
(t) and the sense winding 
voltage i
sense
(t) are measured using appropriate sensors and are 
sampled at a rate to give say 200 to 1000 samples per cycle 
and to record an integral number of cycles, say two. 
Sets of voltage and current measurement are taken from 
zero to the maximum peak flux density value in say six to ten 
steps.  A reading proportional to the peak flux density 
magnitude can be obtained by connecting a standard AC 
voltmeter (not “true RMS”) to the sense coil winding.  This  
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
0 2000 4000 6000 8000 10000 12000
Field Strength (A/m)
Flux Density (T)
 
Fig. 7. Measured BH characteristics based on the peak values of B and H 
measured for each data set. 
0
2
4
6
8
10
12
0.0 0.5 1.0 1.5 2.0
Peak Flux Density (T)
Iron Loss (W/kg)
 
Fig. 8. Measured iron loss characteristics. 
reading can be used to set the supply voltage to obtain sets of 
data at roughly equal steps in peak flux density. 
For each voltage and current data set, the following 
procedure can be used for analysis :  
• remove any DC offsets in the measured voltage 
v
sense
(t) and current i
main
(t) signals by calculating the 
mean of both signals and subtracting them from the 
signals (see Fig. 4); 
• calculate the magnetic field intensity H(t) from 
i
main
(t) using (1); 
• calculate the flux-linkage ?(t) using the integration 
approach shown in (5) and remove the DC offset 
from the calculated flux-linkage; 
• calculate the magnetic flux density B(t) from the 
flux-linkage using (4); 
• plot B(t) versus H(t) to obtain the BH loop (see Fig. 
5), determine the peak values of B and H. 
• calculate the average power loss P
loss
 using (7), the 
loss per kg can be calculated by dividing this by the 
weight of the test core laminations. 
Using the peak values of B and H for each voltage and 
current set (see Fig. 6) and the average power loss, the BH 
curve in Fig. 7 and the iron loss curve in Fig. 8 can be 
obtained. 
IV. REFERENCES 
[1] IEC Standard 60404-2 Magnetic materials – Part 2: “Methods of 
measurement of the magnetic properties of electrical steel sheet and strip 
by means of an Epstein frame,” Ed. 3.0 (Bilingual 1996) 
 
A WORD FOR TODAY 
“Trust in the LORD with all your heart, and lean not on 
your own understanding; in all your ways acknowledge 
him, and he shall direct your paths.” 
  Proverbs 3:5-6 (KJV)