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Magnetic Components in Electric Circuits
Understanding thermal behaviour and stress
Peter R. Wilson, University of Southampton
What are we trying to understand?
How are Magnetic Materials
Affected by Temperature?

What is the impact on Magnetic
Components?

How does this affect electric
circuit behaviour?
B (T)

0.5
0.4
0.3
0.2
0.1
0
-0.1
-0.2
-0.3
-0.4
-150
-100
-50
0
H (A/m)
50
100
150
T=27University
T=95 of T=154
School of Electronics and Computer Science,
Southampton, UK
2
Magnetic Material Characteristics

Ferrous Magnetic Materials exhibit hysteresis

The magnetization of the material is partly reversible (no
loss) and partly irreversible (loss)
Total
Magnetization
(Stored Energy)
M
Reversible
Magnetization
Irreversible
Magnetization
(Lost Energy)
Happlied
School of Electronics and Computer Science, University of Southampton, UK
H
3
Energy Lost in Magnetic Materials

The Material will therefore dissipate energy as heat
under heavy loading:
B (T)
Recovered
Energy
dB
H (At/m)
Dissipated
Energy
BH Curve
Anhysteretic Fn.
School of Electronics and Computer Science, University of Southampton, UK
4
The effect of environmental Temperature?
How does the overall temperature of the material
affect its behaviour?

Eventually the Curie point is reached and the material
ceases to have any effective permeability
Data for a 3F3
Material, 10mm
Toroid obtained by the
author, measured
using a GriffinGrundy oven to
control the
temperature
B (T)

0.5
0.4
0.3
0.2
0.1
0
-0.1
-0.2
-0.3
-0.4
-150
-100
-50
0
50
100
H (A/m)
T=27
T=95
T=154
School of Electronics and Computer Science, University of Southampton, UK
150
5
Modeling Magnetic Materials

Modeling Magnetic Materials is particularly
complex, with several choices


Jiles Atherton, Preisach, Hodgdon, et al
The Jiles Atherton model is often used in circuit
simulators:
H
+
He
Man
  Ms
c
1 c
Mrev
M
+
1
a

tanh( H / a ) H
M an  M
  k  ( M an  M )

Mirr
1
1 c
 0  M S * M  H  / A
School of Electronics and Computer Science, University of Southampton, UK
B
6
Jiles Atherton Model

The results are particularly good at predicting the
BH loop behaviour in ferrites, however the Preisach
model is often better for “square” loop materials
0.4
0.3
0.2
B (T)
0.1
0
-0.1
-0.2
-0.3
-0.4
-150
-100
-50
0
50
100
150
H (At/m)
Measured
Simulated
School of Electronics and Computer Science, University of Southampton, UK
7
Building a Magnetic Component

To build a component (e.g. inductor) for electric
circuits, we need both a core model and a winding:
mmf
F
i
F
p
c
c
Core
p
dF p
vp = np
dt
Electrical
Domain
mmf
p
= n *i
p p
Magnetic
Domain
School of Electronics and Computer Science, University of Southampton, UK
8
Adding the Thermal Dependence

To add dynamic thermal behaviour, use a network
to effectively model the thermal aspects of the
material and the environment
Jiles-Atherton
Non-Linear
Core Model
H
Modified Model
Parameters
Default
Model
Parameters
Parameter
Functions
B
Power
T(°C)
Thermal
Network
Power
Eddy
Current
Loss
Power
Current
Winding
Loss
School of Electronics and Computer Science, University of Southampton, UK
9
Thermal Network Modeling

We have choices to make regarding the thermal
network, in particular a distributed or lumped model

In most cases a lumped model is perfectly adequate
Emission
Tsurface
Hysteresis
+ Eddy Current
+ Winding
Power Loss
Convection
Tair
Cth - Core
Ambient
Temperature
School of Electronics and Computer Science, University of Southampton, UK
10
Characterize the Magnetic Material
It is a relatively simple matter to characterize the
magnetic material model by measuring its
behaviour and calculating the resulting model
parameters
Griffin-Grundy Oven
RS 206-3750
Temperature
Meter
DS345
Signal
Generator
42.00
40.00
TN10 - 3F3
38.00
Power
Amplifier
A (-)

Np
36.00
34.00
Ri
32.00
30.00
Ns
Tektronix
TDS220
Digital
Oscilloscope
CH1
0.0
20.0
40.0
60.0
80.0 100.0 120.0 140.0 160.0
Temperature (Degrees Celsius)
A(Measured)
A(Second Order Fit)
CH2
School of Electronics and Computer Science, University of Southampton, UK
11
Building a Circuit Model…

Using the characterized thermally dependent model
of the core, winding models and a thermal network,
we can make the electric circuit model (in this case
a transformer) dynamically affected by temperature
U1
vp
U2
U3
1
3
1
4
2
5
3
1
3 expja_th6
MMF
I2
2
R4
1k
MMF
4
2
winding_th
5
winding_th
R3
10
tcore
PARAMETERS___
Area
293u
Cth
0.07
D
3.8e-3 R1
1G
PARAMETERS___
C
700
Dens
4750
Vol
188n
1
1
2
tair
U5 emission
U6
ctherm
2
U4
1
2
rconv
+
27
V1
-
School of Electronics and Computer Science, University of Southampton, UK
12
Results of Dynamic Thermal behaviour
At ambient Temperatures, the model behaves very
closely to the measured data
Voltage (V)

0.1
0.08
0.06
0.04
0.02
0
-0.02
-0.04
-0.06
-0.08
-0.1
0
0.005
0.01
0.015
0.02
0.025
Time (s)
Measured
Simulated
School of Electronics and Computer Science, University of Southampton, UK
13
Results of Dynamic Thermal behaviour

At increased temperatures, the transformer output
voltage drops due to reduced permeability
0.08
0.06
Voltage (V)
0.04
0.02
0
-0.02
-0.04
-0.06
-0.08
0
0.005
0.01
0.015
0.02
0.025
Time (s)
Measured
Simulated
School of Electronics and Computer Science, University of Southampton, UK
14
Dynamic Magnetic and thermal behaviour
B (T)

The Flux Density decreases as the magnetic core
temperature increases
0.4
0.3
0.2
0.1
0
-0.1
-0.2
-0.3
-0.4
0
0.05
0.1
0.15
0.2
Time (s)
B
School of Electronics and Computer Science, University of Southampton, UK
15
Conclusions

The magnetic material can be modelled to reflect
not only the complex BH curve, but also its
dependence on temperature

The temperature can be introduced dynamically to
the magnetic material model

The component can be modelled using a thermal
network to accurately predict the dynamic thermal
behaviour

A complete electric circuit can be simulated that
includes dynamic thermally dependent magnetic
component and accurately predicts its behaviour
School of Electronics and Computer Science, University of Southampton, UK
16
References
1.
Wilson, P. R., Ross, J. N. and Brown, A. D. “Magnetic Material Model Optimization and
Characterization Software”. In: Compumag, 2001
2.
Wilson, P. R., Ross, J. N. and Brown, A. D. “Dynamic Electrical-Magnetic-Thermal Simulation
of Magnetic Components”. In: IEEE Workshop on Computers in Power Electronics, COMPEL
2000
3.
P.R. Wilson, J.N Ross & A.D. Brown, “Predicting total harmonic distortion in asymmetric
digital subscriber line transformers by simulation”, IEEE Transactions on Magnetics, Vol. 40 ,
Issue: 3 , 2004, pp. 1542–1549
4.
P.R. Wilson, J.N Ross & A.D. Brown, “Modeling frequency-dependent losses in ferrite cores”,
IEEE Transactions on Magnetics ,Vol. 40 , No. 3 , 2004, pp. 1537–1541
5.
P.R. Wilson, J.N Ross & A.D. Brown, “Magnetic Material Model Characterization and
Optimization Software”, IEEE Transactions on Magnetics, Vol. 38, No. 2, Part 1, 2002, pp. 10491052
6.
P.R. Wilson, J.N Ross & A.D. Brown, "Simulation of Magnetic Component Models in Electric
Circuits including Dynamic Thermal Effects", IEEE Transactions on Power Electronics, Vol.
17, No. 1, 2002, pp. 55-65
7.
P.R. Wilson & J.N Ross, "Definition and Application of Magnetic Material Metrics in Modeling
and Optimization", IEEE Transactions on Magnetics, Vol. 37, No. 5, 2001, pp. 3774-3780
8.
P.R. Wilson, J.N Ross & A.D. Brown, "Optimizing the Jiles-Atherton model of hysteresis using
a Genetic Algorithm", IEEE Transactions on Magnetics, Vol. 37, No. 2, 2001, pp. 989-993
School of Electronics and Computer Science, University of Southampton, UK
17