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Evaluation of magnetization models for simultaneous analysis of flux and temperature distributions in ferrite cores
ELSEVIER
Journal of Magnetism and Magnetic Materials 133 (1994) 516-519
~
journalof magnetism
jR
and
, ~
materials
magnetic
Evaluation of magnetization models for simultaneous analysis of flux and temperature distributions in ferrite cores H. F u k u n a g a a,,, H. Abe a, y . O h t a b, H. Kakehashi b a Department of Electrical Engineering and Computer Science, Nagasaki University, Nagasaki 852, Japan b Matsushita Electric Works, Ltd., Kadoma, Osaka 571, Japan
Abstract The validity of simultaneous analysis of flux and temperature in ferrite cores operating at audio frequencies was evaluated for the magnetization models proposed by Potter and Schmulian and by Jiles and Atherton. It was found that Jiles' model describes the reluctivity vs. flux density characteristic satisfactorily and Potter's the magnetic loss vs. flux density characteristic. When flux and temperature in an inductor were analyzed with the aid of Potter's model or a hybrid model of Jiles' and Potter's, results agreed well with those analyzed by using the measured magnetic properties. These results suggest that flux and temperature in a ferrite core can be analyzed simultaneously from a small number of measured data with the aid of an appropriate magnetization model.
I. Introduction Ferrite cores in electronic devices are often used at high induction levels and then magnetic and joule losses increase their temperature. To clarify the characteristics of such devices, flux and temperature should be analyzed simultaneously by a method such as F E M (Finite Element Method) [1]. Thus huge amounts of information about magnetic properties should be measured in an expected temperature range and stored prior to analysis. This is a time consuming process when we have to analyze a variety of devices made from a variety of materials. Utilization of a simple magnetization model enables us to analyze flux and temperature simultaneously from a small number of measured data for materials. In addition, it will open out analysis combined with a circuit analysis tool such as SPICE. Among many magnetization models proposed previ-
ously [2], models suitable for our purpose are those in which parameters are independent from the magnitude of magnetization and are easily determined. The models proposed by Potter and Schmulian [3] and by Jiles and Atherton [4] are two of those meeting the requirements. Thus we evaluated their validity for the simultaneous analysis and confirmed that flux and temperature distributions in a ferrite core can be analyzed from a small number of experimental data with the aid of a magnetization model.
2. Magnetization model The model proposed by Potter and Schmulian includes three parameters (the saturation magnetization Ms, the ratio S of the remanence to M s, and the coercivity H c) to be determined from measured data. The magnitude of magnetization M in an applied field H is described by using these parameters as
/
[
HcHsgn°t
M = M s sgna-o~ l + t a n h |
* Corresponding author. Fax: + 81-958-46-7379; E-mail: [email protected]. 0304-8853/94/$07.00 © 1994 Elsevier Science B.V. All rights reserved SSDI 0304-8853(94)00197-Y
-Hc
tanh-lS
]/ (1)
H. Fukunaga et al. /Journal of Magnetism and Magnetic Materials 133 (1994) 516-519 where a is calculated from extreme values of H. The parameters were determined from a measured full M - H loop (10 kHz) at 25-140°C for a Co-based amorphous alloy and four kinds of ferrite materials (TDK PC30, PC32, PC38, and PC40). In the model proposed by Jiles and Atherton, M is given by dM
Man - M i r r = ( 1 c ) k 6 _ a ( M an_Mirr dH
dMan ) +C d H '
~'1 ~.
PC40, 40°C, 10kHz
•
Jiles' Model Potter's Model .......... Measured •
,~ /
lOOO
500
1000
500
°°o
i ,,
(2)
500
=
Man(H ) = Ms[COth{ ( H + a M ) / a }
500
517
-~
- a/(H + aM)],
i
~
. . . •. . . . . .• . . . . . -o. . . . . . . o. . .
:
.
•
41-
°-°'''""
(3) '
012 ' 014 Flux Density B ( T ) Fig. 2. Reluctivity calculated from Potter's and Jiles' models for PC40 at 40°C and l0 kHz together with that measured. 0
Mirr = ( M - cM, n ) / ( 1 - c),
(4)
where 8 is a parameter having the value +1 for d H / d t > 0 and d H / d t < 0, respectively. Five parameters (c, k, a, a, and M s) included were determined from measured Rayleigh and full loops.
The discrepancy D between a calculated quantity Qcal and the corresponding measured one Qmes is shown in Tables 1 and 2. D is defined as
3. Results a n d d i s c u s s i o n ,'0
In order to evaluate the validity of the models, hysteresis loops were calculated from the models, and compared with those measured at 10 kHz. Fig. 1 shows typical B - H loops at 40°C for PC40. It is seen that the magnetization curve by Potter's model reaches saturation faster than the measured curve. The minor loop coercivity by Jiles' model is larger than that measured. The reluctivity u and the magnetic loss W reflect these discrepancies as shown in Figs. 2 and 3. The u vs. B characteristic is described satisfactorily by Jiles' model but Potter's simulates the W vs. B characteristic well.
Measured
9B s
~
j
~
z
Qmes dB.
(5)
Flux and temperature distributions were analyzed simultaneously for the inductor shown in Fig. 4 by FEM with the aid of u and W at 10 kHz calculated from the models, and compared with those analyzed by using measured values. Typical results for PC30 and
[x 105]
/"
:/0.
::
9B s
PC40, 40°C, 10kHz
Jiles' Model 3 Potter's Model ......... Measured •
~'//
/
c0
3.2. Simultaneous analysis o f flux and temperature
~
-80
/Jo"
A similar tendency found in Figs. 2 and 3 was observed at almost all the temperatures and for all materials examined. Thus the tendency is expected to be common to soft ferrite materials used at audio frequencies.
A
-160
dB
[xl 05
0.5
Potter's Model
] Qcal - Qrnes ]
D= J0
3.1. Reluctivity and magnetic loss
t
I
I
80
I
I
160
H (A/m)
.o .j
•,,o, / /
2
. ~ ,'~ ¢'
2 •
•
.o C
q-'""
2 _~.=_~.
Jiles' Model
O-
-0.5 Fig. t. Hysteresis loops measured and calculated from Potter's and Jiles' models for PC40 at 40°C.
0.2 o.4 Flux Density B ( T ) Fig. 3. Magnetic loss calculated from Potter's and Jiles' models for PC40 at 40°C and 10 kHz together with that measured.
518
H. Fukunaga et aL /Journal of Magnetism and Magnetic Materials 133 (1994) 516-519
Table 1 Discrepancy D of Eq. (5) between magnetic quantities calculated and measured for PC38 Temp.
Reluctivity
[°C]
Potter
Jiles
Magnetic loss Potter
Jiles
25 40 60 80 100 120 140 Average
0.051 0.049 0.032 0.035 0.104 0.125 0.119 0.074
0.066 0.028 0.023 0.070 0.078 0.072 0.058 0.056
0.114 0.071 0.051 0.053 0.074 0.067 0.078 0.073
0.157 0.204 0.177 0.184 0.150 0.134 0.131 0.162
PC40 cores are shown in T a b l e 3. In the table, ' H y b r i d ' m e a n s t h a t v a n d W were calculated from Jiles' a n d P o t t e r ' s models, respectively. In the analysis c o n d u c t e d with the aid of Jiles' model, the m a x i m u m t e m p e r a t u r e in the PC40 core is m u c h h i g h e r t h a n t h a t analyzed by using m e a s u r e d data. A similar t e n d e n c y was o b s e r v e d for o t h e r materials, too. This discrepancy would be a t t r i b u t e d to the fact t h a t W calculated from Jiles' m o d e l is larger t h a n t h e m e a s u r e d W in the middle B region. O n the o t h e r h a n d , t h e results o b t a i n e d with the aid of P o t t e r ' s m o d e l or the hybrid m o d e l agree well with t h o s e o b t a i n e d by using m e a s u r e d v a n d W. T h e average discrepancies in the m a x i m u m t e m p e r a t u r e for four ferrite materials, which were o b t a i n e d u n d e r the same condition as that indicated in T a b l e 3, were 4.8%, 21.0% a n d 5.1% w h e n Potter's, Jiles', a n d the hybrid m o d e l s were used, respectively. T h e s e results suggest t h a t flux a n d t e m p e r a t u r e distributions in a ferrite core can b e analyzed simultaneously from a small n u m b e r of m e a s u r e d data with the aid of an a p p r o p r i a t e m a g n e t i z a t i o n model. A study to find a b e t t e r m a g n e t i z a t i o n model to m e e t o u r p u r p o s e is in progress.
I oore
~Conductor ~Insulator
Fig. 4. Dimension[in mm]oftheinductoranalyzed.
ated for the m a g n e t i z a t i o n models p r o p o s e d by P o t t e r a n d Schmulian a n d by Jiles a n d A t h e r t o n . Hysteresis loops at 10 kHz calculated for T D K PC30, PC32, PC38 a n d PC40 ferrite materials were c o m p a r e d with those m e a s u r e d , a n d it was f o u n d that the d e p e n d e n c e of the reluctivity v on the flux density B is described satisfactorily by Jiles' model a n d dep e n d e n c e of t h e m a g n e t i c loss W is simulated well by Potter's. Flux a n d t e m p e r a t u r e in an i n d u c t o r m a d e from the above materials were analyzed simultaneously by F E M with the aid of v a n d W calculated from the models, a n d c o m p a r e d with those analyzed by using m e a s u r e d v a n d W. W h e n analysis was c o n d u c t e d with the aid of P o t t e r ' s m o d e l or of a hybrid model of Jiles' a n d Potter's, results a g r e e d well with those c o n d u c t e d by using m e a s u r e d v a n d W. T h e s e results suggest that flux a n d t e m p e r a t u r e distributions in a ferrite core can
4. Summary T h e validity of the s i m u l t a n e o u s analysis of flux a n d t e m p e r a t u r e distributions in ferrite cores was evaluTable 2 D averaged over 25-140°C Material Co-Amor. a PC30 PC32 PC38 PC40
Reluctivity
Magnetic loss
Potter
Jiles
Potter
Jiles
0.397 0.079 0.094 0.074 0.10
0.066 0.046 0.056 0.056 0.060
0.077 0.089 0.111 0.073 0.080
0.120 0.093 0.125 0.162 0.093
a Averaged between 25-100°C.
Table 3 Typical results of simultaneous FEM analysis of flux and temperature in PC30 and PC40 cores. The current density of the conductor was assumed to be 2 A / m m 2 Material
Used data
Max. B [T]
Ave. B [TI
Max. T [°C]
Min. T [°C]
PC30
Measured Potter Jiles Hybrid
0.342 0.309 0.342 0.310
0.098 0.099 0.097 0.099
37.2 37.6 37.2 37.6
29.5 29.6 29.5 29.5
PC40
Measured Potter Jiles Hybrid
0.305 0.300 0.306 0.315
0.099 0.099 0.098 0.098
34.0 36.5 43.2 36.5
27.8 27.3 32.6 29.0
H. Fukunaga et al. /Journal of Magnetism and Magnetic Materials 133 (1994) 516-519 b e analyzed from a small n u m b e r of m e a s u r e d data with the aid of a n a p p r o p r i a t e m a g n e t i z a t i o n model.
References [1] Y. Ohta, H. Kakehashi, M. Fukuhara and H. Fukunaga, Int. J. Appl. Electromagnetics 3 Suppl. (1992) 261.
519
[2] For instance, L.O. Chua and S.C. Bass, IEEE Trans. Circ. Theory 19 (1972) 36. [3] R.I. Potter and R.J. Schmulian, IEEE Trans. Magn. 7 (1971) 873. [4] D.C. Jiles and D.L. Atherton, J. Magn. Magn. Mater. 61 (1986) 48.
Journal of Magnetism and Magnetic Materials 133 (1994) 516-519
~
journalof magnetism
jR
and
, ~
materials
magnetic
Evaluation of magnetization models for simultaneous analysis of flux and temperature distributions in ferrite cores H. F u k u n a g a a,,, H. Abe a, y . O h t a b, H. Kakehashi b a Department of Electrical Engineering and Computer Science, Nagasaki University, Nagasaki 852, Japan b Matsushita Electric Works, Ltd., Kadoma, Osaka 571, Japan
Abstract The validity of simultaneous analysis of flux and temperature in ferrite cores operating at audio frequencies was evaluated for the magnetization models proposed by Potter and Schmulian and by Jiles and Atherton. It was found that Jiles' model describes the reluctivity vs. flux density characteristic satisfactorily and Potter's the magnetic loss vs. flux density characteristic. When flux and temperature in an inductor were analyzed with the aid of Potter's model or a hybrid model of Jiles' and Potter's, results agreed well with those analyzed by using the measured magnetic properties. These results suggest that flux and temperature in a ferrite core can be analyzed simultaneously from a small number of measured data with the aid of an appropriate magnetization model.
I. Introduction Ferrite cores in electronic devices are often used at high induction levels and then magnetic and joule losses increase their temperature. To clarify the characteristics of such devices, flux and temperature should be analyzed simultaneously by a method such as F E M (Finite Element Method) [1]. Thus huge amounts of information about magnetic properties should be measured in an expected temperature range and stored prior to analysis. This is a time consuming process when we have to analyze a variety of devices made from a variety of materials. Utilization of a simple magnetization model enables us to analyze flux and temperature simultaneously from a small number of measured data for materials. In addition, it will open out analysis combined with a circuit analysis tool such as SPICE. Among many magnetization models proposed previ-
ously [2], models suitable for our purpose are those in which parameters are independent from the magnitude of magnetization and are easily determined. The models proposed by Potter and Schmulian [3] and by Jiles and Atherton [4] are two of those meeting the requirements. Thus we evaluated their validity for the simultaneous analysis and confirmed that flux and temperature distributions in a ferrite core can be analyzed from a small number of experimental data with the aid of a magnetization model.
2. Magnetization model The model proposed by Potter and Schmulian includes three parameters (the saturation magnetization Ms, the ratio S of the remanence to M s, and the coercivity H c) to be determined from measured data. The magnitude of magnetization M in an applied field H is described by using these parameters as
/
[
HcHsgn°t
M = M s sgna-o~ l + t a n h |
* Corresponding author. Fax: + 81-958-46-7379; E-mail: [email protected]. 0304-8853/94/$07.00 © 1994 Elsevier Science B.V. All rights reserved SSDI 0304-8853(94)00197-Y
-Hc
tanh-lS
]/ (1)
H. Fukunaga et al. /Journal of Magnetism and Magnetic Materials 133 (1994) 516-519 where a is calculated from extreme values of H. The parameters were determined from a measured full M - H loop (10 kHz) at 25-140°C for a Co-based amorphous alloy and four kinds of ferrite materials (TDK PC30, PC32, PC38, and PC40). In the model proposed by Jiles and Atherton, M is given by dM
Man - M i r r = ( 1 c ) k 6 _ a ( M an_Mirr dH
dMan ) +C d H '
~'1 ~.
PC40, 40°C, 10kHz
•
Jiles' Model Potter's Model .......... Measured •
,~ /
lOOO
500
1000
500
°°o
i ,,
(2)
500
=
Man(H ) = Ms[COth{ ( H + a M ) / a }
500
517
-~
- a/(H + aM)],
i
~
. . . •. . . . . .• . . . . . -o. . . . . . . o. . .
:
.
•
41-
°-°'''""
(3) '
012 ' 014 Flux Density B ( T ) Fig. 2. Reluctivity calculated from Potter's and Jiles' models for PC40 at 40°C and l0 kHz together with that measured. 0
Mirr = ( M - cM, n ) / ( 1 - c),
(4)
where 8 is a parameter having the value +1 for d H / d t > 0 and d H / d t < 0, respectively. Five parameters (c, k, a, a, and M s) included were determined from measured Rayleigh and full loops.
The discrepancy D between a calculated quantity Qcal and the corresponding measured one Qmes is shown in Tables 1 and 2. D is defined as
3. Results a n d d i s c u s s i o n ,'0
In order to evaluate the validity of the models, hysteresis loops were calculated from the models, and compared with those measured at 10 kHz. Fig. 1 shows typical B - H loops at 40°C for PC40. It is seen that the magnetization curve by Potter's model reaches saturation faster than the measured curve. The minor loop coercivity by Jiles' model is larger than that measured. The reluctivity u and the magnetic loss W reflect these discrepancies as shown in Figs. 2 and 3. The u vs. B characteristic is described satisfactorily by Jiles' model but Potter's simulates the W vs. B characteristic well.
Measured
9B s
~
j
~
z
Qmes dB.
(5)
Flux and temperature distributions were analyzed simultaneously for the inductor shown in Fig. 4 by FEM with the aid of u and W at 10 kHz calculated from the models, and compared with those analyzed by using measured values. Typical results for PC30 and
[x 105]
/"
:/0.
::
9B s
PC40, 40°C, 10kHz
Jiles' Model 3 Potter's Model ......... Measured •
~'//
/
c0
3.2. Simultaneous analysis o f flux and temperature
~
-80
/Jo"
A similar tendency found in Figs. 2 and 3 was observed at almost all the temperatures and for all materials examined. Thus the tendency is expected to be common to soft ferrite materials used at audio frequencies.
A
-160
dB
[xl 05
0.5
Potter's Model
] Qcal - Qrnes ]
D= J0
3.1. Reluctivity and magnetic loss
t
I
I
80
I
I
160
H (A/m)
.o .j
•,,o, / /
2
. ~ ,'~ ¢'
2 •
•
.o C
q-'""
2 _~.=_~.
Jiles' Model
O-
-0.5 Fig. t. Hysteresis loops measured and calculated from Potter's and Jiles' models for PC40 at 40°C.
0.2 o.4 Flux Density B ( T ) Fig. 3. Magnetic loss calculated from Potter's and Jiles' models for PC40 at 40°C and 10 kHz together with that measured.
518
H. Fukunaga et aL /Journal of Magnetism and Magnetic Materials 133 (1994) 516-519
Table 1 Discrepancy D of Eq. (5) between magnetic quantities calculated and measured for PC38 Temp.
Reluctivity
[°C]
Potter
Jiles
Magnetic loss Potter
Jiles
25 40 60 80 100 120 140 Average
0.051 0.049 0.032 0.035 0.104 0.125 0.119 0.074
0.066 0.028 0.023 0.070 0.078 0.072 0.058 0.056
0.114 0.071 0.051 0.053 0.074 0.067 0.078 0.073
0.157 0.204 0.177 0.184 0.150 0.134 0.131 0.162
PC40 cores are shown in T a b l e 3. In the table, ' H y b r i d ' m e a n s t h a t v a n d W were calculated from Jiles' a n d P o t t e r ' s models, respectively. In the analysis c o n d u c t e d with the aid of Jiles' model, the m a x i m u m t e m p e r a t u r e in the PC40 core is m u c h h i g h e r t h a n t h a t analyzed by using m e a s u r e d data. A similar t e n d e n c y was o b s e r v e d for o t h e r materials, too. This discrepancy would be a t t r i b u t e d to the fact t h a t W calculated from Jiles' m o d e l is larger t h a n t h e m e a s u r e d W in the middle B region. O n the o t h e r h a n d , t h e results o b t a i n e d with the aid of P o t t e r ' s m o d e l or the hybrid m o d e l agree well with t h o s e o b t a i n e d by using m e a s u r e d v a n d W. T h e average discrepancies in the m a x i m u m t e m p e r a t u r e for four ferrite materials, which were o b t a i n e d u n d e r the same condition as that indicated in T a b l e 3, were 4.8%, 21.0% a n d 5.1% w h e n Potter's, Jiles', a n d the hybrid m o d e l s were used, respectively. T h e s e results suggest t h a t flux a n d t e m p e r a t u r e distributions in a ferrite core can b e analyzed simultaneously from a small n u m b e r of m e a s u r e d data with the aid of an a p p r o p r i a t e m a g n e t i z a t i o n model. A study to find a b e t t e r m a g n e t i z a t i o n model to m e e t o u r p u r p o s e is in progress.
I oore
~Conductor ~Insulator
Fig. 4. Dimension[in mm]oftheinductoranalyzed.
ated for the m a g n e t i z a t i o n models p r o p o s e d by P o t t e r a n d Schmulian a n d by Jiles a n d A t h e r t o n . Hysteresis loops at 10 kHz calculated for T D K PC30, PC32, PC38 a n d PC40 ferrite materials were c o m p a r e d with those m e a s u r e d , a n d it was f o u n d that the d e p e n d e n c e of the reluctivity v on the flux density B is described satisfactorily by Jiles' model a n d dep e n d e n c e of t h e m a g n e t i c loss W is simulated well by Potter's. Flux a n d t e m p e r a t u r e in an i n d u c t o r m a d e from the above materials were analyzed simultaneously by F E M with the aid of v a n d W calculated from the models, a n d c o m p a r e d with those analyzed by using m e a s u r e d v a n d W. W h e n analysis was c o n d u c t e d with the aid of P o t t e r ' s m o d e l or of a hybrid model of Jiles' a n d Potter's, results a g r e e d well with those c o n d u c t e d by using m e a s u r e d v a n d W. T h e s e results suggest that flux a n d t e m p e r a t u r e distributions in a ferrite core can
4. Summary T h e validity of the s i m u l t a n e o u s analysis of flux a n d t e m p e r a t u r e distributions in ferrite cores was evaluTable 2 D averaged over 25-140°C Material Co-Amor. a PC30 PC32 PC38 PC40
Reluctivity
Magnetic loss
Potter
Jiles
Potter
Jiles
0.397 0.079 0.094 0.074 0.10
0.066 0.046 0.056 0.056 0.060
0.077 0.089 0.111 0.073 0.080
0.120 0.093 0.125 0.162 0.093
a Averaged between 25-100°C.
Table 3 Typical results of simultaneous FEM analysis of flux and temperature in PC30 and PC40 cores. The current density of the conductor was assumed to be 2 A / m m 2 Material
Used data
Max. B [T]
Ave. B [TI
Max. T [°C]
Min. T [°C]
PC30
Measured Potter Jiles Hybrid
0.342 0.309 0.342 0.310
0.098 0.099 0.097 0.099
37.2 37.6 37.2 37.6
29.5 29.6 29.5 29.5
PC40
Measured Potter Jiles Hybrid
0.305 0.300 0.306 0.315
0.099 0.099 0.098 0.098
34.0 36.5 43.2 36.5
27.8 27.3 32.6 29.0
H. Fukunaga et al. /Journal of Magnetism and Magnetic Materials 133 (1994) 516-519 b e analyzed from a small n u m b e r of m e a s u r e d data with the aid of a n a p p r o p r i a t e m a g n e t i z a t i o n model.
References [1] Y. Ohta, H. Kakehashi, M. Fukuhara and H. Fukunaga, Int. J. Appl. Electromagnetics 3 Suppl. (1992) 261.
519
[2] For instance, L.O. Chua and S.C. Bass, IEEE Trans. Circ. Theory 19 (1972) 36. [3] R.I. Potter and R.J. Schmulian, IEEE Trans. Magn. 7 (1971) 873. [4] D.C. Jiles and D.L. Atherton, J. Magn. Magn. Mater. 61 (1986) 48.