IEC 60205:2001

INTERNATIONAL IEC
STANDARD
Second edition
2001-04
Calculation of the effective parameters
of magnetic piece parts
Calcul des paramètres effectifs des pièces
ferromagnétiques
Reference number
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INTERNATIONAL IEC
STANDARD
Second edition
2001-04
Calculation of the effective parameters
of magnetic piece parts
Calcul des paramètres effectifs des pièces
ferromagnétiques
 IEC 2001  Copyright - all rights reserved
No part of this publication may be reproduced or utilized in any form or by any means, electronic or
mechanical, including photocopying and microfilm, without permission in writing from the publisher.
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International Electrotechnical Commission
For price, see current catalogue

– 2 – 60205 © IEC:2001(E)
CONTENTS
Page
FOREWORD.3

Clause
1 Scope.4

2 Basic rules.4

3 Formulae for the various types of cores.5

3.1 Ring cores .5
3.2 Pair of U-cores of rectangular section .6
3.3 Pair of U-cores of rounded section.7
3.4 Pair of E-cores of rectangular section .8
3.5 Pair of ETD-cores .9
3.6 Pair of pot-cores .11
3.7 Pair of square cores (RM-cores) .13
3.8 Pair of EP-cores .16
3.9 Pair of PM-cores.18
Annex A (informative) Purpose of revision and how to deal with new effective
parameters .20
Bibliography .24
Table A.1 – Comparison of the effective parameter values of pot-cores (two slots) .21
Table A.2 – Comparison of the effective parameter values of ETD-cores .22
Table A.3 – Comparison of the effective parameter values of PM-cores .22
Table A.4 – Comparison of the effective parameter values of RM-cores.23

60205 © IEC:2001(E) – 3 –
INTERNATIONAL ELECTROTECHNICAL COMMISSION

____________
CALCULATION OF THE EFFECTIVE PARAMETERS

OF MAGNETIC PIECE PARTS
FOREWORD
1) The IEC (International Electrotechnical Commission) is a worldwide organization for standardization comprising

all national electrotechnical committees (IEC National Committees). The object of the IEC is to promote
international co-operation on all questions concerning standardization in the electrical and electronic fields. To
this end and in addition to other activities, the IEC publishes International Standards. Their preparation is
entrusted to technical committees; any IEC National Committee interested in the subject dealt with may
participate in this preparatory work. International, governmental and non-governmental organizations liaising
with the IEC also participate in this preparation. The IEC collaborates closely with the International Organization for
Standardization (ISO) in accordance with conditions determined by agreement between the two organizations.
2) The formal decisions or agreements of the IEC on technical matters express, as nearly as possible, an
international consensus of opinion on the relevant subjects since each technical committee has representation
from all interested National Committees.
3) The documents produced have the form of recommendations for international use and are published in the form
of standards, technical specifications, technical reports or guides and they are accepted by the National
Committees in that sense.
4) In order to promote international unification, IEC National Committees undertake to apply IEC International
Standards transparently to the maximum extent possible in their national and regional standards. Any
divergence between the IEC Standard and the corresponding national or regional standard shall be clearly
indicated in the latter.
5) The IEC provides no marking procedure to indicate its approval and cannot be rendered responsible for any
equipment declared to be in conformity with one of its standards.
6) Attention is drawn to the possibility that some of the elements of this International Standard may be the subject
of patent rights. The IEC shall not be held responsible for identifying any or all such patent rights.
International Standard IEC 60205 has been prepared by IEC technical committee 51: Magnetic
components and ferrite materials.
This second edition cancels and replaces the first edition published in 1966, amendment 1
(1976), amendment 2 (1981), first supplement (1968) and second supplement (1974). This
second edition constitutes a technical revision.
The text of this standard is based on the first edition, amendments 1 and 2, supplements A and
B and the following documents:
FDIS Report on voting
51/582/FDIS 51/594/RVD
Full information on the voting for the approval of this standard can be found in the report on
voting indicated in the above table.
This publication has been drafted in accordance with the ISO/IEC Directives, Part 3.
Annex A is for information only.
The committee has decided that the contents of this publication will remain unchanged until
2005. At this date, the publication will be
• reconfirmed;
• withdrawn;
• replaced by a revised edition, or
• amended.
A bilingual version of this publication may be issued at a later date.

– 4 – 60205 © IEC:2001(E)
CALCULATION OF THE EFFECTIVE PARAMETERS

OF MAGNETIC PIECE PARTS
1 Scope
This International Standard lays down uniform rules for the calculation of the effective
parameters of closed circuits of ferromagnetic material.

2 Basic rules
The following basic rules are applicable to this standard.
2.1 All results shall be expressed in units based on the millimetre and shall be accurate to
three significant figures, but to derive l , A , and V the values of C and C shall be calculated

e e e 1 2
to five significant figures.
NOTE The purpose of specifying this degree of accuracy is only to ensure that parameters calculated at different
establishments are identical, and it is not intended to imply that the parameters are capable of being determined to
this accuracy.
2.2 A is the nominal value of the smallest cross-section. All the dimensions used to
min
calculate A shall be the mean values between the tolerance limits quoted on the appropriate
min
piece part drawing.
2.3 Calculations are only applicable to the component parts of a closed magnetic circuit.
2.4 All dimensions used for the purpose of calculations shall be the mean value within the
tolerance limits quoted on the appropriate piece part drawing.
2.5 All irregularities in the outline of the core, such as small cut-outs, notches, chamfers, etc.
shall be ignored unless otherwise described.
2.6 When the calculation involves the sharp corner of a piece part, then the mean length of
flux path for that corner shall be taken as the mean circular path joining the centres of area of
the two adjacent uniform sections, and the cross-sectional area associated with that length
shall be taken as the average area of the two adjacent uniform sections.
Calculation of effective parameters l , A and V
e e e
The effective parameters can be defined as
2 3 2
l = C /C A = C /C V = l A = C /C
e 1 2    e 1 2    e e e 1 2
where
l is the effective magnetic length of the core (mm);
e
A is the effective cross-sectional area (mm );
e
V is the effective volume (mm );
e
–1
C is the core constant (mm );
–3
C is the core constant (mm ).
60205 © IEC:2001(E) – 5 –
3 Formulae for the various types of cores

3.1 Ring cores
X
α
d /2 d /2
1 1
d /2
β
d /2 d /2 d /2
2 2 2
r
0 r
4x
4x
r
ϕ
h h
h
X
Section X-X
IEC  345/01
2 π
C =
h ln()d d
e 1 2
4π()1 d − 1 d
2 1
C =
h ln()d d
e 1 2
3.1.1 For ring cores of rectangular cross-section with sharp corners
h = h
e
3.1.2 For ring cores of rectangular cross-section with an appreciable average rounding radius r
1,7168 r
h = h (1 – k )   k =
e 1
h()d − d
1 2
3.1.3 For ring cores of rectangular cross-section with sharp corners
h = h (1 – k )
e 2
h (tan α + tan β)
k =
d − d
1 2
3.1.4 For ring cores of trapezoidal cross-section with an appreciable average rounding radius r
h = (1 – k – k )
e 1 2
– 6 – 60205 © IEC:2001(E)
3.1.5 For ring cores of cross-section with circular arc frontal sides

d − d  ϕ sinϕ ϕ 
1 2
h = h − 2 sin − − 
e
ϕ 2 2 2
2  
4 sin
d − d
1 2
ϕ = 2arcsin ;
4r
ϕ, in radians.
NOTE When the winding is uniformly distributed over a ring core, it may be expected that, at all points inside the
ring core, the flux lines will be parallel to its surface.

No leakage flux will therefore leave or enter the ring core. This justifies the use of a theoretically more correct
derivation of the effective parameters which does not make use of the assumption that the flux is uniformly
distributed over the cross-section.
3.2 Pair of U-cores of rectangular section
l
q
l"
4 l'
X
A
Area
YY
h
A
Area
A
Area
Section Y-Y
X
l
l"
l'
Section X-X
IEC  346/01
Length of flux path associated with area A :
l = l′ + l″
2 2 2
Mean length of flux paths at corners:
π
l = l′ + l″ = (p + h)
4 4 4
π
l = l′ + l″ = (s + h)
5 5 5
Mean areas associated with l and l :
4 5
A + A
1 2
A =
A + A
2 3
A =
5 5
l l
i i
C =    C =
1 ∑ ∑
A
A
i
1 1 i
q
l"
l'
p
s
60205 © IEC:2001(E) – 7 –
3.3 Pair of U-cores of rounded section

p
l
l"
l'
X
A
Area
h
YY
A
Area
A
Area
Section Y-Y
X
l
l' s
l"
5 5
Section X-X
IEC  347/01
In calculating A , ignore any ridges introduced for the purpose of facilitating manufacture.

Length of flux path associated with area A :
l = l′ + l″
2 2 2
Mean length of flux path at corners:
π
l = l′ + l″ = (p + h)
4 4 4
π
l = l′ + l″ = (s + h)
5 5 5
Mean areas associated with l and l :
4 5
A + A
1 2
A =
A + A
2 3
A =
5 5
l l
i
i
C =    C =
1 ∑ ∑
A
A
i
1 i
s
l"
l'
– 8 – 60205 © IEC:2001(E)
3.4 Pair of E-cores of rectangular section

l
w
l
X
A
Area
Y
Y
A
l
h 3
Area
A
Area
l
A
Area
A
Area
Section Y-Y
X
Section X-X
IEC  348/01
Area of half the centre limb: A
Mean length of flux paths at corners:
π
l = (p + h)
π  d 
l = + h
 
8 2
 
Mean areas associated with l and l :
4 5
+
A A
1 2
A =
A + A
2 3
A =
5 5
l l
i i
C =    C =
1 ∑ 2 ∑
A
2A
i
1 1 i
w
l
p
d / 2
60205 © IEC:2001(E) – 9 –
3.5 Pair of ETD-cores
l
b
X l
A
c
Y
Y Area
A'
Area
l
h A"
Area
A
l
Area
A
Area
A
Area
Section Y-Y
X
Section X-X
IEC  349/01
 1 
A is equal to the rectangle b  a − c less the cap or segment A
1 c
 
 
1 b 1
2 2
 
A = d arcsin − b d − b
c 2 2
 
4 d 4
 
 
1 1 1 b
2 2
 
A = ab − b d − b − d arcsin
1 2 2
 
2 4 4 d
 
Mean length of flux path at back walls:
1   d
2 2 3
=  + −
l d d b  −
2 2 2
 
4 2
 
NOTE  l is taken from the mean value of ()d − d and ()C − d /2 .
2 2 3 3
Area of half the centre limb:
A = A′ + A″
3 3 3
The condition to obtain
...