IEC 60205:2006

IEC 60205 ®
Edition 3.0 2006-04
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
Calculation of the effective parameters of magnetic piece parts

Calcul des paramètres effectifs des pièces magnétiques

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IEC 60205 ®
Edition 3.0 2006-04
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
Calculation of the effective parameters of magnetic piece parts

Calcul des paramètres effectifs des pièces magnétiques

INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
COMMISSION
ELECTROTECHNIQUE
PRICE CODE
INTERNATIONALE
U
CODE PRIX
ICS 29.100.10 ISBN 978-2-88910-071-2
– 2 – 60205 © IEC:2006
CONTENTS
FOREWORD.0H3
1 Scope.1H5
2 Basic rules.2H5
3 Formulae for the various types of cores.3H6
3.1 Ring cores .4H6
3.2 Pair of U-cores of rectangular section .5H7
3.3 Pair of U-cores of rounded section.6H7
3.4 Pair of E-cores of rectangular section .7H9
3.5 Pair of ETD/EER-cores .8H10
3.6 Pair of pot-cores .9H11
3.7 Pair of RM-cores .10H13
3.8 Pair of EP-cores .11H16
3.9 Pair of PM-cores.12H17
3.10 Pair of EL-cores.13H19
3.11 Pair of ER-cores (low profile) .14H21
3.12 Pair of PQ-cores.15H23
3.13 Pair of EFD-cores .16H25
3.14 Pair of E planar-cores .17H26
Annex A (informative) Purpose of revision .18H29

60205 © IEC:2006 – 3 –
INTERNATIONAL ELECTROTECHNICAL COMMISSION
___________
CALCULATION OF THE EFFECTIVE PARAMETERS
OF MAGNETIC PIECE PARTS
FOREWORD
1) The International Electrotechnical Commission (IEC) is a worldwide organization for standardization comprising
all national electrotechnical committees (IEC National Committees). The object of the IEC is to promote
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International Standard IEC 60205 has been prepared by IEC technical committee 51: Magnetic
components and ferrite materials.
This third edition cancels and replaces the second edition published in 2001, corrigendum 1
(2001). This edition constitutes a technical revision.
This edition includes the following significant technical changes with respect to the previous
edition:
a) unit of angles through the text are described by using “radian”;
b) new words are added in 2.1 “All angles are in radians”;
l ln d g / d ln d g / d
l
2 2 3 2 2 3
c) replacement, Clause 3.9, of the equation = by = ;
A Dπ()h − h A Dπ()h − h / 2
2 1 2 2 1 2
d) new cores “EL, ER, PQ, EFD and E planar” are added in this edition.

– 4 – 60205 © IEC:2006
This bilingual version, published in 2009-01, corresponds to the English version.
The text of this standard is based on the following documents:
FDIS Report on voting
51/848/FDIS 51/857/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.
The French version of this standard has not been voted upon.
This publication has been drafted in accordance with the ISO/IEC Directives, Part 2.
The committee has decided that the contents of this publication will remain unchanged until the
maintenance result date indicated on the IEC web site under "http://webstore.iec.ch" in the data
related to the specific publication. At this date, the publication will be
• reconfirmed;
• withdrawn;
• replaced by a revised edition, or
• amended.
60205 © IEC:2006 – 5 –
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, shall be accurate to three
significant figures, but to derive l , A , and V the values of C and C shall be calculated to
e e e 1 2
five significant figures. All angles are in radians.
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 ).
– 6 – 60205 © IEC:2006
3 Formulae for the various types of cores
3.1 Ring cores
X
α
β
r
r
4×
4×
r
ϕ
h h h
X
Section X-X
IEC  584/06
2π
C =
h ln()d / d
e 1 2
4π()1/ d −1/ d
2 1
C =
2 3
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
1,7168r
h = h()1− k k =
e 1 1
h()d − d
1 2
3.1.3 For ring cores of trapezoidal cross-section with sharp corners
h()tanα + tan β
h = h()1− k k =
e 2 2
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
3.1.5 For ring cores of cross-section with circular arc frontal sides
d − d ϕ sinϕ ϕ
⎛ ⎞
1 2
h = h − 2sin − −
⎜ ⎟
e 2
4sin()ϕ / 2 2 2 2
⎝ ⎠
d /2
d /2
d /2
d /2
60205 © IEC:2006 – 7 –
d − d
1 2
ϕ = 2arcsin .
4r
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
NOTE U + PLT (Plate)-cores use U core formulas.

q
l
l″ l′
4 4
X
A
Area
h
Y Y
A
Area
A
Area
l″ l′
5 5
X
Section Y-Y
l
Section X-X
IEC  585/06
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 ∑ 2 ∑ 2
A
A
= =
i 1 i i 1
i
3.3 Pair of U-cores of rounded section
NOTE U + PLT (Plate)-cores use U core formulas.

q
l″
l′
s p
– 8 – 60205 © IEC:2006
l
p
l″ X
4 l′
A
Area
h
Y Y
A
Area
A
Area
l′
Section Y-Y
l″
5 X
s
l
Section X-X
IEC  586/06
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 ∑ 2 ∑ 2
A A
i=1 i=1
i i
s
l″
l′
60205 © IEC:2006 – 9 –
3.4 Pair of E-cores of rectangular section
NOTE E + I (Plate)-cores use E core formulas.
w
l
X
l
A
Area
Y Y
A
Area
l
h
A
l
Area
A
Area
A
Area
Section Y-Y
X
Section X-X
IEC  587/06
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 2
A 2A
i=1 i=1
i i
w
l
p
d /2
– 10 – 60205 © IEC:2006
3.5 Pair of ETD/EER-cores
b
X l
l
A
c
Area
Y Y
A′
Area
A″
l 3
Area
h
l
5 A
Area
A
Area
A
Area
Section Y-Y
X
Section X-X
IEC  588/06
⎛ ⎞
A1 is equal to the rectangle b a c A .
⎜ − ⎟ less the cap or segment
c
⎝ ⎠
⎛ ⎞
1 b 1
2 2
⎜ ⎟
A = d arcsin − b d − b
C 2 2
⎜ ⎟
4 d 4
⎝ 2⎠
⎛ ⎞
1 1 1 b
2 2
⎜ ⎟
A = ab − b d − b − d arcsin
1 2 2
⎜ ⎟
2 4 4 d
⎝ 2⎠
Mean length of flux path at back walls:
1 d
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 3 3
Area of half the centre limb:
A = A′ + A′′
3 3 3
The condition to obtain A′ = A′′ is
3 3
S = 0,2980d
1 3
Mean length of flux path at corners:
π
l =()p + h
a d
where p = − l −
2 2
b
l
a
d
c
d /2
S
1 p
60205 © IEC:2006 – 11 –
π
l =()2S + h
5 1
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 i=1
i i
3.6 Pair of pot-cores
l
h
a
l′
A″
X l″
Area
A′
Area
A
d /2
1 Area
l
d /2
A
4 6
Area
l″ l′
5 5
d /2
d /2
A″
Area
A′
Area
X
Section X-X
IEC  589/06
Area of outer ring:
′ ′′
A = A + A
1 1 1
′ ′′
The condition to obtain A = A is
1 1
d
2 2
S = − +()d + d
1 1 2
2 8
Area of centre limb:
′ ′′
A = A + A
3 3 3
′ ′′
The condition to obtain A = A is
3 3
d 1
2 2
S = −()d + d
2 3 4
2 8
b
θ
l″
l″
2 6
s
s 1
l′ l′
2 6
– 12 – 60205 © IEC:2006
Area of ring:
2 2
A =()π − nθ()d − d
1 1 2
2b
θ = arcsin
d + d
1 2
where
b is the slot width;
n is the number of slots.
Core factors associated with l :
l 1 a
= ln
A πh d
2 3
l a − d
2 3
=
2 2 2
A π ad h
2 3
Area of centre limb:
π
2 2
A =()d − d
3 3 4
Mean length of flux paths at corners:
π
l = l′ + l′′ =()2S + h
4 4 4 1
π
l = l′ + l′′ =()2S + h
5 5 5 2
Areas associated with l and l :
4 5
1 π
2 2
A =()π − nθ()d − d + d h
4 1 2 2
8 2
π 2 2
A =()d − d + 4d h
5 3 4 3
Core factors associated with l :
l 1 d
6 2
= ln
A()π − nθ h a
l d − a
6 2
=
A ad()π − nθ h
6 2
6 6
l l
i i
C = C =
∑ ∑
1 2
A
A
i=1 i=1
i
i
60205 © IEC:2006 – 13 –
3.7 Pair of RM-cores
NOTE 1 This calculation is also applicable to the core type without hole.
NOTE 2 RM + I (Plate)-cores use RM core formulas.

Type 1 – RM6–S, RM6–R
l′
A 4
8 l″
X
p
ϕ
l
min
l
A
A
β
d /2
l″
l′
d /2 5
l
max
d /2
e
X
l h
c
A /2
Section X-X
Type 2 – RM7
A
X
p ϕ
l
min
A
A
d /2
β
d /2
l
max
d /2
b
e
X
c
A /2
Type 3 – RM4, RM5, RM8, RM10, RM12, RM14
A
p ϕ
A
l A
min 3
l′
max
d /2
β 4
l″ d /2
max 3
d /2
e
c
A /2
l l′ l″
max = max + max
IEC  590/06
α
α
α
a
a
a
l″
l′
– 14 – 60205 © IEC:2006
Total area of the outer leg:
⎧ ⎫
1 ⎛ π⎞ β 2 1
2 2
A = a 1+ tan β − − d − p
⎜ ⎟
⎨ ⎬
1 2
2 4 2 2
⎝ ⎠
⎩ ⎭
e
where β = α − arcsin
d
Core factors associated with l :
d
ln f
l d
2 3
=
A Dπh
A
l min+ l max
where f = , D =
2l min
A
′ ′′
l = l + l
2 2 2
l()1 d −1 d f
2 3 2
=
2 2
π
A ()D h
Type 1:
1 1
2 2
l =()d + d − d d cos()α − β
max 2 3 2 3
4 2
Type 2:
1 1 b
⎛ ⎞
l = d + d − d d ()− −
⎜ ⎟ cos α β
max 2 2 3
4 2 ϕ
⎝ ⎠
2sin
Type 3:
ϕ
e 1⎛ ⎞
l = + 1− sin ()d − c
⎜ ⎟
max 2
2 2 2
⎝ ⎠
Type 1: RM 6-S:
1⎧ β 1 1 ϕ π ⎫
2 ⎛ ⎞ 2
2 2
A = d + e tan β − e tan α − − d
⎜ ⎟
⎨ ⎬
7 2 3
4 2 2 2 2 4
⎝ ⎠
⎩ ⎭
60205 © IEC:2006 – 15 –
Type 1: RM 6-R:
1⎧ β 1 1 ϕ π ⎫
2 2 2
A = d + d d sin()α − β +()c − d tan − d
⎨ ⎬
7 2 2 3 3 3
4 2 2 2 2 4
⎩ ⎭
Type 2:
1⎧ β π 1 ϕ 1 ⎫
2 2 ⎛ ⎞
2 2 2
A = d − d +()b − e tan α − + e tan β
⎜ ⎟
⎨ ⎬
7 2 3
4 2 4 2 2 2
⎝ ⎠
⎩ ⎭
Type 3:
1 β π 1
⎧ 2 2 ⎫
A = d − d + c tan()α − β
⎨ ⎬
7 2 3
4 2 4 2
⎩ ⎭
α
2 2
A =()d − d
8 2 3
Area of centre pole:
π
2 2
A =()d − d
3 3 4
Mean length of flux paths at corners and mean areas associated with these:
π 1 1
⎛ ⎞
l l′ l′′ h a d
= + = + −
⎜ ⎟
4 4 4 2
4 2 2
⎝ ⎠
A =()A + 2βd h
4 1 2
⎧ ⎫
π 1
2 2
l = l′ + l′′ = d + h −()d + d
⎨ ⎬
5 5 5 3 3 4
4 2
⎩ ⎭
1 π
⎧ 2 2 ⎫
A = ()d − d + 2αd h
⎨ ⎬
5 3 4 3
2 4
⎩ ⎭
5 5
l l
i i
C = C =
1 ∑ 2 ∑
A
A
i=1 i=1
i
i
NOTE This calculation ignores the effect of spring recesses and stud recesses. These may have some influence
on the outcome of the calculation, especially for smaller cores.

– 16 – 60205 © IEC:2006
3.8 Pair of EP-cores
l
b l″
l′ 1 4
X
A
l
d /2
α
d /2
l″
l′
5 5
A
h
c
h
X
Section X-X
IEC  591/06
As a pair:
l h
1 2
=
A
ab −πd / 8 − d d / 2
1 1 2
l h
1 2
=
2 2
A
()ab −πd / 8 − d d / 2
1 1 2
l 2 d
2 1
= ln
A ()π −α(h − h) d
2 1 2 2
l 4()d − d
2 1 2
=
2 2 2
A ()π −α(h − h) d d
2 1 2 1 2
4h
l h
3 2
= =
2 2
A
πd
d
3 ⎛ ⎞
π
⎜ ⎟
⎝ ⎠
16h
l h
3 2
= =
2 4 4
A
d π d
⎛ ⎞
3 2
2 2
π
⎜ ⎟
⎝ ⎠
Areas associated with l and l :
4 5
a
l′
l″
60205 © IEC:2006 – 17 –
π d h − h
⎛ ⎞
1 1 2
′ ′′
l = l + l = ⎜γ − + ⎟
4 4 4
2 2 4
⎝ ⎠
2 2
()π −α d + 2()ab −πd /8 − d d / 2
1 1 1 2
γ =
4()π −α
where γ is a hypothetical radius bisecting the cross-sectional area of the ring.
1⎧ π d d h h ⎫
⎛ ⎞
1 2 1 2
A = ab − d − +()π −α d −
⎜ ⎟
⎨ ⎬
4 1 1
2 8 2 2 2
⎝ ⎠
⎩ ⎭
π d h − h
⎛ ⎞
2 1 2
′ ′′
l = l + l = 0,29289 +
⎜ ⎟
5 5 5
2 2 4
⎝ ⎠
⎧ ⎫
π d d
2 2
A = + ()h − h
⎨ ⎬
5 1 2
2 4 2
⎩ ⎭
5 5
l l
i i
C = C =
1 ∑ 2 ∑
A
A
i=1 i=1
i
i
3.9 Pair of PM-cores
c
l″
l 4
l′
b 4 1
X
e
l
d
ϕ
l
max
l″
l′
β
d
A
A
α
h
X
h
Section X-X
IEC  592/06
Total area of the leg:
β
2 2
A =()d − d − 2bt
1 1 2
l
min
t
ƒ
l′
l″
d
d
d
– 18 – 60205 © IEC:2006
f
where β = α − arcsin
d
Core factors associated with l :
l = l′ + l′′
2 2 2
d
ln g
l d
2 3
=
A Dπ()h − h / 2
2 1 2
l min+ l max A
where g = , D =
2l min A
1 1
2 2
l =()d + d − d d cos()α − β
max 2 3 2 3
4 2
l ()1 d −1 d g
2 3 2
=
2 2
A{}Dπ()h − h 2
2 1 2
β 1 1 ϕ π
2 ⎛ ⎞ 2
2 2
A = d + f tan β − f tan α − − d
⎜ ⎟
7 2 3
8 2 16
8 8
⎝ ⎠
α
2 2
A =()d − d
8 2 3
Area of centre limb:
π
2 2
()
A = d − d
3 3 4
Mean length of flux paths at corners and mean areas associated with these:
π
′ ′′
l = l + l =()h − h + d − d
4 4 4 1 2 1 2
A ={}A + 2βd()h − h
4 1 2 1 2
⎧ ⎫
π 1
2 2
′ ′′
l = l + l = d + h − h −()d + d
⎨ ⎬
5 5 5 3 1 2 3 4
4 2
⎩ ⎭
π
2 2
A =()d − d +αd()h − h
5 3 4 3 1 2
60205 © IEC:2006 – 19 –
5 5
l l
i i
C = C =
∑ ∑
1 2
A
A
i=1 i=1
i
i
3.10 Pair of EL-cores
NOTE EL + PLT (Plate)-cores use EL core formulas.

C B
l
D
F
l
l
l
R
IEC  593/06
Area of outer leg:
1 1
⎛ ⎞
2 2
A =()A − E C − 4 R − πR
⎜ ⎟
2 4
⎝ ⎠
Mean length of flux path at outer leg:
l = D
Area of back wall:
A =()C +()F − F + πF /2(B − D)
2 2 1 1
Mean length of flux at back wall:
E F
⎛ ⎞
l = − ⎟
⎜
2 2
⎝ ⎠
Area of centre limb:
1⎧ 1 ⎫
A = πF +()F − F F
3 ⎨ 1 2 1 1⎬
2 4
⎩ ⎭
Mean length of flux path at centre limb:
l = D
F
H
E
A
l
– 20 – 60205 © IEC:2006
Area of outside corner:
A + A
1 21
A =
where A = (B – D)C
Mean length of flux path at outside corner:
π⎛ A E ⎞
⎛ ⎞
l = − +()B − D
⎜⎜ ⎟ ⎟
8 2 2
⎝ ⎠
⎝ ⎠
Area of inside corner:
A + A
23 3
A =
where A =()()F −F + πF /2(B − D)
23 2 1 1
Mean length of flux path at inside corner:
π⎛ A ⎞
⎜ ⎟
l = +()B − D
⎜ ⎟
8 F
⎝ 2 ⎠
5 5
l l
i i
C = C =
1 ∑ 2 ∑
A
2A
i= i=
1 i 1
i
2 3 2
l = C /C A = C /C V = C /C
e 1 2 e 1 2 e 1 2
60205 © IEC:2006 – 21 –
3.11 Pair of ER-cores (low profile)
NOTE ER + PLT (Plate)-cores use ER core formulas.

B
l
C
D
l
l
l
β A
A′
A″
α
A
IEC  594/06
Area of outer leg:
⎛ ⎞
1 αE EG
A = C()A −G −⎜ − sinα⎟
⎜ ⎟
2 4 4
⎝ ⎠
where α = arccos (G/E)
Mean length of flux path at outer leg:
l = D
Area of back wall:
= C(B – D)
A
Mean length of flux path at back wall:
2 2
l =()E + G + C − 2F
Area of centre limb:
G
F
E
A
S
l
– 22 – 60205 © IEC:2006
1 1
⎛ ⎞
A = πF
⎜ ⎟
2 4
⎝ ⎠
Mean length of flux path at centre limb:
l = D
Area of outside corner:
A + A
1 2
A =
Mean length of flux path at outside corner:
π
l =()p + h
where
A E
h = B − D p = −
2 2
Area of inside corner:
A + A
2 3
A =
Mean length of flux path at inside corner:
π
l =()2S + h
5 1
The condition to obtain A′ = A″ is
3 3
S = F()1− sinα = 0,2978F
5 5
l l
i i
C = C =
1 ∑ 2 ∑
A
2A
i=1 i=1
i
i
2 3 2
l = C /C A = C /C V = C /C
e 1 2 e 1 2 e 1 2
60205 © IEC:2006 – 23 –
3.12 Pair of PQ-cores
NOTE 1 This calculation ignores the effect of spring recesses.
NOTE 2 PQ + PLT (Plate)-cores use PQ core formulas.

l′
X 4
l″
A A
7 8
α
β
l
l
max
l′
l″ 5
A
A /2
X
D
l
1 h
C
B
Section X-X
IEC  595/06
Area of outer leg:
βE EG
A = C()A −G − + sin β
2 2
where β = arccos (G/E)
Mean length of flux path at outer leg:
l = 2D
Core factors associated with l :
l
ln()E/F
= f
A Kπ()B − D
l
1/F −1/E
= f
2 2
2 2
A
2K π()B − D
where
A A
7 7
K = =
π
A 2 2
()E − F
l + l
min max
f =
2l
min
NOTE 3 l may be determined by measurement.
max
A
l
min
G
F
E
l″
l′
– 24 – 60205 © IEC:2006
Area of centre limb:
A = πF
Mean length of flux path at centre limb:
l = 2D
Area of outside corner:
A ={}A + 2E()B − D β
4 1
Mean length of flux path at outside corner:
π 1 1
⎛ ⎞
l = l′ + l′′ = B − D + A − E
⎜ ⎟
4 4 4
4 2 2
⎝ ⎠
Area of inside corner:
π F
⎛ ⎞
A = + F()B − D α
⎜ ⎟
2 2
⎝ ⎠
NOTE 4 α in radian, may be determined by measurement.
Mean length off flux path at inside corner:
π ⎧ ⎛ 1 ⎞ ⎫
′ ′′
l = l + l = ()B − D +⎜1− ⎟F
5 5 5 ⎨ ⎬
⎜ ⎟
⎩ ⎝ ⎠ ⎭
l l
i i
C = C =
1 ∑ 2 ∑
A
A
i=1 i=1
i
i
2 3 2
l = C /C A = C /C V = C /C
e 1 2 e 1 2 e 1 2
60205 © IEC:2006 – 25 –
3.13 Pair of EFD-cores
C
B
K
l
F
D
l
l
l
IEC  596/06
Area of outer leg:
C()A − E
A =
Mean length of flux path at outer leg:
l = D
Area of back wall:
A = C()B − D
Mean length of flux at back wall:
E − F
l =
Area of centre limb:
F F − 2q
1 2
A =
where q: chamfer
Mean length of flux path at centre limb:
l = D
Area of out side corner:
F
E
A
q
l
– 26 – 60205 © IEC:2006
()A + A
1 2
A =
Mean length of flux path at outside corner:
π A − E
⎛ ⎞
l = +()B − D
⎜ ⎟
8 2
⎝ ⎠
Area of inside corner:
A + A
2 3
A =
Mean length of flux path at inside corner:
2 2
⎛ ⎞
π F C − F − 2K B − D
⎛ ⎞ ⎛ ⎞
⎜ 1 2 ⎟
l = + ⎟ +
⎜ ⎜ ⎟
⎜ ⎟
4 4 2 2
⎝ ⎠
⎝ ⎠
⎝ ⎠
5 5
l l
i i
C = C =
∑ ∑
1 2
A 2A
i=1 i=1
i i
2 3
C C C
1 1 1
l = A = V =
e e e 2
C C C
2 2 2
3.14 Pair of E planar-cores
NOTE E planar + PLT (Plate)-cores use E planar core formulas.

B
C
l
D
l
R
l
R
l
IEC  597/06
Area of outer leg:
F
E
A
l
60205 © IEC:2006 – 27 –
C()A − E π
⎛ ⎞
2 2
A = − 4 R − × R
⎜ ⎟
1 1 1
2 4
⎝ ⎠
Mean length of flux path at outer leg:
l = D
Area of back wall:
A = C()B − D
Mean length of flux at back wall:
E − F
l =
Area of centre limb:
π
⎛ ⎞
2 2
A = FC − 2 R − × R
⎜ ⎟
3 2 2
⎝ ⎠
Mean length of flux path at centre limb:
l = D
Area of outside corner:
A + A
1 2
A =
Mean length of flux path at outside corner:
...

IEC 60205 ®
Edition 3.1 2009-08
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
Calculation of the effective parameters of magnetic piece parts

Calcul des paramètres effectifs des pièces magnétiques
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IEC 60205 ®
Edition 3.1 2009-08
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
Calculation of the effective parameters of magnetic piece parts

Calcul des paramètres effectifs des pièces magnétiques

INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
COMMISSION
ELECTROTECHNIQUE
PRICE CODE
INTERNATIONALE
CL
CODE PRIX
ICS 29.100.10 ISBN 978-2-88910-073-6
– 2 – 60205 © IEC:2006+A1:2009
CONTENTS
FOREWORD.3
1 Scope.5
2 Basic rules.5
3 Formulae for the various types of cores.6
3.1 Ring cores .6
3.2 Pair of U-cores of rectangular section .7
3.3 Pair of U-cores of rounded section.7
3.4 Pair of E-cores of rectangular section .9
3.5 Pair of ETD/EER-cores .10
3.6 Pair of pot-cores .11
3.7 Pair of RM-cores .13
3.8 Pair of EP-cores .16
3.9 Pair of PM-cores.17
3.10 Pair of EL-cores.19
3.11 Pair of ER-cores (low profile) .21
3.12 Pair of PQ-cores.23
3.13 Pair of EFD-cores .26
3.14 Pair of E planar-cores .27

Annex A (informative) Purpose of revision .30

60205 © IEC:2006+A1:2009 – 3 –
INTERNATIONAL ELECTROTECHNICAL COMMISSION
___________
CALCULATION OF THE EFFECTIVE PARAMETERS
OF MAGNETIC PIECE PARTS
FOREWORD
1) The International Electrotechnical Commission (IEC) 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, IEC publishes International Standards, Technical Specifications,
Technical Reports, Publicly Available Specifications (PAS) and Guides (hereafter referred to as “IEC
Publication(s)“). 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. 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 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 IEC National Committees.
3) IEC Publications have the form of recommendations for international use and are accepted by IEC National
Committees in that sense. While all reasonable efforts are made to ensure that the technical content of IEC
Publications is accurate, IEC cannot be held responsible for the way in which they are used or for any
misinterpretation by any end user.
4) In order to promote international uniformity, IEC National Committees undertake to apply IEC Publications
transparently to the maximum extent possible in their national and regional publications. Any divergence
between any IEC Publication and the corresponding national or regional publication shall be clearly indicated in
the latter.
5) IEC provides no marking procedure to indicate its approval and cannot be rendered responsible for any
equipment declared to be in conformity with an IEC Publication.
6) All users should ensure that they have the latest edition of this publication.
7) No liability shall attach to IEC or its directors, employees, servants or agents including individual experts and
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8) Attention is drawn to the Normative references cited in this publication. Use of the referenced publications is
indispensable for the correct application of this publication.
9) Attention is drawn to the possibility that some of the elements of this IEC Publication may be the subject of
patent rights. 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 consolidated version of IEC 60205 consists of the third edition (2006) [documents
51/848/FDIS and 51/857/RVD] and its amendment 1 (2009) [documents 51/928A/CDV and
51/940/RVC].
The technical content is therefore identical to the base edition and its amendment and has
been prepared for user convenience.
It bears the edition number 3.1.
A vertical line in the margin shows where the base publication has been modified by
amendment 1.
The French version of this standard has not been voted upon.

– 4 – 60205 © IEC:2006+A1:2009
This edition includes the following significant technical changes with respect to the previous
edition:
a) unit of angles through the text are described by using “radian”;
b) new words are added in 2.1 “All angles are in radians”;
l ln d g / d ln d g / d
l
2 2 3 2 2 3
c) replacement, Clause 3.9, of the equation = by = ;
A Dπ()h − h A Dπ()h − h / 2
2 1 2 2 1 2
d) new cores “EL, ER, PQ, EFD and E planar” are added in this edition.
This publication has been drafted in accordance with the ISO/IEC Directives, Part 2.
The committee has decided that the contents of the base publication and its amendments will
remain unchanged until the maintenance result date indicated on the IEC web site under
"http://webstore.iec.ch" in the data related to the specific publication. At this date,
the publication will be
• reconfirmed,
• withdrawn,
• replaced by a revised edition, or
• amended.
60205 © IEC:2006+A1:2009 – 5 –
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, shall be accurate to three
significant figures, but to derive l , A , and V the values of C and C shall be calculated to
e e e 1 2
five significant figures. All angles are in radians.
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 ).
– 6 – 60205 © IEC:2006+A1:2009
3 Formulae for the various types of cores
3.1 Ring cores
X
α
β
r
r
4×
4×
r
ϕ
h h h
X
Section X-X
IEC  584/06
2π
C =
h ln()d / d
e 1 2
4π()1/ d −1/ d
2 1
C =
2 3
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
1,7168r
h = h()1− k k =
e 1 1
h()d − d
1 2
3.1.3 For ring cores of trapezoidal cross-section with sharp corners
h()tanα + tan β
h = h()1− k k =
e 2 2
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
3.1.5 For ring cores of cross-section with circular arc frontal sides
d − d ϕ sinϕ ϕ
⎛ ⎞
1 2
h = h − 2sin − −
⎜ ⎟
e 2
4sin()ϕ / 2 2 2 2
⎝ ⎠
d /2
d /2
d /2
d /2
60205 © IEC:2006+A1:2009 – 7 –
d − d
1 2
ϕ = 2arcsin .
4r
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
NOTE U + PLT (Plate)-cores use U core formulas.

q
l
l″ l′
4 4
X
A
Area
h
Y Y
A
Area
A
Area
l″ l′
5 5
X
Section Y-Y
l
Section X-X
IEC  585/06
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 ∑ 2 ∑ 2
A
A
= =
i 1 i i 1
i
3.3 Pair of U-cores of rounded section
NOTE U + PLT (Plate)-cores use U core formulas.

q
l″
l′
s p
– 8 – 60205 © IEC:2006+A1:2009

l
p
l″ X
4 l′
A
Area
h
Y Y
A
Area
A
Area
l′
Section Y-Y
l″
5 X
s
l
Section X-X
IEC  586/06
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 ∑ 2 ∑ 2
A A
i=1 i=1
i i
s
l″
l′
60205 © IEC:2006+A1:2009 – 9 –
3.4 Pair of E-cores of rectangular section
NOTE E + I (Plate)-cores use E core formulas.
w
l
X
l
A
Area
Y Y
A
Area
l
h
A
l
Area
A
Area
A
Area
Section Y-Y
X
Section X-X
IEC  587/06
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 2
A 2A
i=1 i=1
i i
w
l
p
d /2
– 10 – 60205 © IEC:2006+A1:2009
3.5 Pair of ETD/EER-cores
b
X l
l
A
c
Area
Y Y
A′
Area
A″
l 3
Area
h
l
5 A
Area
A
Area
A
Area
Section Y-Y
X
Section X-X
IEC  588/06
⎛ ⎞
A1 is equal to the rectangle b a c A .
⎜ − ⎟ less the cap or segment
c
⎝ ⎠
⎛ ⎞
1 b 1
2 2
⎜ ⎟
A = d arcsin − b d − b
C 2 2
⎜ ⎟
4 d 4
⎝ 2 ⎠
⎛ ⎞
1 1 1 b
2 2
⎜ ⎟
A = ab − b d − b − d arcsin
1 2 2
⎜ ⎟
2 4 4 d
⎝ 2 ⎠
Mean length of flux path at back walls:
1 d
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 3 3
Area of half the centre limb:
A = A′ + A′′
3 3 3
The condition to obtain A′ = A′′ is
3 3
S = 0,2980d
1 3
Mean length of flux path at corners:
π
l =()p + h
a d
where p = − l −
2 2
b
l
a
d
c
d /2
S
1 p
60205 © IEC:2006+A1:2009 – 11 –
π
l =()2S + h
5 1
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 i=1
i i
3.6 Pair of pot-cores
l
h
a
l′
A″
X l″
Area
A′
Area
A
d /2
1 Area
l
d /2
A
4 6
Area
l″ l′
5 5
d /2
d /2
A″
Area
A′
Area
X
Section X-X
IEC  589/06
Area of outer ring:
′ ′′
A = A + A
1 1 1
′ ′′
The condition to obtain A = A is
1 1
d
2 2
S = − +()d + d
1 1 2
2 8
Area of centre limb:
′ ′′
A = A + A
3 3 3
′ ′′
The condition to obtain A = A is
3 3
d 1
2 2
S = −()d + d
2 3 4
2 8
b
θ
l″
l″
2 6
s
s 1
l′ l′
2 6
– 12 – 60205 © IEC:2006+A1:2009
Area of ring:
2 2
A =()π − nθ()d − d
1 1 2
2b
θ = arcsin
d + d
1 2
where
b is the slot width;
n is the number of slots.
Core factors associated with l :
l 1 a
= ln
A πh d
2 3
l a − d
2 3
=
2 2 2
A π ad h
2 3
Area of centre limb:
π
2 2
A =()d − d
3 3 4
Mean length of flux paths at corners:
π
l = l′ + l′′ =()2S + h
4 4 4 1
π
l = l′ + l′′ =()2S + h
5 5 5 2
Areas associated with l and l :
4 5
1 π
2 2
A =()π − nθ()d − d + d h
4 1 2 2
8 2
π 2 2
A =()d − d + 4d h
5 3 4 3
Core factors associated with l :
l 1 d
6 2
= ln
A()π − nθ h a
l d − a
6 2
=
A ad()π − nθ h
6 2
6 6
l l
i i
C = C =
∑ ∑
1 2
A
A
i=1 i=1
i
i
60205 © IEC:2006+A1:2009 – 13 –
3.7 Pair of RM-cores
NOTE 1 This calculation is also applicable to the core type without hole.
NOTE 2 RM + I (Plate)-cores use RM core formulas.

Type 1 – RM6–S, RM6–R
l′
A 4
8 l″
X
p
ϕ
l
min
l
A
A
β
d /2
l″
l′
d /2 5
l
max
d /2
e
X
l h
c
A /2
Section X-X
Type 2 – RM7
A
X
p ϕ
l
min
A
A
d /2
β
d /2
l
max
d /2
b
e
X
c
A /2
Type 3 – RM4, RM5, RM8, RM10, RM12, RM14
A
p ϕ
A
l A
min 3
l′
max
d /2
β 4
l″ d /2
max 3
d /2
e
c
A /2
l l′ l″
max = max + max
IEC  590/06
α
α
α
a
a
a
l″
l′
– 14 – 60205 © IEC:2006+A1:2009
Total area of the outer leg:
⎧ ⎫
1 ⎛ π ⎞ β 2 1
2 2
A = a 1+ tan β − − d − p
⎜ ⎟
⎨ ⎬
1 2
2 4 2 2
⎝ ⎠
⎩ ⎭
e
where β = α − arcsin
d
Core factors associated with l :
d
ln f
l d
2 3
=
A Dπh
A
l min+ l max
where f = , D =
2l min
A
′ ′′
l = l + l
2 2 2
l()1 d −1 d f
2 3 2
=
2 2
π
A ()D h
Type 1:
1 1
2 2
l =()d + d − d d cos()α − β
max 2 3 2 3
4 2
Type 2:
1 1 b
⎛ ⎞
l = d + d − d d ()− −
⎜ ⎟ cos α β
max 2 2 3
4 2 ϕ
⎝ ⎠
2sin
Type 3:
ϕ
e 1 ⎛ ⎞
l = + 1− sin ()d − c
⎜ ⎟
max 2
2 2 2
⎝ ⎠
Type 1: RM 6-S:
1 ⎧ β 1 1 ϕ π ⎫
2 ⎛ ⎞ 2
2 2
A = d + e tan β − e tan α − − d
⎜ ⎟
⎨ ⎬
7 2 3
4 2 2 2 2 4
⎝ ⎠
⎩ ⎭
60205 © IEC:2006+A1:2009 – 15 –
Type 1: RM 6-R:
1 ⎧ β 1 1 ϕ π ⎫
2 2 2
A = d + d d sin()α − β +()c − d tan − d
⎨ ⎬
7 2 2 3 3 3
4 2 2 2 2 4
⎩ ⎭
Type 2:
1 ⎧ β π 1 ϕ 1 ⎫
2 2 ⎛ ⎞
2 2 2
A = d − d +()b − e tan α − + e tan β
⎜ ⎟
⎨ ⎬
7 2 3
4 2 4 2 2 2
⎝ ⎠
⎩ ⎭
Type 3:
1 β π 1
⎧ 2 2 ⎫
A = d − d + c tan()α − β
⎨ ⎬
7 2 3
4 2 4 2
⎩ ⎭
α
2 2
A =()d − d
8 2 3
Area of centre pole:
π
2 2
A =()d − d
3 3 4
Mean length of flux paths at corners and mean areas associated with these:
π 1 1
⎛ ⎞
l l′ l′′ h a d
= + = + −
⎜ ⎟
4 4 4 2
4 2 2
⎝ ⎠
A =()A + 2βd h
4 1 2
⎧ ⎫
π 1
2 2
l = l′ + l′′ = d + h −()d + d
⎨ ⎬
5 5 5 3 3 4
4 2
⎩ ⎭
1 π
⎧ 2 2 ⎫
A = ()d − d + 2αd h
⎨ ⎬
5 3 4 3
2 4
⎩ ⎭
5 5
l l
i i
C = C =
1 ∑ 2 ∑
A
A
i=1 i=1
i
i
NOTE This calculation ignores the effect of spring recesses and stud recesses. These may have some influence
on the outcome of the calculation, especially for smaller cores.

– 16 – 60205 © IEC:2006+A1:2009
3.8 Pair of EP-cores
l
b l″
l′ 1 4
X
A
l
d /2
α
d /2
l″
l′
5 5
A
h
c
h
X
Section X-X
IEC  591/06
As a pair:
l h
1 2
=
A
ab −πd / 8 − d d / 2
1 1 2
l h
1 2
=
2 2
A
()ab −πd / 8 − d d / 2
1 1 2
l 2 d
2 1
= ln
A ()π −α(h − h) d
2 1 2 2
l 4()d − d
2 1 2
=
2 2 2
A ()π −α(h − h) d d
2 1 2 1 2
4h
l h
3 2
= =
2 2
A
πd
d
3 ⎛ ⎞
π
⎜ ⎟
⎝ ⎠
16h
l h
3 2
= =
2 4 4
A
d π d
⎛ ⎞
3 2
2 2
π
⎜ ⎟
⎝ ⎠
Areas associated with l and l :
4 5
a
l′
l″
60205 © IEC:2006+A1:2009 – 17 –
π d h − h
⎛ ⎞
1 1 2
′ ′′
l = l + l = ⎜γ − + ⎟
4 4 4
2 2 4
⎝ ⎠
2 2
()π −α d + 2()ab −πd /8 − d d / 2
1 1 1 2
γ =
4()π −α
where γ is a hypothetical radius bisecting the cross-sectional area of the ring.
1 ⎧ π d d h h ⎫
⎛ ⎞
1 2 1 2
A = ab − d − +()π −α d −
⎜ ⎟
⎨ ⎬
4 1 1
2 8 2 2 2
⎝ ⎠
⎩ ⎭
π d h − h
⎛ ⎞
2 1 2
′ ′′
l = l + l = 0,29289 +
⎜ ⎟
5 5 5
2 2 4
⎝ ⎠
⎧ ⎫
π d d
2 2
A = + ()h − h
⎨ ⎬
5 1 2
2 4 2
⎩ ⎭
5 5
l l
i i
C = C =
1 ∑ 2 ∑
A
A
i=1 i=1
i
i
3.9 Pair of PM-cores
c
l″
l 4
l′
b 4 1
X
e
l
d
ϕ
l
max
l″
l′
β
d
A
A
α
h
X
h
Section X-X
IEC  592/06
Total area of the leg:
β
2 2
A =()d − d − 2bt
1 1 2
l
min
t
ƒ
l′
l″
d
d
d
– 18 – 60205 © IEC:2006+A1:2009
f
where β = α − arcsin
d
Core factors associated with l :
l = l′ + l′′
2 2 2
d
ln g
l d
2 3
=
A Dπ()h − h / 2
2 1 2
l min+ l max A
where g = , D =
2l min A
1 1
2 2
l =()d + d − d d cos()α − β
max 2 3 2 3
4 2
l ()1 d −1 d g
2 3 2
=
2 2
A{}Dπ()h − h 2
2 1 2
β 1 1 ϕ π
2 ⎛ ⎞ 2
2 2
A = d + f tan β − f tan α − − d
⎜ ⎟
7 2 3
8 2 16
8 8
⎝ ⎠
α
2 2
A =()d − d
8 2 3
Area of centre limb:
π
2 2
()
A = d − d
3 3 4
Mean length of flux paths at corners and mean areas associated with these:
π
′ ′′
l = l + l =()h − h + d − d
4 4 4 1 2 1 2
A ={}A + 2βd()h − h
4 1 2 1 2
⎧ ⎫
π 1
2 2
′ ′′
l = l + l = d + h − h −()d + d
⎨ ⎬
5 5 5 3 1 2 3 4
4 2
⎩ ⎭
π
2 2
A =()d − d +αd()h − h
5 3 4 3 1 2
60205 © IEC:2006+A1:2009 – 19 –
5 5
l l
i i
C = C =
∑ ∑
1 2
A
A
i=1 i=1
i
i
3.10 Pair of EL-cores
NOTE EL + PLT (Plate)-cores use EL core formulas.

C B
l
D
F
l
l
l
R
IEC  593/06
Area of outer leg:
1 1
⎛ ⎞
2 2
A =()A − E C − 4 R − πR
⎜ ⎟
2 4
⎝ ⎠
Mean length of flux path at outer leg:
l = D
Area of back wall:
A =()C +()F − F + πF /2(B − D)
2 2 1 1
Mean length of flux at back wall:
E F
⎛ ⎞
l = − ⎟
⎜
2 2
⎝ ⎠
Area of centre limb:
1 ⎧ 1 ⎫
A = πF +()F − F F
3 ⎨ 1 2 1 1⎬
2 4
⎩ ⎭
Mean length of flux path at centre limb:
l = D
F
H
E
A
l
– 20 – 60205 © IEC:2006+A1:2009
Area of outside corner:
A + A
1 21
A =
where A = (B – D)C
Mean length of flux path at outside corner:
π ⎛ A E ⎞
⎛ ⎞
l = − +()B − D
⎜⎜ ⎟ ⎟
8 2 2
⎝ ⎠
⎝ ⎠
Area of inside corner:
A + A
23 3
A =
where A =()()F −F + πF /2(B − D)
23 2 1 1
Mean length of flux path at inside corner:
π ⎛ A ⎞
⎜ ⎟
l = +()B − D
⎜ ⎟
8 F
⎝ 2 ⎠
5 5
l l
i i
C = C =
1 ∑ 2 ∑
A
2A
i= i=
1 i 1
i
2 3 2
l = C /C A = C /C V = C /C
e 1 2 e 1 2 e 1 2
60205 © IEC:2006+A1:2009 – 21 –
3.11 Pair of ER-cores (low profile)
NOTE ER + PLT (Plate)-cores use ER core formulas.

B
l
C
D
l
l
l
β A
A′
A″
α
A
IEC  594/06
Area of outer leg:
⎛ ⎞
1 αE EG
A = C()A −G − ⎜ − sinα ⎟
⎜ ⎟
2 4 4
⎝ ⎠
where α = arccos (G/E)
Mean length of flux path at outer leg:
l = D
Area of back wall:
A = C(B – D)
Mean length of flux path at back wall:
2 2
l =()E + G + C − 2F
Area of centre limb:
G
F
E
A
S
l
– 22 – 60205 © IEC:2006+A1:2009
1 1
⎛ ⎞
A = πF
⎜ ⎟
2 4
⎝ ⎠
Mean length of flux path at centre limb:
l = D
Area of outside corner:
A + A
1 2
A =
Mean length of flux path at outside corner:
π
l =()p + h
where
A E
h = B − D p = −
2 2
Area of inside corner:
A + A
2 3
A =
Mean length of flux path at inside corner:
π
l =()2S + h
5 1
The condition to obtain A′ = A″ is
3 3
S = F()1− sinα = 0,2978F
5 5
l l
i i
C = C =
1 ∑ 2 ∑
A
2A
= i=1
i 1 i
i
2 3 2
l = C /C A = C /C V = C /C
e 1 2 e 1 2 e 1 2
60205 © IEC:2006+A1:2009 – 23 –
3.12 Pair of PQ-cores
NOTE 1 This calculation ignores the effect of spring recesses.
NOTE 2 PQ+PLT (Plate)-cores use PQ core formulas.
NOTE 3 The equations below are consistent with those given in IEC 62317-13.

′
″
l
A
8 l 4
A 4
α
β l
l
max
′
″
l
l
A
A /2
h
l
D 1
C
B
IEC  014/09
Area of outer leg:
βE 1
A = C(A − G) − + GI
2 2
where
G
⎛ ⎞
β = arccos
⎜ ⎟
E
⎝ ⎠
I = E sin β
Mean length of flux path at outer leg:
l = 2D
Core factors associated with l :
For l , A the elemental radius dr shown in the figure is elemental length of the flux path in the
2 2
integral below. The radius vector extends from F/2 to E/2 for the entire circle. The effective
length l for the section is multiplied by f. The area is the physical area multiplied by K.
2i
A
l
min
J
G
F
E
″
l
′
l
– 24 – 60205 © IEC:2006+A1:2009

r
dr
IEC  015/09
E
l f f ⎛ E ⎞
2i
= dr = ln
⎜ ⎟
∫F
A K2πr()B − D 2πK()B − D F
⎝ ⎠
1 1
⎛ ⎞
−
E ⎜ ⎟
l f F E
2i ⎝ ⎠
= dr = f
2 ∫F 2 2
A []2πK()B − D r 2[]πK()B − D
From this A is computed. The total magnetic length of this section is 2l for the top and
2i
bottom halves together.
B − D ⎛ E ⎞
A = πKEF ln
⎜ ⎟
E − F F
⎝ ⎠
⎛ ⎞
EF E
⎛ ⎞
l = 2l = f ⎜ln ⎟
⎜ ⎟
2 2i
⎜ ⎟
E − F F
⎝ ⎠
⎝ ⎠
where
A A
7 7
K = =
π
A
2 2
()E − F
2 2
A =()β ⋅ E − α ⋅ F + G ⋅ L − J ⋅ I
⎛ L ⎞
α = arctan⎜ ⎟
J
⎝ ⎠
l + l
min max
f =
2l
min
2 2
E + F − 2EF cos()α − β
l =
max
E
F
60205 © IEC:2006+A1:2009 – 25 –
Define the other two physical areas in the flux path at back wall.
A = 2α ⋅ F()B − D
A = 2β ⋅ E()B − D
The mathematical area A is given as A >A >A .
2 10 2 9
Area of centre limb:
A = πF
Mean length of flux path at centre limb:
l = 2D
Area of outside corner:
1 1
A =()A + A =[]A + 2E()B − D β
4 1 10 1
2 2
Mean length of flux path at outside corner:
π 1 1
⎛ ⎞
' "
()
l = l + l = ⎜ B − D + A − E ⎟
4 4 4
4 2 2
⎝ ⎠
Area of inside corner:
1 π ⎛ F ⎞
A =()A + A = ⎜ ⎟ + F()B − D α
5 3 9
2 2 2
⎝ ⎠
Mean length of flux path at inside corner:
⎛ ⎞
⎛ ⎞
π 1
' "
⎜ ⎟
l = l + l = ()B − D + ⎜1− ⎟F
5 5 5
⎜ ⎟
⎜ ⎟
⎝ ⎠
⎝ ⎠
5 5
l l
i i
C =      C =
1 ∑ 2 ∑
A
A
i
i
i=1 i=1
The minimum physical cross-section area A is given as:
min
A = min (A , A , A , A , A )
min 1 3 4 5 9
2 3
C C C
1 1 1
l =      A =      V =
e e e
C C
C
2 2
– 26 – 60205 © IEC:2006+A1:2009
3.13 Pair of EFD-cores
C
B
K
l
F
D
l
l
l
IEC  596/06
Area of outer leg:
C()A − E
A =
Mean length of flux path at outer leg:
l = D
Area of back wall:
A = C()B − D
Mean length of flux at back wall:
E − F
l =
Area of centre limb:
F F − 2q
1 2
A =
where q: chamfer
Mean length of flux path at centre limb:
l = D
F
E
A
q
l
60205 © IEC:2006+A1:2009 – 27 –
Area of out side corner:
()A + A
1 2
A =
Mean length of flux path at outside corner:
π A − E
⎛ ⎞
l = +()B − D
⎜ ⎟
8 2
⎝ ⎠
Area of inside corner:
A + A
2 3
A =
Mean length of flux path at inside corner:
2 2
⎛ ⎞
F C − F − 2K
π ⎛ ⎞ B − D
⎛ ⎞
⎜ 1 2 ⎟
l = + +
⎜ ⎟ ⎜ ⎟
⎜ ⎟
4 4 2 2
⎝ ⎠ ⎝ ⎠
⎝ ⎠
5 5
l l
i i
C = C =
1 ∑ 2 ∑
A 2A
i=1 i i=1 i
2 3
C C C
1 1 1
l = A = V =
e e e
C C C
2 2 2
3.14 Pair of E planar-cores
NOTE E planar + PLT (Plate)-cores use E planar core formulas.

B
C
l
D
l
R
l
R
l
IEC  597/06
F
E
A
l
– 28 – 60205 © IEC:2006+A1:2009
Area of outer leg:
C()A − E π
⎛ ⎞
2 2
A = − 4 R − × R
⎜ ⎟
1 1 1
2 4
⎝ ⎠
Mean length of flux path at outer leg:
l = D
Area of back wall:
A = C()B − D
Mean length of flux at back wall:
E − F
l =
Area of centre limb:
π
⎛ ⎞
2 2
A = FC − 2 R − × R
⎜ ⎟
3 2 2
⎝ ⎠
Mean length of flux path at centre limb:
l = D
Area of outside corner:
A + A
1 2
A =
Mean length of flux path at outside corner:
π A − E
⎛ ⎞
()
l = + B − D
⎜ ⎟
8 2
⎝ ⎠
Area of inside corner:
()A + A
2 3
A =
...