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• Dongbu CNI

Dongbu CNI

Dongbu CNI

Dongbu CNI

Dongbu CNI

Inductance of Wound Cores

The inductance of a core and the number of turns can be calculated by using the following formula.

Magnetic Design Formula

L = Where L = induntance (H) = core permeability N = number of turns A = core cross section area (cm2) l = mean magnetic path length (cm) LN = inductance for N turns (H) AL = nominal inductance(nH/N2)

Where H = magnetizing force (Oersteds) N = number of turns I = peak magnetizing current (A) = mean magnetic path length (cm) Bmax = maximum flux density (Gauss) Erms = voltage across coil (V) A = core cross section area (cm2) f = frequency (Hz) = material permeability

N = 10 turns (our standard wound turns for M040-066A) A = 0.100cm2 (please see the page 56) = 2.380cm (please see the page 56) LN = 66 x 10

2 x 10-3 = 6.60(H)

0.4N2A x 10-2

Required N =

0.4NI

LN = AL x N2

103

L1

Example) M040066A

L = = 6.60(H)0.4 x 125 x 102 x 0.100 x 10-2

2.380

The relations of Permeability-Flux Density(B)-Magnetizing Force(H)

H = (Amperes Law)

4.44fANBmax =

BH

=

2

L2

2=

Amperes Law : The law is the magnetic equivalent of Gausss law. It relates the circulating magnetic field in a closed loop to the electric current passing through the loop

Faradays Law : The law that defines the relationship of the voltage induced across the winding of a core to the flux density within the core

( )1/2desired L(nH)

AL(nH / N2)N1 N2

10 11

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Technical Information

Core : M040066AApplied current : 3A

The total core losses are made up of three maincomponents : Hysteresis, eddy current and residual losses.

1) Inductance Calculation at 0A

Inductance calculation by Permeability vs. DC bias curves Specification

L = = 6.60(H)

N = 10 turns (our standard wound turns for M040-066A) A = 0.100cm2 (please see the page 56) = 2.380cm (please see the page 56) LN = 66 x 10

2 x 10-3 = 6.60(H)

Where Rac = effective resistance (Ohm) a = hysteresis loss coefficient c = residual loss coefficient e = eddy current loss coefficient = same as before mentioned L = inductance Bmax = maximum flux density f = frequency

Eddy current loss

Residual loss

Hysteresis loss

Total loss factor

0.4 x 125 x 102 x 0.100 x 10-22.380

RacL

2) Magnetizing force (H : Oe) is calculated by Ampere law to achieve the roll off

H = = = 15.8(Oe)0.4 x x N x I

0.4 x x 10 x 3

2.38

3) When the magnetizing force(H) is 15.8 Oe, yielding 85% of initial permeability. Therefore, the Inductance at 3A is

L(3A) = 6.6 x 0.85 = 5.6(H)

Core loss

= aBmaxf + cf + ef2

10 11

• Dongbu CNI

Dongbu CNI

Dongbu CNI

Dongbu CNI

Dongbu CNI

Window Area = x

The Q factor is the ratio of reactance to the effective resistance and is often used as measure of performance. So, the Q factor represents the effect of electrical resistance.

Q Factor

Q =

Where Q = quality factor = 2f (Hz) L = inductance (H) Rdc = DC winding resistance (Ohm) Rac = resistance due to core losses (Ohm) Rd = resistance due to winding dielectric

losses (Ohm)

Le = effective mean magnetic path length (cm) Ae = effective core cross section area (cm2 ) Ve = effective core volume (cm3) OD = core outer diameter before coating (cm) ID = core inner diameter before coating (cm) HT = core height before coating (cm)

LRdc + Rac + Rd =

ReactanceTotal Resistance

x HT

Le = (OD-ID)

Physical constant of core

In ODID

Ve = Le x Ae

CGS (unit) By To obtain (unit) Factor

Magnetic Flux Density (B) Gauss (G) 10-4 Tesla (T) 1T=104G

Magnetizing Force (H) Oersted (Oe) 79.58 Amperes per Meter (A/m) 1A/m=4/103Oe

Conversion Table

ID2( )

2

Ae = OD-ID

2

12 13

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Technical Information

The increase in surface temperature of a component in free-standing air due to the total power dissipation (both copper and core loss). The following formula has been used to approximate temperature rise:

Total Power Loss = Copper Loss + Core LossSurface Area means in case of wound core

Nominal DC Resistance, in ohm/mH, at any given winding factor can be calculated by using the following equations:

Temperature Rising Calculation

Temperature Rise(oC) =

Where /mhwf = mh for chosen winding factor /mhu = unity value, listed for each core size wf = chosen winding factor Kwf = length/turn for chosen wf* Ku = length/turn for unity(100%) wf*

* see Winding Turn Length on core size pages

Total Power Loss (milliwatts)Surface Area(cm2)

/mhuwf

KwfKu

Nominal DC Resistance

/mhwf = x

The value of Rdc for any given winding factor can be computed as follows:

Where Rdcwf = Rdc for chosen winding factor Rdcu = unity value, listed for each core size(ohms) wf = chosen winding factor Kwf = length/turn for chosen wf* Ku = length/turn for unity(100%) wf* * see Winding Turn Length on core size pages

KwfKu

Rdcwf = Rdcu x wfx

( )0.833

12 13

• Dongbu CNI

Dongbu CNI

Dongbu CNI

Dongbu CNI

Dongbu CNI

MPP

10

High Flux

100 1000 10000

Frequency (kHz)

Frequency (kHz)

Per

cent

Per

mea

bilit

y(%

)P

erce

nt P

erm

eabi

lity(

%)

10 100 1000 10000

100

90

80

70

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50

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20

10

0

100

90

80

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60

50

40

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10

0

14 26 60

125

14

26

60

125

Permeability vs. Frequency

14 15

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Technical Information

Permeability vs. Frequency

Sendust100

98

96

94

92

90

88

86

84

82

80

100

90

80

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60

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40

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20

10

0

Frequency (kHz)

Per

cent

Per

mea

bilit

y(%

)P

erce

nt P

erm

eabi

lity(

%)

Power Flux

60

90

14 26

35 60

75

125

90

Frequency (kHz)

10 100 1000 10000

10 100 1000 10000

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• Dongbu CNI

Dongbu CNI

Dongbu CNI

Dongbu CNI

Dongbu CNI

MPP

Normal Magnetizing Curves

8000

7000

6000

5000

4000

3000

2000

1000

0

High Flux

Flux

Den

sity

(Gau

ss)

1 10 100 1000

14000

13000

12000

11000

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9000

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1000

0

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125

60

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26

Flux

Den

sity

(Gau

ss)

1 10 100 1000

Magnetizing Force (Oersteds)

Magnetizing Force (Oersteds)

16 17

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Technical Information

Sendust

16000

14000

12000

10000

8000

6000

4000

2000

01 10 100 1000

Magnetizing Force (Oersteds)

Magnetizing Force (Oersteds)

11000

10000

9000

8000

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6000

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0

90

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Flux

Den

sity

(Gau

ss)

Flux

Den

sity

(Gau

ss)

Power Flux

1 10 100 1000

125

90

75

60

26

Normal Magnetizing Curves

16 17

• Dongbu CNI

Dongbu CNI

Dongbu CNI

Dongbu CNI

Dongbu CNI

MPP4

3

2

1

0

-110 100 1000 10000

10 100 1000 10000

AC Flux Density (Gauss)

Per

cent

Cha

nge

of P

erm

eabi

lity

(%)

125

60

26

High Flux30

25

20

15

10

5

0

-5

-10

AC Flux Density (Gauss)

Per

cent

Cha

nge

of P

erm

eabi

lity

(%) 125

60

26

Permeability vs. AC Flux Density

18 19

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Permeability vs. AC Flux Density

4

3

2

1

0

-1

4

3

2

1

0

-1

AC Flux Density (Gauss)

Per

cent

Cha

nge

of P

erm

eabi

lity

(%)

perc

ent c

hang

e of

per

mea

bilit

y(%

)

Sendust

Power Flux

AC Flux Density (Gauss)

125

90

75

60

26

60

Technical Information

10 100 1000 10000

10 100 1000 10000

18 19

• Dongbu CNI

Dongbu CNI

Dongbu CNI

Dongbu CNI

Dongbu CNI

MPP100

90

80

70

60

50

40

30

20

10

0

100

90

80

70

60

50

40

30

20

10

0

DC Mangnetizing Force (Oe)

DC Mangnetizing Force (Oe)

Per

cent

Per

m e

abili

ty (%

)P

erce

nt P

erm

eab

ility

(%)

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