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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)

(Faradays Law)Ermsx102

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

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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

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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

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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

60

50

40

30

20

10

0

100

90

80

70

60

50

40

30

20

10

0

14 26 60

125

14

26

60

125

Permeability vs. Frequency

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Technical Information

Permeability vs. Frequency

Sendust100

98

96

94

92

90

88

86

84

82

80

100

90

80

70

60

50

40

30

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

10000

9000

8000

7000

6000

5000

4000

3000

2000

1000

0

125

60

125

60

26

26

Flux

Den

sity

(Gau

ss)

1 10 100 1000

Magnetizing Force (Oersteds)

Magnetizing Force (Oersteds)

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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

7000

6000

5000

4000

3000

2000

1000

0

90

60

Flux

Den

sity

(Gau

ss)

Flux

Den

sity

(Gau

ss)

Power Flux

1 10 100 1000

125

90

75

60

26

Normal Magnetizing Curves

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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

(%)