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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

    10 11

  • Dongbu CNI

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    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

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    Frequency (kHz)

    Frequency (kHz)

    Per

    cent

    Per

    mea

    bilit

    y(%

    )P

    erce

    nt P

    erm

    eabi

    lity(

    %)

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    125

    14

    26

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    Permeability vs. Frequency

    14 15

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    Technical Information

    Permeability vs. Frequency

    Sendust100

    98

    96

    94

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    90

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    cent

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    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

    14 15

  • Dongbu CNI

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    MPP

    Normal Magnetizing Curves

    8000

    7000

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    0

    High Flux

    Flux

    Den

    sity

    (Gau

    ss)

    1 10 100 1000

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    125

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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

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    2000

    01 10 100 1000

    Magnetizing Force (Oersteds)

    Magnetizing Force (Oersteds)

    11000

    10000

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    0

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    Flux

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    sity

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    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

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    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

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    20

    10

    0

    100

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    0

    DC Mangnetizing Force (Oe)

    DC Mangnetizing Force (Oe)

    Per

    cent

    Per

    m e

    abili

    ty (%

    )P

    erce

    nt P

    erm

    eab

    ility

    (%)