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## 磁材设计公式

Inductance of Wound Core
Inductance(L) can be figured out by the inductance factor(AL).

A = inductance factor (nH/N2)
N = number of turns

Inductance can also be determined by the relative permeability and the effective core parameters.

A = effective cross section area (cm2)
l  = mean magnetic path length (cm)
μ = relative permeability ( no dimensions)

Effective Magnetic Path Length
For toroidal powder cores, the effective area (A) is as the same as the cross sectional area. According to the definition and Ampere ’ s Law, the effective magnetic path length is the ratio of ampere-turns (NI) to the average magnetizing force. Using Amper

OD = outside diameter of core (cm)
ID  = inside diameter of core (cm)

Magnetic Flux Density
Using the Faraday's Law, the maximum flux density(Bmax) is figured out by the following fomular

Bmax = maximum flux density ( gausses)
Erms  = voltage across coil (volts)
f       = frequency (hertz)

Magnetizing Force
Using Ampere's law, the magnetizing force(H) is:

N = number of turns
I  = peak magnetic current ( amperes)
l  = mean magnetic path length (cm)

Permeability
The magnetizing force determines the estimate of magnetic flux density. The relative permeability is, by definition:

μ = relative permeability
B = magetic flux density (gausses)
H = magnetizing force ( oersteds)

Q Factor
The quality factor (Q) is defined as the ratio of reactance to the effective resistance for an inductor and thus indicates its quality. The Q of wound core can be figured out with the following formula, when the effects of selfresonance caused by the dis

ω    = 2πfrequency (hertz)
L    = inductance (henries)
Rdc = DC winding resistance (ohms)
Rac = resistance due to core loss (ohms)
Rd  = resistance due to winding dielectric loss (ohms)

Core Loss
Total core loss at low flux densities is the sum of three losses of hysteresis, residual, and eddy current.

a = hysteresis loss coefficient
c = residual loss coefficient
e = eddy current loss coefficient
μ,L,Bmax,f = as above

Inductance Calculation

Electrical Specifications
Core: NPF157060
AL: 81 nH/N
Number of winding: 75T
Current: DC 15A

By permeability vs DC Bias Curves
Inductance at non-biased:     DC magnetizing force (H) at 15A:
L = AL N2                             H = 0.4πNI/l
= 81x752/1000                       = 0.4x3.14x75x15/9.84
= 455.6 (μH)                          = 143.6 (Oe)

When magnetizing force is 143.6 Oe, the yield is 54% of initial permeability according to Permeability vs DC Bias Curves .
The inductance at 15A will decrease the inductance by 54% compared with at 0A.
Therefore, L(@15A)=455.6x0.54=246(μH)
By AL vs NI Curves
CaCalculate NI:
NI= 75x15
= 1125

Using the AL vs NI Curves on core data of 1.57", the yield of AL value is 43.8 when NI is 1125.
According to the formula: L=ALN
L(@15A)=43.8x752/1000=246 (μH)