常见问题
制备电磁元件的设计公式
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)
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