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                The calculation of inductance and core

                Date:2014-03-06 Tag:2013 Source:POCO

                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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