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Example 1 MPP core
Using the permeability versus DC bias data provided by Magnetics , multiple iterations and curve tting techniques, a closed form solution for the 60u material was found to be approximated by %Ui = 1.77e .021H 0.77e .031H where Ui is the initial inductance of the core and H is the magnetizing force in oersteds. C= L= N 1000 where AL is the inductance reference of the core. B1 = 0.4 NI (V I ) lm
B2 = 1.77e .012V(B1 ) 0.77e .031V(B1 ) + 0.02 B3 = R2 = V 3, 4 V ( B2 ) 1 2 f eddy C
The following circuit uses the above derivation to model a Magnetics R 55121 MPP core with 21 turns. The constants given in the data book for the 55121 core provide the following values: AL =35 mH, lm =4.11 cm, core weight=0.015 lb, feddy = 7 MHz, and Ui =60. We can calculate the components of the model as C= B1 = R1 = 21 1000 35 mH = 15.4 F
0.4 21 I (V1 ) 4.11 1 = 0.0015 2 7 MHz 15.4 F
The SPICE netlist is provided later (Fig. 2.29). Note that R1 represents the winding s DC resistance. The test circuit sweeps the current Two
MPP: MODELING A MAGNETICS 55121 MPP CORE * PSpice version .DC I1 .1 100 .10 .AC DEC 20 100HZ 10MEGHZ .PROBE .PRINT AC V(4) VP(4) * Node 4 Impedance .PRINT DC V(6) V(5) * Node 6 = H, Node 5 = % Permeability G2 3 1 9 0 1 V1 1 0 G1 0 9 2 1 1 C1 9 8 15.4U R2 8 0 1.5M E1 5 0 Value = { ABS(1.256*21*I(V1)/4.11) } E2 6 0 Value = { (1.77*Exp((.012*V(5))))(.77*Exp((.031*V(5))))+.01 } E3 2 0 Value = { V(3,1)/V(6) } I1 0 4 AC 1 R1 4 3 .04 RT4 4 0 1G RT3 3 0 1G RT9 9 0 1G .END Netlist for a 55121 MPP core.
through the core while the percent permeability and magnetizing force are monitored and displayed in Fig. 2.30. Actual data points are plotted as dots, while the calculated results are plotted using line style. An AC impedance plot is also performed (Fig. 2.31). Calculating the inductance from the impedance curve yields 1 = 15.6 H, which agrees with the expected 2 10.19 kHz 15.4 H. The percent permeability versus magnetizing force curve was integrated and multiplied by the initial permeability [59]. The resulting graph is the DC BH curve shown in Fig. 2.32. The curve shows a maximum ux density of approximately 7500 G, which agrees with the speci ed value of 7000 G. L= Ferrite Cores The same principles apply to ferrite cores as well as MPP cores. In this example, a model is generated for ferrite F material. Again, trialanderror and curve tting techniques may be used in order to obtain a closedform expression of percent permeability versus magnetizing force. Graphical data are provided in the Magnetics Ferrite Data Book.

