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will model, is I= 1 L %U Vdt
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The results have shown that the B-H characteristics properly represent the hysteresis and remenance effects of the core. Core loss must be represented at a single operating condition or may be entered outside of the model. This can be accomplished via the use of parameter passing. In this case, the 3-dB point on the permeability versus frequency graph was used. The con guration of the model is shown in Fig. 2.28. In PSpice, the SPICE 3 B-elements are replaced by voltage-controlled voltage or current source equivalents (E or G elements). B1 calculates the magnetizing force in the inductor using the relationship H= 0.4 NI lm
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where N is the number of turns, I is the current through the element (measured by V1), and lm is the magnetic path length of the core. Because H is a real value, its absolute value is used. B2 calculates the percent permeability using the equation de ned above. B3 calculates the voltage across the element, divided by the percent permeability. G1 integrates the value of BS3 and presents it to G2, which forces a current ow through the element. With the values of G1 and G2 both established as 1, the current through the element is I=
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B1 V(5)=ABS(1.256*21*I(V1)/4.11)
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B2 V(6)=(1.77*E^ (.012*V(5)))-(0.77*E(0.031*V(5)))+.01)
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Schematic of the SPICE 3 core model. V(6) = % Permeability, V(5) = H.
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Because this is in the desired form, we can solve for all of the variables.
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
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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 B-H 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, trial-and-error and curve- tting techniques may be used in order to obtain a closed-form expression of percent permeability versus magnetizing force. Graphical data are provided in the Magnetics Ferrite Data Book.
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