Non-Linear Saturable Kool Mu Core Model

Transcription

1 Non-Linear Saturable Kool Mu Core Model Scott Frankel, AEi Systems, LLC Iron Powder cores have been well suited for applications such as switching regulator inductors, in-line noise filters, and flyback converter transformers, where high flux density capacity is the key characteristic in the magnetic core performance Unfortunately, when using Iron Powder cores at higher frequencies (> 100 Khz) the Iron Powder Core losses tend to be prohibitive As the switching frequency of power converters increases, the need for cores that can produce high flux densities with reasonable core losses increases Magnetics (r) designed the Kool Mu (r) series of cores in order to meet this demand The Kool Mu cores have magnetic characteristics resembling the Iron Powder with significantly decreased core losses When using SPICE to model such cores, the saturation characteristics of the core can become extremely important Unfortunately, the SPICE primitive L (Inductor) element only models linear inductance, and not the non-linear characteristic of a real magnetic core Fortunately for designers, SPICE is versatile enough to be able to create a subcircuit of the magnetic core that very accurately represents the non-linear saturation characteristics of the core Several approaches to modeling the saturation characteristics of magnetic cores are discussed in [3] In that text, saturable core models for MPP (molypermalloy powder) and Ferrite cores are generated In this article, we will apply these techniques to generate a saturable core model for the Kool Mu family of cores We will use the SPICE model discussed in [3] that was used for the MPP core models That model is shown below in Figure /09/00

2 G1 1 7 B3 Input 1 R1 C1 V G2 1 R2 Output B1 B2 B4 Inductance 10 Figure 1: SPICE model of Kool Mu core The B elements are equation blocks that we will use to calculate the core characteristics The elements and their representative equations are shown in Tabular form in Table 2 The core characteristics for this example will be the Kool Mu core The constants we need to extract to complete the model are shown in Table 1 Inductance per Mean Magnetic Eddie Current Permeability[Ui] 1000 Turns [A L ] Path Length [Lmean] Loss Coefficient [Feddy] Core 26 mh 0817 cm 707 MHz 125 Table 1: Core parameters Extracted 2 07/09/00

3 Spice element name Description Equation SPICE equivalent Expression R1 DCR of Inductor = Ohms (entered by user) R1 1 4 {DCR} B1 Magnetizing Force H 04 π N I Lmean B1 5 2 V = ABS(1256*{N}*I(V1)/0817) N=Number of turns (entered by user) I = current in inductor Lmean=Mean magnetic path (cm) B2 % Permeability %U E1 Perm H A1 e ( ) B1 e ( E2 Perm H ) H= Magnetizing Force Perm = Permeability of core A1, B1, E1, E2 = Constants to be derived B3 Vcore/% Permeability Vcore %U 02 B2 6 2 V=(096402*E^-(125*V(5,2)*00017))-(- 0893*E^-(125*V(5,2)*000047)) B3 7 2 V=(4,3)/(V(6,2)+002) Vcore=Voltage applied to core %U=% Permeability 3 07/09/00

4 C1 Inductance 2 N L A L 1000 C1 8 9 {N^2*26*1N} IC={IC} N=Number of turns A L =Inductance per 1000 turns R2 Eddie Current Losses R2 1 2 π Feddy C R2 9 2 {1/(6283n*707MEG*26*N^2)} Feddy=Eddie Frequency C = L = Inductance B4 Inductance (used for measuring Ind %U N A L B V=V(6,2) * {N^2*13*1N} inductance external to the %U=Percent Permeability model; Not required for N=Number of turns subcircuit operation) A L =Inductance per 1000 turns Table 2: SPICE elements and Equations 4 07/09/00

5 The most difficult part of deriving the core model is modeling the saturation characteristics of the core This is performed in this model by curve fitting the data provided in the databook to a non-linear equation that closely resembles this characteristic The data used is provided in the % permeability vs Magnetizing Force graph in the Magnetics data book The equation that was found (by trial and error) to closely resemble the saturation characteristics of the Kool Mu material is given below: E1 Perm H %U A1 e ( ) B1 e ( E2 Perm H ) In order to derive the constants A1, B1, E1, and E2, an Excel spreadsheet, along with the SOLVER function, was utilized The Excel spreadsheet used is shown in Table /09/00

6 Table 3: Excel spreadsheet used to curve fit % Permeability The Magnetizing force (H) from the data book is shown in cells A9 through A45 The % permeability corresponding to this Magnetizing force is shown in cells G9 through G45 The curve fit equation for % permeability above was translated into an Excel equivalent equation and inserted into cell E9 6 07/09/00

7 E1 Perm H %U A1 e ( ) B1 e ( E2 Perm H ) [Normal Equation format] =(($K$11*EXP(-$K$12*$E$5*$A9))-($K$13*EXP(-$K$14*$E$5*$A$9) [Excel Equivalent Format] This equation was then copied from E9 down to cell E45 In order to optimize the constants to curve fit to the % permeability equation, the error squared was calculated for each point in cells I9 through I45 and summed in cell I46 The constants A1, A2, E1, and E2 are entered in cells K11 through K14 In order to optimize the constants solution, a guess must be entered into the constant cells (K11 through K14) Any numbers should be sufficient, so entering 1 for each of the constants should be a good start We are now ready to invoke the solver function of Excel Select the TOOLS menu in Excel and select the SOLVER function The settings for the SOLVER dialogue box are shown below: Equal to: MIN Value of: 0 By Changing Cells: $K$11:$K$14 Set Target Cell: $I$46 And under the OPTIONS dialogue box, Iterations = Max time = 100 Sec Precision = 0001 Tolerance = 5% These settings will vary the values of the constants (A1, A2, E1, E2) until the sum of all the errors (cell 7 07/09/00

8 I46) is optimally close to zero As shown in Table 3, the constants are iterated to be: A1= E1= B1= E2=4708E-05 These are substituted into the B2 element as shown in Table 2 In order to show the excellent results of the curve fit, the data was plotted against the curve fit equation The resulting plot is shown in Figure 2 Magnetics Inc Kool Mu Core 77XXX u=125 % Permeability H - Oersteds Curve Fit Results Data Sheet Values Figure 2: % Permeability vs Magnetizing Force for U=125 We now have all the parameters and equations needed to construct our SPICE equivalent model of the Kool Mu core The IsSpice netlist is shown in Table 4 The SPICE subcircuit is compatible with the 8 07/09/00

9 parameter passing capabilities of IsSpice N (Turns), DCR (DC resistance), and IC (initial current) are passed to the model by the schematic Initial current is passed in case the user wants to utilize the convergence aid of an initial condition Table 4: Spice 3 compatible Netlist of core ********** *SRC=77140;ku77140;Magnetic Cores;Koolmu; *SYM=MPP1 SUBCKT {N= DCR=01 IC=0} R1 1 4 {DCR} V1 3 2 G G C1 8 9 {N^2*26*1n} IC={IC} R2 9 2 {1/(6283n*0707meg*26*N^2)} B1 5 2 V=ABS(1256*{N}*I(V1)/817) B2 6 2 V=(096402*E^-(125*V(5,2)*00017))-(-00893*E^-(125*V(5,2)*000047)) B3 7 2 V=V(4,3)/(V(6,2)+02) B V=V(6,2)*{N^2*26*1n} ENDS ********** In order to test the accuracy of the saturation characteristics, a test circuit was constructed that would generate % permeability vs Magnetizing Force The SPICE model is shown in Figure 3 and the netlist is shown in Table 5 The resulting plot is shown in Figure V U X H3 V3 3 V(3) H V1 0 Figure 3: Saturation test circuit 9 07/09/00

10 Table 5: Netlist for test circuit C:\DATA\CIRCUITS\Ku_tst1 *SPICE_NET DC V SUBCKT 77140# R M V1 3 2 G G C U IC=0 R M B1 5 2 V=ABS(1256*20000 *I(V1)/817) B2 6 2 V=(096402*E^-(125*V(5,2)*00017))-(-00893*E^-(125*V(5,2)*000047)) B3 7 2 V=V(4,3)/(V(6,2)+02) B V=V(6,2)*10400U ENDS PRINT DC V(6:X11) OP *ALIAS V(2)=L *ALIAS V(3)=H *ALIAS V(5)=VINP PRINT AC V(2) VP(2) V(3) VP(3) PRINT DC V(2) V(3) PRINT TRAN V(3) V(5) V3 5 6 H3 3 0 V X #0 *{N=20 DCR=01 IC=0 } V1 5 0 END 10 07/09/00

11 9000M 7000M % Permeability 5000M 3000M 10000M Magnetizing Force [Oersteds] in Volts 1 Figure 4: SPICE result of % Permeability vs Magnetizing Force As Figure 4 shows, the SPICE model closely represents the saturation characteristics of the core The techniques used above may be used across the Kool Mu family When using this model, remember the model characteristics are only valid at room temperature About the Author Scott Frankel is a Sr Staff Analyst at Analytical Engineering Inc AEI specializes in worst case analysis, simulation, and design for spacecraft electronics Scott is also a co-author of a book on SPICE simulations, soon to be published by McGraw-Hill Acknowledgements The author would like to graciously thank Steven Sandler for his invaluable assistance and insight regarding this topic 11 07/09/00

12 References [1] Magnetics Technical Bulletin No KMC-S [2] Magnetics Kool Mu Powder Cores Data book 1994 [3] Sandler, Steven M SPMS Simulation with SPICE 3 McGraw Hill /09/00