1. Pg 1 PEmag Assorted Features

2. Pg 2 Overview  PEmag is the “Advanced Modeling module” for PExprt  Based on finite element analysis  Considers geometry, frequency, and material effects neglected by PExprt  Can change the winding configuration to consider geometrical affects  Standalone application or directly coupled to PExprt

3. Pg 3 3D 2D 1D Layers InterleavedTop Down Toroids Planar AnalyticalAnalytical FEAFEA Analysis of Magnetic Components

4. Pg 4 Classical Procedure Actual Component Measurement Equipment Classical Model PEmag Component Description PEmag 1D Model 2D Model FEA solver Analytical  Using PEmag, no component is built until expected performance is obtained  Influence of the winding cofiguration can be verified Modeling Procedure

5. Pg 5 To obtain an accurate frequency dependant model of a ferrite core device To obtain an accurate frequency dependant model of a ferrite core device Magnetic fields Electric fields Current Voltage Frequency Waveform Geometry & Materials Distributionof depend strongly on Basic goal of PEmag models

6. Pg 6 Main Effects to be considered Produce Energy storage (electric+magnetic) and losses Physical effects Skin Proximity Gap effects End effects Typically known as: Leakage inductance + AC resistance + parasitic capacitances

7. Pg 7 Skin effect Skin depth At high frequency, current tends to flow through the surface

8. Pg 8 Proximity effect Opposite currents Parallel currents Opposite currents tend to flow together Parallel currents tend to separate

9. Pg 9 Flux distribution Current density distribution Air Gap Effect

10. Pg 10 PEmag Analytical 1D model

11. Pg 11 PEmag 1D model features  Fast model generation  Easy to implement  Frequency effects are taken into account  2D effects neglected (gap, end...)  Only valid in 1D winding strategies Advantages Drawbacks Very useful to model 1D winding strategies

12. Pg 12 z2 z1 Surface S  ’ b d e e ConcentricConcentric Top down PEmag 1D model description

13. Pg 13 Actualshape1Dshape Actualshape1Dshape Actualshape1Dshape Window filling: turns spacing Note: If turns fill window height, the equivalent 1D foil is nearly same width Note: If turns DO NOT fill window height, the equivalent 1D foil is thinner

14. Pg 14 Magnetic Field Distribution Note: If turns fill window height, the H-field is nearly vertical in 1 direction or 1D Note: If turns DO NOT fill window height, the H-field has strong radial component and is 2D

15. Pg 15 uzuz urur uu Concentric structure Hz z r Short Circuit “Concentric” Structure: Magnetic Field

16. Pg 16 uzuz urur uu Hr z Short Circuit Planar structure (top down) Hr r “Top Down” structure: Magnetic Field

17. Pg 17 H 1D Maxwell equations Transmission line equations 1D Maxwell equations PEmag 1D model description

18. Pg 18 Ampere’s Law: PEmag 1D model implementation Note: Each winding layer is represented by its own transmission line

19. Pg 19 TL_0 TL_2 X_conv_W_0 X_conv_W_2 // --- Interface electrical-magnetic --- // --- Xconv_W_0 ---... Xconv_W_0 definition // --- tline_0 ---... tline_0 definition INTERN C c_ais_prev_0 N1:=m_0, N2:=GND ( C:=4.552965e-014, V0:= ); INTERN C c_ais_next_0 N1:=m_1, N2:=GND ( C:=5.130374e-014, V0:= ); INTERN C c_ais_m_1 N1:=m_1, N2:=GND ( C:= 4.608742e-013, V0:= ); Simplorer Analytical Winding Model (1D)

20. Pg 20 // Core model generation // Windings // --- Xconvint0 ---... Xconvint0 definition // --- Xconvext0 ---... Xconvext0 definition // --- MODEL FOR LINEAR CORE --- INTERN L l_int N1:=wint, N2:=GND ( L:=2.497640e-009, I0:= ); INTERN R R_Eddy_int N1:=wint, N2:=GND ( R:=5.596031e-001 ); INTERN L l_ext N1:=wext, N2:=GND ( L:=2.497640e-009, I0:= ); INTERN R R_Eddy_ext N1:=wext, N2:=GND ( R:=5.596031e-001 ); upmconv Transmision Lines 0V upmconv Simplorer Analytical Core Model (1D)

21. Pg 21 PEmag FEA based 2D model

22. Pg 22 Model Structure 12 (s) i 1 Z 11 Z (s) 12 2 (s) iZ 22 Z (s) ++ W1 W2 R w1 + N dt 1 + u 1 u 2 R w 2 i 1 i 2 ++ N 1 i 1 i N 2 2 1  2  d 1  N dt 2 d 2  R 12 cc gg aa  11  22 PEmag 2D model (FEA based) description

23. Pg 23 LINEAR PROBLEM!! Superposition theorem applies for CURRENT, but not for LOSSES Winding resistance modeling using FEA FEA losses Z 11 (s) Z 22 (s) W1W2 1 2 3 4 Z 12 (s) Model losses TEST 1 TEST 2  J 2

24. Pg 24 FEA magnetic energyModel magnetic energy Z 11 (s) Z 22 (s) W1W2 1 2 3 4 Z 12 (s) LINEAR PROBLEM!! Superposition theorem applies for CURRENT, but not for ENERGY TEST 1 TEST 2  B 2  H 2 Winding inductance modeling using FEA

25. Pg 25 FEA Electric Energy     IDEdD+D DE DE DEDE III off   d       1 2 1 2 1 2 1 2 1 11 11 11    () (   E +E d off  1 ) () d d  ICVCVVVC CCV CCV CVV III off      1 2 1 2 1 2 1 2 1 2 11 22 1 2 1 111 2 1 2 11 11 () () () 1 2 Model Electric Energy Capacitive modeling using FEA

26. Pg 26 Core losses modeling (2D) IEEE Transactions on Magnetics, vol 27, NO. 6, November 1991 Ferrite Core Loss for Power Magnetic Components Design Waseem Roshen XSIMP1_1XMIMP1_2 isens1 Kcore

27. Pg 27 Frequency dependent core resistivity  Since energy and losses in the core are now frequency dependent, it is needed to use a frequency dependent resistivity in the core  PEmag 4 20 100 kHz 1 MHz 10 MHz  f MnZn Ferrites

28. Pg 28 Modeling Assumptions in PEmag

29. Pg 29 2D RZ model of 3D device Actual DeviceRZ Model

30. Pg 30 d1 d2 d3 d4 Modification of Simulated Dimensions  Window Height and Window With are the same in both structures  d1 is modified in order to obtain the same central leg area in both structures  d2 is modified in order to obtain the same external leg area in both structures  d3 is modified in order to obtain the same core volume in both structures 2D RZ model of 3D device

31. Pg 31 Core Conductor Actual Device RZ Model Modification Conductor Resistance

32. Pg 32 Modification Window Air Permittivity Insulator (   2-3) Copper Real Simulated Air (  = 1) Air (   1) Copper Note: Since the insulation on a conductor is not explicitly modeled, the permitivity of the conductor is adjusted slightly

33. Pg 33 Example: 94 turns each layer Use of Equivalent Layers  For transformers with > 500 total turns, it is difficult to solve for every turn  An equivalent layer can be used as an approximation  Equivalent layers with the same DC resistance and ampere-turns are created in order to help the FEA solver to obtain a solution

34. Pg 34 CONNECTION WIRES CONNECTION WIRES CURRENT DISTRIBUTION FOIL Foil conductors in PEmag  Current crowds at the end of a foil winding where the lead connects  Note: this is a 3D effect which cannot be calculated using a 2D FEA solver

35. Pg 35 AC and time domain models  Choose the appropriate model based on the Simplorer simulation that will be performed  In general, the time domain model is simpler than the frequency domain model, and may converge better

36. Pg 36 AC and time domain models Time Domain: Frequency Domain: Foster Network

37. Pg 37 Magnetic Circuit name Magnetic Circuit nodes Magnetic Definition //+---------------------------------------------------+ //| PExprt FEA based MODEL FOR MAGNETIC COMPONENT. | //| SIMPLORER(C) VERSION 6 LANGUAGE VERSION | //| GENERATED BY PExprt (C) UPM-Ansoft 1992-2004 | //| Version 6.0.11 | //+---------------------------------------------------+ //| Frequency Domain Model Version | //+---------------------------------------------------+ MODELDEF Course { // Model Type FEA PORT electrical: ap_center; PORT electrical: am_center; // Magnetic circuit definition } Simplorer FEA based (2D) Model

38. Pg 38 // Model Type: FEA PORT electrical: ap_center; PORT electrical: am_center; PORT electrical: bp_center; PORT electrical: bm_center; INTERN AM AMsens1 N1:=ap_centerx, N2:=N1_1; // --- Winding 1 --- // Winding wind_1 … Winding definition // END Winding wind_1 INTERN R REddy_W_1 N1:=N1_4, N2:=am_center ( R:=1.998186e+005 ); // --- MODEL FOR LINEAR CORE RM12/I --- INTERN R RMAGLINEAR_PExprt_Core N1:=M4, N2:= GND ( R:= 1.613822e+005 ); // --- Mutual and Self Impedances --- // --- Z1_1 --- // Self Impedance 1 … Self Impedance definition // END Self Impedance 1 // --- Z1_2 --- // Mutual Impedance 1 2 … Mutual Impedance definition // END Mutual Impedance 1 2 } W_1 SIMP1_1 MIMP1_2 REddy1 ap am AMsens1 core Simplorer FEA based (2D) Model

39. Pg 39 // Self Impedance 1 R Rser_1_1_0 N1:=N1_1, N2:=N1_1_0 ( R:=1.442450e-002 ); L Lser_1_1_0 N1:=N1_1_0, N2:=N1_1_1 ( L:=2.465325e-006, I0:= ); R Rpar_1_1_1 N1:=N1_1_1, N2:=N1_1_2 ( R:=1.567802e-001 ); L Lpar_1_1_1 N1:=N1_1_1, N2:=N1_1_2 ( L:=2.518019e-007, I0:= ); R Rpar_1_1_2 N1:=N1_1_2, N2:=N1_1_3 ( R:=5.753948e+001 ); L Lpar_1_1_2 N1:=N1_1_2, N2:=N1_1_3 ( L:=8.082232e-007, I0:= ); R Rpar_1_1_3 N1:=N1_1_3, N2:=N1_2 ( R:=3.008290e-003 ); L Lpar_1_1_3 N1:=N1_1_3, N2:=N1_2 ( L:=5.587515e-009, I0:= ); // END Self Impedance 1 Foster Network a p Self-Impedance Simplorer FEA based (2D) Model

40. Pg 40 Foster Network isens EDROP N1_3 N1_2 // Mutual Impedance 1 2 INTERN I IIsens_1_2 N1:=GND, N2:=z_1_2 ( IS := AMsens2.I, PARTDERIV := 1, AC_PHASE := 0, AC_MAG := AMsens2.I ); INTERN VM VMZ_1_2 N1:=z_1_2, N2:=GND ; INTERN E EUdrop_1_2 N1:=N1_3, N2:=N1_2 ( EMF := VMZ_1_2.V, PARTDERIV := 1, AC_PHASE := 0, AC_MAG := VMZ_1_2.V ); R Rser_1_2_0 N1:=z_1_2, N2:=N12_1_0 ( R:=-1.931039e-003 ); L Lser_1_2_0 N1:=N12_1_0, N2:=N12_1_1 ( L:=2.769650e-006, I0:= ); R Rpar_1_2_1 N1:=N12_1_1, N2:=N12_1_2 ( R:=-1.545651e-004 ); L Lpar_1_2_1 N1:=N12_1_1, N2:=N12_1_2 ( L:=-1.022399e-009, I0:= ); R Rpar_1_2_2 N1:=N12_1_2, N2:=N12_1_3 ( R:=-2.835523e-001 ); L Lpar_1_2_2 N1:=N12_1_2, N2:=N12_1_3 ( L:=-3.918711e-008, I0:= ); R Rpar_1_2_3 N1:=N12_1_3, N2:=GND ( R:=-9.547027e-002 ); L Lpar_1_2_3 N1:=N12_1_3, N2:=GND ( L:=-9.382589e-008, I0:= ); // END Mutual Impedance 1 2 Mutual-Impedance Simplorer FEA based (2D) Model

41. Pg 41. // --- C1_1 [F] --- INTERN C c1_1 N1:=ap_center, N2:=am_center ( C:=1.797270e-012, V0:= ); // --- C1_2 [F] --- INTERN C c1_2 N1:=ap_center, N2:=bm_center ( C:=-7.521580e-015, V0:= ); // --- Co1_2. [F]. --- INTERN C co1_2 N1:=am_center, N2:=bm_center ( C:=5.781070e-011, V0:= ); Magnetic Model ap am bp bm Capacitive Model Simplorer FEA based (2D) Model

42. Pg 42 Connection wires Short circuit wires Typical values of the connections (using a solid wire of 0.75 mm diameter) @1MHzRL 5mm 8m  26nH 10mm 14m  63nH 15mm 22m  107n H Winding Connection Effects  Note: Not considered in the FEA simulation, but can be added as parasitic R,L

43. Pg 43 W_1 SIMP1_1 MIMP1_2  Choose Modeler / External Connections to specify extra lead resistance and inductance Winding Connection Effects

44. Pg 44 With connections Transformer Studied Geometric parameters : Core shape and size: custom made Core material: 3F3 Conductors: foils, 70  m thick Windings: Two in 11 layers Turns: Primary: 5; Secondary: 11 Substracting connections PEmag model vs measurements Winding Connection Effects

45. Pg 45 Extra Features in PEmag

46. Pg 46 Twisted wire type  This can be used to model every strand in a Litz wire for actual skin and proximity effect  Practical limit is <1000 strands total in the model

47. Pg 47 Extra Core Shapes: T, I, DRUM  These are not available in PExprt

48. Pg 48 Shield Electrostatic shields modeling  Shields should be modeled as an extra winding

49. Pg 49 Center tap  Must be modeled as two independent windings  Connect together later in the Simplorer simulation Center tapped windings modeling

50. Pg 50 Al value calculation  PEmag can calculate the Al value for the core  Based on the IEC calculation method

51. Pg 51 Effective values calculation  PEmag can calculate the effective area and length of a core  Based on the IEC calculation method

52. Pg 52 Margin tapes  Can add top or center margin tapes to the winding

53. Pg 53 Numbering bobbin pins

54. Pg 54 Move layer feature

55. Pg 55 Parallel layer feature

56. Pg 56 Integrated Magnetics

57. Pg 57 Integrated Magnetics

58. Pg 58 Integrated Magnetics

59. Pg 59 Three Phase Components