Minimum Loss Design of a 100 khz Inductor with Litz Wire

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1 IEEE IAS Annual Meeting New Orleans, LA, Octber 5-9, 1997 Minimum Lss Design f a 100 khz Inductr with Litz Wire Ashkan Rahimi-Kian Ali Keyhani Jeffrey M. Pwell Student Member, IEEE Senir Member, IEEE Department f Electrical Engineering Research and Develpment The Ohi State University Liebert Crpratin Clumbus, OH 4310 Clumbus, OH 439 Phne ( , {ashkan, keyhani@ee.eng.hi-state.edu} Abstract - In this paper, a minimum lss design f a 100 khz inductr with litz wire using an iterative design prcedure is presented. The finite element analysis methd has been used t investigate the effects f air-gaps and number f turns n the field distributin, perating flux density, leakage flux and cre lsses. I. INTRODUCTION A cnsiderable effrt has been directed twards highfrequency inductr and transfrmer design [1,,3,4,5,6]. The minimum lss design f a 100 khz inductr with fil windings and Ferrite cre has been perfrmed by A.Nysveen and M.Hernes [1]. In this paper, the minimum lss design f a 100 khz inductr with litz wire and Permally80 (Cut-C cre is presented. In high-frequency inductrs, winding lsses are nrmally kept under cntrl by using fil cnductrs r multi-strand litz wire. When such cnductrs are prperly designed, additinal lsses defined as skin effect and prximity effect (eddy rrents can be kept at very lw values. Bth fil cnductrs and litz wire have their advantages and draw backs. Litz wire is fairly easy t wind up and terminate and is adaptable t varius windw gemetries; n the ther hand, litz wire is expensive and gives a pr fill factr (area f the bare cnductr t the area f the wire. Fil cnductrs are fairly easy t prduce in a variety f heights and weights, and if ptimum fil height fr a given number f turns is used, the winding becmes cmpact an has a ptential fr lw lsses. Hwever, the ptimal fil winding tends t becme very wide where high rrent, high frequency and a large number f turns are presented at the same time. The additinal winding lsses are induced by the fringing flux near air-gaps. Fringe field causes eddy rrents in the fil winding when trying t penetrate the winding. A quasi-distributed air-gap, built by a high number f small discrete air-gaps, is used t avid this prblem [1]. II. PROBLEM DESCRIPTION The bjective f this study is t develp an iterative inductr design prcedure and t minimize the cre and winding lsses f an inductr using the finite element methd. The tw fundamental issues in the design f any highpwer high-frequency inductr are minimum lsses and lw leakage flux. Cre lsses and winding lsses are strngly related t the frequency. Cre lss, fr a given frequency and flux density, is material dependent. Therefre, as a first step in the design prcess, an investigatin f varius high frequency cre materials is essential. Cpper lss in the inductr is extremely sensitive t the leakage flux distributin in the windw area, which in turn is dependent n the cre and winding gemetry. The characteristics f a gd cre material include lw specific lsses (defined as lsses per unit vlume r per unit mass at high perating frequencies, high saturatin flux density, high pwer/weight rati, and gd thermal and mechanical prperties. In high-frequency inductr design, lw lss materials such as Ferrite, Permally80 and Metglas605SC are clearly the best chices. Table 1 lists sme f their salient prperties. Hwever, the Ferrite material has higher lsses than the Permally80, it has a wide range f cre gemetries and lwer cst than Permally80. III. COMPUTER-AIDED DESIGN OF HIGH- FREQUENCY INDUCTORS A transfrmer generally appraches ptimum efficiency fr a given vlume, if its cpper lsses are equal t the cre lsses. The same rule applies fr maximizing the Q-factr in an inductr. The Q-factr f an inductr is the tangent f the

2 TABLE 1 CORE MATERIAL PROPERTIES phase angle between its vltage and rrent. At very high frequencies, the inductive reactance is very high and the effect f winding resistance (R s is very small. The inductr Q-factr is maximized at a frequency that the cre lsses are equal t the cpper lsses []. A cmputer prgram was develped t design an inductr based n area prduct (A p apprach [3]. The prgram selects ne cre material frm the data base (48 cres frm the Magnetics Cut-Cres catalgue at a time and implements the design steps fr all the wires (31 litz wires frm the New England Electric Wire catalgue. Thse cre materials and wires that can satisfy the cnditin, P P (within 10% tlerance, will be selected by the prgram. The flw chart f the design prcedure is shwn in figure 1. IV. DESIGN STEPS The design specificatins fr the inductr are shwn in Table. TABLE SPECIFICATIONS FOR THE INDUCTOR The design steps f the cmputer prgram are as fllws: 1. Callatin f the inductr vltage: V π f L I (V (1. Callatin f the energy: 1 Eng L I (W.s ( 3. Callatin f the windw area: W a G F (cm (3 G Inner cre height (cm F Inner cre width (cm Cre type Ferrite (P Permally80 Metglas605SC B m (T Ω-m Shape E, I, U, Trids Trids,Cut C-cres Trids,Cut C-cres 4. Callatin f the area prduct: Ap Wa Ac cm (4 A c Cre crss sectin (cm 5. Callatin f the initial utilizatin factr: K u s1 s s (5 A s 1 A + A 055. Inductance ( L 10 H Current ( I 75 Arms Frequency ( f 100 khz fe ins A Cpper area (cm A ins Insulatin area (cm s Fill factr 0.6 s 3 Usable windw area / Windw area Callatin f the maximum perating flux density: Eng 1e4 Bm (T (6. 86 A K K p u j K j Thermal cefficient 486 at T c 50 K u Callatin f the rrent density: J K ( A.14 (A/cm (7 j p 8. Callatin f the number f turns: V 1e4 N 4. 44Bm f Ac (8 9. Callatin f the air-gap length: N Ac 1e lg L (cm (9 4π 1e Callatin f the fringe flux effect cefficient: lg G FFC 1+ lg(. 5 ( A l (10 c 11. Recallatin f the number f turns: lg L N (. 5 Ac FFC 1e 1. Recallatin f the perating flux density: B ac N I 1e l g g (11 (T (1 13. Callatin f the cre lsses: P ( f ( B 1e4 W (W (13 fe ac e W e Cre weight (lb. 14. Callatin f the mean length f each turn:

3 [ ] MLT E + D + 4 ( OD + Bbbin (cm (14 E Cre leg width (cm D Cre leg thickness (cm OD Wire utput diameter (cm Bbbin Bbbin thickness (cm 15. Callatin f the litz wire ac-resistance:.5 ID f G 4 s ( ( Rac NSTRD ID Fs H + ( Gs (16 R OD dc G s Eddy rrent basis factr H Single strand R ac Rdc 1 ID Diameter f the individual strands ver cpper (cm NSTRD Number f strands Rac Fs Rdc N MLT ( 38. e 5 (Ω ( Callatin f the winding lsses: P Rac I (W ( Check if: P P fe (within 10% tlerance 18. Callatin f the number f layers: N OD M G M arg in (19 M arg in Distance between the winding and the tp cre leg (yke (cm 19. Callatin f the windw utilizatin factr: Wttal Ku Wa (0 W ttal Winding area + Bbbin area Wh Ww W h Winding height G M arg in (cm W w Winding width M OD + Bbbin (cm 0. Callatin f the ttal inductr lsses: Pttal P + Pfe (W (1 1. Callatin f the inductr Q-factr: X L RP Q R R + X ( P ac L R P Cre resistance ρ lc (Ω Ac 1e ρ Cre resistivity 0.57 (Ω.m X L Inductr reactance π f L (Ω l c Magnetic path length (cm. Select anther cre and repeat steps 1-1. Select anther cre size Cre Data Wire Data Determine: 1. windw area (W a. cre crss sectin (A c 3. perating flux density (B m 4. number f turns (N 5. air-gap length (lg 6. new perating flux density (B p 7. cre lsses (P fe 8. Litz wire ac-resistance (R ac 9. winding lsses (P 10. windw utilizatin factr (K u P P fe Yes Stre the results End Figure 1. Design prcedure flw chart V. FINITE ELEMENT ANALYSIS N, select anther wire size A finite element package FLUXD [7] was used t evaluate the acracy f the inductr analytical design. FLUXD has the ability t callate magnetic field and eddy rrent lsses by slving the vectr ptential equatin, 1 ( j ωσa + rt[ rt( A] J (3 r The bundary cnditin was set t Dirichlet cnditin with a zer value f vectr ptential ( A 0 alng the bundary line. The selected crss sectin f the inductr gemetry used in the finite element analysis is shwn in figure. The materials used in the bbbin and insulatin between layers are nnmagnetic. Therefre, they were mdeled as air ( r 1. VI. MAGNETO-THERMAL ANALYSIS Cre lsses and winding lsses determine the thermal lsses. High lsses due t high frequency peratin will result in very high temperature that can exceed the safe perating temperature fr the inductr. Therefre, fr safe peratin, the thermal analysis shuld be perfrmed t determine the perating temperature fr the resulting lsses.

4 FLUXD has the ability t cmpute the temperature gradient f an inductr using magnet-thermal analysis. In thermal analysis f an inductr, hysteresis, eddy rrents and winding rrent are cnsidered as heat surces. There are tw ways f heat transfer between the inductr and its surrundings: 1. Cnvectin heat transfer: The cnvectin heat transfer crs between a fluid in mtin and a bunding surface when the tw are at different temperatures. q h ( Ts T (W/m (4 q Cnvective heat flux h Cnvectin heat transfer cefficient T s Surface temperature ( c T Fluid temperature ( c. Radiatin heat transfer: The thermal radiatin is energy emitted by matter that is at a finite temperature. The energy f the radiatin field is transprted by electrmagnetic waves. q εσt 4 s (W/m (5 q Radiative heat flux frm the surface ε Emissivity f the surface σ Bltzmann cnstant T s Abslute temperature f the surface ( c VII. RESULTS OF THE ANALYTICAL DESIGN The numerical results f the analytical design fr ne f the selected cres by the prgram (cre n. 13 are shwn in Table 3. It can be seen frm the results that cre lsses and winding lsses are clse tgether. Therefre, the Q-factr f this inductr is nearly maximum (100. At high frequencies, litz wire can imprve the Q-factr f the gapped inductr cnsiderably. The diameter f the litz wire is abut 40% greater than slid wire f the same crss sectinal cnductr area because f its cmplex twisted structure and the presence f a large amunt internal insulatin. The results shw that the windw utilizatin factr is relatively lw (0.345 which is the penalty fr using litz wire. TABLE 3 LITZ WOUND CUT-C CORE (1MIL-PERMALLOY80 INDUCTOR WITH AIR-GAP Cre # 13 Winding lsses (W 6.6 Cre lsses (W 4.7 Operating flux density (T.15 Cre crss sectin (cm Cre weight (g 408. Cre vlume (cm Windw area (cm 14.5 Windw utilizatin factr.345 Air-gap length (mm 10.7 Number f turns 13 Number f layers 1 Ac-resistance (mω 4.7 Q-factr 100 Current density (A/cm 93 Wire AWG # 38 Wire diameter (mm 4.8 Wire bare area (cm.095 N. f strands 1050 VIII. FINITE ELEMENT RESULTS The finite element analysis results f the candidate inductr are presented in Table 4. They clearly shw that the results f the analytical inductr design (area prduct apprach are in gd agreement with the finite element results except in cre lsses. The eddy rrent lsses can nt be callated in the analytical design, but at high frequencies they can nt be neglected. The finite element results shw that cre lsses (Hysteresis and eddy rrent lsses are cnsiderably larger than winding lsses. Therefre, this inductr is nt a minimum lss design. The equi-flux lines f the candidate inductr are shwn in figure. XI. ITERATIVE DESIGN STEPS The iterative design steps are as fllws: Step 1. Select all the cres and wires such that, P P. When this cnditin is satisfied, the inductr Q-factr will be maximized. Step. D the finite element analysis fr the candidate inductr designed in step 1. Step 3. Increase the number f turns t reduce the perating flux density and cnsequently the cre lsses. Step 4. Increase the air-gap length t reduce the inductance t the desired value. fe

Step 5. Change the single big air-gap t small distributed air- gaps t reduce the fringe fields in the winding area. Step 6. D the magnet-thermal analysis fr the minimum lss inductr.

5 Step 5. Change the single big air-gap t small distributed air- gaps t reduce the fringe fields in the winding area. Step 6. D the magnet-thermal analysis fr the minimum lss inductr. TABLE 4 FINITE ELEMENT ANALYSIS RESULTS OF THE CANDIDATE INDUCTOR Design # 1 Number f air-gaps 1 Length f air-gaps (mm 10.7 Number f turns 13 Winding resistance (mω 4.7 Current (Arms 73 Inductance (H 10.9 Operating flux density (T 0.3 Winding lsses (W 5 Cre lsses (W 61 Current density (A/cm 308 Eddy rrent (Arms.45 Fr a given cre size and frequency, cre lsses are prprtinal t the perating flux density []. As the flux density is reduced by increasing the number f turns, cre lsses decrease. The increment f the number f turns will increase the amunt f inductance which is nt desirable. N Ac L (6 l g It can be seen frm equatin (6 that the inductance can be reduced t its desired value by increasing the air-gap length. As it was mentined earlier, the prblem with big single air-gap is high magnetic fringe field in the winding area. This prblem can be slved by using many small airgaps instead f ne big air-gap. It is imprtant that there be a certain distance between air-gaps when there are many f them in ne cre leg. Otherwise, the air-gaps will be shrt cirited and als the manufacturing cst will be increased. It is recmmended that the distance between the tw air-gaps be greater than fur times f ne air-gap length [1]. In the secnd design, the number f turns was increased t 16 and the air-gap length t 17.8 mm. The finite element analysis results are shwn in clumn f Table 5. It can be seen frm the results that the cre lsses (Hysteresis and eddy rrent lsses have been reduced frm 61 watts t 40.8 watts which is cnsiderable. Figure. Equi-flux lines f the candidate inductr In the third design, the number f turns was increased t 0 and the single big air-gap (17.8 mm was changed t five small distributed air-gaps (3.56 mm each. The finite element analysis results are shwn in clumn 3 f Table 5. They shw that the cre lsses are reduced t 19.7 watts and all design specificatins are als met. This design can be cnsidered as a minimum lss design fr this cre size. If we wanted t increase the number f air-gaps mre than five, the manufacturing csts wuld be much higher. The inductr gemetry and equi-flux lines f design n. 3 (minimum lss design are shwn in figure 3. The temperature gradient f design n. 3 is shwn in figure 4. It can be seen frm the graph that the temperature is maximum between the winding and the cre leg (8.5 c. X. CONCLUSION In this paper, an iterative design prcedure t design minimum lss high-frequency inductrs with litz wire is presented. The finite element analysis methd is used t minimize the inductr cre lsses (Hysteresis and eddy rrent lsses. A 10 H, 75 Arms inductr with 100 khz perating frequency is designed thrugh the develped iterative design prcedure. It is shwn that the cre lsses can be reduced cnsiderably by increasing the number f turns and using small distributed air-gaps as shwn in Table 5.

6 TABLE 5 FINITE ELEMENT ANALYSIS RESULTS OF DIFFERENT DESIGNS Design # 1 3 Number f air-gaps Length f air-gaps (mm Number f turns Winding resistance (mω Current (Arms Inductance (H Operating flux density (T Winding lsses (W Cre lsses (W Current density (A/cm Eddy rrent (Arms Figure 3. Equi-flux lines f design n. 3 Figure 4. Temperature gradient f design n. 3

7 ACKNOWLEDGMENT This wrk was supprted by the Liebert C., Clumbus, OH. The use f FLUXD sftware frm the MAGSOFT C. is gratefully acknwledged. REFERENCES [1] N. Nysveen, M. Hernes, Minimum Lss Design f a 100 khz Inductr with Fil Windings, EPE Cnference Prceedings 1993, pp [] Dnald E. Pauly, Selecting Transfrmer/Inductr Cre Material, Pwer Supply Magnetics, January 1996, pp [3] W. T. McLyman, Transfrmer and Inductr Design Handbk, New Yrk: Mercel Dekker, [4] M. A. Prestn, R. W. De Dncker, R. C. Oney, C. M. Stephens, High-Current High-Frequency Inductrs fr Resnant Cnverters, EPE Cnference Prceedings 1991, pp [5] W. A. Rshen, R. L. Steigerwald, R. J. Charles, W. G. Earls, G. S. Claydn, C. F. Saj, High-Efficiency, High- Density MHz Magnetic Cmpnents fr lw Prfile Cnverters, IEEE Trans. Industry Applicatins, vl. 31, n. 4, July 1995, pp [6] M. S. Rauls, D. W. Nvtny, D. M. Divan, Design Cnsideratins fr High Frequency C-Axial Winding Pwer Transfrmers, Research Reprt, WEMPEC, June [7] FLUXD user manual, MAGSOFT C., Nv

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