PEDS2009. Index Terms-- leakage inductance, magneto motive force (MMF), finite element analysis (FEA), interleaving, half turn, planar transformer

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1 PEDS9 The Analysis and Comparison of Leakage Inductance in Different Winding Arrangements for Planar Transformer Ziei Ouyang, Ole C. Thomsen, Michael A. E. Andersen Department of Electrical Engineering, Technical University of Denmark Kgs. Lyngy, 8, Denmark Astract -- The coupling of the indings can e easily increased y using multiply stacked planar indings connection. Interleaving is a ell-knon technique used to reduce leakage inductance and minimize high-frequency inding losses. The paper aims to analyze leakage inductance ased on magneto motive force (MMF and energy distriution in planar transformer and correct the formula of leakage inductance proposed y previous pulications. The investigation of different inding arrangements shos significant advantages of interleaving structure. In this ork, a novel half turn structure is proposed to reduce leakage inductance further. Some important issues are presented to acquire desired leakage inductance. The design and modeling of kw planar transformer is presented. In order to verify the analytical method for leakage inductance in this paper, finite element analysis (FEA and measurement ith impedance analyzer are presented. Good matching eteen calculation, FEA D simulation and measurement results is achieved. Index Terms-- leakage inductance, magneto motive force (MMF, finite element analysis (FEA, interleaving, half turn, planar transformer I. INTRODUCTION In recent years, planar transformers have ecome increasingly popular in high frequency poer converter design ecause of the advantages they achieved in terms of increased reliaility, reproduciility, and increased poer density. In terms of circuit performance one of the advantages of planar transformer is lo profile and repeatale leakage inductance []. The leakage inductance causes the main sitch current at the device input to vary at a lo slope eteen zero and rated value and reduces the rate of commutation eteen output diodes. In addition, the stored energy in the leakage inductance leads to the generation of voltage spikes on the main sitch hich, esides creating EMI prolems, increases the sitching losses and loers the efficiency []. Therefore, most designers expect the leakage inductance to e as small as possile. Hoever, in some applications such as a phase-shift-modulated soft sitching DC/DC converter, the magnitude of the leakage inductance determines the achievale load range under zero-voltage operation, and a relatively large leakage inductance is desirale. This paper aims to calculate the leakage inductance stored in planar transformer y analyzing magneto motive force (MMF and energy distriution. Section ІІ defines leakage inductance using the perspective of energy. The energy associated ith leakage inductance should e equal to the sum of energy stored in each element layer inside the core indo. The section also analyzes the magnetic field strength in each layer and finite element analysis D model is simulated to demonstrate the correctness of the analytical method. As presented in previous pulications [3-5], the formula (see eqn.6 is generally used to calculate the leakage inductance. Hoever, it must e noted that the formula doesn t provide precise results. It assumes that the magnetic field strength along the height of insulator layer eteen noninterleaved sections varies linearly ut actually it should keep constant during the hole area of insulator layer. In order to correct the previous formula, a ne formula suited for symmetrical inding arrangement is proposed in this paper. The error analysis on the to calculations is also presented. Section ІІІ proposes a novel half turn structure to reduce leakage inductance further. The MMF distriution curve for half turn arrangement is analyzed and leakage inductance is computed. Section ІV descries some important issues to require desired leakage inductance including copper thickness, the thickness of insulator layer and the numer of turns. Section V evaluates the good matching eteen calculation, FEA D simulation and measurement ith impedance analyzer (PSM735+ Impedance Analysis Interface and Kelvin Fixture hich indicates the correctness of the analytical method and the proposed calculation. Section V provides the conclusion. II. BASIC DEFINITION AND CALCULATION FOR LEAKAGE INDUCTANCE A. Basic Definition of Leakage Inductance Not all the magnetic flux generated y AC current excitation on the primary side follos the magnetic circuit and link ith the other indings. The flux linkage eteen to indings or parts of the same inding is never complete. Some flux leaks from the core and returns to the air, inding layers and insulator layers, thus these flux causes imperfect coupling. If the secondary is short-circuited, the main flux hich links oth indings ill e negligile ecause the primary and secondary ampere turns almost cancel. So the leakage flux parts don t lose their individual identities. It is seen from Fig. that ithin the inding area the mutual repulsion causes the leakage flux to lie approximately parallel to the inding interface. The leakage inductance referred to the primary can e accessed y the energy stored in a 43 Authorized licensed use limited to: Danmarks Tekniske Informationscenter. Donloaded on August 3, at 8:7:3 UTC from IEEE Xplore. Restrictions apply.

2 PEDS9 magnetic field, E energy = B H dv = L I lk p ( total symmetry axis d x ٠ P MMF Distriution N I S N I Fig. The leakage flux paths and magneto motive force variation (MMF B. Leakage Inductance Calculation For simplification to analyze MMF created y the indings, turns ratio : and total numer of turns 8 are used as example. The MMF varies linearly in inding layers (see Fig. can e assumed hen operation frequency is not very high. When the frequency is increased, MMF distriution ill concentrate on the surface of rectangle conductor ecause of eddy current effect. In practice, as frequency gros, the leakage inductances slightly decrease. Indeed, relative variation of leakage inductance as the frequency changes is quite small [6]. The leakage inductance for non-interleaving structure can e calculated as follos: Fig. Analytical scheme of MMF distriution for non-interleaving structure The differential volume of each turn is l dx, therefore the total energy is sum of the energy stored in each elementary layer hich can e expressed y μ h E = H l dx ( energy here l is the length of each turn, is the idth of each turn, h represents the thickness of each inding layer. Fig. shos the thickness d x, situated at a distance x from the inner surface of the secondary inding. The field strength along the flux path hich includes this layer depends on the numer of ampere turns linked y the path. Since the flux disperses rapidly on leaving the inding, the associated energy is much reduced and the reluctance of the path ithin the magnetic core can e ignored compared ith that of the path in the inding, therefore the flux path can e expressed y the idth rather than the full closed flux path. H may e taken as the field strength in the inding layer hich is assumed to e constant along the plane of layer, thus, for first primary layer, I x H = (3 h according to the eqn., the energy in the total inding space can e deduced then 4 h I ( x 4 h I ( x I dx + dx + ( ( h + h + h h h μ I 3I E ( ( h ( energy = l h h ( h h h I ( + h μ l 46( h + h = 44h I + 3 p (4 here h and h are the thickness of primary and secondary respectively, h is the height of insulator layers. Fig.3, Fig.4 and Fig.5 sho energy distriution (a and magnetic field strength distriution ( in non-interleaving structure, P-P-S- S-P-P-S-S structure and P-S-P-S-P-S-P-S structure respectively. Fig.4 and Fig.5 represent partial interleaving and complete interleaving inding arrangements respectively. It is ovious to see that interleaving structure provides significant advantage in reducing leakage inductance. The analytical MMF distriution (c can e verified y magnetic field strength distriution ased on FEA simulation results (. The good matching eteen ( and (c illuminates the correctness of analytical method. Based on the aove calculation, a ne general formula suited for symmetrical inding arrangement (symmetrical MMF distriution is proposed hich can e expressed y, l K + = h K h K K K K K L ( ( leakage μ M( h h h ( ( h h 3 = K = K here N N K K = ; M =, M N, N are the numer of turns on the primary and secondary respectively, M is the numer of section interfaces. C. The error analysis The formula (see eqn.6 as pulished in the previous reference [3-5] to compute the leakage inductance for the symmetrical interleaving structure, hich has een generally used to compute leakage inductance for most of designers. l N x L = leakage μ + x (6 M 3 here N is the numer of turns on the inding hich the leakage inductance is to e referred; M is the numer of section interfaces; x is the sum of all section dimensions perpendicular to the section interfaces and x is the sum of all inter-section layer thickness. It must e noted that the P-P- (5 44 Authorized licensed use limited to: Danmarks Tekniske Informationscenter. Donloaded on August 3, at 8:7:3 UTC from IEEE Xplore. Restrictions apply.

3 PEDS9 Fig.3 Non-interleaving structure (a Energy distriution in FEA D simulation ( Magnetic field strength distriution in FEA simulation (c Analytical MMF distriution Fig.4 P-P-S-S-P-P-S-S structure (a Energy distriution in FEA D simulation ( Magnetic field strength distriution in FEA simulation (c Analytical MMF distriution Fig.5 P-S-P-S-P-S-P-S structure (a Energy distriution in FEA D simulation ( Magnetic field strength distriution in FEA simulation (c Analytical MMF distriution S-S-S-S-P-P and P-S-S-P-P-S-S-P structures mentioned in pulication [3] have same leakage energy ith the P-P-S-S-P- P-S-S and P-S-P-S-P-S-P-S structures respectively. Hoever, it assumes that the magnetic field strength along the height of insulator layer eteen non-interleaved sections varies linearly hich is shon y the lue line in the Fig.6. Actually there is no extra flux path link ith the insulator layer, the MMF curve should, therefore, keep constant in the area of insulator layer (see lack line in Fig.6. The correctness of the latter analytical MMF distriution can e proved y FEA D simulation. Fig.6 Comparison of MMF distriution in to different analytical methods As an example, a planar transformer has een uilt ith EI 64/5/5 core, the length of each turn is mm, copper idth is mm and the thickness of primary and secondary are oth 45 Authorized licensed use limited to: Danmarks Tekniske Informationscenter. Donloaded on August 3, at 8:7:3 UTC from IEEE Xplore. Restrictions apply.

4 PEDS9.mm, the thickness of insulator layer is.3mm. The inding arrangements P-P-P-P-S-S-S-S, P-P-S-S-P-P-S-S and P-S-P-S-P-S-P-S ill e seen as case, case and case 3 respectively. Tale I descries the error eteen the proposed eqn.5 and the previous eqn.6. TABLE I. THE ERROR ANALYSIS TABLE Previous Calculation (eqn.5 The error Calculation (eqn.6 Case 45 nh 9 nh 9% Case 6.6 nh 8.9 nh 3% Case 3 nh 5.8 nh 7% III. NOVEL HALF TURN STRUCTURE The interleaving, partial interleaving and non-interleaving structures cause a significant difference in leakage inductance ecause of MMF distriution. From the MMF distriution curve, maximal magnetizing force in each layer determines the value of leakage inductance. Therefore half turn structure could e proposed to optimize leakage inductance further. One solution is to physically form half turn in top layer and ottom layer respectively. The other solution is to parallel the top layer ith ottom layer so as to sustain half current to flo, the other layers are still in series, only one turn in each layer. As can e seen from Fig.7, the MMF distriution has een shifted to e a symmetrical curve on the X axis. The maximal magnetizing force is reduced to half of primary current. Taken together eqn.-3, the energy in the total inding space can e found as follos, h I ( 8 / / x h I h ( x I x dx+ 6 ( dx+ dx h h μ h E energy = l I + 8( h μ l h + 4h = h I + 48 p (7 Fig.7 Analytical scheme of MMF distriution for half turn structure Oviously, the energy enclosed in the inding space gets a significant deduction, the leakage inductance therefore can e computed y l h + 4 h L leakage = μ h = 8. 4 nh + 48 This structure not only reduces the leakage inductance, ut also enefits the inding loss caused y skin effect and proximity effect. Referring to Doell equation [7], the quantity m represents the ratio of the MMF F (h to the layer ampere-turns NI. The value of m can directly affect proximity loss of inding [7-]. Interleaving indings can significantly reduce the proximity loss hen the primary and secondary currents are in phase. Regarding the interleaving structure, the value of m is equal to for each layer. Further, the value of m also can form to.5 y the half turn structure hich ill decrease proximity loss a lot. Of course, the maximal magnetizing force can e reduced further y paralleling more layers. The MMF curve can almost e distriuted into a line hich overlaps ith X axis if there are sufficient layers to e parallel. Hoever, I have to mention that it doesn t make sense ecause of sacrificing inding space. Fig.8 Magnetic field strength distriution and flux vector for half turn structure IV. IMPORTANT ISSUES FOR LEAKAGE INDUCTANCE A. The thickness of copper foil As e can see from eqn.5, leakage inductance can e influenced y the thickness of copper foil. It should e as small as possile if leakage inductance is to e reduced. Fig. 9 shos that the thicker the copper, the higher the leakage inductance ill e achieved. Hoever, the inding loss might e sacrificed if the thin copper foil is used. It is necessary to note that the ratio of ac-resistance and dcresistance ill e reduced ecause of the loer skin effect, although dc-resistance is increased. Therefore, there is an optimal value on the thickness of copper foil hich can alance leakage inductance and inding loss. B. The thickness of insulator layer Leakage inductance can e influenced further y the thickness of insulator layer hich also can e oserved from the equ.5. From Fig.9, the leakage inductance decreases hen the thickness of insulator layer is reduced. Considering capacitor effect eteen intra-indings and insulator strength, the thickness of insulator on t e too lo. The designer should find a alance eteen leakage inductance 46 Authorized licensed use limited to: Danmarks Tekniske Informationscenter. Donloaded on August 3, at 8:7:3 UTC from IEEE Xplore. Restrictions apply.

5 PEDS9 Fig.9 and self-capacitor. Reducing the insulation layer thickness elo a certain level ill result in a considerale increase of the total losses []. C. The numer of turns Comparing the charts (a, ( and (c in Fig.9, it can e seen that the numer of turns provide a significant difference in leakage inductance. The more numer of turns, the higher the leakage inductance ill e. Hoever, if the numer of turns is increased, inding loss ill e increased hich is not desirale. In reverse, core loss ill e reduced ecause of the variation of flux density is decreased. Therefore trade-off ecomes an essential design property. D. The others As knon from eqn.5, the permeaility of copper foil and insulator, the length and idth of conductor are also related to the leakage inductance. The relative permeaility can e controlled y different materials. Therefore, a leakage layer hich consists of ferrite film could e used to realize higher leakage inductance ithout sacrificing inding loss. This leakage layer can e used in half ridge resonant converter and many phase-shift applications to realize ZVS. FEA simulation results for interleaving structure ith different issues Fig. The prototype of kw planar transformer using in DC-DC converter V. EXPERIMENTAL VERIFICATION The design and modeling of kw planar transformer is uilt (see Fig.. The fold technique on the planar copper inding is adopted to avoid some undesirale prolem caused y the terminal connection. Furthermore, the different inding arrangements are quite flexile to e realized if the fold technique is used. In order to verify the analytical method for leakage inductance in this paper, the results ased on measurement ith impedance analyzer (PSM735+ Impedance Analysis Interface and Kelvin Fixture is presented. Fig. shos good matching eteen calculation, FEA D simulation and measurement results is achieved. The proposed novel half turn structure has een seen as case 4. Oviously half turn arrangement has est result in leakage inductance. There is no dout that small error exists eteen measurement and calculation ecause of complex magnetic flux in actual model. The tolerance of insulator thickness and short-loop in secondary side also might cause a slight error eteen measurement and calculation. In addition, extra connection also leads inaccuracy result. Fig. Comparison eteen calculation, FEA simulation and measurement VI. CONCLUSION The purpose for this paper is to find a solution to acquire a desired leakage inductance. An analytical computation of leakage inductance has een introduced. Several different inding arrangements have een investigated. Computed results are in good agreement ith those otained y FEA D simulation. The interleaving structure provides significant advantage in reducing leakage inductance. The previous formula has een corrected. In order to optimize leakage inductance and inding loss further, a novel half turn as proposed in this paper. Computed results shos a half turn structure enefit lo leakage inductance extremely. Some important issues including copper thickness, insulator thickness and numer of turns ere concluded to guide designer to otain desired value. The analytical method has een experimentally validated ased on a planar core transformer. Good matching is achieved eteen calculation, FEA simulation and measurement. 47 Authorized licensed use limited to: Danmarks Tekniske Informationscenter. Donloaded on August 3, at 8:7:3 UTC from IEEE Xplore. Restrictions apply.

6 PEDS9 ACKNOWLEDGMENT The authors gratefully acknoledge the support of this ork y Niels O. Christensen, Ole Poulsen, and Ee B. Hansen, Flux A/S company of Denmark. REFERENCES [] Meinhardt. M, Duffy. M, O'Donnell. T, O'Reilly. S, Flannery. J, O Mathuna. C. Ne method for integration of resonant inductor and transformer-design, realisation, measurements IEEE Applied Poer Electronics Conference and Exposition, APEC '99, vol., pp , March 999. [] William G. Hurley, David J. Wilcox. Calculation of leakage inductance in transformer indings IEEE Transactions on Poer Electronic, vol. 9, no., pp. 6, January, 994. [3] E. C. Snelling. Soft Ferrites, Properties and Applications, Butterorths, second edition, 988. [4] Ferrell. J, Lai. J.-S, Nergaard. T, Huang. X, Zhu. L, Davis. R. The role of parasitic inductance in high-poer planar transformer design and converter integration IEEE Applied Poer Electronics Conference and Exposition, APEC '4, vol., pp. 5 55, 4. [5] Ning. Zhu, van Wyk. J. D, Wang. F. Design of integrated parallel resonant transformers IEEE Poer Electronics Specialists Conference, PESC '5, vol., pp , June, 5. [6] Margueron. X, Keradec. J.-P, Magot. D. Analytical caculation of satic leakage inductances of HF transformers using PEEC formulas IEEE Transactions on Industry Applications, vol. 43, no. 4, pp , July, 4. [7] Roert W.Erickson, Dragan Maksimovic. Fundamentals of Poer Electronics, second edition, 4. [8] William Gerard Hurley, Eugene Gath, John G. Breslin, Optimizing the ac resistance of multilayer transformer indings ith aritrary current aveforms IEEE Transactions on Poer Electronics, vol. 5, No., March. [9] Alerto Reatti, Marian K. Kazimierczuk, Comparison of various methods for calculating the ac resistance of inductors IEEE Transactions on Magnetics, vol. 38, No. 3, May. [] Jan A. Ferreira, Improved analytical modeling of conductive losses in magnetic components IEEE Transactions on Poer Electronics, Vol. 9, No., January 994. [] Ackermann. B, Lealter. A, Waffenschmidt. E. Analytical modelling of inding capacitances and dielectric losses for planar transformers Proceedings of Computers in Poer Electronics, 4 IEEE Workshop, vol., pp. 9, Aug, 4. [] Maxell D Field Simulator, Ansoft Corporation, 48 Authorized licensed use limited to: Danmarks Tekniske Informationscenter. Donloaded on August 3, at 8:7:3 UTC from IEEE Xplore. Restrictions apply.