Optimum design of high frequency transformer for compact and light weight switch mode power supplies (SMPS)

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1 Optimum design o high requenc transormer or compact and light weight switch mode power supplies (SMS Karampoorian. H. R api. Gh Vahedi. A Zadehgol. A Islamic Azad Uniersit o Khorramabad, Iran Iran Uniersit o science and technolog, Tehran, Iran Abstract in this paper a new approach or optimization o high requenc transormer design is presented. The presented design method is based on a restatement o the traditional transormer design equations to include non-sinusoidal switching waeorms and high requenc skin and proximit eects. In this optimization procedure both electric and thermal eects in the transormer is considered. Wae orm o oltage and current, and imum acceptable temperature rise, are used as input data. The aim o this procedure is the selection o the smallest that can delier desired power, and determination o optimum lux densit and current densit to reach a transormer with high power densit and admissible temperature rise. Since the transormer is the maor contributor to the olume and weight o the ower Suppl, the results o this transormer analsis can be used or entire power suppl optimization as well. Finall the alidit o presented method is analzed. Index terms losses, optimization method, proximit, skin, switch mode power supplies, thermal model, transormer I. INTRODUCTION Magnetic component technolog has receied considerable attention in recent ears. It is widel recognized that the abilit to manuacture small and eicient magnetic components is the ke to achieing high power densit that is important actor or power suppl in application such as satellite, airplane, computer or an compact and mobile sstems. It is a well-known act that reduction in the size o magnetic components hae been achieed b operating at higher requencies, mainl in switching circuits. Howeer the high-requenc transormer is the maor contributor in the size o an SMS since it determines about 5% o the oerall olume and more than 0% o the oerall weight []. Fundamental issues in the design o an high-power, high-requenc transormer are to minimize the power loss, olume and weight. This paper explores the optimum design o a high-power and high-requenc transormer, which contains: Selection o the smallest standard size releant to the throughput power, requenc, and transormer operating temperature. Calculation o the optimum lux and current densit proiding minimum transormer loss. In order to accomplish such a complex optimization procedure, inestigations were carried out in the ollowing areas: Core loss determination Copper loss determination Thermal modeling 4 Optimization II LOSS COMONENT The total loss o a transormer consists o two basic parts: copper loss and loss. In two ollowing subsection both o these components are discussed in detail. A Core loss The total loss is a result o three loss mechanisms: hsteresis, edd current and stra losses. Each o them computed as bellow []: hs α.. n ( ( π h edd ( 6ρ l stra 68. ( edd h ( Whereα, n, ρ, h and l are constants depend on material propert and dimensions o the, is requenc and is lux densit. As can be seen, all aboe equation are unction o and thus we can approximate the sum o them b: x loss cv.. (4 Where V is the olume o the and c, x and result rom the manuacturer data sheet b cure itting method [,]. Copper loss deinition, the copper loss in a two winding transormer carring high requenc current with an eectie alue I rms and I rms in primar and secondar side is: cu rms RIrms F RdcI rms F RdcI rms R I (5

2 Where: F i Rei Rdci (6 Is called an ac-resistance coeicient or i th harmonic and model skin and proximit eect in the conductor []. This coeicient is calculated b improed ormulation based on Dowell work [4]. This ormulation is as ollows: I K ni F i n I (7 n rms Where I ni, because o the nonsinuosoidal nature o the current wae orm o these transormers, are th n harmonic component o the current o i th winding. K n is calculated as ollows[]: K n sinh nδ cosh nδ sin nδ cos ( m nδ nδ (8 sinh nδ sin nδ cosh nδ cos nδ Where m is the number o laer and Δ is normalized diameter and shown as: h Δ K laer (9 δ Whereδ σμ0ω is skin depth at undamental requenc, h is thickness o the laer, μ0 is permeabilit o air, σ is the conductiit o the conductor and K laer is the porosit actor and is equal to the ratio o the total net height o the copper to the height o the window. Following picture illustrate these parameters. III TRANSFORMER TEMERATURE RISE Transormer temperature estimation is needed in design process in order to eri that material temperature speciications are not exceeded and also to take temperature dependence o loss mechanisms into account. Linear thermal resistances are requentl used in electronic design. Howeer, these should be used onl or conductie heat transer. ut in transormer thermal modeling there are another mechanisms in heat transer that are conection and radiation. These two phenomena are nonlinear and depend on the instantaneous temperature dierences between the obect and ambient. In this work heat transer mechanisms is considered and the transormer temperature rise is calculated as ollows [6]. Dissipated power cnection radiation A Conection Conectie heat transer capacit conection (W o a cube with dimensions in millimeter is: con con up con bottom con side (0 Those are dissipated power rom up, bottom and side surace o the bod. Each o them is: con con.5 up.4 Aup ΔT (.5 bottom.6 Abottom ΔT ( con.5 side.9 Aside ΔT ( h Core h hw Where and so on. Aup is the area o the upper surace o the bod ΔT is temperature rise and is: Δ T T surace T ambient (4 Substituting (, ( and ( into (0 ield:. 5 (.4A.6A.9A. ΔT con up up bottom side (5 RIMARY WINNDING SECONDARY WINDING M, K laer h/hw M4, K laer h/hw Fig..schematic diagram o transormer window Radiation Radiatie heat transer capacit radiation (w o an obect with emissie actor o 0.85 and dimensions in millimeter is: 4 [( Tsurace ( T ] 4 8 rad Atotal ambient (6

3 IV THERMAL SYSTEM Total dissipated power is a unction o three parameters as: T, T, obect dimention (7 total ( surace ambient (, EI E I K. F R dc I cv. ( F R dci x ( We can utilize o this unction in two orms as shown below: ploss Tambient Thermal Tsurace dimension model Tsurae Tambient dimension V OTIMIZATION The aim o this paper is to reach minimum size and imum eicienc or transormer, thus the obect unction that has to minimize is as: olum loss (8 Since McLman s work [7] it is obious that the product o area and winding area is a stand or transormer olume. Thus we use area product, A p instead o olume in our obect unction. Ap is calculated as below: A A A (9 Thermal model Fig.. Thermal sstem cu loss E A (0 K N Where E is the eectie alue o primar oltage, N is number o turn o primar and K is the orm actor o the oltage waeorm that is 4.44 or sinusoidal and 4 or square waeorm [7,8]. NI N I ( Acu K cu K cu Where Kcu is copper ill actor and is the current densit that assume to be equal at primar and secondar winding. Substitution o (0 and ( into (9 ields: E I E I A ( K J. And K K Kcu Substitution (4, (5 and ( into (8 or gien requenc results in : In ( R and dc Rdc are directl depend on and indirectl to. To replace them with their equialents the ollowing substitution is done: R dc l l ρ ρ a a a N (4 Where l a is aerage length o one turn o the primar winding and N and a are number turn and copper cross section o it respectiel and so on or secondar. Now there is: Where: (, F ρlani a a. I, a. I and EI EI K. cv. N i F ρ l ( a a x Substituting these into (5 ields: (, F ρl K A E I EI K. a E I cv. I N Ei K.. A. F ρ l ( K A x E I a In (6 all the parameters except and constant thus it can be written: (5 (6 are K (, K( K (7 Where: EI EI K K. [ F ρ l E I F ρl E I ]/( K A K a a x (8 (9 K cv (0 Eq. (7 is a two ariable unction that can be optimized b partial deriation but since is in the denominator o one term, i it become larger, the better result obtained. ut is in denominator o one term and nominator o another, thus it has an optimum alue

4 and is our deriatie ariable: K K. opt K K ( ( ( 0 K ( Substitution o ( into equation that is the sum o all loss component ield ( K loss. total K ( K ( I: seen rom this table, to achiee desired throughput power T will be higher than 00 o C or E4 that is smaller than E55. In case E65, surace temperature is o 89 C that is smaller than00 o C. This means that E65 don t use in optimum operating point and its ull capacit is not used. TALE I. optimum design or EE o Core tpe opt (g J opt ( a mm T c E E E Then: K 4 (4 loss. total K4K ( K (5 loss K (6 K K 4 From thermal model we can calculate the imum alue o loss. total that reach transormer temperature rise to the saet margin. Substitution this loss. total in (6 ield imum admissible and b ( the optimum can be calculated. Substituting this and in ( gie minimum Ap or minimum size. The Fig. lowchart, shows the optimization procedure. VI OTIMIZATION METHOD VALIDATION The proposed optimization procedure is utilized or design a transormer that must operate in the circuit that shows in Fig 4. the oltage and current wae orm o this transormer is illustrated in Fig.5. ecause the rms alue o oltage and current are 8.58 olt and 6.8 ampere respectiel, apparent power o the designed transormer is VA at 0 khz. It is assumed that transormer temperature not exceeds o 00 o C. This means that T surace 00 o C. For this transormer, EE errite made o manier98a material is used. These s are aailable in standard range such as E5, E, E4, E55, E65, and other standard size. The optimization routine propose E55, 57 gauss and. a mm. ower loss and temperature rise or E4, E55 and E65 are calculated. The result is showed in Table I. as can be A OT A current no A. OT A smaler no Fig..Optimization procedure

5 00 i R load 50 high requenc transormer Fig. 4 Simulated circuit or high requenc oltage generation a Voltage (gauss Fig.6 loss (watt s. (gauss Fig. 5. avoltage (olt, bcurrent (ampere,s. time (sec In another test an inestigatie analsis is done b plotting power loss ersus and or E55 (which according to Table I and because o obtained temperature, is the optimum size around optimum operating point. For this, because o close relation between and, at irst is set to gien alue b change in primar turn, then since dimensions o window are speciied, and loss can be calculated. Table II shows the result o this inestigation. TALE II. operation o E55 around optimum point (G ( A/mm b Current loss (w η % o T surace c Fig. 6 shows the result o this analsis in a graph. As can be seen rom Table I, Table II and Fig. 6 the optimization algorithm accuratel determine the smallest that can operate at gien condition, and the design parameter ( and or selected. Howeer it must be considered that correspondence between analtical result and experimental result is depend on the accurac o equation that use or calculation o transormer speciication such as and copper loss and thermal model. Since these equation can predict the transormer speciication with error less than 0 %[6], the whole procedure is reliable up to 90%. The authors is engaged in implementation a set up to test prototpe optimized transormers and ealuation o alidit o proposed optimization procedure in practice. VII CONCLUSION A new methodolog or designing transormers has been described. The design procedure so optimized to determine the smallest possible and to minimize the and winding losses b selection optimum current densit and lux densitie based on the electrical and thermal analsis o the transormer. The design procedure lowchart is suitable or use in a computer application in conunction with a database o size and materials. Analtical inestigation showed that optimization procedure is accurate but because o the approximation in thermal and loss equations, accordance between analtical result and practical result could not be completel expected. In terms o that, the main adantage o the design procedure deeloped is that it allows us to select the and calculate winding parameters, i.e., it proides (with acceptable accurac the most necessar design inormation. This inormation can be urther used or more precise (inite element or inite dierence analsis, i necessar.

6 REFERENCES [] R. etko, Optimum design o a high-power highrequenc transormer, IEEE Trans. ower Electronic., ol., no., pp. 4, 996. [] S. A. Mulder, Loss Formulas or ower Ferrites and Their Use in Transormer Design. The Netherlands: hilips Components, 994. [] F. F. Judd and D. R. Kressler, Design optimization o small lowrequenc power transormers, IEEE Trans. Magn., ol., no. 4, pp , 977. [4]. L. Dowell, Eects o edd currents in transormer windings, roc.inst. Elect. Eng., ol., no. 8, pp , 966. [5] W. J. Muldoon, Analtical design optimization o electronic power transormers, in roc. ower Electronics Specialists Con., June 978, pp [6] Sippola M., Sepponen R., Accurate prediction o High Frequenc ower Transormer Losses and Temperaturerise, IEEE Transactions on ower Electronic, ol. 7, no. 5, September 00 [7] W. T. McLnam, Transormer and Inductor Design Handbook. New York: Marcel Dekker, 978. [8] E. C. Snelling, Sot Ferrites roperties and Applications, nd ed.london, U.K.: utterworths, 988, ch..

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