DESIGN OPTIMIZATION OF TRANSFORMERS OF HIGH-EFFICIENCY SWITCHING POWER SUPPLIES SRIKANTH POTLURI, B.E. A THESIS ELECTRICAL ENGINEERING

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1 DESIGN OPTIMIZATION OF TRANSFORMERS OF HIGH-EFFICIENCY SWITCHING POWER SUPPLIES by SRIKANTH POTLURI, B.E. A THESIS IN ELECTRICAL ENGINEERING Submitted t the Graduate Faculty f Texas Tech University in Partial Fulfillment f the Requirements fr the Degree f MASTER OF SCIENCE IN ELECTRICAL ENGINEERING August, 1999

2 1' ^ ACKNOWLEDGEMENTS / 9^7 - _ ^ I wuld like t thank all whm had direct r indirect rle in this prject. As a firm believer in Gd, I wuld first thank him fr the pprtunity and the cntinuus supprt thrugh ut my master's degree and this prject. I wuld like t first thank Dr. James C. Dickens fr giving me this pprtunity and supprt. This prject wuld nt have cmpleted withut his advcacy. I wuld als like t thank Dr. Michael Giesselmann, whse cntinuus supprt was indispensable fr the success f this prject. Als amng the prfessrial staff, I wuld like t thank Dr. Nancy Van Cleave fr being n my thesis cmmittee and fr helping me in cmpleting my master's thesis. Amng the technical and secretarial staff, I wuld like t first thank Christpher Hatfield fr his guidance and supprt, withut which this prject wuld nt have been what it is nw. I wuld like t thank Daniel Garcia, and Marie Byrd fr their friendship. I wuld like t thank Lnnie Stephensn, Russel Martin, and Dean fr their expertise and supprt. Amng my friends and family, I we special thanks t my parents fr their supprt and patience since I left hme. I wuld like t thank all f my friends and my brther whse supprt was vital fr the success f the prject. Finally, I thank all thse persns wh have helped me knwingly r unknwingly, and I wish everyne mentined here the best f luck fr their future endeavrs. 11

3 TABLE OF CONTENTS ACKNOWLEDGEMENTS ABSTRACT LIST OF TABLES LIST OF FIGURES ii v vi vii L INTRODUCTION Overview f the Thesis Cntents 3 n. BASIC PRINCIPLES AND THEORY OF TRANSFORMERS Basic Relatinships Intrductin t Transfrmers Cre Lss Cnductr Lsses Basics f Switch Mde Pwer Supplies Shape f the Wavefrm in Switch Mde Pwer Supplies 40 IIL OPTIMIZATION OF TRANSFORMER Cre Dimensins Needed fr Optimizatin Assumptins Made in Transfrmer Optimizatin Design fr Minimum (Cpper) Winding Lss Optimum Value f the Winding Lss Optimum Current Density f the Windings Transfrmer Optimizatin fr Minimum Pwer Lss

4 rv. TEST PLATFORM Auxiliary Pwer Supply Sectin Main Pwer Supply Sectin Efficiency f the Pwer Supply Imprvements 70 V. MEASUREMENTS AND RESULTS 71 VL CONCLUSIONS, REFERENCES APPENDDC IV

5 ABSTRACT Cnventinal transfrmers designed fr nrmal line frequencies will nt be any gd fr high frequencies in the rder f tens f kilhertz, which are the mst cmmn perating frequencies fr high-efficiency switching pwer supplies. Designs f these high- frequency switch-mde transfrmers need special care regarding the size f wire, cre, type f cre material, perating flux density, etc. The prblem statement can be redefined as btaining the highest pssible efficiency using the smallest pssible cre. It is knwn fact that as the perating frequency increases, the size f magnetic cmpnents decreases which enables us t design cmpact applicatins. Skin effect and prximity effects can cause serius effects by increasing the AC resistance f the wire in the rder f tens t hundreds in magnitude, in a prly designed high-frequency transfrmer. Design ptimizatin f high-frequency, high-efficiency transfrmers cnsidering skin and prximity effects is being discussed in this thesis. The applicatins f this include design f high efficiency DC/DC switching pwer supplies, design f high frequency pwer electrnic applicatins, etc. We can extend this wrk t high-frequency magnetic cmpnents design such as inductrs, which are the majr cmpnents in pwer electrnics. The Visual Basic applicatin develped can be used fr future designs.

6 LIST OF TABLES 2.1 Curve fit results fr typical ferrite materials Cmparisn f different factrs Pwer supply measurements 74 VI

7 LIST OF FIGURES 2.1 A tw-winding transfrmer Magnetic circuit that mdels the tw-winding Ideal transfrmer symbl Transfrmer mdel including magnetizing A tw-winding transfrmer with the leakage flux Tw-winding transfrmer equivalent circuit, including magnetizing inductance referred t primary and primary and secndary leakage inductances Cmplete transfrmer equivalent circuit Hysteresis lp illustrating areas f stred and dissipated energy Skin effect - Islated cnductr Prximity effect - Oppsite currents Prximity effect - Same currents Schematic diagram f a linear pwer supply Example f pulse width mdulatin Different pulse widths and duty cycles Example f a buck regulatr Example f a bst regulatr Schematic f a Cuk cnverter Cuk cnverter fr n state f MOSFET Cuk cnverter circuit fr MOSFET in turn ff state 37 vu

8 2.20 Example f a fly-back cnverter Push-pull cnverter Auxiliary pwer supply Cmmn implementatin f RC snubbers Transient vltage and current (a) with ut snubber circuit (b) with snubber Pulse width mdulatr The pwer supply test setup P and ETD cres next t each ther (a) P42/29 (b) P 36/ The cling f P and ETD transfrmers Tp view f (a) Existing ETD (b) Optimized POT cre transfrmers... r. 5.5 Thermal image f the cmplete pwer supply under test -^ Vlll

9 CHAPTER I INTRODUCTION The main idea f this prject is t develp high efficiency, high frequency switching pwer supplies. In the designing f a high efficiency switching pwer supply, the lsses shuld have t be really small all ver the supply. As the size f the cmpnents is decreased, there is a necessity fr ptimum design f each and every cmpnent with in the pwer supply and the verall system. Here we are attempting t shw the imprtance f the magnetic cmpnents, we are ging t discuss the selectin f varius parameters, imprtant cnsideratins in high-frequency and high-efficiency switching pwer supplies in rder t reduce the lsses in the magnetic cmpnents. T make the switching pwer supplies cmpact, reliable and less weight we need t minimize the magnetic cmpnents as they ccupy larger ft print area and weigh a lt. Operating the pwer supply at higher frequencies we can reduce the size f inductrs, capacitrs and transfrmers. Up t 25kHz we can neglect the adverse effects f prximity and skin effect. Hwever at frequencies greater than 25 khz bth the Prximity and Skin effects cme int the picture and makes the design f a transfrmer cmplex. As the size f these elements decrease, the heat dissipatin becmes a prblem and reliability f the circuit will be at stake. As the frequency f the peratin is increasing, the AC resistance f the wire increases and may be disastrus that is 1000 times mre than the DC resistance fr a prly designed magnetic cmpnents. The efficiency f the transfrmer decreases t as lw as 50% and especially in lw pwer supplies this leads t an

10 inefficient pwer supply. The main bjective f the thesis is t develp high efficiency magnetics fr the high frequency switching pwer supplies. We will find the switch-mde pwer supplies everywhere in the real wrld. Sme f the appucatins are in hand calculatrs, laptps, camcrders, satellites, cellular phnes, speed cntrl f DC machines, etc. The apphcatin f this thesis is nt nly in switchmde pwer supplies but als everywhere where high-frequency magnetics are used. The previus wrk dne in this area was mre theretical cmpared t this thesis. This thesis gives theretical apprach t the prblem, relates with the physical quantities and the practical cnsideratins and gives a feasible slutin. The ptimizatin prcess was tested n the test setup and the results were prvided. The results shw that there is a cnsiderable amunt f imprvement nt nly in the efficiency but als in the size f the transfrmer and ft print area f the PCB. Typical factrs that affect the designing f magnetic cmpnents are the fllwing: 1. Winding vltages: Amplitude, wavefrm and frequency, 2. Winding currents: Amplitude, wavefrm and frequency, 3. Pwer level, 4. Magnetizing inductance, 5. Leakage inductance, 6. Efficiency, 7. Temperature rise, 8. Insulatin class, 9. Thermal envirnment,

11 10. Mechanical envirnment, 11. Dimensinal cnstraints, 12. Weight limits, 13. Shielding and islatin, 14. Safety requirements, 15. Cst. We have t cnsider all f the abve things in designing high-frequency magnetics that makes the transfrmer design cmplex, which made us t cncentrate n this tpic. 1.1 Overview f the Thesis Cntents The first chapter f this thesis gives an intrductin t the thesis, verview f the thesis, and the imprtance f magnetic cmpnents. As explained earlier the next generatin switching pwer supplies are ging t be cmpact, efficient and reliable. Once the frequency f peratin is chsen, we need careful design f each and every cmpnent in the system. Once the frequency is higher than 25 khz, the high frequency effects are ging t play majr rle, which we can neglect under lw frequency analysis. The secnd chapter discusses the basic thery f magnetics, fundamentals f transfrmers, the applicatins f transfrmers, cre lsses, cpper lsses, basics f switching pwer supplies, the applicatins f switching pwer supplies, and the shape f wavefrm in switch mde pwer supplies. The third chapter is n the ptimizatin f high frequency switching pwer transfrmer. Here we are ging t discuss abut the cre dimensins needed fr

12 ptimizatin, assumptins made in the ptimizatin prcedure, design f transfrmer fr minimum winding lsses, hw t determine the ptimum current density, and the design f transfrmer fr minimum pwer lss that is maximum efficiency. This gives an idea hw this thesis is helpful in future designs. The furth chapter explains abut the test platfrm used fr measurements and calculatins. This explains the unique features f the pwer supply, the varius sectins f the pwer supply, efficiency measurements, suggestins t imprve the efficiency. The fifth chapter explains the measurements and results f this thesis. This was dne n different types f transfrmers t shw the effectiveness f ur results. The sixth chapter wraps up the thesis and gives the cnclusins. The references used fr the successful cmpletin f this thesis were given in the references. The appendix gives sme material n perfrmance factr, and sme f the Mathcad files used fr ptimizatin.

13 CHAPTER n BASIC PRINCIPLES AND THEORY OF TRANSFORMERS This chapter gives the brief intrductin t all the necessary tpics that are required t understand the thesis. This includes discussin n basic relatinships and principles f magnetics, thery f transfrmers, discussin n lsses in the transfrmers, and basics f switch-mde pwer supplies. 2.1 Basic Relatinships The basic magnetic quantities and relatinships are ging t be illustrated in this part. Magnetic quantities are analgus t the electrical quantities Culmb's Law fr magnetic ples The frce f attractin r repulsin between tw magnetic ples f strength my and m2 is directly prprtinal t the prduct f their strength and is inversely prprtinal t the square f the distance between them. F = ^ (2.1) Mr where F is the frce f attractin r repulsin depending n the plarity. r is the distance between the magnetic ples ju is the cnstant f prprtinality, called permeability. "Like ples repel and unlike ples attract" decides the directin f the frce.

14 Magnetizing frce is defined as the frce per unit ple strength. That is F mj _., A nil //= = -V ~2 (2.2) m2 //r and the unit f magnetizing frce is Oersted and is defined as the frce experienced by a magnetic ple f unit strength separated frm a unit ple by a distance f ne meter in air. The permeability fr air is 1. Flux density is btained by multiplying bth sides f Eq. (2) by \i. The unit f flux density is gauss. B = juh=^ (2.3) r The relatinship between B and H is determined by the cre characteristics. Fr free space r air: B = juh (2.4) Where ji is the permeability f the free space and is equal t 47i. 10" Henries per meter in MKS units. The B-H characteristic fr any ther cre is f/4. B = juh. (2.5) The cre permeability i is expressed as a prduct f relative permeability //^ and M=MMr (2.6) The magnetmtive frce mmf, r Scalar Ptential between tw pints pi and p2 is given by the integral f the magnetic field H alng the path cnnecting the tw pints. p^ mm" if = j H.dl (2.7) pi

15 where dl is a vectr length element pinting in the directin f the path. The dt prduct yields the cmpnent f H in the directin f the path. If the magnetic field is f unifrm strength H passing thrugh an element f length / as illustrated, then the abve equatin reduces t mmf=hj (2.8) This is similar t the electric field f unifrm strength E, which induces a vltage V = E./ between tw pints separated by distance /. The ttal flux emanating frm the ple will be the flux density at a distance r frm the ple multiplied by the area f the sphere f radius r with the ple mi at the center O = 5A = r!- = 4mn. (2.9) r If a ttal magnetic flux O is passing thrugh a surface S having an area A, then the ttal flux O is equal t the integral f the nrmal cmpnent f the flux density ver the surface. <D= JB.dA (2.10) surfaces where da is the vectr area element and its directin is nrmal t the surface. Fr a unifrm flux density f magnitude B as shwn, the integral reduces t ^ = B.Ac (2.11) Flux density B is similar t the electrical current density J, and the flux O is analgus t the electrical current I and magnetmtive frce is analgus t the vltage. If a current density f magnitude J passes thrugh a surface f area Ac, then the ttal

16 current is I = J.Ac. This similarity between electrical and magnetic quantities suggests the Ohm's law fr magnetic circuits. mmf=^r (2.12) In magnetic circuits, the prprtinality cnstant is called reluctance, symbl R. reluctance is directly prprtinal t the length f the magnetic path and is inversely prprtinal t the area thrugh which the flux flws. R = (2.13) M Faraday's Law The emf induced v(t) in a circuit is determined by the time rate f change f the magnetic flux thrugh that circuit. JO v(t) = -- (2.14) dt Fr a unifrmly distributed flux regin, using Eq. (2.14) we can rewrite the abve equatin as: dbjt) v(t) = A^ -. (2.15) dt Lenz's Law An induced Current flws in a directin t create a Magnetic Field, which will cunteract the change in Magnetic Flux.

17 2.1.5 Ampere's Law This states that a current carrying cnductr placed in a magnetic field will have a frce exerted upn it in accrdance with the fllwing relatinship: F = Bil (2.16) where F is the frce n the wire in dynes perpendicular t bth directin f current flw and magnetic field. B is the flux density in gauss perpendicular t the wire. i is the current in amperes / is the length f the wire in centimeters. 2.2 Intrductin t transfrmers Magnetic cmpnents such as inductrs and transfrmers are the vital parts f switching pwer supplies. A transfrmer will have tw r mre windings n the magnetic material where as inductr will have ne (r mre windings) n the magnetic material. Switching pwer supply transfrmers and inductrs require the use f high perfrmance cre materials. Chsing the prper cre material fr a specific applicatin requires an understanding f cre material technlgy. In this sessin we are ging t study the fundamentals f transfrmers. In general transfrmers are either single phase (l-cj)) r three phase (3-([)). Hwever we are ging t study abut the single-phase transfrmers. Transfrmers are necessary t prvide the islatin needed, r t step up the vltage (t a very high vltage level), r t step dwn (t a very lw vltage level).

18 2.2.1 Principle f Operatin Cnsider a cil t which a varying vltage is applied which generates a varying flux. If a secnd cil is placed in clse prximity s that the flux generated by the first cil passes thrugh the secnd cil, then accrding t the Faraday's law a vltage will be develped acrss the secnd cil prprtinal t the rate f change f flux and the number f turns in the secnd cil. If the ends f the secnd cil are cnnected t a resistance, a current flws in the secnd cil in a directin that ppses the change in flux. The current that flws in the secnd cil tends t reduce the net flux linking bth cils. T cntinue t satisfy faraday's law, an additinal current must flw in the first cil that will ffset the reductin in the flux caused by the current flw in the secnd cil. The first cil is called the primary winding and the secnd cil is called the secndary winding. The vltage and current equatins are given belw. N y _ secndary y ^2 An) sec ndary -.j primary ^ ' ' primary I, = ^'""^^ I. (2.18) * secndary, r primary "^ ^ ^lec ndary where Vprimary is the vltage applied t the primary winding, Nprimary''^^ the numbcr f turns in the primary winding, Iprimary IS the currcut flwing in the primary winding, Vsecndary is thc vltagc iuduccd in the secndary winding, Nsecndary is the numbcr f turns in the secndary winding, ^secndary is the currcut flwing in the secndary winding. Multiplying Eq. (2.17) by Eq. (2.18) 10

19 sec ndary ' sec ndary primary primary 2.19) Dividing Eq. (2.17) by Eq. (2.18) V sec ndarv sec ndary = z secndary f N \ secndary N \ primary i primary (2.20) where Zsecndary, Zprimary ^Tc the impcdanccs f the secndary and the primary windings, respectively Transfrmer Mdeling Cnsider the tw-winding transfrmer f Fig The cre has crss-sectinal area Ag, mean magnetic path length /m, and permeability //. An equivalent magnetic circuit is given in Fig.2.2. The cre reluctance is R = IJjuAc (2.21) #^ Flux 1 1 ' i -) '^m., 0 turns, 1 ~--"\ i J 0 ~ : -\2 :> :urns + v2i:t: - Figure 2.1. A tw-winding transfrmer 11

20 .^lux Re > / V /- + rc n1.i1 ( ^ ) ' ^^ -2.i2 Figure 2.2. Magnetic circuit that mdels the tw-winding Since there are tw windings in this example, it is necessary t determine the relative plarities f the MMF generatrs. Ampere's law states that Fc = niii + n2i2 - (2.22) The MMF generatrs are additive, because the currents /; and (2 pass in the same directin thrugh the cre windw. Slutin f Fig. 2 yields 0.R = niii + n2i2. (2.23) This expressin culd als be btained by substitutin f Fc = 0R int Eq. (2.22) The Ideal Transfrmer In the ideal transfrmer, the cre reluctance R appraches zer. This causes the cre MMF Fc = OR t als apprach zer. Eq. (2.22) then becmes 0 = mil + «2i'2. (2.23) Als, by Faraday's law, we have 12

21 Vl ^2 -n, = «2 JO dt JO J? (2.24) Nte that ^is the same in bth equatins abve: the same ttal flux links bth windings. Eliminatin f 0 leads t JO ^ Vi ^ V, dt n^ «2 (2.25) Equatins (2.23) and (2.25) are the equatins f the ideal transfrmer: ^ = ^and (2.26) The ideal transfrmer symbl f Fig. 2.3 is defined by Eq. (2.26). i1 Ideal j2_ ^ + i { ( v2 n1 : n2 Figure 2.3. Ideal transfrmer symbl. 13

22 2.2.4 The Magnetizing Inductance Fr the actual in which the cre reluctance R is nnzer, we have O/? = «jzj +«2^*2 ^^^ ^1 = «1 JO dt (2.27) Eliminatin f 0 gives This equatin is f the frm «; J R dt «2 (2.28) dim. (2.29) where "2 (2.30) are the magnetizing inductance and the magnetizing current, referred t the primary winding. An equivalent circuit is illustrated in Figure 2.4. Figure 2.4 cincides with the transfrmer mdel. The magnetizing inductance mdels the magnetizatin f the cre material. It is a real, physical inductr, which exhibits saturatin and hysteresis. All physical transfrmers must cntain a magnetizing inductance. Fr example, suppse that we discnnect the secndary winding. We are then left with a single winding n a magnetic cre-an inductr. Indeed, the equivalent circuit f Figure 2.4 predicts this behavir, via the magnetizing inductance. The magnetizing current causes the rati f the winding currents t differ frm the turns rati. 14

23 i1 (n2/nl; 'deal jii. A Lmp=n1''2/R < J v2 n1 : n2 Figure 2.4. Transfrmer mdel including magnetizing The transfrmer saturates when the cre flux density B(t) exceeds the saturatin flux density Bsat- When the transfrmer saturates, the magnetizing current Impit) becmes large, the impedance f the magnetizing inductance becmes small, and the transfrmer windings becme shrt circuits. It shuld be nted that large winding currents ii(t} and i2{t) d nt necessarily cause saturatin: if these currents bey Eq. (2.24), then the magnetizing current is zer and there is n net magnetizing f the cre. Rather, saturatin f a transfrmer is a functin f the applied vlt-secnds. The magnetizing current is given by (t)=-^\v,{t)dt (2.31) mp mp Equatin (2.31) can be expressed in terms f the cre flux density B(t) as Bit) «ia ]v,it)dt (2.32) 15

24 The flux density and magnetizing current will becme large enugh t saturate the cre when the applied vlt-secnd Ay is t large, where Aj is defined fr a peridic ac vltage wavefrm as '2 A,=jv,(r)dt. (2.33) The limits are chsen such that the integral is taken ver the psitive prtin f the applied peridic vltage wavefrm. T fix a saturating transfrmer, the flux density shuld be decreased by increasing the number f turns, r by increasing the cre crss-sectinal area A^. Adding an air gap has n effect n saturatin f cnventinal transfrmers, since it des nt mdify Eq. (2.32). An air gap simply makes the transfrmer less ideal, by decreasing Lmp and increasing Imp(t) withut changing B(t). Saturatin mechanisms in transfrmers differ frm thse f inductrs, because transfrmer saturatin is determined by the applied winding vltage wavefrms, rather than the applied winding currents Leakage Inductance In practice, there is sme flux that links ne winding but nt the ther, by "leaking" int the air r by sme ther mechanism. As illustrated in Figure 2.5, this flux leads t leakage inductance, that is, additinal effective inductances which are in series with the windings. A tplgically equivalent structure can be deduced, in which the leakage fluxes 0ii and 0i2 are represented explicitly as separate inductrs. 16

25 ii(t) :. Flux i 7lf: 1 Flux vi(t) 11 il f^ k.._ 1 1 J- r V 1 J Flux Figure 2.5. A tw-winding transfrmer with the leakage flux. Figure 2.6 illustrates a transfrmer electrical equivalent circuit mdel, including series inductrs Ln and La, which mdel the leakage inductances. These leakage inductances cause the terminal vltage rati V2(t)/vi(t) t differ frm the ideal turns rati «2/«7. In general, the terminal equatins f a tw-winding transfrmer can be written v,(0".^2(0. ^11 ^12 _-^21 ^22 _ d dt 'hit)'.hit). (2.34) The quantity L/2 is called the mutual inductance, and is given by M2 - - ^ mp R n (2.35) given by The quantities Ln and L22 are called the primary and secndary self-inductances. A, -L «, «2 A 2 (2.36) ^22 ~ ^12 «1 -Lj2 17

26 i1 L11 T 1 ideal + 7-* L.inp=(n1/n1)L12; J > > ( i' 1 -/2 n1 :n2 Figure 2.6. Tw-winding transfrmer equivalent circuit, including magnetizing inductance referred t primary and primary and secndary leakage inductances. Nte that Eq. (2.34) des nt explicitiy identify the physical turns rati w/";. Rather, Eq. (2.34) expresses the transfrmer behavir as a functin f electrical quantities alne. Equatin (2.34) can be used, hwever, t define the effective turns rati " =? (2.37) and the cupling cefficient k= ^'^ ^J^lL 22 (2.38) The cupling cefficient k lies in the range 0<k <1, and is a measure f the degree f magnetic cupling between the primary and secndary windings. In a transfrmer with perfect cupling, the leakage inductances Lu and La are zer. The cupling cefficient k is then equal t 1. Cnstructin f lw-vltage transfrmers having cupling cefficients in excess f 0.99 is quite feasible. When the cupling cefficient is 18

27 clse t 1, then the effective turns rati rig is apprximately equal t the physical turns rati n2/ni The Transfrmer Equivalent Circuit Referred t Primary Transfrmer equivalent circuit referred t the primary is shwn in Figure 2.7. The current transfrmatin fr the ideal transfrmer neglects the current that flws in the primary independent f the lad current. This current is required t prduce the magnetic flux and is called the magnetizing current. The magnetizing current can be accunted fr by an inductance in parallel with the ideal transfrmer and is represented as Lmp. This is the n-lad current flwing thrugh the primary winding. The current assciated with the cre lss is in additin t the lad current. Therefre cre lss can be represented by a resistance in parallel with the primary f the ideal transfrmer and is represented as Rep. The value f this resistance will vary in the perating cnditins f the transfrmer. Since primary and secndary windings are made f wire with finite resistance, the resistance f primary and secndary can be calculated and are represented as R^ and R^. Hwever the secndary resistance is transfrmed t the primary side using Eq. (2.20). As the transfrmers are cmpsed f clsed spaced turns with the primary and secndary ften very clse tgether and bth clse t the cre and grund, there is a appreciable amunt f stray capacitance present. This is represented by a cmbinatin f parallel and series capacitance, C and Cp, respectively. 19

28 :D L11 w LI2i'n' r\r\r- L n Cp 'l 1 -r > _mtd ;^ ff;:cp 1 >,7 1 -I 1 r c L i Figure 2.7. Cmplete transfrmer equivalent circuit. Althugh we are assuming a 100% cupling in ideal transfrmers, there exists a small amunt f leakage flux in actual, real wrld transfrmers. The presence f this leakage flux is evidenced by the failure f the inductance f the device t be exactly prprtinal t the square f the number f turns, the failure f the vltage transfrmatin t be exactly equal t the turns rati, and the existence f small inductance delectable in the primary when secndary is shrted, at which time there wuld therwise be zer change in flux. These factrs suggest a equivalent tw series inductances called leakage inductance represented by L/; and L/2/n. 2.3 Cre Lss In mst f the pwer electrnic applicatins, the efficiency and size f the pwer circuitry are f primary cncern. In rder t achieve high circuit efficiency and small cmpnent size, the circuit has t be perated at higher frequencies. Here we are ging t discuss abut the magnetic cre lsses and its relatin with the perating frequency. 20

29 The pwer lss in the cre is called as cre lss. This has basically tw cmpnents. Hysteresis and Eddy current. The energy used t align and rtate the elementary magnetic particles f the cre cntinuusly is the Hysteresis lss. The energy delivered t a cil cntaining a ferrmagnetic cre during an interval x, the time spent in ne traverse f the hysteresis lp, is E = jvidt. (2.39) 0 In Eq. (2.39) v is in vlts, i is in amperes, t is in secnds, and E is in jules. T describe E in magnetic quantities, v and i are expressed as belw. v = A^-^xlO~^ (2.40) dt The flux in a ferrmagnetic circuit is apprximately unifrm acrss the crsssectinal area f the cre, s that 0 = 5A. (2.42) By rearranging the terms in equatin (2.41), it becmes HI. 1 = '. (2.43) 0.4;rA^ Substituting Eqs. (2.40), (2.42) and (2.43) in Eq. (2.39) yields 21

30 E = db^ NA x\0-'x-^^dt dt 0.4nN - ^xi-hi^j5 0.4;r l (2.44) The integral prtin f Eq. (2.44) may be separated int intervals with the aid f Figure 2.8 as fllws: ^ *1 B2 0 B3 B4 0 \HdB=jHdB-\HdB+JHdB+JHdB-JHdB+JHdB. (2.45) 0 0 Bl fi2 0 B3 B4 Figure 2.8. Hysteresis lp illustrating areas f stred and dissipated energy. Shaded areas represent stred energy. In Eq. (2.45), the psitive terms indicate energy supplied t the cil, and the negative terms indicate energy returned t the circuit. Thus the net energy absrbed by the cre due t hysteresis is prprtinal t the area enclsed by the hysteresis lp. The prduct AH in Eq. (2.44) is the vlume f the cre, called V belw. If the cre 22

31 magnetizatin is repeated with a frequency f, then Eq. (2.44) may be written as a pwer lss: P = /VxlO"^ JHdB. (2.46) 0.4;r In Eq. (2.46), P is in watts,/is in hertz, Vis in cubic centimeters, H is in ersteds, and B is in gauss. Frm the abve equatin, it can be bserved that the hysteresis pwer lss is prprtinal t the frequency. The energy lss per cycle is (almst) cnstant and is equal t the area f the B-H lp. This lss increases, as the frequency increases. Circulating currents in a cnductive magnetic cre cause Eddy current lss. The currents are caused by vltages induced by changing magnetic flux in the cre in the same manner that vltages are induced in the secndary windings f the transfrmers. Eddy currents tend t fllw circular paths nrmal t the directin f the magnetic flux. These currents represent a pwer lss, which is independent f lad current. Three input-vltage cases are f particular interest: a sine wave vltage, a symmetrical square wave vltage, and a pulse vltage f single plarity. Fr each f these cases, the rate f change f flux density must be determined t estimate the eddy current lsses The effect f cre material n bandwidth The achievable bandwidth f transfrmers depends n the prperties f cre materials. The lw cutff frequency is determined by the shunt inductance. The high cutff frequency is determined by the leakage inductance and distributed capacitance. The shunt inductance is determined by the permeability f the magnetic cre, the number 23

32 f primary turns, and the cre gemetry. Open circuit inductance will be high, as the permeability and the number f turns increase. The leakage inductance and distributed capacitance are bth rughly prprtinal t cil vlume. T btain wide bandwidth, a cre material f high permeability is needed t btain high shunt inductance. The smaller the number f turns used t achieve the shunt inductance needed fr the lw-frequency respnse, the lesser will be the leakage inductance and distributed capacitance, the prduct f which determines the high-frequency cutff. As frequency decreases, the flux density increases fr a fixed vltage. The permeability f the cre decreases with the nset f saturatin. This places the additinal requirement n the cre material t have a high samratin flux density fr gd lwfrequency respnse. Cre lss is represented by specific cre lss, which is defined, as the pwer lss per unit vlume. Specific pwer lss depends n the type f material, perating flux density, the frequency f peratin and the perating temperature. Cre lss in ferrite materials is related t the switching frequency by: Pcr._^c^ = Kj''-B''{cu.r- -cr, J- + cr) (2.47) where P^^^ ^^-^^ is the specific pwer lss f a cre that is cre lss per unit vlume. f is the switching frequency B is the perating flux density A'j, ^2' ^d kj^ are the cnstants and depend n the type f material T is the perating temperature in degrees centigrade ct2, cti and ct are the temperature cefficients. 24

33 C/5 i-t s 4 > 4 > * < D l-h 3 u (N H 1/3.<-J 3np Ul DH <+-( (/2 Pwer Ls ^ ^^ Spec ^^ C3 O ^H Cl. Ui O (4-1 V^.1:^ 3 ti LX, <D ^ 3 u CJ *-> O,_^ ^ N ffi ^ >> c 3 a- T3 c3 i-i CO q tn 1 X (N 1 X in i (Ti I> \D O 1 U en d CN 1 X en d X in r4 ^ r-- O 1 00 U m r- ON ts 1 O X 00 q 1 X d in CO -: '"' (N in U en r- O) n d 1 H X 00 q d CN»n in < 1 VO CN (N d T-H X in p 1 d in VD in d en 1 CS en PLH en 00 cs ts d ^-^ X in p 1 X d in c^ q ra 1 O CN O in 1 en ^ ts d ^H X 00 d d "x d in CN CN CN t^ d X VO en CD O in «n tn d» ^ X 1 X in ON d ON CN in ts 1 O X CN ' O 6 in Tt S en O X d 1 'x en d CN 00 CN 1 O X ' CN ts d y - ^ X p en 1 X (N in CN CN in en ON 6 en E ^ 25

34 2.4 Cnductr Lsses The inherent resistance f the cnductr is the main cause fr this type f lss. Basically, this is I R lss, where I is the current flwing thrugh the cnductr, and R is the AC resistance at high frequencies. The increase in cnductr lsses is appreciable when the winding cnductr thickness becmes cmparable t the 'skin depth' f the high frequency currents. This skin depth in cpper is cm at 10 khz and cm at 1 MHz. The increase in the cnductr lss at high frequency is because f a number f interrelated effects, such as 1. Skin Effect, 2. Prximity Effect, 3. End Effects, 4. Cre Gap Effects. In the fllwing sectin, we are ging t discuss these effects Skin Effect This is the fundamental effect at higher frequencies. A current I(t) flwing thrugh a cnductr induces a magnetic flux 0it), which causes eddy currents inside the cnductr. Accrding t the Lenz's law, these eddy currents ppse their cause, i.e., I(t). S the net current density inside the cnductr starts decreasing as the frequency increases. The current density is an expnentially decaying functin f distance int the cnductr, with characteristic length <^knwn as penetratin depth r skin depth. The penetratin depth is given by 26

35 ^ = Sqrt (2.48) And fr cpper it is 6.623/Vf cm. where f is in Hz. The current distributin due t Skin effect fr an islated cnductr is illustrated in Figure 2.9. S the high frequency currents d nt penetrate t the center f the cnductr and there will nt be prper utilizatin f the cnductr besides these lsses. Hwever by using litz wire (generally having a number f insulated strands), we can increase the eddy current path resistance many times. Braiding r weaving f insulated strands f wire tgether frms Litz wire in a way that causes each strand t spend equal time at the surface and each lcatin in the crss-sectin and will take care f the skin effect lsses. This makes all the strands t carry equal amunt f current. The size (AWG) f the strand depends n the perating frequency. Figure 2.9. Skin effect - Islated cnductr Prximity Effect This is anther type f lss when a cnductr is in the vicinity f ther current carrying cnductrs. Eddy currents are induced in the cnductr by the currents flwing in the prximity cnductrs, in turn causes the lsses in the cnductr. When the 27

36 windings are multi-layered, the prximity effect is the dminant cnductr lss at higher frequencies. Prximity effect is a phenmenn that can greatly increase magnetic winding lsses ver DC resistance r skin effect alne. In ther wrds, we can say that bth Skin Effect and Prximity Effect are due t the eddy currents induced inside the cnductr: ne because f the current carried by itself and the ther because f the current in the near by cnductrs. Decreasing the number f layers needed culd minimize prximity Effect (this can be dne by increasing the number f windings per layer). Harmnic analysis must be used in calculating the Prximity lss r the lss estimates are ff by many rders f magnitude End Effects Mre current tends t flw thrugh the uter (end) windings cmpared t the middle (inner) windings because f the nn-unifrm magnetic fields in transfrmer r inductr windings. This can be bserved in ETD, E and P cre and is absent in tridal cres as the windings are distributed unifrmly Cre Gap Effects The presence f discrete air gaps in a cre creates nn-axial magnetic fields, which intersect the windings inducing additinal eddy current lsses. The presence f air gap makes the end windings (windings near t the air gap) t carry mre current than the neighbring cnductrs as the flux leaving the magnetic material is maximum. These 28

37 effects are ften a majr lss mechanism in transfrmer and inductrs with gapped cre. We have nt tried using gapped cre t increase the efficiency. It is nt nly difficult but als almst impssible t accunt the lsses separately. We are cnsidering the first tw types f lsses (Skin and Prximity Effects) which are respnsible fr the lsses in the cnductrs at high frequencies. Typical current distributins fr prximity effect with current flw bth in and the same directin and in ppsite directins were shwn in Figures 2.10 and Figure Prximity effect - Oppsite Currents Figure Prximity effect - Same Currents Prximity Effect is nt nly mre serius than skin effect, but als the analysis f its lsses is bscure and mathematically difficult. We can say that the cre lss and prximity effect are the tw mst cnsideratins in high frequency magnetics design. Prximity effect limits the high frequency current density as the perating flux density f the cre is limited by the cre lss at high frequencies. Even cnductrs nt carrying any 29

38 amunt f current experience eddy current lsses when they are in an external AC magnetic field. In every cnductive element inside a transfrmer, inductr, r any AC magnetic device. Skin and Prximity effects are extremely imprtant. 2.5 Basics f Switch-Mde Pwer Cnversin An ideal pwer supply wuld be characterized by supplying a smth and cnstant utput vltage regardless f variatin in line vltage, lad current r ambient temperature Linear Pwer Supplies The linear regulatr behaves as a variable resistance between the input and the utput as it prvides the precise utput vltage. One f the limitatins t the efficiency f this circuit is due t the fact that the linear device must drp the difference in vltage between the input and the utput. Linear regulatrs will have a linear (variable) resistr in series with the lad. And frm the maximum pwer transfer therem, we can deliver maximum pwer t the lad when the regulatr resistance equals the lad resistance. This means we are ging t lse arund 50% f the pwer in the regulatr itself These linear regulatrs are easy t design hwever inefficient cmpared t switching pwer supplies (ging t be discussed). The schematic f a linear pwer supply is shwn in Figure We can use the linear regulatrs t change the DC vltage levels up-t sme extent. We cannt step up the vltage in Linear Pwer Supplies. 30

39 'PLIX _PS L.near Pc'.ver SUJCi^'' I.C3C 1 erratic i::ia:jr3m jf a _ine?,r r-'me- i-iuplv Figure 2.12 Schematic diagram f a Linear Pwer Supply While these supplies have many desirable characteristics, such as simplicity, lw utput ripple, excellent line and lad regulatin, fast respnse time t lad r line changes and lw EMI, they suffer frm lw efficiency and ccupy large vlumes. Switching pwer supphes are becming ppular because they ffer better slutins t these prblems Switching Pwer Supplies Here we are ging t discuss the fundamentals and basic types f switch-mde pwer suppues. Switch-mde pwer cnverters are used fr varius applicatins and the purpse in general is t step up r dwn the DC vltage. Hwever these are used even t prvide the islatin between the input (DC) and the utput (DC). Yu can fmd these in ur daily appuances like PCs, rganizers, cameras, and even in cellular phnes. 31

40 We can use transfrmers t step up and step dwn and even t prvide islatin between the input and utput in case f AC supply. With the increasing use f prtable and cmpact devices we need t find prtable pwer supplies t. We can nt use transfrmers t step up r step dwn the DC vltage levels. In switching pwer supphes we will have MOSFETs, Transistrs r IGBTs which are perated either in the cutff regin (high impedance, pen circuit) r in the saturatin regin (lw n resistance, shrt circuit) and acts as switches. Whenever the switch is clsed, the vltage drp acrss the switch is ging t be zer, hence the pwer lss (prduct f vltage drp acrss it and the current thrugh it) is zer, ideally. Whenever the switch is pen, the current thrugh it is zer, hence the pwer lss in it. Ideally, lss in the switch-mde pwer supplies is zer. There are three basic types f switch-mde cnverters frm which all ther types are derived: 1. Buck Cnverter, 2. Bst Cnverter, 3. CUK Cnverter Pulse width mdulatin Pulsed width mdulatin is the heart f any switching pwer supply. One way t cntrl the average pwer t a lad is t cntrl the average vltage applied t it. This can be dne by pening and clsing a switch in rapid fashin as being dne in Figure Pulses fr different duty factrs were shwn in Figure

41 V A Tn V1 -= > Lad (3vg> --I! - t Figure 2.13 Example f pulse width mdulatin Pulse Width Mdulatin (PWM) (a). 25% Duty Cycle / A (c). 75% Duty Cycle -^ v / \ :b;l 50%. Duty Cycle -> Figure Different Pulse Widths and Duty cycles The average vltage sent t the lad is equal t: (T ^ V =V n (avg) I T (2.49) Buck regulatr 33

42 This is the basic type f switching regulatr, als knwn as step dwn regulatr and is shwn in Figure A typical applicatin is t reduce the standard military bus vltage f 28V t 5.1V t pwer CMOS lgic. At time t(0), the cntrller, having sensed that the utput vltage VQ is t lw, turns n the pass transistr t build current in L, which als starts t recharge capacitr C. At a predetermined level f VQ, the cntrller switches ff the pass transistr Q, which frces the current t free wheel arund the path cnsisting f L,C, and the ultra fast rectifier d. This effectively transfers the energy stred in the inductr L t the capacitr. The utput equatin is given by Eq. (2.49). Q2N2222 -/'W"V~>. Vi -=: IC ^'' C -u T +, > '' '''= \ J Lead Figure Example f a Buck regulatr. Inductr and capacitr sizes are inversely prprtinal t the switching frequency, which accunts fr the increasing pwer density f switching pwer supplies. Because f Pwer MOSFET's quality at higher frequencies, they replaced the bi-plar transistrs Bst regulatr 34

43 This is anther basic type f switching regulatr, als knwn as step-up regulatr and is shwn in Figure AppUcatins fr this circuit wuld be t increase 5V-battery surce t 15V fr CMOS circuits r even t 150V fr electr-luminescent displays. 71 L IC H>f Q2N2222 H" ^ + ^ L j a d Figure Example f a Bst regulatr Transfer f energy stred in the inductr int the capacitr is the principle fr this t. The inductr current ramp up quickly when the transistr switch is clsed at time t(0), since the full input vltage is applied t it. The transistr is turned ff at time t(l) which frces the inductr current t charge up the capacitr thrugh the ultra fast dide d. since the energy stred in the inductr is equal t, the PWM IC can increase VQ by increasing its wn n-time t increase the peak inductr current befre switching. The transfer functin is: V = Vm v r-r n (2.50) Cuk Cnverter 35

44 This cnverter perfrms a DC cnversin functin, which is similar t bth Bst and Buck cnverter. That is it can step up and step dwn the magnitude f DC vltage, and inverts its plarity. Practical realizatin using a MOSFET is shwn in Figure This cnverter perates via capacitive energy transfer unlike Bst and Buck cnverters, wh perate n inductive energy transfer. in -I- _jad Cuk Cnverter Figure Schematic f a Cuk Cnverter When the MOSP^T is turned n, the cnverter circuit reduces t Figure _1 r^. r"-} r'-t r'-< L2 + Vin 1 i C1 - i_ i 1 n.... ^. -^^ ^DSC Figure Cuk Cnverter circuit fr n state f MOSFET. When the MOSFET is turned ff, the cnverter circuit reduces t Figure

45 ->i-^.,-^r"-! L2 01 -:; _j.i :J Figure Cuk Cnverter circuit fr MOSFET in tumff state Flyback cnverter This is a unsymmetrical vltage regulatr with islatin. In this a transfrmer is used in place f the inductr. The flyback cnverter is shwn in Figure 2.20 and is cmmnly used in pwer supphes up t 150W, which is sufficient fr mst persnal cmputers, many test instruments, vide terminals, etc. Since transfrmer perates at high frequency, its size is much smaller than a 50/60 Hz transfrmer. Within certain limits, transfrmer size is inversely prprtinal t frequency. Figure Example f Flyback cnverter. 37

46 Here the transfrmer is like a tw-winding inductr, ne fr string energy in the transfrmer and the ther fr dumping the cre energy in t the utput capacitr. Current increase in the primary f the transfrmer during the n time f the transistr (t(o)-t(l)) but nte that n secndary current flws because the secndary vltage reverse biases dide d. When the transistr turns ff, the transfrmer vltage plarities reverse because its magnetic field wants t maintain current flw. Secndary current can nw flw thrugh the dide t charge up the capacitr. The utput vltage is given by the basic PWM equatin times the transfrmer turns rati V =v. in ^n '^2 T-T N, (2.51) The majr disadvantages that limit its use t lwer wattage supplies are: 1. The utput vltage is high because f half-wave charging f the utput capacitr. 2. The transistr must blck 2 xy. during mmff 3. The transfrmer is driven in nly ne directin, which necessitates a larger cre Symmetrical Cnverters These are the cnverters in which the transfrmer is driven in bth directins symmetrically (under ideal cnditins). Basically, these are three types and are derived frm the basic regulatrs: 1. Push-pull cnverter, 2. Half-Bridge cnverter, 3. Full-Bridge cnverter. 38

47 Here we are ging t deal nly with the Push-Pull cnverter as ur test platfrm has islated Push-Pull n it Push-Pull Cnverter The circuit is well knwn and widely used cnverter and is shwn in Figure Transistrs Ql and Q2 are alternatively switched n fr time perid t(n). This subjects the transfrmer cre t an alternating vltage plarity t maximize its usefiilness. The transfer functin still fllws the basic PWM frmula but there is the added factr 2 because bth transistrs alternately cnduct fr a prtin f the switching cycle. d n MOO'Til ft I / N -y I 1+ (N2 d ^J Ii L Q2N2222 FT -OH d d Figure Push-Pull Cnverter v^.=2xv;. (2.52) The presence f a dead time perid td is required t avid having bth transistrs cnduct at the same time, which wuld be the same as turning the transistrs n nt a shrt circuit. The utput ripple frequency is twice the perating frequency, which reduces the size f the LC filter cmpnents. The purpse f the anti-parallel dides acrss the 39

48 transistrs is t remm the magnetizatin energy t the input vltage whenever a transistr turns ff The disadvantage is that the transfrmer center-tap cnnectin cmplicates the transfrmer design and the primary windings must be tightly cupled in rder t avid vltage spikes when each transistr is turning ff. 2.6 Effect f Shape f the Wavefrm in Switching Pwer Supplies The shape f the wavefrm has a definite imprtance in switching pwer supplies. The initial analysis was made using the sinusidal wavefrm, which is nt the real wavefrm in switch-mde pwer supplies. The actual wavefrm is either rectangular r square in shape with finite rise and fall times. This can be decmpsed using Furier series that cntains the fundamental frequency alng with the higher harmnics. Using the Pspice, the effect f rise time and fall time n different aspects f switching pwer supplies such as stress n input capacitr, Electr Magnetic Interference (EMI) level, the level f harmnics, the switching lsses were studied and were tabulated which can be used in chsing the right cnfiguratin. The mn plar wavefrms will have the DC cmpnent, which is bserved in fly-back cnverter, frward cnverter, etc. (asymmetrical cnverters). This sets an upper limit n the flux density f peratin and we need t reset the cre after each cycle. And in symmetrical cnverters like push-pull, full-bridge and half-bridge cnverters we need nt reset the cre as the wavefrm des this. Table 2.2 cmpares sme f the imprtant issues and gives an idea abut the effect f shape f the wavefrm. 40

49 Input Capacitr value Table 2.2. Cmparisn f different factrs With rise time = falltime=l% Highest With rise time = fall time = 5% High With rise time = fall time = 10% Lw Switch Lsses Lw High Highest EMI Highest High Lw 41

50 CHAPTER m OPTIMIZATION OF TRANSFORMER High-frequency transfrmer is the majr cntributr in the size f any Switchmde Pwer Supply as it ccupies abut 25% f the vlume and 50% f the verall weight. The perfrmance f MOSFETs at high-frequency has enabled the switching pwer supplies t perate in excess f 50 khz. As the frequency increases, the size f the transfrmers, and filtering cmpnents decreases. This gives us the cmpact design f pwer supplies. Hwever, as the size f transfrmers becmes small, the amunt f surface area available t dissipate the pwer lss decreases, increasing the stress n the insulating material, and the care t be taken in designing these high-frequency transfrmers. Operating at higher frequencies has a significant effect n the cre lss f the magnetic material. Cre lss in ferrite materials is related t the switching frequency by: P., =K,f'^B'' (3.1) cre _ specific i J ^ where P^^^^, ^^^^ is the specific pwer lss f a cre that is cre lss per unit vlume. / is the switching frequency B is the perating flux density K^,K^, and K^ are the cnstants and depend n the type f material. The cre lss als depends n the temperature at which the circuit is perated. It was bserved that the values f bth ^2 ^^ ^3 ^^^^ greater than 1 fr the ferrite 42

51 magnetic materials, which means a strng dependency f cre lss n frequency and perating flux density. Transfrmer design at lw frequencies assumes that the cre lss is lw enugh that the samratin flux density cnstraint can be used as a basis fr chsing the peak perating flux density. The transfrmer is designed and the temperamre rise is calculated. If it is nt in the permissible regin, current density is decreased and design is checked. This prcess is repeated until a feasible slutin is btained. As the number f variables changed frm iteratin t iteratin is nly ne, ptimizatin f a lw-frequency transfrmer is nt hard. At higher frequencies, cre lss is high enugh that a transfrmer designed using the lw-frequency design prcedure wuld verheat due t excessive cre lss. Skin and prximity effects have a significant effect n the cpper lss. Peak flux density must be decreased t reduce the verheating due t cre lss. The current density has t be ptimum in rder t ensure lw lsses, size f transfrmer is cmpact. Here we have mre than a single variable and the prblem is multidimensinal. Fr a given temperature rise, the amunt f pwer that can be dissipated depends n the size f the transfrmer. The prblem f minimizing transfrmer size reduces t minimizing pwer lss f a transfrmer. Optimum design f high-frequency transfrmer includes the selectin f the smallest standard cre that is apprpriate fr the given pwer rating, frequency f peratin, and perating temperature. This als includes calculatin f the ptimum flux density fr minimum lsses f the transfrmer. 43

52 This transfrmer ptimizatin is derived frm, and based n the papers f Dwell[6], and Petkv[15]. Winding resistance cefficient K^, rati f AC resistance t DC resistance is used in the ptimizatin prcess. This depends n the frequency, the number f layers and shape f the cnductr. K, = ^ = Q.5y[M{y)+(2m-\)\D{y)\ (3.2) he where v = is the nrmalized cnductr thickness. 8 Fr a fil cnductr, he is the cnductr thickness, and 5is the skin depth. And fr a rund cnductr, he = d (d is the cnductr diameter), and ^is the skin depth. S = ' (/"is the perating frequency) (3.3) V7 m is the number f layers ^^^^^sinh(y) + sm(y) csh(y)-cs(>') ^^^^^sinh(y)-sin(y) ^3 ^^ ^3 5^ csh(>') + cs(>') M(y} is called the skin effect term and D{y) is called the prximity effect term. The relatinship K^ (m, >') is pltted in Figure 3.1. We can bserve that bth the number f layers, m and the nrmalized cnductr thickness, y have significant effect n the K^. At high frequencies the skin effect restricts the cnductr thickness, y. Litz wire pracfically slves this prblem by having a number f small strands f permissible thickness. Our discussin will nt include much abut fil cnductrs. 44

53 3.1 Cre Dimensins Needed fr Optimizatin The fllwing list f parameters are needed fr high-frequency transfrmer ptimizatin. c cil frmer width hw height f the primary winding rj Outer radius f the primary (inner radius f the secndary) rf Inner radius f the bbbin Vg Vlume f the cre Ae crss-sectinal area f the cre and Wa winding area f the bbbin. 3.2 Assumptins Made in Transfrmer Optimizatin The fllwing assumptins are made in the transfrmer ptimizatin. 1. The transfrmer has nly tw-windings: primary and secndary. That is, we have nly ne secndary, which is a reasnable assumptin in high pwer transfrmers. 2. The cil frmer is fully utilized. 3. Pwer dissipatin due t cpper lss is cncentrated mainly in the inner radius f the winding. 4. The winding has a cylindrical shape, which is true fr EC, ETD, P, EP, RM, PM, trid shapes. 3.3 Design fr Minimum (Cpper) Winding Lss The pwer lsses f primary and secndary are: 45

54 n ^ j^ p ^w\ ~ * 1 '^ac\ "Y>2 ~ ^2-^ac2 (3.6) and we knw Rac as Kr times Rdc. Rac=RdcKr (3.7) and Rdc is: ^dc=^^^ (3.8) where p is the cnductivity f the cpper, la is the average length f turn, Acu is the pure cpper crss-sectinal area f the wire, and N is the number f turns. Ttal winding lsses is defines as Pw, which becmes P = P + P Kx -A -^rl- 2 ^ PKV^X ^cu\ p _j2j. P-K2'^2 (3.9) 'Si'2 ~ -* 2 "'^ r2, \u2 (IN IN ^ Pw -^r'p- 'h ^. h V ^cul ^cu2 We can define x as the rati between ri and rp. x = (3.10) Andiri=l +. (3.11) fp Using Eqs. (3.11 and 3.12), we can rewrite Eq. (3.10) as belw: 46

55 P^,=4.I^.Nf.K^.p. P^,=4.ll.Nl.K^.p. 1 + x h^.k^.{x-\) h^.k^.[k,-x) (3.12) And we knw frm Ampere-turn balance f the transfrmer h.ni = I2.N2. (3.13) Substituting Eq. (3.14) in Eq. (3.13) and cmbining the tw equatins yields P = P +P 2»T2 _S.I,\N;.K^.p K'^w {x-\).[k,-\)_ (3.14) This gives a the minimum pwer lss value fr the windings, which is P wmin 2 KT2 S.I,\N,\K^.p k...k. (3.15) The ptimum pwer distributin between primary and secndary windings is t have the lss distributed unifrmly that is lsses in the primary is equal t the lsses f the secndary. This keeps the temperature f the transfrmer cnstant. This sectin discusses varius utilizatin factrs used in transfrmer design with the necessary examples. Cnsider a primary winding f A^y turns f wire with a diameter di, which are unifrmly distributed in my layers and a secndary winding f A^2 turns f wire diameter d2 distributed in m2 layers. Assume A^yy as the number f primary windings in a layer. A^n = h K " w " axial (3.16) 47

56 Kaxiai is a space utilizatin factr in an axial directin, due t incmplete cmpacting f the wire in the axial directin f the winding. This depends n the wire diameter and varies between 0.88 and 0.96 fr wire diameters between 0.1mm and 3mm. The numbers f primary and secndary layers are ^ _ VI ~ ^F h^ radial'^ insulatin _ ^P-[^ ~V-^ radial'^ insulatin ^ _ V2 ~^\)-^ radial'^insulatin _ ^p\^\ ~ ^)-^radial'^insulatin Kinsuiatin is a spacc utilizatin factr f the winding in a radial directin, due t insulatin between the winding layers. Insulatin thickness and the wire diameter determine this value, and vary between 0.71 and 0.96 fr an insulatin thickness between 0.02 and 0.2mm and a wire diameter between 0.1mm and 3mm. Kradiai is a spacc utilizatin factr f the wire in the radial directin, due t the incmplete cmpacting f the wire in the radial directin f the winding and depends n the wire diameter and varies between 0.77 and 0.98 fr wire diameters between 0.1m and 3inm. Ttal number f primary turns, A^y = my.a^yy»r _ "'w-^p'kp^ ^r^ radial'^ axial'^insulatin /a 1 0\ d^ Similarly, N^ = ^" '^^ '^^' ^)'^radial -^axial -f^insulatin (3^9) ^2 Let us assume the area f crss-sectin f the wires f the wires as A^y and Aw2' These are given by 48

57 _ 7t.d{ _ K.h^,.rp.(X - \\K^^i 'J^axial -^insulatin - " 4 4.N, 2 / X (3.20) ^'^ 4 4.N, Kiitz is an area utiuzatin factr f the "litz" wire, due t incmplete cmpacting f the strands inside the "Utz" bundle. It is the rati between ttal area f the strands and area f the "litz" bundle and its value is 7i/4 = The pure crss-sectinal area f the primary and secndary wires is gixen by A - ^-^H- -fp '{X - ij-^fe K,^ -f^ radial '^ axial '^^ insulatin _K.h^..r,.{x-\\K^. 4.N, ^ _ ^'K'^P'\K\ ~ X\^ litz'^cu'^ radial'^ axial'^insulatin (3.21) ^7r.h^..rj..{K,-x).K^. 4.N, Kcu is an area utihzatin factr f a single "litz" wire strand. It is the rati f pure cpper crss-sectinal area f the strand t ttal crss-sectinal area f the strand and depends n the strand diameter. This is usually fr cmmnly used highfrequency strand diameters. Let us define Kw as area utilizatin factr f the windings. This describes the pure cpper crss-sectinal area t the ttal r windings crss-sectinal area and includes varius factrs, w here '^w ~ ^cu'^utz'^ radial'^axial'^ insulatin ' ^"^ ) 49

58 3.4 Optimum Value f the Winding Lss as Frm Eq. (3.16), we bserved that the ptimum diameter f the primary winding fipt=^p'xpt=rp.^ll + j -. (3.23) Transfrmer equatins are: /, = V, N,= -L A.K,,.B.A,.f (3.24) where P is the Vlt-Ampere rating f the transfrmer Vi is the RMS value f the primary vltage Ksh is the cefficient f the shape factr. This is equal t 1 fr rectangular vltages and is 1.11 fr sinusidal waves. B is the magnitude f the perating flux density in the cre Ae is the crss-sectinal area f the cre / is the perating frequency. Multiplying the tw terms in the Eq. (3.18), we will get h.n,= ^ -. (3.25) 4.K^,.B.AJ Substituting Eq.(3.19) in Eq.(3.16) we will get the winding lss as P^=K,,.-f-^ (3.26) rl ^2 jr2 where 50

59 K.,= -t\ K,.p '^'^sh-^e'k'^w 1-h +1 ll + -^-l (3.27) 3.5 Optimum Current Density f the Windings Current density in a wire is given by j=-l (3.28) where / is the current and Acu is the area f the cpper. Current densities f the windings are given by J.= J.= I^ cul I. ^cu2 (3.29) where Ac^y and Acu2 are pure cpper crss-sectinal areas f the primary and secndary windings. Cmbining the equatins f Eq. (3.23), we will get ^cu2-a ^cul '^2 ^l + ^pt (3.30) ^pt + 1 Substimting the ptimum value f jc in the abve equatin yields This gives lpt =4^=h- (3.31) 2pt 51

60 7,= 4./,.Arj ^'K'rp-KJx^p,-l) 4.7,.A^i r ^'K'fp-K, 11+^ -1 \ (3.32) Expressing in terms f pwer, using Eq. (3.19) ''lpr ~ ^'Ksh'BJA'K-rp'K^ r 11+^-1 (3.33) And the current density f the secndary is given by T _ ^t _ 'lpr 2pt 11+^ (3.34) 3.6 Transfrmer Optimizatin fr Minimum Pwer Lss This sectin gives the ptimizatin prcess t design a transfrmer f highest efficiency. The pwer lss in a transfrmer has tw cmpnents: cre lss and the cpper lss. We knw frm ur previus discussin, cre lss depends n the frequency, perating flux density and vlume f the cre. Cpper lss depends n the resistance f the wire, current density, which in turn are based n the utput pwer, perating frequency and the flux density. P =P +P t cre cpper = P V +P cre _ specific' e cpper = K,.V^.f'\B''+K,,-^ B\f (3.35) 52

61 The ptimum slutin gives the ptimum flux density fr a given frequency t have the minimum lsses. The abve equatin has t be differentiated with respect t B and equate it t zer t btain the ptimum flux density. dp, -(/= cnstant) = 0 (3.36) db This results in Bpt^ = r 2.K,,.P: it 2+2 Kl.V^.K3.f V ^^3 J +2 (3.37) and the calculated minimum transfrmer lss is nniii 1 e J 2\K2zMr ^3+2 Ki+2 ^^tvk r A:3+2 2.^,1 F^ ^K^.K^W^ y / 2(^2-^3) A'3+2 (3.38) 53

62 Enter the details f the transfrmer. Vin, Vinmax, Vinmin, frequency f peratin and Cnfiguratin. Suggests the material depending n the frequency f peratin. Calculate the Area Prduct required t fit the cre depending n the maximum flux density allwed by the material. B Take the user's respnse i.e. cre details. Vlume f the cre, Crss-sectinal area. Winding area. Outer radius f the bbbin, Inner radius f the bbbin, Height f bbbin. Obtain the Optimum flux density using the ptimizatin prcess. Recalculate the Electrical Area prduct needed if Bpt is less than the Bmax. Cmpare Ape with Amechanical. Figure 3.1 Flw Chart fr Transfrmer Optimizatin 54

63 Calculate Number f turns in primary and secndary. Calculate the Wire area needed fr primary and secndary. Check whether we can fit the windings in the available winding area. N Yes Calculate the Operating Flux Density. Calculate Cpper lsses, Cre lss, ttal lss, efficiency, regulatin, etc. Stp Figure 3.1 Flw Chart fr Transfrmer Optimizatin. (Cntinued) 55

64 CHAPTER IV TEST PLATFORM This sectin explains mre abut the test platfrm used fr ur experiment, its unique feamres, the prblems faced during implementatin, etc. The test setup under cnsideratin is a switching pwer supply, f 1.5kW, with input vltage between 24 and 32 vlts, utput vltage f 500 vlts and utput current between 0 and 3 amperes. The pwer supply has three identical sectins, whse utputs are cnnected in series, and each sectin gives an utput vltage f 167 vlts and current f 3 amperes. This gives a ttal utput vltage f 500 vlts and 3 amperes f current. 4.1 Auxiliarv Pwer Supply Sectin An auxiliary switching pwer supply is cnstructed in rder t pwer up the pulse width mdulatin chips f the three sectins f the supply. This is a simple push-pull cnverter with its input vltage being between 24 vlts and 32 vlts and utput at a cnstant level f 28vlts. This has 2 MOSFETs cnnected n the primary side f the transfrmer. The secndary f the transfrmer is rectified using a full wave rectifier and is subjected t a lw pass filter, which eliminates the high frequency harmnics and gives a nice direct current (DC) vltage at the desired level. The auxiliary pwer supply is shwn in Figure

65 ZiJ'-CC 'I5S2J '* ="13 :; j-va- vt G».J 'I- ;5:t.,':!, '1-- i -lov M322D' 39 3 ^A ^ - t D1 ;J3S3 +- tuju9?u! 35 '1. ;i I P,3 ;^ r 1 \- -Wv -pcflld > I 'vvv * rw anpi+.i I ' N'r-i- ^*rrr ^5fnpi-. ;ntt7«i J<3 llt ~^ >-.vr n F J!L i = -.:=-v:c -I '-'"^ \u Old '! II I- ^* * ^//^ i_ Jl :;^ -i It- 3; 3 UUU:: V UUU:: ^^ ^3 Figure 4.1 The AuxiUary Pwer Supply 4.2 Main Pwer Supply Sectin The main pwer supply has three identical push-puu cnfigured sectins. Here we are ging t discuss ne f the sectins. And each sectin gives an utput vltage f 170 vlts and a current f 3 amperes. These sectins are cnnected in series, which makes the utput vltage 500 vlts and utput current as 3 amperes. Figure 4.1 shws die schematic f the main pwer supply. We can divide each f the sectins in t different parts as fllws: 1. Input Filter, 2. Pwer MOSFETs, 3. Pwer Transfrmer, 57

66 4. Rectifiers and Snubbers, 5. Output Filter, 6. Cntrl Sectin, 7. Feedback lp, 8. Lad Input Filter The input filter fr these is just a capacitr f large value t reduce the vltage fluctuatins at the input because f external effects. The switch-mde pwer supply appears as a negative resistance t the utput f the filter capacitr. The negative resistance is due t the fact that with the increasing vltage, the input current decreases, the utput pwer and input pwer d nt vary. The decreasing input current with an increasing input vltage implies a negative input resistance. Capacitrs C12, C13, C15, C16, C18 and C19 represent the input filter Pwer Switches The pwer switches used were Internatinal rectifier's MOSFETs 2N6764 and the n resistance f this MOSFET was Ohms. These MOSFETs are quickly switched between the saturatin and the cut-ff states. They serve as a "gate" fr the energy entering the supply that is subsequently delivered t the lad. The pulse width mdulatr regulates the energy flw by changing the n time and ff time f the pwer MOSFETs. Each sectin has tw MOSFETs in parallel t distribute the current flwing unifrmly 58

67 between the MOSFETs, t reduce the stress n each MOSFET, t reduce the static lsses (lsses due t I^R) and t increase the reliability. The switching lsses are f cnsiderable amunt, as the switches are carrying large currents. The MOSFETs are munted via a heat sink, which helped us t dissipate the switching lsses Pwer Transfrmer The pwer transfrmer used has center-tap n bth primary and secndary. The transfrmer des nt stre energy in this cnfiguratin and nly transfers energy frm primary t secndary. The push-pull cnverter ffers a relatively small transfrmer cmpared t asymmetrical cnverters, due t the fact that the cre f the transfrmer is excited in bth directins equally. The initial testing f the circuit was dne with ETD cres. The prblem with these cres was with the heat dissipatin. The amunt f surface area available t dissipate the heat generated was small cmpared t the Pt cres, which later replaced ETD cres. The test set up was built t pwer up a Hall-Effect thruster used in satellites. The lsses in the transfrmer have t be dissipated using radiatin nly in vacuum, as there is n chance fr cnductin r cnvectin. We can nt use frced ventilatin fr cling. The windings were made f Litz wire, 175/40 wire fr primary and 38/40 wire fr the secndary. Litz wire used has nyln serving fr additinal insulatin. We prvided additinal insulatin by using mylar fil between the layers. 59

68 4.2.4 Output Rectifier The secndary f the pwer transfrmer is rectified using dide rectifier and is fed t a secnd rder lw pass filter made f Inductr and Capacitr, which gives a smth DC utput at cnstant vltage. The rectifier circuit was cnstructed with XTS 30-12A. These dides cnduct at the same time as the pwer switches, and they act as free wheeling dides when nne f the transistrs are cnducting. The peak value f the current thrugh these rectifiers is higher than the average value f the current. The rectificatin circuit is causing a cnsiderable amunt f lsses because f the V-I drp Snubber Netwrks A snubber netwrk is used t reduce the transient ver vltage spike and thereby reducing the EMI. This als helps in reducing the transient lsses. If nt reduced, the transient vltages may exceed the ratings f the semicnductrs, resulting in device failure. A snubber circuit was implemented by using a resistr-capacitr netwrk, was placed acrss the pwer MOSFETs and the secndary side rectificatin dides t aid in reducing the switching stress and EMI prblems caused by mming the device n and ff. This kind f snubber circuit is called Passive Snubber as it is ging t dissipate the energy stred in the capacitr in the resistr. Additinally, pwer lsses during switching are reduced because f the snubber circuits [3]. The snubber netwrks, seen in the main schematic in Figure 4.2, were implemented by R23 and C5, R24 and C6, R33and C14, R34 and C7, R37 and C8. and 60

69 R38 and C17 fr switches. Snubber netwrks ensure that secndary breakdwn, re\ erse bias, and safe perating range f the transistr are nt exceeded [3]. i I in Switching Cntrl i iq + Vce D Ic i R Figure 4.2 Cmmn Implementatin f RC Snubbers The snubber netwrk shwn in Figure 4.2 shws a cmmn implementatin f the netwrk. When the MOSFET is in the n state the vltage acrss it and the snubber netwrk is nearly zer. The snubber netwrk is used t increase the time it takes fr the transistr vltage t rise during the turn ff state. This is because, nce the transistr begins t turn ff, the dide will be frward biased and the capacitr wiu begin t charge up. The resistr is used t limit the discharge current f the capacitr thrugh the transistr, nce the transistr is turned back n. This circuit is knwn as a turn ff snubber since it aids in reducing the turn ff stress. A similar circuit referred t as a turn n snubber, can be used fr the same purpse during the turn n prcedure. Altemative 61

70 placements f the netwrk are pssible. One example wuld be t place the netwrk acrss the transfrmer. Figure 4.3 shws hw the vltage begins t rise acrss the transistr when the switch begins t turn ff During this tumff, time switching stresses and pwer lss are high. By adding in the snubber netwrk, the pwer lss and switching stresses are reduced as can als be seen in Figure 4.3. Tum-Off (a) Figure 4.3. Transient Vltage and Current (a) with ut Snubber circuit (b) with Snubber Circuit T determine the apprpriate values fr the capacitrs in snubber netwrk Eq. 4.1 was used [6]. Ip is the expected peak current thrugh the switches and was calculated during the transfrmer design. The time it takes fr the switch t clse is indicated as tf and Vf is the desired capacitr vltage when the transistr current reaches zer [6]. Vf was chsen t be twice the surce vltage supplied by the input filter t the pwer 62

71 cnverter. This is due t the fact that twice the supply vltage drps acrss the switch when it is pen. ^ _ ^P tf fr...vs=vf@is=0 ^P'^tf 2*Vf 2*Vs ^^4*(44«)^ (4.1) 2*200y T select the resistr value Eq. 4.2 was used [6]. The resistr value was chsen such that the capacitr wuld fully discharge befre the switch tums back n. r >\OORC r 8.3*10'^ >R< n looc 5*62pF (4.2) R < 26KQ >R = 20KQ Output Filter The utput filter used was a secnd-rder lw-pass LC filter cnstructed with an inductance f loouh and a capacitance f 20uF. This was dne t keep the highfrequency radiatin and cnducted ripple and RF interference within reasnable bunds. "T prvide a steady DC utput, and reduce ripple and nise, LC lw-pass filters will nrmally be prvided n switching supply utputs. In switching cnverters, these filters carry ut tw main functins. The prime requirements is energy strage, s as t maintain a nearly steady DC utput vltage thrughut the pwer switching cycle. A secnd, and perhaps less bvius, functin is t reduce high-frequency cnducted series and cmmn-mde utput interference t acceptable limits." [3] 63

72 4.2.7 Cntrl Sectin Pulse Width Mdulatr A pulse width mdulatr (PWM) is the heart f the switch-mde pwer supply, and cntrls the duty cycle f the switches. The PWM chsen fr the switching pwer supply (fr bth auxiliary and main pwer supply circuits) is an UC2856 frm Unitrde. The UC2856 is a current mde cntrller that feamres sft start, under vltage lck ut, current mde cntrl, and a built-in dual drive circuit. The dual drive circuit prvides a 1.5A peak current t quickly turn n the pwer MOSFETs. The sensing blck f the diagram, shwn in Figure 4.4, takes a reference vltage (V(desired)) and the utput vltage and amplifies the difference between them. The difference signal is then sent t a cmparatr, which is then cmpared with a repetitive wavefrm. Figure 4.4 shws hw such a circuit might lk. This type f circuit is called V(desired) V(actual) ^ Repetitive Wavefrm Cmparatr Vcntrl (amplified errr) Switch > Cntrl Signal Switch Cntrl Signal Figure 4.4 Pulse-Width Mdulatr a pulse-width mdulatr. The switch frequency is l/tg. "This frequency is kept cnstant in a PWM cntrl and is chsen t be a few kilhertz t a few hundred kilhertz range. 64

73 When the amplified errr signal, which varies very slwly with time relative t the switching frequency, is greater than the saw-tth wavefrm, the switch cntrl signal becmes high, causing the switch t tum n. Otherwise the switch is ff "[5] Current Mde Cntrl The UC2856 als ffers the ability f pulse by pulse current limiting. Current mde cntrl is the prcess f limiting the maximum amunt f current passing thrugh the switches. The peak current allwed is determined. By using this equatin the maximum current thrugh the transfrmer was determined. Thus, the values f the current cntrl circuitry were determined. Current-mde cntrl prvides a fast acting inner feedback lp this makes the cnverter int a cnstant current supply. The currentmde cntrl has several advantages ver the cnventinal direct duty rati PWM cntrl. 1. It limits peak switching current. Since either the switch current is directly measured r the current is measured smewhere in the circuit where it represents the switch current with ut delay, the peak value f the switch current can be limited by simply putting an upper limit n the cntrl vltage. 2. It remves ne ple (crrespnding t the utput filter inductr) frm the cntrlt-utput transfer functin, thus simplifying the cmpensatin in the negative feedback system, especially in the presence f right-half-plane zer. 3. It allws a mdular design f pwer supplies by equal current sharing where several pwer supplies can be perated in parallel and prvide equal currents, if the same 65

74 cntrl vltage is fed t all the mdules. (Fr high pwer appucatins, pwer stages can be cnnected in parallel. Since the utput currents are prprtinal t the cntrl vltages, the pwer stages can be frced t share equally by simply cnnecting the cntrl vltages t a cmmn bus. This can be achieved using fixed frequency current mde cntrl peratin.) 4. It results in a symmetrical flux excursin in a push-pull cnverter, thus eliminating the prblem f transfrmer cre saturatin. In push-pull cnverters bth quadrants f the B/H curve are used. Any flux excursin in ne directin f the transfrmer that is nt symmetric with the reverse directin will cause the center pint, which is desired t be zer flux, t shift. Because f the flywheel actin the utput dides the winding vltage f the transfrmer is clamped t zer and there is n DC restratin f the cre between cycles. As a result any unbalanced flux-density swing results in a increasing flux density ffset. This causes the transfrmer t "staircase" int saturatin. By sensing and cntrlling the peak primary currents in the switches any tendency fr unbalanced flux density swings will result in a change in the magnetizatin current, and by maintaining the peak current cnstant stafrcase saturatin will nt ccur [3]. 5. It prvides input vltage feed-frward. An input vltage feed-frward is autmatically accmplished, resulting in an excellent rejectin f input line transients. A perfect feed frward can be achieved fr particular slpe cmpensatin. 66

75 Feedback The circuit has tw different feedback lps. The inner lp is because f the current mde cntrl, which was discussed earlier. The secnd and uter lp is the vltage feedback lp. As we need islatin between the input t the supply and the utput f the supply, Islated feedback was prvided using Unitrde's UC1901. The features f the chip are in the appendix [81. The utput vltage is sampled using a vltage divider circuit having tw resistrs in series. The utput f the chip is given t RF cupling transfrmer, whse utput is averaged and fed t the PWM cntrller Lad The pwer supply was tested with a resistive lad, which is cmmn fr all the three sectins. The lad resistrs are made f pwdered carbn and each ne is a standard resistr f 60 Ohms. Varius values were btained fr the lad by cnnecting these resistrs in different cnfiguratins. The supply was tested with 180, 150 and 120 hms f lad. 4.3 Efficiencv f the Pwer Supply One f the bjectives f tiiis prject was t design an efficient pwer supply. As was discussed earlier, switching pwer supplies ffer greater efficiency than linear pwer supplies. Since the system was fully integrated, efficiency measurements were prvided in Chapter V, "Measurements and Results." 67

76 The pwer MOSFETs, used n the pwer cnverter have their biggest lsses during tum n and tum ff. The energy stred in the snubber netwrk capacitr can be seen in Eq. (4.3). During the n time f the MOSFETs, the energy is transferred mstly t the snubber resistr. This can be calculated, theretically, as seen in Eq. (4.4) W =-CVs' =.5^^ uf * 64 ~ = /// (4.3) -CVs ^ _ Energy 2 1 ru. 2 r Time T 2 ^^'^^ Pr = /// * (40kHz ) = 81.9milliWatts The pwer absrbed by the transistr during tum-ff is given be Eq. (4.5) I.'tf'f 9-*(25*10"^)-*40*10' PMsFet = = ^ = 2.025Watts (4.5) MsFet ^QQ^ 100*0.001*10"^ It shuld be mentined that a cnsiderable amunt f pwer is als lst t the transistr during the n state. This is due t the transistrs n resistance, and calculated as fllws: ^MOSFET ~ ^verage^n^rtsistbjice ' \^-^) And the resistance f the MOSFET is Ohms. P = ^ (4.7) input r s\stem /v-- effieiency Assuming an efficiency f 95 %, we knw that Put as 1500 watts, and taking a vltage f 28 vlts, input current is 1500 ^ ner^.e = ""' ' 0.95*28 ampercs. 68

77 This gives us a current f amperes and as the units are in parallel, current thrugh each unit is ne third f this current that is amperes. And tw MOSFETs are in parallel in each bridge f the push-pull giving a current f 9.4 amperes thrugh each f these MOSFETs. Hence the lsses per MOSFET are (9.4)'(0.055) = 4.858war/5. This is a cnsiderable amunt f pwer as we have 12 MOSFETs n the supply. The ther cause f pwer lss, in the designed circuit, is the utput dides. With a lad current f 3 amps, the lss in the dides is apprximately 9watts, assuming a frward vltage f 1 vlt per dide. The ther majr cause f pwer lss is the transfrmer. The primary cpper lsses fr the transfrmer are given in Eq.(4.8) and the secndary cpper lsses in Eq. (4.9) The derivatin f die values Rpr^,nar^Rs' ^^ ^peak can all be fund in this authrs prject ntebk in the transfrmer sectin. P,^^MI,.^^2^D^'R^^^M2(>j2^S)'{0.0034S) = \.336Watts (4.8) p, = I -R = 3- *.1574 = Watts (4.9) sec ndary s s The cre lsses is given by prduct f vlume times the specific pwer density, i.e. 18.2*0.2 = 3.64 watts. This brings die ttal cnsidered lsses t watts. Fr the desired utput pwer f 1500 watts, the efficiency f the system was 88%. This is die result btained in the practical experiment. This is nt high enugh because f the lsses n the secndary side snubbers. Our calculatin des nt include the lsses n the secndary side dide snubbers. 69

78 4.4 Imprvements Suggested imprvements t increase the efficiency f the pwer supply include synchrnus rectificatin, and a weaving snubber cnfiguratin. Synchrnus rectificatin is the prcess f replacing the utput rectifier with cntrlled switches. Since ne f the causes f decreased efficiency is the utput rectifier, with 9 watts f pwer lss t the rectifier, replacing the rectifier with cntrlled switches wuld increases the efficiency f the system. This imprvement culd easily be implemented by using the drive circuit f the PWM t cntrl the synchrnus rectifier switches. The ther thing t cnsider is design f efficient (active) snubbers t replace the present (passive) snubbers. 70

79 CHAPTER V MEASUREMENTS AND RESULTS This chapter cver the efficiency and perating temperature measurements as a result f ptimizatin n the test set up discussed in the previus chapter. The experiment cnsists f testing the pwer supply with replacing ne f the existing transfrmers with the ptimized transfrmer. The main bjective f the experiment is t shw the ptimizatin f the transfrmer in terms f efficiency and temperature f the individual cmpnents. The temperature was measured using infrared thermal imaging camera. The rate f temperature rise and fall were bserved. The POT cres have better perfrmance in terms f thermal stability because f large surface area available fr dissipatin f heat. The lad fr the switch-mde pwer supply was a 200 hm pwdered carbn resistance and the system ran fr mre than 15 minutes t achieve the steady state. Figure 5.1 shws the pwer supply test semp. Figure 5.2 shws the ptimized transfrmer and the existing transfrmer besides each ther. This picmre was taken with thermal imaging camera, which shws the difference in temperamres. Figure 5.2 (a) shws the existing ETD and P 42/29 cre, whereas Figure 5.2 (b) shws the existing and P 36/22 cre. In bth cases, the temperature f windings and the cre f the ptimized transfrmer are gd cmpared t the existing transfrmer. Optimized transfrmer is wund using POT cre where as the existing transfrmer is ETD cre. POT cre has certain advantages cmpared t the ETD in terms f EMI, amunt f surface area, and munting. Here the POT cre transfrmer is munted temprarily n the pwer supply bard and is nt fixed. 71

80 Figure 5.1. The pwer supply test setup. The ptimized transfrmer has nt nly better efficiency, but als has unifrm distributin f heat, which is necessary fr space appucatins. Because f large surface area available the cling is much faster, which can be seen in Figure

81 (a) (b) Figure 5.2 P and ETD cres next t each ther (a) P42/29 (b) P36/22. Figure 5.3. The cling f P and ETD transfrmers 73

82 The system was tested with bth P42/29 cre and P36/22 cres. Thugh the cre lsses are lw fr P36/22 because f lw vlume, the winding lsses are high due t higher resistance f the windings. T fit the windings in the cre, tw wires were in parallel n the primary side, and ne wire in secndary fr a P36/22 cre. Where as the P42/29 cre has enugh winding area t fit three wires in parauel n the primary side and ne n the secndary side. This gives us almst equal lsses in primary and secndary, which in tum gives unifrm distributin f heat. Figure 5.4 shws the tp view f the tw different transfrmers. Figure 5.4 (a) shws the tp view f the existing transfrmer where as Figure 5.4 (b) shws the tp view f the ptimized POT P442/29 cre. Frm this picture we can bserve the cre and windings temperature f the ptimized transfrmer are less than the existing ne. (a) (b) Figure 5.4 Tp view f (a) Existing ETD and (b) Optimized POT cre transfrmers 74