Exclusive Technology Feature. Eliminate The Guesswork When Selecting Primary Switch V DD Capacitors. ISSUE: May 2011

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1 Excluive Technlgy Feature Eliminate The Guewrk When Selecting Primary Switch DD aacitr by Ed Wenzel, STMicrelectrnic, Schaumburg, ll. SSUE: May 2011 A rimary witch, ued fr ff-line alicatin, ften cntain a cntrller and a high-vltage MOSFET. The engineering dcument f rimary witch familie tate that the caacitr at DD mut be ized accrding t the time needed t tart-u. Sme rvide a frmula fr the caacitr at the DD in t enure tart-u and me d nt have a frmula. The frmula given in me rimary witch ecificatin cntain an undefined tart-u time, t, which deend n many arameter! The fllwing examle i frm a rimary witch ecificatin: The external caacitr DD n the DD in mut be ized accrding t the time needed by the cnverter t tart-u, when the device tart witching. Thi time t deend n many arameter, including tranfrmer deign, utut caacitr, ft tart feature, and cmenatin netwrk imlemented n the OMP in and ible ecndary feedback circuit. The fllwing frmula can be ued fr defining the minimum caacitr needed: DD > DD t / DDhyt 1 n thi article, we derive an equatin t determine a caacitr value at DD uing knwn circuit cmnent value and arameter frm ne rimary witch ecificatin. The derivatin begin with a calculatin f the time it take t charge u the utut caacitr, t. We then ue thi arameter, tgether with the required DD witching current, DD1, and the DDhyt ( DDn DDff ), t determine the value fr the DD caacitr. Tyical tart-u wavefrm frm the engineering ec are hwn in the figure. Figure. Tyical tart-u wavefrm fr a rimary witch in an ffline cnverter alicatin Hw2Pwer. All right reerved. Page 1 f 5

2 Excluive Technlgy Feature Amng the arameter we will need t calculate DD are utut vltage factr and back mde. The utut vltage factr, x, i the utut vltage at turn-n divided by the ecified utut vltage in teady-tate eratin. The back mde, M, i a number ranging frm M 4 in dicntinuu-mde eratin t M 2 in cntinuu mde. After calculating DD, we will determine a nminal caacitr value by auming a 20% tlerance fr the DD ca and the utut ca. The firt equatin, DD, i fr a wer uly with a knwn number f tranfrmer turn. The ecnd equatin, DD1, can be ued fr an etimate where the turn rati i unknwn. Thi etimate i baed n the aumtin that the back vltage i uually equivalent t the minimum dc inut vltage fr a wer uly erating with a 50% duty cycle. The rimary witch tart witching when the DD reache DDn ( DDt n the grah). The utut vltage rie and the current DD1 i drawn frm the DD ca. The time t i the time it take fr the utut vltage t rie, which mut be befre the DD dr t DDff ( DDd n the grah). The DD ca i then calculated frm dv r dt dt dv where i DD1, dt i t and dv i the hyterei ( DDn DDff ). Derivatin Of Primary Switch DD aacitr alue The fllwing derivatin i ued t calculate the value f the DD caacitr required n the auxiliary winding uing infrmatin frm a rimary witching engineering ec and circuit value. We tart with the equatin fr ecndary eak current, k : k Dk ( ) Eqn (1) where Dk i the ecified eak drain current, i the number f rimary turn, and i the number f ecndary turn. ext, we define an utut vltage factr, x: chg x Eqn (2) where chg i the utut vltage at turn-n and ecified i utut vltage. chg i ne ymbl rereenting the lad current at chg fr a reitive lad with the ame factr x: chg x. Eqn (3) chg i equal t the average f the ecndary eak current, k /M, minu the lad current, chg : chg k chg Eqn (4) M where chg i the current int the utut caacitr, and M i a cntant equal t 4 fr dicntinuu-mde eratin and 2 fr cntinuu-mde eratin. Subtituting equatin 1 and 3 int equatin 4 yield 2011 Hw2Pwer. All right reerved. Page 2 f 5

3 Excluive Technlgy Feature chg ( Dk ) ( M ) x. Eqn (5) Frm the familiar equatin dv/dt, r dt dv/ we btain an exrein fr the time t charge the utut caacitr: t ( chg chg ). Eqn (6) Then, ubtituting equatin 2 and 5 int equatin 6, we btain t ( x) ( ) Dk x ( M ). Eqn (7) ext, frm the equatin dv/dt r dt/d we btain a value fr the auxiliary caacitr value, DD : ( t ) DD1 DD Eqn (8) DDhyt where DD1 i the ecified DD current during witching and DDhyt i the ecified DD hyterei vltage. Then, ubtituting equatin 7 int 8, we arrive at DD DDhyt ( x ) DD1 ( ) Dk x ( M ). Eqn (9) Fr the cae where the turn rati i nt knwn, we can etimate the DD caacitr value by relacing / with an exrein baed n the back vltage,. We tart with + ( ) d. Eqn (10) Slving fr / yield ( + ) d. Eqn (11) Finally, ubtituting equatin 11 int equatin 9, we btain DD1 DDhyt ( x ) DD1 ( ) M Dk x ( + ) d w, let cnider the examle f a rimary witch with a univeral inut and the fllwing circuit value: Dk 2.0 A 2011 Hw2Pwer. All right reerved. Page 3 f 5

4 Excluive Technlgy Feature DD1 9 x 10-3 A DDhyt A d x 10-6 F 90 turn 11 turn M 3 X 0.7 DD DDhyt DD 5 ( x ) Dk M F. DD1 x Fr a 20% tlerance n bth the auxiliary and the utut caacitr DDnm DD r 20 µf. Or frm 100, we can etimate the DD value DD ( x ) DD ( Dk ) x DDhyt M ( + d ). Again, auming a 20% tlerance, we btain DD 1 nm DD r 20 µf. F Reference: 1. Per53-E Offline Primary Switch dataheet, age 22, available nline at htt:// 2. Per53-E Offline Primary Switch dataheet, age Hw2Pwer. All right reerved. Page 4 f 5

5 Excluive Technlgy Feature Abut The Authr Ed Wenzel i an alicatin engineer fr STMicrelectrnic in Schaumburg, ll. He jined the cmany in June 1998 in the wer lab fr variu wer uly alicatin. He ha mre than 40 year exerience in the wer field with variu tlgie and emicnductr. Ed ha a BSEE degree frm rtheatern Univerity in Btn. He ha ublicatin and a nte in the wer uly area and fr LED alicatin. Ed ha been awarded tw atent Hw2Pwer. All right reerved. Page 5 f 5