POWER ELECTRONIC APPLICATIONS

Transkript

1 POWER EECTRONIC APPICATION Assoc. Prof. Dr. H. İbrahim OKUMUŞ Karadeniz Technical Universiy Engineering Faculy Deparmen of Elecrical and Elecronics 1

2 Conens Inroducion ACAC Phase Conrol Circuis Inegral awe Conrol Phase Conrol for Resisive oads Harmonics wich Mode DCDC Converers

3 Course Maerials Tex book, ecure noes, PowerPoin Presenaions References Power Elecronics, Circuis, Devices, and Applicaions, by M. H. RAHID. Nik Rumzi Nik Idris, ecure Noes, Deparmen of Energy Conversion, Universii Teknologi Malaysia kudai, JOHOR Power Elecronics: Converers, Applicaions and Design by N. Mohan, T.M. Undeland and W.P. Robbins, John Wiley & ons, Inc Power wiching Converers by imon. Ang, Marcel Dekker, Inc., 1995 Power Elecronics and AC Drives by B.K. Bose, Prenice Hall, 1986 Power Elecronic Conrol of AC Moors by J.M.D. Murphy, F.G. Turnbull, Pergamon Press, 1989 Principles of elecric machines and power elecronics by P.C. Şen, John Wiley and ons, 1997 Power elecronics : devices, drivers, and applicaions by B.W Williams, Macmillan Educaion d okumus@ku.edu.r 3

4 Web sie for he course: EE 408 Power Elecronic Applicaions 4

5 Wha is Power Elecronics? A field of Elecrical Engineering ha deals wih he applicaion of power semiconducor devices for he conrol and conversion of elecric power Inpu ource AC DC unregulaed Reference Power Elecronics Converers Conroller sensors Oupu AC DC oad POWER EECTRONIC CONERTER he hear of power a power elecronics sysem Doç.Dr. H. İbrahim OKUMUŞ okumus@ku.edu.r 5

6 Why Power Elecronics? Power semiconducor devices Power swiches i sw v sw = 0 P loss = v sw i sw = 0 osses ideally ZERO! ON or OFF i sw = 0 v sw Doç.Dr. H. İbrahim OKUMUŞ okumus@ku.edu.r 6

7 Why Power Elecronics? Power semiconducor devices Power swiches K K K ak ak G ak G i a A i a A A i a Doç.Dr. H. İbrahim OKUMUŞ okumus@ku.edu.r 7

8 Why Power Elecronics? Power semiconducor devices Power swiches G D i D D G C i c CE E Doç.Dr. H. İbrahim OKUMUŞ okumus@ku.edu.r 8

9 Why Power Elecronics? Passive elemens High frequency ransformer i Inducor C 1 i C Doç.Dr. H. İbrahim OKUMUŞ okumus@ku.edu.r 9

10 Why Power Elecronics? Inpu ource AC DC unregulaed Power Elecronics Converers sensors IDEAY OE oad! Oupu AC DC Reference Conroller Doç.Dr. H. İbrahim OKUMUŞ 10

11 Why Power Elecronics? Oher facors: Improvemens in power semiconducors fabricaion Power Inegraed Module (PIM), Inelligen Power Modules (IPM) Decline cos in power semiconducor Advancemen in semiconducor fabricaion AICs FPGA DPs Faser and cheaper o implemen complex algorihm Doç.Dr. H. İbrahim OKUMUŞ okumus@ku.edu.r 11

12 ome Applicaions of Power Elecronics : Typically used in sysems requiring efficien conrol and conversion of elecric energy: Domesic and Commercial Applicaions Indusrial Applicaions Telecommunicaions Transporaion Generaion, Transmission and Disribuion of elecrical energy Power raing of < 1 W (porable equipmen) Tens or hundreds Was (Power supplies for compuers /office equipmen) kw o MW : drives Hundreds of MW in DC ransmission sysem (HDC) Doç.Dr. H. İbrahim OKUMUŞ okumus@ku.edu.r 1

13 ACAC FAZ KONTRO Şekil 1.1 Yükün gücünün, emel dalga frekansı değişmeden konrol edilmek isendiğinde, bir AC anahar kullanılır. Bu anahar, şekil 1.1 de görüldüğü gibi, bir riyak veya ers paralel bağlanmış iki ade risör olabilir. Birkaç isisna dışında, konrolun sonucu anaharlama işleminden bağımsız olarak amaçlanır. Praikeki mevcu riyak anma değerleri çok yüksek güç uygulamalarını sınırlamakadır. 13

14 1.1 GİRİŞ Yükün gücünün konrolünde iki emel meo kullanılabilir. Birincisi, belirli sayıda am dalgayı ileime geçirir. Daha sonra yine belirli sayıda am dalganın ileimi engellenir. Böylece, ileim ve kesimdeki am dalgaların sayısı ile yüke giden oralama güç ayarlanabilir. Şekil 1. de böyle bir kullanıma ai ipik bir dalga şekli görülmekedir. Yük epkisinin zaman sabii, yükün oralama güce epki verebileceği kadar uzun olmalıdır. Genel olarak, epki zamanı saniyeden daha düşük zamanlar olmayıp saniye seviyesindedir. İki ade uygulama yeri olarak, 1. Bir haznedeki sıvıyı belirli bir sıcaklıka sabi umak için ısımak,. Hava kanalına yerleşirilmiş bir ısııcı ile kanaldaki havayı ısımak. Her iki uygulama da kapalıdöngü şeklinde olup, am dalgaların ileim ve kesimdeki sayılarına bağlı olarak isenilen sıcaklık konrol edilebilir. 14

15 Şekil

16 Bu işlem bazı uygulamalarda kullanışlı değildir ve faz konrolünün periyoaki her yarım dalga için yapılması gereklidir. Şekil 1.3, yükün omik olduğu durumları gösermekedir. Bu işlem, bazı uygulamalar için uygun olan faz konrollü bir çıkış üreir. Işık kararma ve moor hız konrolu buna bir örnekir. Moor hız konrol meodu, ork un hızın karesi ile değişiği fan lar ve pompalar gibi sadece değişken momenli yükler için uygundur. Şekil

17 Temel AA Faz Konrol Devreleri 17

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21 1

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23 1. İNTEGRA DAGA KONTRO Şaye yüke giden dalgaların şekil 1. de görüldüğü gibi ileimi ve kesimi yapılırsa, yükün oralama gücü değişebilir. İleim dalga şeklinin ekrarlandığı, ileim zamanının, oplam dalga zamanına oranı; yükün oralama gücünü konrol eder. Şekil 1. de, k yükün enerjili olduğu dalga sayısı ve n ise operasyonun am periyodundaki dalga sayısıdır. k süresince anahar ileimde ve güç maksimumdur. Kalan (nk) dalga süresince, anahar ileimde değil ve güç sıfırdır. Omik yük durumunda oralama güç 1.1 eşiliği ile verilir: P or R k n (1.1) k sayısı sadece bir am sayı olarak değişiğinden, yükün oralama gücü sadece sonlu kademelerde değişir. Oralama gücün regülasyondaki mevcu adımlarının sayısı, ekrarlama şekli içerisindeki dalgaların oplam sayısına bağlıdır. okumus@ku.edu.r 3

24 Kapalı bir döngü sisemi, k değerini ayarlanan bir nokada veya nokaya yakın umaka kullanılabilir. Böyle bir sisem, konrolün abiaından gelen açık ve kapalılığın bir sonucu olan değişimleri düzelmek için konrol edilen sisemde yeerli enerji depolamaya bağlıdır. Bu konrol meodunun bir avanajı, omik yüklerde sıfır gerilimde anaharlama oluşmasıdır. Yük akımının değişim oranı sisemin frekansı arafından idare edilir ve bu değişim oranı, diğer konroller ile elde edilen oranla karşılaşırıldığında küçük olabilir. onuçaki elekriksel gürülü diğer meodlara göre küçük olabilir. okumus@ku.edu.r 4

25 ÖRNEK 1.1 Omik bir yük, yük gücünün büün dalgalarda üreilmesi için konrol edilecekir. Kaynak, 30 RM, 60 Hz dir. Yük gücünün 10 kw arası değişmesi gerekmekedir. Tekrarlamanın maksimum aralığı 0,5 sn dir. R =5,9. Aşağıdakileri bulunuz: a. Anaharın akım oranı b. Maksimum gücü elde emek için yükün enerjili olacağı zamanın yüzdesi c. Minimum gücü elde emek için n ve k değerleri d. Yükeki mümkün olabilen en küçük arış nedir? okumus@ku.edu.r 5

26 (a) ÇÖZÜM I m ( 30)( 1, 414) 615, A epe değer 5, 9 61, 5 I RM 43, 5 1, 414 (b) Anahar devamlı ileimde olduğu zaman, P or ( 30)( 43, 5) Anahar, maksimum gücü elde emek için zamanın %100 ünde ileimde olmalıdır. k (c) P=000 W için, n , Şaye n = 30 dalga seçilirse, k = (0,)(30) = 6 dalga (d) k nın bir birim değişimi için, yükeki en küçük değişim, P W 333 W dan daha aşağı bir çıkış güç değişimi için, k değerinin iki am sayı arasında değişirilmesi gerekir. W okumus@ku.edu.r 6

27 Dönüşürücü Animasyonları 7

28 1.3 OMİK YÜKERİN FAZ KONTROU Şekil 1.1 deki emel devre, omik bir yükün gücünü konrol emek için kullanılabilir. Şekil 1.3 deki grafikler, omik yüklü am dalga bir doğrulucudakilere benzemekedirler. Buradaki farklılık, her ikinci yarım dalganın poziif değerinin olmayıp negaif kısmının olmasıdır. Bununla birlike, gücün bir kareli fonksiyon olmasından dolayı gerilimdeki negaif kısmın güç üzerinde azalıcı bir ekisi yokur. Şekil 1.1 Her yarım dalgadaki ileimin gecikmesi, açısıdır ve 1. eşiliği ile verilir. 1 (1.) Yük akımının RM değerinin eşiliği omik yüklü AC faz konrol durumu için 1.3 eşiliği olarak yeniden ifade edilmişir: I I () m 0,5 sin 1 RM (1.3) 0,5 Şekil 1.3 8

29 Yük gücü 1.4 eşiliği ile verilir: P I R or RM (1.4) Yük geriliminin RM değeri, I nin RM değeri için 1.3 eşiliğinde verilen ifadesine benzemekedir. 1.3 eşiliği R ile çarpılarak 1.5 eşiliğindeki sonuç elde edilir: RM () m 0,5 sin 1 0,5 (1.5) ve 1.4 eşiliklerinin incelenmesi, yük gücünün 0 ile 180 arasındaki üm aralık için nın değişirilmesi ile ayarlanabileceğini göserir. erilen bu aralık için ileimin ayarlanmasını yapabilecek uygun eikleme devreleri mevcuur. Akım sinüzoidal olmadığından dolayı, AC kaynağına yansıyan güç fakörü, yük omik bile olsa birim değerden daha azdır. Tanıma göre güç fakörü 1.6 eşiliğinde verilmişir: Oralama Güç Güç Fakörü (1.6) I RM RM okumus@ku.edu.r 9

30 Bu anımın, 1.3 ve 1.4 eşiliklerindeki ifadeler kullanılarak değerlendirilmesi yapılır. 1.6 eşiliğindeki RM in değeri sinüzoidal kaynak gerilimidir. Bu eşiliklerin birkaçı 1.7 eşiliğini oluşurmak için birleşirilebilir: Güç Fakörü 0, 5 sin 1 (1.7) onuç güç fakörü, sıfır olduğu zaman 1 ve sıfırdan armaya başladığında ise azalır. Kaynak geriliminin sıfır olduğu aynı zamanda, anahar akımı sıfır olur, çünkü yük omikir. Bundan dolayı, akımın sıfır olduğu zaman anahar ıkamaya başladığında, ihmal edilebilir kaynak gerilimi vardır. Kesim anındaki büyük dv/d problemi yokur ve elemanın erminal uçlarında gerilimin birikme oranını azalmayı gerekiren bir koruyucu devreye gerek yokur. okumus@ku.edu.r 30

31 Yük omik olduğundan dolayı, ileimde yük akımının arışında gecikme yokur. Şaye =0 de anaharın ileimi gerekmiyorsa, akımı uabilmek için yeerli uma akımını sağlama da bir problem değildir. Bu özellikle sınırlayıcı bir gereksinim değildir. nın çok küçük bir değeri için, yarıileken anaharı ileim durumunda umaya neden olacak yeerli gerilim ve akım genelde bulunmakadır. >90 değeri için, anaharın ileiminden önce anahar kaynak geriliminin epe değerini ıkar. Böylece anaharın minimum gerilim kapasiesi, kaynak geriliminin epe değeridir. Aynı ıkama kapasiesi, abiiki, anaharın CR veya riyak uygulamalarının her iki yönü içinde gereklidir. 31

32 ÖRNEK 1. Şekil 1.1 deki devrede, anahar 460 RM, 60 Hz lik bir kaynakan, omik bir yükün gücünü konrol emekedir. Yük direnci 0 ve =35 dir. Aşağıdakileri bulunuz: (a) epe yük akımı (b) yük akımının ekin değeri (c) anahar gerilim oranı (d) devrenin güç fakörü ÇÖZÜM (b) I RM (a) I m m ( 460)( 1, 414) 3, 53 R 0 3,53 35 sin P I RM ( ) W 0,5,48 A (c) Anaharın, kaynak geriliminin epe değeri olan 650 a dayanabilmesi gerekir. Bundan dolayı minimum anahar anma gerilimi en azından 800 olmalıdır. A (d) Güç Fakörü sin , okumus@ku.edu.r 3

33 1.4 HARMONİKER: TEK FAZI OMİK YÜKER Şekil 1.3 deki akımın dalga biçimi, özellikle nın değeri ararken yüksek dereceli harmonikleri içerir. Harmonik içeriği dalganın Fourier serilerinin analizi yapılarak belirlenir: imerik yarım periyoaki inceleme dalga biçiminin sadece ek sayılı harmonikleri içerdiğini göserir. Orijin kaydırılamadığından dolayı fonksiyon ek veya çif olur. Bundan dolayı A n ve B n erimlerinin ikiside birden mevcu olabilir. imerik olma durumu ile T/ aralığında inegral alınarak kasayılar belirlenebilir. Formüllerde zaman yerine açı değişkeni kullanılmışır: A B n n I m sin cos n d (1.8) I m sin sin n d (1.9) okumus@ku.edu.r 33

34 1.8 ve 1.9 eşiliklerinin çözümü ile aşağıdaki sonuçlar elde edilir: I m A1 cos 1 (1.10) B I m 1 sin (1.11) A n Im n 1 n 1 cosn 1 n 1 cosn 1 (1.1) I m Bn n 1 sinn 1 n 1 sinn 1 (1.13) n 1 Şekil 1.4 deki grafik, ile değişen bazı harmoniklerin davranışlarını gösermekedir. Her değer her bir harmoniğin bağıl genliğidir ve A ve B kasayılarının bilinen yolla birleşirilmesi ile elde edilir. okumus@ku.edu.r 34

35 ÖRNEK 1.3 Tek fazlı omik bir yük 460 RM, 60 Hz lik bir kaynak arafından bir faz konrol anaharı ile beslenmekedir. Faz konrolsüz yükün gücü 15 kw ır. Aşağıdakileri bulunuz: (a) oralama gücü 9 kw a düşürecek değeri (b) nın bu değeri için akımın emel dalgasının epe genliği (c) 3. ve 5. derece harmonik akımlarının epe genlikleri ÇÖZÜM = 0 iken yük direncinin değeri bulunabilir: okumus@ku.edu.r 35

36 R , 1 P=9000 W ile 1.4 eşiliği kullanılarak, I RM , 0, 5 5, eşiliği kullanılarak ve bir irdeleme işlemi ile, bulunabilir: =1,414 rad = 80, ve 1.11 eşilikleri kullanılarak: 4614 A , cos (,414), A A Şekil okumus@ku.edu.r 36

37 4614 B , (,414) sin (,414),68 A C A B 3116, A 1 1 (c) 1.1 ve 1.13 eşilikleri kullanılarak 1 A B 46, cos3 1 (1,414) 3 1 cos3 1 (1,414) 11, , sin3 1 (1,414) 3 1 sin3 1 (1,414) 4, 46 A A C 3 A3 B3 1,59 A okumus@ku.edu.r 37

38 A 5 46, cos5 1 (1,414) 5 1 cos5 1 (1,414) 3, 16 A B 46, sin5 1 1, sin5 1 (1,414) 4, 17 5 A C 5 A5 B5 5,3 A okumus@ku.edu.r 38

39 1.5 FAZ KONTRO: İNDÜKTİF YÜKER İndükif bir yük için devre şeması şekil 1.5(a) da ve ilgili grafikler 1.5(b) de göserilmişir. 1 okumus@ku.edu.r Şekil

40 Yük akımının grafiğine bakıldığı zaman yük akımının, gerilimin sıfır oldukan belli bir zamandan sonraya kadar sıfır olmadığı görülür. Bu, yükün indükansından kaynaklanmakadır. Yük akımı sıfıra erişip kaldığı zaman, anahar uçlarındaki gerilim ideal bir süreksizliğe sahipir. Bu, CR ve riyak uçlarındaki gerilimde ani değişmelerin sonucu ileim ihimalinden daha önce bahsedilmişir. Böyle bir durumda kuupsuz bir koruyucu devre, akım sıfır olduğu zaman isenilmeyen bir ileimden korunmak için genel olarak isenilir. Şekil 1.5 deki yük akımı sandar devre analizi meoları ile bulunabilir. / da başlanarak, akım 1.14 eşiliği ile bulunabilir: i m Z sin Ae / (1.14) 1.14 eşiliği, sadece şekil 1.5(b) de göserilen 1 aralığı için geçerlidir, burada 1 (1.15) (1.16) okumus@ku.edu.r 40

41 Z R j R an (1.17) (1.18) sin( ) ( / ) e A (1.19) 1.14 eşiliğinde akımın sıfır olduğu zamanının bulunmasıyla açısı bulunabilir. Bu kapalı formda ifade edilemez faka bir irdeleme işlemi ile kolaylıkla bulunabilir. bir kere bulundukan sonra, yük akımının RM değeri ve yükün oralama gücü belirlenebilir. Yük akımı için, 1.14 eşiliğindeki büün erimler bilinmeke ve bir akımın RM değeri 1.0 eşiliği kullanılarak hesaplanabilir: I RM Z m T / / sin Ae / d 0,5 (1.0) okumus@ku.edu.r 41

42 Power Elecronic Applicaions / / / / cos sin 1 4 cos sin 1 4 sin sin e A e A e e A Z m I RM (1.1) Yük akımının RM değerinin bilinmesiyle yükün oralama gücü kolaylıkla bulunur. onuç 1. eşiliğinde verilmişir. P I R or RM (1.)

43 Güç fakörü oralama güç I RM RM I R (1.3) RM Güç fakörü (1.4) m / I RM Güç fakörü R Z sin A / e e / 4A e sin 1 / 4A e sin 1 sin / cos cos 0.5 (1.5) okumus@ku.edu.r 43

44 Power Elecronic Applicaions / / / / cos sin 1 4 cos sin 1 4 sin sin cos e A e A e e A fakörü Güç (1.6) 1.6 eşiliğinden, güç fakörünün, iki erimin çarpımından oluşuğu görülmekedir. Birincisi, faz konrolü olmaksızın devrenin güç fakörü. İkincisi ise faz konrolünün ekisidir. Güç fakörünün faz konrolü yapılmadan önceki durumdan daha az olduğuna dikka emek gerekir.

45 ÖRNEK 1.4 Şekil 1.5(a) daki devrede kaynak 460 RM, 60 Hz dir. Yük 10 luk bir direnç ile 0,05 H lik bir indükansan oluşmakadır. Düzenek, = 75 ile çalışmakadır. Aşağıdakileri bulunuz: (a) arasında geçerli yük akımının denklemi (b) nın değeri (c) Yük akımının RM değeri (d) Yükün oralama gücü (e) faz konrolunun ekili olduğu nın minimum değeri (f) devrenin güç fakörü okumus@ku.edu.r 45

46 (a) 1.14 eşiliği kullanılarak, yük akımı aşağıdaki gibi bulunur m Z R j 1, 34 cos 6 R Z 10 1,34 1,083rad 75 1,309 0,4686 rad A R an 1,885 sin( ) sin(75 6) / ) (1,309/1,885) e e ( 0,449 i 650 sin 1,083 0,449e 1,34 / okumus@ku.edu.r 46

47 (b) (a) daki yük akımının değeri, 4,1757 radyanda sıfır olur. Bu, bir irdeleme işlemi ile bulunur. Açı olarak ifade edildiği zaman, 39 dir. Faz konrolu yapılmaksızın am ileimde, yük akımı (180=) 4 de sıfır olacakı. (c) 1.1 eşiliği kullanılarak, yük akımının RM değeri bulunabilir: I RM 18,68 A (d) Yük gücü 1. eşiliği ve (c) deki akım kullanılarak bulunabilir: Por I R 18, RM W (e) an 1 R an ,05 6 nın bu değerden daha küçük yapılması başarısızlıkla sonuçlanır. nın dan küçük olmaması gerekir. okumus@ku.edu.r 47

48 (f) Güçfakörü Güç fakörünün gerekir. oralama güç I RM RM cos cos (460)(18,68) 0,470 0,406 den küçük olduğuna dikka emek arasındaki eşilikler ile ifade edilen sonuçlar çok kullanışlı değildir. Şekil 1.6 ve 1.7 deki grafikler devre analizi ve dizaynı için kullanışlı olabilir. Şekil 1.6, bir paramere olarak devre için cos değerini kullanan, nın bir fonksiyonu olarak, ileim açısı () yı vermekedir. Şekil 1.7, yine bir paramere olarak cos değerini kullanan, nın bir fonksiyonu olarak, yük akımının bağıl RM değerini vermekedir. Grafik, verilen eşiliklerin sayısal çözümünü sağlamakadır. Örnek 1.6 bu grafiklerin nasıl kullanıldığını gösermekedir. okumus@ku.edu.r 48

49 Şekil

50 Şekil

51 Inroducion wichmode dcdc Converers One or Three Phase wichmode dcodc converers are used Buck (Azalıcı) o conver unregulaed dc inpu ino a conrolled dc oupu a a desired volage level. Conrolled or Unconrolled Half or Full Wave Recifier Boos (Arırıcı) Converers swichmode dc power supplies, dc moor drives AC line volage (1phase or 3phase) Recifier Filer (or baery) PID Fuzzy DC (unregulaed) dcdc converer sysem Neural Nework DCDC Converer v conrol Conroller DC (regulaed) v measure v ref oad Arificial Inelligen okumus@ku.edu.r 51

52 Basic converer opologies: sepdown (buck) and sepup (boos) converers. Oher converer opologies are combinaion of he wo basic opologies or derived from one of he wo. Oher converer opologies: epup/sepdown (buckboos) converer combine he wo basic converers Cuk converer obained by using he dualiy principle on he circui of he buckboos converer flyback converer derived from he buckboos converer wih ransformer forward converer derived from he buck converer wih ransformer pushpull converer derived from he buck converer wih ransformer halfbridge converer derived from he buck converer wih ransformer fullbridge converer derived from he buck converer 5

53 Noe: 1. Fullbridge converer is ofen used for dc moor drives.. Pushpull, halfbridge and fullbridge converers can be used as inverers for dcoac conversion. 3. All converers are possible o be used as resonan converers by adding in circui resonan elemens. Analysis assumpions: in seady sae operaion, ideal swiches, negleced losses in inducive and capaciive elemens, zero inernal impedance of he dc inpu source, an oupu filer capacior as an inegral par of he converer, an equivalen resisance o represen a load in he case of M dc power supplied and a dc volage in series wih a resisor and an inducor o represen a dc moor load. okumus@ku.edu.r 53

54 Basic wiching Principles (Animaions) v o v o R (1D)T closed open 0 DT T (a) (b) (c) Figure 1.1: (a) basic dcdc swiching converer, (b) swiching equivalen, (c) oupu volage v o In a swiching converer circui, he ransisor operaes as an elecronic swich by being compleely on or off. This circui is known as a dc chopper circui. Assuming he swich is ideal in Figure 1.1, he oupu is he same as he inpu when he swich is closed, and he oupu is zero when he swich is open. Periodic opening and closing of he swich resuls in he pulsed oupu shown in Figure 1.1 (c). The average or dc componen of he oupu is o 1 T T 0 v o ( ) d 1 T 0 DT R v ( ) d D (1.1) okumus@ku.edu.r 54

55 The dc componen of he oupu, o is conrolled by varying he duy raio D, which is he fracion of he period ha he swich is closed, i.e. D on on off T on on f (1.) where f is he swiching frequency in herz. The dc componen of he oupu will be less han or equal o he inpu for his circui. The power absorbed by he ideal swich is zero. When he swich is open, here is no curren in i; when he swich is closed, here is no volage across i. Therefore, all power is absorbed by he load, and he energy efficiency is 100%. osses will occur in a real swich because he volage across will no be zero when i is on, and he swich mus pass hrough he linear acive region of he oupu I characerisics when making from one sae o he oher. okumus@ku.edu.r 55

56 The Buck (epdown) Converer (Animaions) wich D i v v X i C C i R R o Figure 1. (a): The Buck dcdc converer Conrolling he dc componen of a pulsed oupu of he ype in Fig 1.1 (c) may be sufficien for some applicaions, bu ofen he objecive is o produce an oupu ha is purely dc. One way of obaining a dc oupu from he circui of Fig 1.1 (a) is o inser a lowpass filer afer he swich. Figure 1. (a) shows an inducorcapacior (C) lowpass filer added o he basic converer. The diode provides pah for he inducor curren when he swich is opened and is reverse biased when he swich is closed. The circui is called a buck converer or a sepdown converer because he oupu volage is less han he inpu. Is main applicaions is in he regulaed dc power supplies and he dc moor speed conrol. okumus@ku.edu.r 56

57 olage and Curren Relaionships If he lowpass filer is ideal, he oupu volage is he average of he inpu volage o he filer. The inpu o he filer, v X is when he swich is closed and is zero when he swich is open, provided ha he inducor curren remains posiive, keeping he diode on. If he swich is closed periodically a a duy raio D, he average volage a he filer inpu is D, Eq This analysis assumes ha he diode remains forward biased for he enire ime ha he swich is open, implying ha he inducor curren remains posiive. An inducor curren ha remains posiive hroughou he swiching period is known as coninuous curren or coninuous conducion. Conversely, disconinuous curren or disconinuous conducion is characerized by he inducor curren reurning o zero during each period. okumus@ku.edu.r 57

58 eady sae operaion and assumpions for analysis The buck converer (and dcdc converers in general) has he following properies when operaing in he seady sae: 1. The inducor curren is periodic: i ( T ) i ( ) (1.3). The average inducor volage is zero: 1 T T v ( l ) d l 0 (1.4) v o o i I,max I,min i C ame area DT T i ame area i I = I R 3. The average capacior curren is zero: I C 1 T T i C ( l ) d l 0 (1.5) 4. The power supplied by he source is he same as he power delivered o he load. For nonideal componens, he source also supplies he losses: P s = P o (ideal) & P s = P o losses (nonideal) (1.6) okumus@ku.edu.r 58

59 Analysis of he buck converer of Fig 1. (a) begins by making hese assumpions: 1. The circui is operaing in he seady sae.. The inducor curren is coninuous (always posiive) 3. The capacior is very large, and he oupu volage is held consan a volage o. This resricion will be relaxed laer o show he effecs of finie capaciance. 4. The swiching period is T; he swich is closed for he ime DT & open for ime (1 D)T. 5. The componens are ideal. The key o he analysis for deermining he oupu o is o examine he inducor curren and inducor volage firs for he swich closed and hen for he swich open. The ne change in inducor curren over one period mus be zero for seadysae operaion. The average inducor volage is zero. okumus@ku.edu.r 59

60 Analysis for he swich closed wich D i v i C v X C i R o R v s o o wich is closed wich D i v = v o i C v X = C i R o R i I,max I,min i C DT T i i R I R i I = I R Fig 1. (b) Equivalen circui during swich closed okumus@ku.edu.r 60

61 When he swich is closed in he buck converer circui of Fig 1. (a), he diode is reverse biased, as shown in he equivalen circui in Fig 1. (b). The volage across he inducor is v di s o d Rearranging wih swich closed di s o d ince he derivaive of he curren is a posiive consan, he curren increases linearly, i waveform. The change in curren while he swich is closed is compued by modifying he preceding equaion: di i i s o d DT ( s i ) o ( ) DT closed (1.7) okumus@ku.edu.r 61

62 Analysis for he swich open wich wich D D i v v X i v = v o v X = 0 i C C i C C i R o R i R o R v s o o i I,max I,min i C wich is open DT T i I = I R i i R I R Fig 1. (c) Equivalen circui during swich open okumus@ku.edu.r 6

63 When he swich is open, he diode becomes forward biased o carry he inducor curren, and he equivalen circui of Fig. 1. (c) applies. The volage across he inducor when he swich is open is v di o d di Rearranging wih swich open o d The derivaive of curren in he inducor is a negaive consan, and he curren decreases linearly. The change in inducor curren when he swich is open is okumus@ku.edu.r i i o ( 1 D ) T ( i ) ( o )( 1 D ) T open (1.8) 63

64 Oupu volage eadysae operaion requires ha he inducor curren a he end of he swiching cycle be he same as ha a he beginning, meaning ha he ne change in inducor curren over one period is zero. This requires Using Equaion 1.7 and 1.8, ( i ) ( open i ) closed 0 ( s o ) DT o ( 1 D ) T 0 olving for o, D (1.9) o s which is he same resul as Eq.11. The bulk converer produces an oupu which is less han or equal o he inpu. Oher approaches o ge Eq. 1.9 are (1) average v = 0 and () average v x = o. Noe ha he oupu volage depends only on he inpu and he duy raio D. If he inpu volage flucuaes, he oupu volage can be regulaed by adjusing he duy raio appropriaely. A feedback loop is required o sample he oupu volage, compare i o a reference and se he duy raio of he swich accordingly. okumus@ku.edu.r 64

65 Boundary beween coninuous and disconinuous curren o v o DT T (a) (c) i I = I R I = I R i s o v o (d) (e) (b) Figure 1.3: Inducor volage, v, in coninuous (a), boundary (a) and disconinuous (b) operaions. Inducor curren, i, in coninuous (c), boundary (d) and disconinuous (e) operaions. v x volage (f) v x o (f) okumus@ku.edu.r 65

66 The average inducor curren mus be he same as he average curren in he load resisor, since he average capacior curren mus be zero for seadysae operaion: I I R o R (1.10) ince he change in inducor curren is known from Eqs. 17 and 18, he maximum and minimum values of he inducor curren are compued as i 1 I I, max 1 ( 1 D ) o o ( 1 D ) T R o R f (1.11) i 1 I I, min 1 ( 1 D ) o o ( 1 D ) T R o R f (1.1) where f = 1/T is he swiching frequency in herz. okumus@ku.edu.r 66

67 Equaion 11 can be used o deermine he combinaion of and f ha will resul in coninuous curren. ince I,mim = 0 is he boundary beween coninuous and disconinuous curren. 1 ( 1 D ) I 0 (1.13) o 0 R f f ( 1 D ) R ( 1 D ) R > f ( 1 D ) R f ( 1 D ) R f (1.14) ( 1 D ) R f Coninuousconducion mode The boundary Disconinuousconducion mode okumus@ku.edu.r 67

68 Disconinuous curren operaion s o 0 v DT I M i 1 T T o T Figure shows he regions for i > 0 (during DT and 1 T) and i = 0 ( T). During he inerval T, he power o he load is supplied by he filer capacior alone. Again, equaing he inegral of he inducor volage over one T o zero (Eq. 1.4) yields ( s o )DT ( o ) 1 T = 0 o s D D 1 (1.14) The oupu volage does no depend on D alone. okumus@ku.edu.r 68

69 Oupu volage Ripple In he preceding analysis, he capacior was assumed o be very large o keep he oupu volage consan. In pracice, he oupu volage canno be kep perfecly consan wih a finie capaciance. The variaion in oupu volage, or ripple, is compued from he volage curren relaionship of he capacior. The curren in he capacior is i C i i R as shown in Fig. 1.4a The average curren I C = 0, I = I R. Assume o / o << 1, hence I R /I R << 1, hen I C ~ I, as shown in Figure 1.4(a). While he capacior curren is posiive, he capacior is charging. From he definiion of capaciance, i C I C = 0 v o o Q T/ I / o Q (a) (b) C o Q C o o Q Figure 1.4: (a) Capacior curren, i, C (b) capacior ripple volage C okumus@ku.edu.r 69

70 The change in charge, Q is he area of he riangle above he ime axis: resuling in Using Eq 1.8 for i, Q o 1 T i T i 8 T i 8 C okumus@ku.edu.r T o ( 1 D ) T o ( 1 D ) (1.15) o 8 C 8 Cf In his equaion, is he peakopeak ripple volage a he oupu, as 0 shown in Fig. 14b. i is also useful o express he ripple as a fracion of he oupu volage: ( 1 D ) o (1.16) o 8 Cf ince we se a maximum limi o he ripple volage, he minimum C required o limi his oupu can be given by ( 1 D ) C min 8 f o o 70

71 If he ripple is no large, he assumpion of a consan oupu is reasonable and he preceding analysis is essenially valid. Noe ha he low pass C filer has a corner frequency, f C of 1 f C C 1 C 4 ubsiue equaion (1.17) ino equaion (1.16) gives f C (1.17) o (1 D) (1 8 f [ 1 o ] 4 fc D) f f o, a low pass C filer wih a relaively much smaller f C han he swiching frequency will give a small ripple volage, i.e f C << f for ripple < 1% C okumus@ku.edu.r 71

72 Conrol of dcdc Converers o = D (coninuous mode) shows ha o changes wih if D is fixed. Negaive feedback echnique is used o conrol o o equal o a desired level. Many mehods for conrolling he oupu volage can be used. Pulsewidh modulaion (PWM): consan frequency and varying duy cycle. ref v sam Amplifier _ v conrol v s Repeiive waveform Comparaor _ wich conrol signal v sc (a) s, m v conrol awooh waveform, v s on off wich conrol signal, v sc T s on Pulsewidh modulaor: (a) General block diagram, (b) comparaor signals. (b) okumus@ku.edu.r 7

73 ref is he referen volage fed from an inpu prese circui. v sam is he sampling volage sampled from he oupu of a dcdc converer. The amplifier is someimes called error amplifier (amplifying he error). The repeiive waveform can be any shape bu sawooh is used because of proporionaliy of conrolling of D. s, m and T s are consan and he variaion of v conrol is much slower han 1/T s. v conrol = A ( ref v sam ), A = volage amplificaion. If v sam = k o, k < 1, hen v sam = kd. From he waveform, D = on /T s = v conrol / s, m. Hence, v conrol = D s, m = A ( ref kd ). D Rearrange, ref for = consan and ref D D decreases wih increasing for ref = consan. s, m k A o = D = (v conrol / s, m ), hence o v conrol for = consan, v conrol is he direc conrol inpu for dc moor speed conrol. okumus@ku.edu.r 73

74 Overvolage snubber circui i C wich v C D i v v X i C C i R R o ray inducance and capaciance C a he inpu circui. R O i D O C C O wich v C D i v v X i C C i R R o Overvolage snubber circui a he inpu circui. okumus@ku.edu.r 74

75 I i R ON OFF v C I R i v C v C wihou snubber, v C wih snubber The snubber circui suppresses: (1) overshooing volage () i harmonics okumus@ku.edu.r 75

76 The Boos (epup) Converer (Animaions) v i i wich i C C v C i R R v o Figure.1(a) Boos dcdc converer. The circui in Figure.1(a) is a boos converer or sepup converer. I is socalled because he oupu volage of he converer is larger han he inpu volage. Is main applicaion is in dc regulaed power supplies. When he swich is closed or on, he diode is reversebiased and hus isolaing he oupu sage. When he swich is opened or off, he oupu sage receives energy from he inducor as well as from he inpu. okumus@ku.edu.r 76

77 olage and Curren Relaionships (a) v s closed open ame area The analysis of he I characerisics of he boos converer follow hese assumpions: 1) eadysae condiions exis. ) The swiching period is T & he swich is closed for ime DT & opens for ime (1D)T. 3) The inducor curren is always posiive (i.e. coninuous). 4) The componens used are ideal. 5) The capacior C is infiniely large and hus he oupu can be held consan a he average value o. (b) (c) s o I i,max I,min i R i C I R DT Q Figure.: (a) Inducor volage, v, (b) Inducor curren, i, (c) Capacior curren, i C. T Q i I I R I R okumus@ku.edu.r 77

78 When he swich closed v i i wich i C C v C i R R v o v s s o I i,max closed open DT T i ame area i v = i wich i C C v C i R R v o I,min i R i C I R Q Q I I R I R Figure.1(b) Equivalen circui for swich closed, okumus@ku.edu.r 78

79 When he swich is closed, he diode is reversebiased by he source and hus by K around he loop conaining, and he swich, we have v di d di d (.1) ince he rae of change of he inducor curren is a consan, he inducor curren increases linearly while he swich is closed, as shown in Figure.(b). From he waveform, he change in he inducor curren can be esimaed o be: i i DT olving for i for he swich closed, we ge i closed DT (.) okumus@ku.edu.r 79

80 When he swich open v i i wich i C C v C i R R v o v s s o i I,max closed open DT T i ame area I,min I I R v = o i i wich i C C v C i R R v o i R i C I R Q Q I R Figure.1(c) Equivalen circui for swich open. okumus@ku.edu.r 80

81 When he swich is opened, he curren can no change insanly, so he diode is forwardbiased o provide a pah for he inducor curren. Assuming ha dc/average oupu volage o is consan, hen he volage across he inducor is given as di v o d di d i i (1 D) T olving for i for he swich opened, we ge ( o )(1 D) T i open o (.3) ince he rae of change of he inducor curren is a consan, he inducor curren mus change linearly while he swich is open, as shown in Figure.(b). From he waveform, he change in he inducor curren can be esimaed o be: o (.4) okumus@ku.edu.r 81

82 Oupu volage For seadysae operaion, he ne change in he inducor curren mus be zero. o, from equaion (.) and equaion (.4): i i 0 closed open okumus@ku.edu.r olving for o, we ge DT ( o )(1 D) T 0 ( D 1 D) (1 D) 0 o o 1 D (.5) Equaion (.5) shows ha if he swich is always open/off, i.e. D = 0, hen he oupu is he same as he inpu.thus, as D increases, he oupu becomes larger: hus he name boos converer. As D approaches uniy, he oupu volage goes infiniy bu bearing in mind ha his analysis is based on he assumpion of ideal componens. Real componens which include losses will preven his o happen. Eq..5 can also be obained by average v = 0. 8

83 Average inducor curren I The oupu power of he converer circui wih a load R is given by The inpu power of he converer circui wih a load R is given by P i o Po R I I The average curren in he inducor can be deermined by recognising ha he power provided by he source mus be he same as he power absorbed by he load resisor. (Ideal) Thus, equaing he inpu power o he oupu power of he converer: Using equaion (.5) o 1D I R R or rearranging for he average inducor curren I R( 1 D) R( 1 D) (.6) okumus@ku.edu.r 83

84 The boundary The maximum inducor curren can be esimaed from he average value and he change in he inducor curren as in equaion (.) during he onime (or equaion (.4) during he offime since i also gives same magniude of change) as : I i, max I R(1 D) DT I i,max I,min DT T i I The minimum inducor curren can be esimaed from he average value and he change in he inducor curren as in equaion (.) during he onime in he same way as : I i, min I R(1 D) DT okumus@ku.edu.r 84

85 One of he assumpions made in his analysis is ha he inducor curren is coninuous. o, i is necessary for he minimum inducor curren I,min o be posiive (zero or above). Therefore, he boundary beween he coninuous and disconinuous inducor curren is deermined from DT Thus, okumus@ku.edu.r I, min R(1 D) DT R(1 D) or D R(1 D) f D(1 D) R f D(1 D) R f coninuous boundary D(1 D) R disconinuous f Disconinuous curren operaion Average inducion volage = 0 DT ( o ) 1 T = 0 o 1 D 1 0 o v 0 DT (.7) T i 1 T T 85

86 Oupu olage Ripple One of he earlier assumpion in he analysis is ha he capacior is infiniely large and hus he oupu volage is consan dc. In pracice, he capaciance is finie and hus here will be some flucuaion in he oupu volage waveform or ripple. The peak o peak oupu volage ripple can be calculaed from he capacior curren waveform, as shown in figure.(c). Assume o >> o, hen I R >> I R, means I R ~ consan. Almos all ac componen of he diode curren flows hrough he capacior. okumus@ku.edu.r 86

87 The change in he capacior charge is o Q IRDT DT R Q C o R o o o Thus, for he ripple volage DT C DT RC o D RCf (.8) i D i D = I R i C i C = I R v o Q Q Q Q o o o DT DT T or closed open o where = RC is he ime consan, hus, as C increases, he ripple decreases and for very small ripple, need >> T, i.e large C Noe: Boos circui does no require snubber circui. okumus@ku.edu.r 87

88 The BuckBoos (epdownepup) Converer i wich i v i D i C C v C i R R o Noe on he curren direcions and volage polariy Figure 3.1(a) BuckBoos dcdc converer, The circui in Figure 3.1(a) is a buckboos converer. I is socalled because he oupu volage of he converer can be smaller (Buck) or larger (Boos) han he inpu volage depending on he duy raio of he swich. When he swich is closed or on, he diode is reversebiased and hus isolaing he oupu sage from he inpu source. The energy is firs sored in he inducor while he capacior which is previously charged up will provide energy o he oupu load. When he swich is opened or off, he diode is forward biased and he oupu sage receives energy from he inducor. The energy sored in he inducance is charging up he capacior and ransferred o he load a he same ime. The oupu has a negaive polariy w.r.. he common erminal of he inpu volage. okumus@ku.edu.r 88

89 The converer has he following properies when operaing in he seady sae: 1. he inducor curren is periodic: i ( T ) i ( ) (3.1). The average inducor volage is zero: 1 T T v ( l ) d l 0 (3.) 3. The average capacior curren is zero: I C 1 T T i C ( l ) d l 0 (3.3) v o i I, max I, min i R I R closed open DT T i I I R I Q Q I R i C 4. The power supplied by he source is he same as he power delivered o he load. For nonideal componens, he source also supplies he losses: P s = P o (ideal) & P s = P o losses (nonideal) ( 3.4) okumus@ku.edu.r 89

90 olage and Curren Relaionships The analysis of he I characerisics of he boos converer follow hese assumpions: 1) eadysae condiions exis. ) The swiching period is T & he swich is closed for ime DT & opens for ime (1D)T. 3) The inducor curren is always posiive (i.e. coninuous). 4) The componens used are ideal. 5) The capacior C is infiniely large and hus he oupu can be held consan a he average value o. okumus@ku.edu.r 90

91 i i When he swich closed wich wich i i i D v i D v = i C C i C C v C v C i R R i R R o o Figure 3.1(b) Equivalen circui for swich closed, v o i I, max I, min i R i C I R closed open DT T i I I R Q I R Q Figure 3.: (a) Inducor volage, v, (b) Inducor curren, i, (c) Capacior curren, i C. I okumus@ku.edu.r 91

92 When he swich is closed, he diode is reversebiased by he source. The oupu sage is isolaed from he inpu sage.thus by K around he loop conaining, and he swich, we have di di v (3.5) d d ince he rae of change of he inducor curren is a consan, he inducor curren increases linearly while he swich is closed, as shown in Figure 3.(b). From he waveform, he change in he inducor curren can be esimaed o be: i i DT i closed DT (3.6) okumus@ku.edu.r 9

93 When he swich open i wich i i D v i C C v C i R R o v o i I, max closed open DT T i I I R I, min I i wich i i D v = o i C C v C i R R o i R i C I R I R Q Q Figure 3.1(c) Equivalen circui for swich open. okumus@ku.edu.r 93

94 When he swich is opened, he curren can no change insanly, so he diode is forwardbiased o provide a pah for he curren ino he capacior and he resisor. The volage across he inducor is given as v o di d (3.6) ince he rae of change of he inducor curren is a consan, he inducor curren mus change linearly while he swich is open, as shown in Figure 3.(b). From he waveform, he change in he inducor curren can be esimaed o be: di d o i i (1 D) T olving for i for he swich opened, we ge o o ( 1 D) T i (3.7) open okumus@ku.edu.r 94

95 Oupu volage For seadysae operaion, he ne change in he inducor curren mus be zero. o, from equaion (3.5) and equaion (3.7): i 0 DT (1 D) T i o closed open 0 olving for o, we ge D D o o 0 o D [ ] 1 D (3.8) Noe ha he oupu volage always has an opposie polariy o he inpu volage. In addiion, he oupu magniude of he converer can be smaller or larger han he inpu, depending on he duy raio, D. If D is > 0.5, i.e. he swich is closed for more han half he swiching period, he oupu is larger han he inpu and if D is < 0.5, hen he oupu is smaller han he inpu. Thus, his converer combines he capabiliy of boh he Buck and Boos converers and hus he name. Noe ha he inpu source is never direcly conneced o he load bu raher energy is sored in he inducor when he swich is closed and ransferred o he load from he inducor when he swich is open. When D 1, o, bu his does no occur in a real circui due o losses. Eq. 3.8 can also be obained by considering average v = 0. okumus@ku.edu.r 95

96 Average inducor curren I The oupu power of he converer circui wih a load R is given by P o o R The inpu power of he converer circui wih a load R is given by P I The average curren in he inducor can be deermined by recognising ha he power provided by he source mus be he same as he power absorbed by he load resisor. (Ideal) okumus@ku.edu.r 96

97 I Thus, equaing he inpu power o he oupu power of he converer: o I R Bu, he average inpu/source curren is relaed o he inducor curren by o RD D R[1 D] I DI I o D R olving for I using o D 1 D RD I 1 T I 1 T 0 1 T DT I, max I, min 1 T i ( ) d T 0 1 T i ( ) d i T DT DT 1 i ( ) d 0 0 T i i I, max I, min 1 T i ( ) d DT i 0 1 T I I R I ( ) d DT DT i ( ) d i( ) d [ DT. I ] 0 0 DI okumus@ku.edu.r 97

98 The maximum inducor curren can be esimaed from he average value and he change in he inducor curren as : I i D, max I R(1 D) The minimum inducor curren can be esimaed from he average value and he change in he inducor curren as : I i D, min I R(1 D) DT DT okumus@ku.edu.r 98

99 The boundary One of he assumpions made in his analysis is ha he inducor curren is coninuous. o, i is necessary for he minimum inducor curren I,min o be posiive (zero or above). Thus, (1 D) > f (1 D) f (1 D) f Disconinuous curren operaion Average inducion volage = 0 DT ( o ) 1 T = 0 o D 1 R R R coninuous boundary disconinuous I D R(1 D) DT, min D DT R(1 D) D D or R(1 D) f 0 o v (3.10) DT T i 1 T 0 T okumus@ku.edu.r 99

100 Oupu olage Ripple One of he earlier assumpion in he analysis is ha he capacior is infiniely large and hus he oupu volage is consan dc. In pracice, he capaciance is finie and hus here will be some flucuaion in he oupu volage waveform or ripple. The peak o peak oupu volage ripple can be calculaed from he capacior curren waveform, as shown in he following figure. Assume o >> o, hen I R >> I R, means I R ~ consan. Almos all ac componen of he diode curren flows hrough he capacior. The change in he capacior charge when swich is closed is (can do he same for when swich is open bu more roublesome) okumus@ku.edu.r 100

101 Q I R o DT DT R Q C o i D i D = I R Q Q Thus, for he ripple volage o R DT C o i C i C = I R Q Q o or o o o DT RC o DT D RCf (3.11) DT T closed open where = RC is he discharging ime consan, hus, as C increases, he ripple decreases and for very small ripple, need >> T, i.e large C v o o okumus@ku.edu.r 101

102 R O Overvolage snubber circui D O C v w v C C O i D v D i C C i R R v w o 0 o Turnoff Afer urnoff, v w = v = ( o ) = o Effec of parasiic elemens The parasiic elemens are due o he losses associaed wih he inducor, he capacior, he swich and diode. The acual volage ransfer raios are qualiaively shown in figures below for buck, boos and buckboos converers in coninuousconducion mode. Ideal 0 Ideal D Real D Real D 1 D To have higher oupu volages, sepup ransformers are required. 0 1 Ideal D 1 D 0.5 Real 1 D okumus@ku.edu.r 10

103 The Flyback Converer (Manyeik Kublajlı Kıyıcılar) All he dcdc converer menioned previously do no has elecrical isolaion beween he inpu sage & he oupu sage. If he inpu supply is grounded, he oupu sage will share he same ground poin. One of he dcdc converers ha provides isolaion beween he inpu and oupu is he flyback converer. We begin he evoluion of a flyback converer from a basic BuckBoos converer as shown below: A) ar wih a basic BuckBoos converer C o B) Inducor may be produced by windings in parallel on same core C o okumus@ku.edu.r 103

104 C) As here is igh magneic coupling beween boh coils of he inducor, i is no longer necessary o have hem linked elecrically, also no really necessary o have same number of urns on each winding. Rearranging winding polariy N P N o D) wich could be pu in he reurn side of he supply in he primary windings o give he basic Flyback converer circui N P N o E) The inpu & oupu relaionship is given by (he facor N /N P is added o he buckboos formula) o N N p D 1 D okumus@ku.edu.r 104

105 A basic flyback converer wih is equivalen ideal ransformer model incorporaing he equivalen magneizing inducance M. M ~ he inducance of primary winding when he secondary erminal is opencircuied, ofen called opencircui inducance. The operaion of he flyback converer is similar o ha of he buckboos converer. The oupu volage of he converer can also be smaller or larger han he inpu volage depending on he duy raio of he swich as well as on he urn raio of is ransformer. When he swich is closed or on, he diode is reversebiased & hus isolaing he oupu sage from he inpu source and he ransformer. The energy is firs sored in he magneizing inducance m (or he ransformer core) while he capacior which is previously charged up will provide energy o he oupu load. When he swich is opened or off, he diode is forward biased & he oupu sage receives energy from he inducance m via he ransformer. okumus@ku.edu.r i v w i M v M M i 1 v 1 N P N i v D v i D C i C v C R Transformer model (neglec winding resisance and leakage inducance) i R o 105

106 1. The inducor curren is periodic: i ( T ) i ( ) M (4.1) M. The average inducor volage is zero: M 1 T T v M ( l ) d l 0 (4.) 3. The average capacior curren is zero: I C 1 T T i C ( l ) d l 0 (4.3) N N v M P o I,max I,min o /R i C closed DT i M Q DT open (1D)T T Q i I M 4. The power supplied by he source is he same as he power delivered o he load. For nonideal componens, he source also supplies he losses: P s = P o (ideal) & P s = P o losses (nonideal) (4.4) okumus@ku.edu.r 106

107 In addiion, he analysis of he I characerisics of he flyback converer follows hese assumpions: 1. eadysae condiions exis, i.e. All volage and currens are periodic, beginning and ending a he same poins over one swiching cycle.. The duy raio of he swich is D and he swiching period is T. The swich is closed for ime DT & open for ime (1D)T. 3. The inducor curren is always posiive (i.e. Coninuous and above zero). 4. The componens used are ideal (i.e. no resisance for and C and hus no resisive losses and zero volage drop across he diode and swich when on/forward biased). 5. The capacior C is infiniely large and hus he oupu can be held consan a he average value o. okumus@ku.edu.r 107

108 When he swich closed i i v w v w i M v M M i M v M M v 1 i 1 i 1 v 1 N P N N P N v D v Fig 4.: A basic Flyback converer wih is equivalen model when he swich is closed. i v i D C v D i = 0 i 1 = (N /N P )i = 0, i M = i v 1 = v = v 1 (N /N P ), v D = v v C = (N /N P ) o i i D C i C v C i C v C R R i R o i R o N N closed open v M DT (1D)T P o i i M I,max I,min i D I R i C I R i R Q I R DT Q T i Figure 4.4: (a) Inducor volage, v M, (b) ource curren, i, (c) Inducor curren, i M, (d) Diode curren, i D, (e) Capacior curren, i C, (f) oad curren, i R. I M 108

109 On he source side of he ransformer (Figure 4.1 and 4.): When he swich is closed, he diode is reversebiased by he source. The oupu sage is isolaed from he inpu sage and he ransformer. Thus by K around he loop conaining, m and he swich, we have di di M M v1 vm (4.5) M d d ince he rae of change of he inducor curren is a consan, he inducor curren increases linearly while he swich is closed, as shown in Figure 3.(b). From he waveform, he change in he inducor curren can be esimaed o be: M i M i DT M M M i closed DT M (4.6) okumus@ku.edu.r 109

110 On he load side of he ransformer (Figure 4.1 and 4.): By K around he loop conaining v, C//R and he diode, we have v N [ N N from v v v1 ] [ ] v D 0 where o v1 N P N N hus & vd v o [ ] N p i 0 i okumus@ku.edu.r i i 1 N N N P P o ince he diode is reversebiased and off (i.e. Open circui), i = 0 and hus i 1 = 0 since hey are coupled magneically by he windings. o, while he swich is closed, curren is increasing linearly in he magneizing inducance m bu here is no curren in he windings of he ideal ransformer. In he acual ransformer, he curren is increasing linearly in he primary winding bu here is no curren in he secondary winding. i P v w i M v M M i 1 v 1 N P N v D v Fig 4.: A basic Flyback converer wih is equivalen model when he swich is closed i i D C i C v C R i R o 110

111 i i v w When he swich open i M v M M i M v M M i 1 v 1 i 1 v 1 N P N N P N i i v D v i D C v D v i D C i C v C i C v C R R i R i R o o N N v M P o i i M I,max I,min i D I R i C I R closed DT Q DT open (1D)T Q T i I M v w Fig 4.3: A basic Flyback converer wih is equivalen model when he swich is open. i R I R i 1 = i M i = (N P /N )i 1 i D = i i C = i D i R v = o v 1 = (N P /N )v v w = v 1 okumus@ku.edu.r 111

112 When he swich opens (Figure 4.1 and 4.3), he curren can no change insanly in he inducance m, so he conducion pah mus be hrough he primary winding of he ideal ransformer. The curren i m mus ener he undoed erminal of he primary winding and mus exi he undoed erminal of he secondary (rules for he ideal ransfomer analysis). This is possible because he diode is forwardbiased o provide a pah for he curren ino he capacior and he load resisor. Thus, looking a he load side of he ransformer and he oupu sage of he circui, we have v o Thus di d M NP o[ ] N o M & olving for i m for he swich closed, we ge N [ N v v P M ] [ i M M ] 1 dim d i open M o N [ N P ] v v 1 N N im o NP [ ] ( 1 D) T M N o (1 D) T M from N [ N P ] P (4.7) okumus@ku.edu.r 11

113 Power Elecronic Applicaions 113 Currens of ineres while he swich is open are (Fig. 4.1 & 4.3), by KC a he load side: P N N i i 1 ] [ ] 1[ P M P D N N i N N i i i R N N i i i i o P M R D C ] [ i i M 1 On he source side of he ransformer (Fig 4.3): By K around he loop conaining m, (or primary winding), he source and he swich, we have v w v 1 ] [ 1 P o w N N v v D N N N N D D N N v P P P o w 1 1 D C R i i i R i o R where from & & hus hus Noice ha he swich is experiencing a volage which is larger han he source volage when he swich is open Eq. 4.8