Switched Mode Converters (1 Quadrant)
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- Antony Morton
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1 (1 Quadran) Philippe Barrade Laboraoire d Elecronique Indusrielle, LEI STI ISE Ecole Polyechnique Fédérale de Lausanne, EPFL Ch-1015 Lausanne Tél: Fax: Philippe.barrade@epfl.ch
2 Summary Inroducion DC supplies: principle Linear or Swiched Mode Converers Swiched Mode Converers: main challenges DC/DC direc converers Buck, boos, buck-boos converers Muli channels converers Transformers for DC/DC converers Principle, Model Sizing of a ransformer: weigh, power and frequency DC/DC converers wih ransformers Forward Flyback DC/AC/DC converers
3 Inroducion DC supplies: principle Swiched mode converers are DC/DC converers They are generally supplied from an AC nework, via: A ransformer For a galvanic insulaion For volage level adapaion A recifier In order o obain a DC volage source Swiched mode converers are used o generae conrolled and adjusable DC volage levels
4 Inroducion DC supplies: principle Typical (and possible) archiecure Recifier Filer Oupu filer Transformer: Volage adapaion Galvanic insulaion DC/DC converer
5 Inroducion DC supplies: principle Typical (and possible) archiecure Transformer : size and weigh (?) Recifier: generally a diode recifier Filer No regulaion of he oupu volage Theoreically, a LC filer is needed Taking ino accoun he parasiic inducances of he AC nework or he leakage inducances of he ransformer, a single capacior is generally used The aim of his filer is o supply he DC/DC converer wih a volage source DC/DC converer: dedicaed for he conrol and regulaion of he oupu volage. Theoreically, wo soluions can be invesigaed: Linear converer Swiched mode converer: hen an LC (or C) oupu filer is needed o lower ripple.
6 Inroducion DC supplies: principle Anoher ypical (and possible) archiecure Recifier Filer LC resonan circui Non-conrolled recifier Oupu filer Transformer: Volage adapaion Galvanic insulaion DC/AC converer Middle-frequency ransformer: Volage adapaion Galvanic insulaion
7 Inroducion DC supplies: principle Anoher ypical (and possible) archiecure Inpu Transformer (opional) Recifier, Filer DC/AC converer In order o obain ransmi energy o an AC sage LC resonan circui (opional): For efficiency reasons, o obain sof-swiching condiion for he DC/AC converer Middle-frequency ransformer: Volage adapaion, Galvanic insulaion Middle-frequency: reducion of weigh and size Should avoid he use of he inpu ransformer Recifier: Conrolled or non-conrolled, o obain DC oupu volage A LC (or C) filer is needed o lower ripple
8 Inroducion Linear or Swiched mode converers Linear converer Transisor driven in is linear characerisics AC Nework Transisor (Linear conrol) ref Transformer Recifier Filer Swiched mode converer Oupu filer o lower oupu volage ripple Swiched Mode Converer Oupu Filer AC Nework Transformer Recifier Filer ref
9 Inroducion Linear or Swiched mode converers Main properies: comparison Swiched mode Linear Efficiency 65 à 90% 35 à 55% Power per kilo 30 à 300W/kg 10 à 30W/kg Power per l 50 à 300W/l 20 à 50W/l Inpu volage range 0.85 à 1.2 n 0.9 à 1.1 n Dynamic 5% - 1ms 1% - 50us Oupu volage ripple 1% 0.1% EMC Imporanes Négligeables Main ineres for using swiched mode power converers Efficiency Power densiy
10 Inroducion Swiched Mode Converers: main challenges Swiched mode converer: Main opology Low frequency inpu filer (50Hz, 60Hz, 400Hz): size and weigh! Swiched Mode Converer Oupu Filer AC Nework Transformer Recifier Filer Swiched mode converer: DC/DC converer wih ransformer Middle frequency ransformer: Swiching frequency of he converer: size and weigh AC Nework Swiched Mode Converer Oupu Filer Recifier Filer Transformer
11 Inroducion Swiched Mode Converers: Convenion This conribuion will focus on Swiched Mode converer opologies (Inpu ransformer) + Recifier + Filer Ideal volage source
12 DC/DC converers Inroducion The aim of his presenaion is o describe 1 quadran swiched mode converers s is he oupu volage I s is he oupu curren The power provided o he load is: P s I s s 4 I s 1 Depending on he opology and he componens, DC/DC converers can be reversible or non-reversible Converers affiliaed wih quadran 1 ( s >0 and I s <0) will be considered P s <0 P s >0 P s >0 P s <0 s 3 2
13 DC/DC converers Inroducion The aim of direc DC/DC converer is o manage an energy ransfer beween A DC volage source and a DC curren source (Buck or sep-down converer) Such a converer allows he supply of loads wih an adjusable volage, lower han he inpu volage A DC curren source and a DC volage source (Boos or sep-up converer) Such a converer allows he supply of loads wih an adjusable volage, higher han he inpu volage A DC volage source and a second DC volage source (Buck-boos or sep-up/down converer) The conrol of he energy ransfer beween wo volage sources is allowed by an inernal inducance, used as energy buffer in he energy flow process Such a converer allows he supply of loads wih an adjusable volage, higher or lower han he inpu volage The buck-boos converer is no he associaion of a buck and a boos converers
14 DC/DC Converers Buck (sep-down) converer: Topology I e T e I s L s I cs I so D s C s R s so 1 Swiching cell: ransisor + Diode Main parameer: swiching period T s
15 DC/DC Converers Buck (sep-down) converer: Coninuous conducion mode: The oupu curren I s is always posiive Each off-swiching of he diode is rigged by he on-swiching of he ransisor Disconinuous conducion mode: Each off-swiching of he diode is due o a naural decrease of he oupu curren o 0, while he ransisor is no immediaely swiched on. Coninuous conducion mode Criical conducion mode Disconinuous conducion mode I s I s I s I s > I s /2 I s /2 <I s > I s /2 I s /2 <I s > I s DT s (1-D)T s DT s (1-D)T s DT s (1-D)T s
16 Buck (sep-down) converer: Summary: DC/DC Converers Coninuous conducion mode : s so D Criical conducion : e Normalized Variables y D I Disconinuous conducion mode slim s e 2L f so s ( 1 D)D e L f D s 2 I e s y x s s e L f I e s so e x lim y 1 2 y 1 2x 1 + ( 1 y) 2 D
17 DC/DC Converers Buck (sep-down) converer: Oupu characerisics
18 DC/DC Converers Boos (sep-up) converer: Topology I s D I cs I so L e I e s C s R s so ei e T 1 Swiching cell: ransisor+diode Main parameer Swiching period T s
19 Boos (sep-up) converer: Coninuous conducion mode: The inpu curren is always posiive DC/DC Converers Each off-swiching of he diode is rigged by he on-swiching of he ransisor Disconinuous conducion mode Each off-swiching of he diode is due o a naural decrease of he inpu curren o 0, while he ransisor is no immediaely swiched on. Coninuous conducion mode ei l ei Criical conducion mode l Disconinuous conducion mode ei l ei- so ei - so ei - so I e I e I e I e I e I e DT s (1-D)T s DT s (1-D)T s DT s (1-D)T s T s T s T s
20 DC/DC Converers Boos (sep-up) converer: Summary Coninuous conducion mode : Criical conducion I 1 1 D Disconinuous conducion mode : so slim s s ei 2L f e ei ( 1 D)D + ei 2 so ei 1 D 2Lef Is y x Normalized Variables e s ei L f I ei s so ei x y lim 1 1 D 1 2 y 1+ y 1 2 y 2 D 2x
21 DC/DC Converers Boos (sep-up) converer: Oupu Characerisics
22 DC/DC Converers Buck-Boos (sep-up/down) converer: Also know as DC/DC inverer Topology d I e I T I l D I d e L l C s R s s I cs I so I s Energy ransfer beween 2 volage sources is allowed by he inernal inducance L 1 Swiching cell: ransisor+diode Main parameer Swiching period T s
23 DC/DC Converers Buck-Boos (sep-up/down) converer: Coninuous conducion mode: The curren in he inducor is always posiive Each off-swiching of he diode is rigged by he on-swiching of he ransisor Disconinuous conducion mode Each off-swiching of he diode is due o a naural decrease of he curren in he inducor o 0, while he ransisor is no immediaely swiched on. Coninuous conducion mode Criical conducion mode Disconinuous conducion mode l l l e e e - so - so - so I l I l I l I l <I l > I l <I l > I l <I l > DT s (1-D)T s DT s (1-D)T s DT s (1-D)T s T s T s T s
24 Buck-Boos (sep-up/down) converer: Summary DC/DC Converers Coninuous conducion mode : Criical conducion : I Disconinuous conducion mode : s so slim so s 1 2Lf e D 1 D ( + ) 2 e e 2 e 2Lf so e so I s D 2 y x Normalized Variables Lf s e I e s so e x lim y y D 1 D 1 2 y ( 1 + y) 2 2 D 2x
25 DC/DC Converers Buck-Boos (sep-up/down) converer: Oupu Characerisics
26 DC/DC Converers Muli channels converers Convenional buck or boos opologies, Reducion of cooling devices Increase of he efficiency Sof-swiching condiions This can be obained in he disconinuous conducion mode he off-swiching of diodes is naural, and no due o he on-swiching of ransisors Swiching curren is 0A when ransisors are swiched on.
27 DC/DC Converers Muli channels converers Example of a muli-channel boos converer
28 DC/DC Converers Muli channels converers Example of a muli-channel boos converer Each channel works in disconinuous conducion mode The associaed coil is hen reduced (few micro-henri) Srong curren ripple, poor averaged value On he low-volage source: averaged values of currens are summed As each leg is phase-shifed, curren ripple are cancelled. Such a soluion offers high efficiency for applicaions of few kw.
29 DC/DC Converers Muli channels converers Example of a muli-channel boos converer Vin 18 V Vou V Iin max 255 A (maximal power 4600 W) Swiching frequency : 20 khz 8 channels Inducors used : 7.8 uh (ypical inducor for a classical converer : some mh) Curren shown for 4 channels
30 Transformers for DC/DC converers Principle, Model In swiched mode converers, ransformers are needed To adap volage/curren levels To offer galvanic insulaion In several applicaions, ransformers are he firs devices in he energy-flow chain: Sizing? Volume? Weigh?
31 Transformers for DC/DC converers Principle, Model General equaions of a ransformer: Principle of a 2 windings ransformer ϕ f1 ϕ f2 i 1 ϕ i 2 u 1 u 2 Sign convenions Volages and currens are posiives regarding convenions adoped in he figure
32 Transformers for DC/DC converers Principle, Model General equaions of a ransformer: Firs hypohesis: No leakage flux Relucance of he magneic circui is 0 Windings wih no elecric resisance u n 1 1 u2 n2 d dϕ d u n dϕ u n m ni ni R ϕ i i n n m i 1 m i 2 u 1 u 2
33 Transformers for DC/DC converers Principle, Model General equaions of a ransformer: Second hypohesis: No leakage flux Relucance of he magneic circui Windings wih no elecric resisance n2 R ni 11 ni 2 2Rϕ i1 i2 + ϕ n { 1 n { 1 Ideal ransformer 2 n1 ϕ n1ϕ ϕ i µ { R L m : magneic inducance of he ransformer L m iµ
34 Principle, Model Transformers for DC/DC converers General equaions of a ransformer: L m : magneic inducance of he ransformer The primary mean value of he volage mus be 0 Magneic energy sored ino a ransformer: W 1 L 1 Mi R µ ϕ The energy sored ino he ransformer canno be disconinuous Currens: diµ u L d 1 M The flux is hen a sae variable ni 11 ni 2 2Rϕ Each disconinuiy of he inpu curren mus be compensaed by an equivalen disconinuiy of he secondary side curren
35 Transformers for DC/DC converers Principle, Model General equaions of a ransformer: hird hypohesis: Leakage flux Relucance of he magneic circui Windings wih no elecric resisance dϕ u n + n { d dϕ u n + n { d e e 2 dϕ d f1 dϕ d f2 e e n m n
36 Principle, Model Transformers for DC/DC converers General equaions of a ransformer: hird hypohesis: Leakage flux Relucance of he magneic circui Windings wih no elecric resisance Inroducing he noion of leakage inducances (considering ha ϕ f1 and ϕ f2 are direcly proporional o he primary and secondary currens) dϕf1 di1 di1 n1 l1 u1 e1+ l1 d d d dϕ di di n l u e + l d d d f
37 Transformers for DC/DC converers Principle, Model Model Resisance of windings are negleced Hyserese and iron losses are no akien ino accoun i 1 l 1 i 1 ' l 2 m i 2 u 1 e 1 e 2 L m i µ u 2 i 1 l1 and l2 Lm i 1 ' m l f i 2 u 1 L m e 2 u 2 i µ
38 Transformers for DC/DC converers Sizing of a ransformer: Main equaions: S f 1 n 1 n 2 2 S b S f : secion of he magneic circui S b : surface allowed for windings
39 Transformers for DC/DC converers Sizing of a ransformer: Main equaions: surface of he magneic circui () u1 n1 d B () BSf u1 n1sf d 1 ns f M 1 f B S dϕ ϕ u ()d 1 nsf 1 f nb f 1 M db
40 Transformers for DC/DC converers Sizing of a ransformer: Main equaions: surface allowed for windings S n s K + n s K + L+ n s K b 1 1 b1 2 2 b2 N N bn I I I S n K + n K + L+ n K 1eff 2eff Neff b 1 b1 2 b2 N bn J1 J2 JN using:n I a n I i ieff i 1 1eff S b N n1i 1eff i 1 ak i J i bi
41 Transformers for DC/DC converers Sizing of a ransformer: Main equaions: definiion of A TR, defining he volume of he ransformer A S TR f S b A TR I B 1eff M f N i 1 a i K J i bi A TR B P 1 M f N The volume of he ransformer (and is weigh) are direcly linked o The power The frequency The frequency has o be increased o lower volume and weigh i 1 a i K J i bi
42 DC/DC converers wih ransformers General principle Such converers are idenified from he convenional DC/DC converers In convenional energy ransfer chain, ransformers are direcly coupled o a low frequency power nework Converisseur DC/DC Réseau Transformaeur Converisseur AC/DC Filre Filre ref The ransformer can be inegraed direcly ino he DC/DC converer (when possible) Réseau Converisseur AC/DC Filre Converisseur DC/DC Filre The working frequency is given by he swiching frequency of he converer ref
43 DC/DC converers wih ransformers General principle Such converers are locaed direcly of recifier and an inpu filer Convenion: I e I s e s so DC/DC Converer Filer
44 DC/DC converers wih ransformers Flyback: Converer deduced from he DC/DC Buck-boos converer d When he ransisor is ON, L is coupled o e e I e I T I l D I d L l C s R s s When he diode is ON, L is coupled o he oupu Magneic energy is alernaively sored in L from e, and hen provided o he oupu I s I cs I so The mean value of l is 0 When he ransisor is ON, he primary side of he ransformer is coupled o e When he diode is ON, he secondary side is coupled o he oupu e I e l i 1 2 d D I d C s I s I cs I so R s s Magneic energy is alernaively sored in L m and hen provided o he oupu T i 2 The mean value of u 1 is 0 I
45 DC/DC converers wih ransformers Flyback: Coninuous conducion mode: I 1 I 1 I m e 1 Volages and currens waveforms I 2 I m /m - s m s 2 Transisor ON: <I s > Energy is sored ino he ransformer I m -m e T Transisor OFF: I 1 s m Par of he sored energy is ransmied o he oupu e DT (1-D)T DT (1-D)T
46 Flyback: Coninuous conducion mode: DC/DC converers wih ransformers Volages and currens waveforms The ransisor has o be able o suppor no only he inpu volage bu: 1 > + m T e s As energy needs o be sored ino he ransformer, he magneic circui can be huge Srong flucuaions of secondary and primary currens, wi leakage inducances: srong consrains on he componens
47 Flyback: Coninuous conducion mode: Main equaions: DC/DC converers wih ransformers Duy cycle D: raio beween ransisor conducion ime and he swiching period Oupu volage D 1 T D m 1 D so s e Curren ripple: linked o he magneizaion inducance Inpu and oupu currens I l M e L f D D D I I I 1 D 1 D e s so
48 DC/DC converers wih ransformers Flyback: Disconinuous conducion mode: 1 Volages and currens waveforms e Transisor ON: Energy is sored ino he ransformer - s m 2 Transisor OFF: I 1 I m s Par of he sored energy is ransmied o he oupu I 1 I 2 I m /m -m e T The demagneizaion of he ransformer is compleed before he ON swiching of he ransisor <I s > I 1 I m s m e DT (1-D)T DT (1-D)T
49 Flyback: DC/DC converers wih ransformers Disconinuous conducion mode: Volages and currens waveforms The ransisor has o be able o suppor no only he inpu volage bu: 1 > + m T e s As energy needs o be sored ino he ransformer, he magneic circui can be huge, bu less han he case of he coninuous conducion mode Srong flucuaions of secondary and primary currens, regarding heir mean values The oupu volage is no more dependan of he ransformaion raio m, bu dependen of he load: R so s De 2L m f
50 DC/DC converers wih ransformers Forward Converer deduced from he DC/DC Buck converer I e D m D 1 L s I d I cs I so l 2 D 2 s C s R s so e I s T I Energy flows direcly from he primary side o he secondary side of he ransformer when he ransisor is ON. A hird winding is needed o conrol he magneizaion curren when he ransisor is swiched off. From he volage s he behaviour is ha one of a buck converer.
51 DC/DC converers wih ransformers Forward Volage and curren waveforms e 1 I Ls -m 13 e 2 m 12 e I 1, m 12 I 2 -m 23 e s I Dm m 12 e I m e (m 13 +1) e T DT (1-D)T DT (1-D)T
52 Forward Volage and curren waveforms DC/DC converers wih ransformers When he ransisor is ON: The secondary volage and s are m 12 e The primary curren is he sum of he secondary curren (modulo he raio m 12 ) and he magneizaion curren. When he ransisor is swiched off: Primary and secondary currens are 0 The demagneizaion circui is ON Primary and secondary volages are negaive Transisor volage is m 13 e + e When he demagneizaion is compleed: Primary and secondary volages and currens are 0 (free-wheeling mode) Condiion for a complee demagneizaion of he ransformer (before he conducion of he ransisor) m13 D < 1+ m 13
53 DC/DC converers wih ransformers Forward From he volage s, he behaviour of he forward is close of he buck Limi: leakage inducances, wih conducion of boh D 1 and D 2 during he commuaions of he ransisor Oupu characerisics of idenical he he Buck, where he only difference is he facor m 12 applied o e Compared o he flyback, smaller ransformer Three windings are needed (more complex) Leakage inducances need o be reduced as possible.
54 DC/DC converers wih ransformers DC/AC/DC Converers: Principle: Inpu Recifier + inpu filer : volage source DC/AC converer Recifier e s
55 DC/DC converers wih ransformers DC/AC/DC Converers: Principle: Firs sage: Volage inverer Able o manage energy ransfer beween a DC volage source : from an inpu filer (C) an AC curren source : he primary side of a ransformer Second sage: medium frequency ransformer Galvanic insulaion, Volage/curren level adapaion Third sage: recifier Able o manage energy ransfer beween 1 quadran converer: An AC volage source (secondary of he ransformer. Leakage inducances?) A DC curren source Diodes for he recifier Oupu volage level will be adjused by he volage inverer
56 DC/DC converers wih ransformers DC/AC/DC Converers: H-bridge volage inverer + full H-bridge diode recifier I Ls D D 3 1 T 1 T 3 I 2 D 1 ' D 3 ' L s m e A 1 2 s C s R s so B T 2 D 2 T 4 D 4 D 2 ' D 4 ' Volage inverer 2 swiching cells: (T 1,D 1 ),(T 2,D 2 ) and (T 3,D 3 ),(T 4,D 4 ) Each swiching cell is conrolled wih he same swiching frequency, duy cyle 50% The 2 nd swiching cell can be phase-shifed from he firs one
57 DC/DC converers wih ransformers A DC/AC/DC Converers: H-bridge volage inverer + full H-bridge diode recifier The duy cycle D defines he ime delay beween he wo swiching cells The Widh of he posiive and negaive pulse varies from 0 o T/2 when D varies from 0 o 1 e e B 2 m 1 m e I 2 e 1 m e m e s I Ls D T 2 T - e D T 2 T
58 DC/DC converers wih ransformers DC/AC/DC Converers: H-bridge volage inverer + full H-bridge diode recifier From he volage s, he behaviour is close o ha one of a Buck Converer: Averaged oupu volage Curren ripple in L s : Averaged oupu curren: md so s e m ( ) e ILs 1 D D 2LsF Defines mainly he magniude of he AC curren in he secondary side of he ransformer
59 DC/DC converers wih ransformers DC/AC/DC Converers: H-bridge volage inverer + full H-bridge diode recifier Transformer Primary side currens 1 I 1 mi 2 I m The mean value of 1 mus be 0 o conrol he magneizaion curren of he ransformer The widh of posiive and negaive pulse mus be idenical in one swiching period I m D T 2 T
60 DC/DC converers wih ransformers DC/AC/DC Converers: H-bridge volage inverer + diode recifier I 2 I Ls D D 3 1 T 1 T 3 D 1 ' L s e m 2 s C s R s so A B 1 2 ' T 2 D 2 T 4 D 4 D 2 ' I 2 ' Equivalen soluion compared o he full-bridge recifier
61 DC/DC converers wih ransformers DC/AC/DC Converers: H-bridge volage inverer + diode recifier: Efficiency: Conducion losses Swiching losses: Can be reduced if ZVT (Zero Volage ransiion) is possible Can be reduced if ZCS (Zero Curren swiching) is possible Swiching process mus be analyzed o idenify: If naural ZVT and/or ZCS occur The devices o add in order o allow ZVT and ZCS
62 DC/DC converers wih ransformers DC/AC/DC Converers: H-bridge volage inverer + diode recifier: Taking ino accoun leakage inducances of he ransformer swiching cells (T 3,D 3 ),(T 4,D 4 ) : ZVT hanks o he free-wheeling phase swiching cells (T 1,D 1 ),(T 2,D 2 ): ZVT only due o he leakage inducances of he ransformer D 1 1 I 1 D 3 D 2 D 4 T 1 T 2 T 1 T 4 T 3 T 4
63 DC/DC converers wih ransformers DC/AC/DC Converers: H-bridge volage inverer + diode recifier: Adding a dc blocking capacior and a saurable inducor o allow ZCS condiions I 2 I Ls e D D 3 1 T 1 T 3 c l m D 1 ' L s s C s R s so A B T 2 D 2 T 4 D 4 D 2 ' I 2 '
64 DC/DC converers wih ransformers DC/AC/DC Converers: H-bridge volage inverer + diode recifier: Adding a dc blocking capacior and a saurable inducor o allow ZCS condiions swiching cells (T 3,D 3 ),(T 4,D 4 ) : Each Turn ON of a ransisor is made wih ZCS and ZVS condiions Each urn OFF of a ransisor, capaciors are needed o limi he du/d swiching cells (T 1,D 1 ),(T 2,D 2 ) : Each Turn ON of a ransisor is made wih ZCS condiions Each urn OFF of a ransisor is also made wih ZCS condiions 1 I 1 T 1 T 2 T 1 T 4 T 3 T 4
65 DC/DC converers wih ransformers DC/AC/DC Converers: H-bridge volage inverer + diode recifier: Adding a dc blocking capacior and a saurable inducor o allow ZCS condiions Reducion of swiching losses, Componens such as IGBTs can be used High volage, high power applicaions.
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