R. W. Erickson. Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder
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1 R. W. Erckson Department of Electrcal, Computer, and Energy Engneerng Unersty of Colorado, Boulder
2 3.5. Example: ncluson of semconductor conducton losses n the boost conerter model Boost conerter example L C C R DT s T s Models of on-state semconductor deces: MOSFET: on-resstance R on Dode: constant forward oltage V D plus on-resstance R D Insert these models nto subnteral crcuts Fundamentals of Power Electroncs 25 Chapter 3: Steady-state equalent crcut modelng,...
3 Boost conerter example: crcuts durng subnterals and 2 L C C R DT s T s swtch n poston swtch n poston 2 L R L L C L R L R D L C V D R on C R C R Fundamentals of Power Electroncs 26 Chapter 3: Steady-state equalent crcut modelng,...
4 Aerage nductor oltage and capactor current L IR L IR on DT s D'T s IR L V D IR D V t C I V/R V/R t L C = D( IR L IR on )D'( IR L V D IR D V)= = D(V/R)D'(I V/R)= Fundamentals of Power Electroncs 27 Chapter 3: Steady-state equalent crcut modelng,...
5 Constructon of equalent crcuts IR L IDR on D'V D ID'R D D'V = R L DRon D'V D D'R D IR L IDR on ID'R D I D'V D'I V/R = V/R D'I V R Fundamentals of Power Electroncs 28 Chapter 3: Steady-state equalent crcut modelng,...
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7 Complete equalent crcut R L DRon D'V D D'R D I D'V D'I V R R L DRon D'V D D'R D D' : I V R Fundamentals of Power Electroncs 29 Chapter 3: Steady-state equalent crcut modelng,...
8 Soluton for output oltage R L DRon D'V D D'R D D' : I V R V = D' D'V D D' 2 R D' 2 R R L DR on D'R D V = D' D'V D R L DR on D'R D D' 2 R Fundamentals of Power Electroncs 3 Chapter 3: Steady-state equalent crcut modelng,...
9 Soluton for conerter effcency P n =( )(I) R L DRon D'V D D'R D D' : P out =(V)(D'I) I V R η = D' V = D'V D R L DR on D'R D D' 2 R Condtons for hgh effcency: /D' > V D D' 2 R > R L DR on D'R D Fundamentals of Power Electroncs 3 Chapter 3: Steady-state equalent crcut modelng,...
10 Accuracy of the aeraged equalent crcut n predcton of losses Model uses aerage currents and oltages To correctly predct power loss n a resstor, use rms alues Result s the same, proded rpple s small MOSFET current waeforms, for arous rpple magntudes: I (c) (b) (a) DT s 2 I. I T s t Inductor current rpple MOSFET rms current Aerage power loss n R on (a) = (b) =. I (c) = I I D D I 2 R on (.67) I D (.33) D I 2 R on (.55) I D (.3333) D I 2 R on Fundamentals of Power Electroncs 32 Chapter 3: Steady-state equalent crcut modelng,...
11 Summary of chapter 3. The dc transformer model represents the prmary functons of any dc-dc conerter: transformaton of dc oltage and current leels, deally wth % effcency, and control of the conerson rato M a the duty cycle D. Ths model can be easly manpulated and soled usng famlar technques of conentonal crcut analyss. 2. The model can be refned to account for loss elements such as nductor wndng resstance and semconductor on-resstances and forward oltage drops. The refned model predcts the oltages, currents, and effcency of practcal nondeal conerters. 3. In general, the dc equalent crcut for a conerter can be dered from the nductor olt-second balance and capactor charge balance equatons. Equalent crcuts are constructed whose loop and node equatons concde wth the olt-second and charge balance equatons. In conerters hang a pulsatng nput current, an addtonal equaton s needed to model the conerter nput port; ths equaton may be obtaned by aeragng the conerter nput current. Fundamentals of Power Electroncs 33 Chapter 3: Steady-state equalent crcut modelng,...
12 Chapter 4. Swtch Realzaton 4.. Swtch applcatons Sngle-, two-, and four-quadrant swtches. Synchronous rectfers 4.2. A bref surey of power semconductor deces Power dodes, MOSFETs, BJTs, IGBTs, and thyrstors 4.3. Swtchng loss Transstor swtchng wth clamped nducte load. Dode recoered charge. Stray capactances and nductances, and rngng. Effcency s. swtchng frequency Summary of key ponts Fundamentals of Power Electroncs Chapter 4: Swtch realzaton
13 SPST (sngle-pole sngle-throw) swtches SPST swtch, wth oltage and current polartes defned wth SPDT swtch: 2 Buck conerter L L C R V All power semconductor deces functon as SPST swtches. wth two SPST swtches: A A B A L B B L C R V Fundamentals of Power Electroncs 2 Chapter 4: Swtch realzaton
14 Realzaton of SPDT swtch usng two SPST swtches A nontral step: two SPST swtches are not exactly equalent to one SPDT swtch It s possble for both SPST swtches to be smultaneously ON or OFF Behaor of conerter s then sgnfcantly modfed dscontnuous conducton modes (chapter 5) Conductng state of SPST swtch may depend on appled oltage or current for example: dode Fundamentals of Power Electroncs 3 Chapter 4: Swtch realzaton
15 Quadrants of SPST swtch operaton Swtch on state current Swtch off state oltage A sngle-quadrant swtch example: ON-state: > OFF-state: > Fundamentals of Power Electroncs 4 Chapter 4: Swtch realzaton
16 Some basc swtch applcatons Snglequadrant swtch swtch on-state current swtch off-state oltage Currentbdrectonal two-quadrant swtch swtch on-state current swtch off-state oltage swtch on-state current swtch on-state current Voltagebdrectonal two-quadrant swtch swtch off-state oltage Fourquadrant swtch swtch off-state oltage Fundamentals of Power Electroncs 5 Chapter 4: Swtch realzaton
17 4... Sngle-quadrant swtches Acte swtch: Swtch state s controlled exclusely by a thrd termnal (control termnal). Passe swtch: Swtch state s controlled by the appled current and/or oltage at termnals and 2. SCR: A specal case turn-on transton s acte, whle turn-off transton s passe. Sngle-quadrant swtch: on-state and off-state are unpolar. Fundamentals of Power Electroncs 6 Chapter 4: Swtch realzaton
18 The dode Symbol on off nstantaneous - characterstc A passe swtch Sngle-quadrant swtch: can conduct poste onstate current can block negate offstate oltage proded that the ntended on-state and off-state operatng ponts le on the dode - characterstc, then swtch can be realzed usng a dode Fundamentals of Power Electroncs 7 Chapter 4: Swtch realzaton
19 The Bpolar Juncton Transstor (BJT) and the Insulated Gate Bpolar Transstor (IGBT) BJT C on off An acte swtch, controlled by termnal C Sngle-quadrant swtch: can conduct poste onstate current IGBT C nstantaneous - characterstc can block poste off-state oltage proded that the ntended on-state and off-state operatng ponts le on the transstor - characterstc, then swtch can be realzed usng a BJT or IGBT Fundamentals of Power Electroncs 8 Chapter 4: Swtch realzaton
20 The Metal-Oxde Semconductor Feld Effect Transstor (MOSFET) An acte swtch, controlled by termnal C C on off on (reerse conducton) Normally operated as snglequadrant swtch: can conduct poste on-state current (can also conduct negate current n some crcumstances) can block poste off-state oltage Symbol nstantaneous - characterstc proded that the ntended onstate and off-state operatng ponts le on the MOSFET - characterstc, then swtch can be realzed usng a MOSFET Fundamentals of Power Electroncs 9 Chapter 4: Swtch realzaton
21 Realzaton of swtch usng transstors and dodes Buck conerter example A A A B B B L L C R V Swtch A: transstor Swtch B: dode A B SPST swtch operatng ponts Swtch A on L Swtch A off Swtch B off Swtch B on L A B Swtch A Swtch B Fundamentals of Power Electroncs Chapter 4: Swtch realzaton
22 Realzaton of buck conerter usng sngle-quadrant swtches A A B L L L B A B Swtch A on L Swtch B on L Swtch A off Swtch B off A B Fundamentals of Power Electroncs Chapter 4: Swtch realzaton
23 4..2. Current-bdrectonal two-quadrant swtches C BJT / ant-parallel dode realzaton on (transstor conducts) off on (dode conducts) nstantaneous - characterstc Usually an acte swtch, controlled by termnal C Normally operated as twoquadrant swtch: can conduct poste or negate on-state current can block poste off-state oltage proded that the ntended onstate and off-state operatng ponts le on the composte - characterstc, then swtch can be realzed as shown Fundamentals of Power Electroncs 2 Chapter 4: Swtch realzaton
24 Two quadrant swtches on (transstor conducts) off on (dode conducts) swtch on-state current swtch off-state oltage Fundamentals of Power Electroncs 3 Chapter 4: Swtch realzaton
25 MOSFET body dode on (transstor conducts) off C on (dode conducts) Power MOSFET characterstcs Power MOSFET, and ts ntegral body dode Use of external dodes to preent conducton of body dode Fundamentals of Power Electroncs 4 Chapter 4: Swtch realzaton
26 A smple nerter A Q D A = (2D ) L L V g D 2 C R Q 2 B B Fundamentals of Power Electroncs 5 Chapter 4: Swtch realzaton
27 Inerter: snusodal modulaton of D = (2D ) Snusodal modulaton to produce ac output: D=.5 D m sn ( t).5 D The resultng nductor current araton s also snusodal: L = R = (2D ) R Hence, current-bdrectonal two-quadrant swtches are requred. Fundamentals of Power Electroncs 6 Chapter 4: Swtch realzaton
28 The dc-3øac oltage source nerter (VSI) a b c Swtches must block dc nput oltage, and conduct ac load current. Fundamentals of Power Electroncs 7 Chapter 4: Swtch realzaton
29 Bdrectonal battery charger/dscharger D L bus Q spacecraft man power bus Q 2 D 2 batt bus > batt A dc-dc conerter wth bdrectonal power flow. Fundamentals of Power Electroncs 8 Chapter 4: Swtch realzaton
30 4..3. Voltage-bdrectonal two-quadrant swtches C BJT / seres dode realzaton Fundamentals of Power Electroncs off (dode blocks oltage) on off (transstor blocks oltage) nstantaneous - characterstc 9 Usually an acte swtch, controlled by termnal C Normally operated as twoquadrant swtch: can conduct poste on-state current can block poste or negate off-state oltage proded that the ntended onstate and off-state operatng ponts le on the composte - characterstc, then swtch can be realzed as shown The SCR s such a dece, wthout controlled turn-off Chapter 4: Swtch realzaton
31 Two-quadrant swtches on swtch on-state current off (dode blocks oltage) off (transstor blocks oltage) swtch off-state oltage C Fundamentals of Power Electroncs 2 Chapter 4: Swtch realzaton
32 A dc-3øac buck-boost nerter L ab bc a b c Requres oltage-bdrectonal two-quadrant swtches. Another example: boost-type nerter, or current-source nerter (CSI). Fundamentals of Power Electroncs 2 Chapter 4: Swtch realzaton
33 4..4. Four-quadrant swtches swtch on-state current swtch off-state oltage Usually an acte swtch, controlled by termnal C can conduct poste or negate on-state current can block poste or negate off-state oltage Fundamentals of Power Electroncs 22 Chapter 4: Swtch realzaton
34 Three ways to realze a four-quadrant swtch Fundamentals of Power Electroncs 23 Chapter 4: Swtch realzaton
35 A 3øac-3øac matrx conerter 3øac nput 3øac output a an bn b cn c All oltages and currents are ac; hence, four-quadrant swtches are requred. Requres nne four-quadrant swtches Fundamentals of Power Electroncs 24 Chapter 4: Swtch realzaton
36 Power Processng Functons of a Swtch In a PWM DC-DC conerter: The man swtch performs the functon of conerson of DC power to AC power at the swtchng frequency The rectfer (dode or synchronous rectfer) performs the functon of conerson of AC (swtchng frequency) power to DC power As a result of the aboe processes, the conerter DC oltage and current leels are changed. Buck conerter example 2 L CCM waeforms 2 Ts 2 Ts g 2 C R dt s T s t Swtch network 2 2 Ts The buck conerter reduces the dc oltage, and exhbts current gan dt s T s t
37 Buck conerter example Q L Q L Q D C D D Transstor oltage: Q = V Q ṽ Q where V Q = h Q and hṽ Q = L (dc component) (ṽ Q s the ac component) Smlarly, the transstor current s Q = I Q ĩ Q The power p Q flowng nto the transstor s: p Q = Q Q = = V Q ṽ Q I Q ĩ Q Now multply out and aerage oer one perod: = V Q I Q hṽ Q ĩ Q R V Transstor waeforms Q Q L trans ĩ Q MOSFET hon DT s ṽ Q MOSFET off The transstor consumes power at DC, and generates power at the swtchng frequency. The transstor functons as an nerter. V Q I Q = hṽ Q ĩ Q T s V Q I Q t
38 DC components of transstor current and oltage Q DC component of Q ṽ Q V Q V Q = D Q L trans ĩ Q DT s T s I Q t DC component of Q I Q = DI L MOSFET on MOSFET off
39 Dode waeforms Q Q Q C D D! B@ L L D CA R V k k k k k k L Dode waeforms D dode ṽ D ) V D t Dode oltage: D = V D ṽ D where V D = h D and hṽ D = Smlarly, the dode current s D = I D ĩ D (dc component) (ṽ D s the ac component) The power p D flowng nto the dode s: p D = D D = = (V D ṽ D ) I D ĩ D Now multply out and aerage oer one perod: = V D I D hṽ D ĩ D D Dode off h DT s Dode on Note that V D s negate. Hence the dode consumes power at the swtchng frequency, and generates power at DC. The dode functons as a rectfer. V D I D = hṽ D ĩ D L ĩ D T s I D
40 Indrect power Q L Q L Q D C D D The transstor conerts power from DC to AC form. Ths power s transmtted to the dode, whch rectfes ths AC power to produce DC power. Ths power that s conerted to AC and then back to DC, s called ndrect power. The ndrect power s equal to: L R V Lossless or low-loss conerters that change the oltage exhbt gan Buck conerters exhbt current gan Boost conerters exhbt oltage gan The ndrect power path s responsble for ths gan. For the buck conerter: the DC nput current s I Q The output current I L s greater than I Q, by the amount I D. Rectfcaton of the ndrect power by the dode s the mechansm that generates ths addtonal output current. For the boost conerter: the DC nput oltage s The output oltage V s greater than, by the amount V D. Rectfcaton of the ndrect power by the dode s the mechansm that generates ths addtonal output oltage. P ndrect = V Q I Q = (D )(D I L ) = DD I L
41 4..5. Synchronous rectfers Replacement of dode wth a backwards-connected MOSFET, to obtan reduced conducton loss C off on (reerse conducton) on deal swtch conentonal dode rectfer MOSFET as synchronous rectfer nstantaneous - characterstc Fundamentals of Power Electroncs 25 Chapter 4: Swtch realzaton
42 Buck conerter wth synchronous rectfer A Q A C C Q 2 B B L L MOSFET Q 2 s controlled to turn on when dode would normally conduct Semconductor conducton loss can be made arbtrarly small, by reducton of MOSFET onresstances Useful n low-oltage hgh-current applcatons Fundamentals of Power Electroncs 26 Chapter 4: Swtch realzaton
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