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Power Electronics Chapter 6: Convertercircuits1
here do the boost,uck-boost, and other
onverters originate?
How can we obtain aconverter having givendesired properties?
6.1. Circuit manipulations
converters6.2. A short list of
6.3. Switch realization How SPDTs and SPSTs
can be implemented with real
semiconductor devices
Chapter6ConverterCircuits
(Chapter 6Erickson)
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Power Electronics Chapter 6: Convertercircuits2
6.1. CircuitManipulations
L1
+
+
Vg Vo
Begin with buck converter: previously derived from first principles
Switch changes dc component, low-pass filter removesswitching harmonics
Conversion ratio is M = D
2C R
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Power Electronics Chapter 6: Convertercircuits3
6.1.1.Inversionofsource and load
Interchange power input and output ports of a converter
Buck converter exampleV =DV2 1
Port1 Port2
L1
+
V1
+
V2
+
Power low
2
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Power Electronics Chapter 6: Convertercircuits4
Interchange power source and load:
Port1
1
Port2L
+
V1
+
V2
Power flow
1D
V1= V2V2=DV1
2
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Power Electronics Chapter 6: Convertercircuits5
Realization ofswitches
Port1 Port2 Reversal of powerflow requires newrealization ofswitches
Transistor conductswhen switch is inposition 2
L
+
V1
+
V2
Power flow Interchange ofand D
D
1D'
V1= V2 Inversion of buck converter yields boost converter
+_
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Power Electronics Chapter 6: Convertercircuits6
6.1.2. Cascade connection ofconverters
+
Vg
V1=M1(D)Vg
VoVg =M(D) =M (D)M (D)1 2
Vo=M2(D)V1
D
Converter 1
V1 =M(D)Vg
1
Converter 2
Vo =M2 (D)V1
+
V1
+
Vo
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Power Electronics Chapter 6: Convertercircuits7
Example: buck cascaded byboost
L1 L2 21
+ +
+
Vg
Vo
Buck converter Boost converter
V1
Vg
Vo
=D
VoVg
D1D
=1
1D=
V1
{ {
2C1
1
V1
C2 R
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Power Electronics Chapter 6: Convertercircuits8
Buckcascaded byboost:
simplification ofinternalfilter
Remove capacitorC1
1 L1 L2 2
+
+
VoVg
Combine inductorsL1 and
L
L2
iL 21
+
Noninvertingbuck-boost
converter
+
Vg Vo
2 1
2 1C2 R
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Power Electronics Chapter 6: Convertercircuits9
Noninverting buck-boost converter
L iL 21
+
+
Vg Vo
subinterval 1 subinterval 2
+ +L
+
+
Vg Vo Vg Vo
iL
i
2 1
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Power Electronics Chapter 6: Convertercircuits10
subinterval 1 subinterval 2
+ +L
+
+Vg VoVg Vononinverting
buck-boost
+ +iL
L
inverting
buck-boost
+
+
Vg
Vo Vg Vo
i
iL
i
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Power Electronics Chapter 6: Convertercircuits11
Reduction ofnumberofswitches:inverting buck-boost
Subinterval1 Subinterval2
+ +iL
L
+
+
Vg
Vo Vg Vo
One side of inductor always connected to ground hence, only one SPDT switch needed:
+1
V0 =
DiL Vg+ 1DVg Vo
2
i
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Power Electronics Chapter 6: Convertercircuits12
Discussion:cascadeconnections
Properties of buck-boost converter follow from its derivationas buck cascaded by boost
Equivalent circuit model: buck 1:D transformer cascaded by boostD:1 transformer
Pulsating input current of buck converter
Pulsating output current of boost converter
Other cascad e connections are possible
uk converter: boost cascaded by buck
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Power Electronics Chapter 6: Convertercircuits13
6.1.3.Rotationofthree-terminalcell
Treat inductor andSPDT switch as three-terminal cell:
A a b B1
+
2+
Vg vo
c
a-A b-B c-C
a-C b-A c-B
a-A b-C c-B
buck converter
boost converter
buck-boost converter
C
Three-terminal cell can be connected between source and load in six ways out of whichthree are nontrivial and distinct:
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Power Electronics Chapter 6: Convertercircuits14
Rotation of a dual three-terminalnetwork
A capacitor and SPDTswitch as a three-terminal cell:
1
+A a b B
2+
Vg vo
C
Three-terminal cell can be connected between source and load in threenontrivial distinct ways:
a-A b-B c-C
a-C b-A c-B
a-A b-C c-B
buck converter with L-C input filter
boost converter with L-C output filter
uk converter
c
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Power Electronics Chapter 6: Convertercircuits15
6.1.4. Differentialconnection ofload
to obtain bipolar output voltage
dc source load
+
Differential loadvoltage is+
Vo
Vo=V
V1 2+
Vg The outputsV1 andV2
may both be positive,but the differentialoutput voltageVo can bepositive or negative.
2
D'
Converter 1
V1= M(D)Vg
V1
D
Converter 2
V2= M(D')Vg
+
V
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Power Electronics Chapter 6: Convertercircuits16
Differential connectionusing twobuck converters
Buck converter1
1
Converter #1 transistordriven with duty cycleD
Converter #2 transistor
driven with duty cyclecomplement D
Differential load voltageis
Vo=DVgD'Vg
+
V1+
Vo
+
Vg
+
V2
1
Simplify:Vo= (2D1)Vg
Buck converter2
}
{
2
2
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Power Electronics Chapter 6: Convertercircuits17
Conversion ratioM(D),differentially-connected buckconverters
Vo= (2D1)Vg
M(D)1
00.5 1 D
1
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Power Electronics Chapter 6: Convertercircuits18
Simplification offilter circuit,
differentially-connected buckconverters
g g
}
{
Bypass load directly with capacitor
1
+
Vo
V +
1
2
2
Original circuit
Buck converter1
1
+
V1+
Vo
V +
2
1 +
V2
Buck converter2
2
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Power Electronics Chapter 6: Convertercircuits19
Re-draw for clarity
+ Vo
Commonly used in single-phase inverterapplications and in servo amplifier applications
Simplification offilter circuit,
differentially-connected buckconverters
+Vg
iL 1
+Vg
1
Combine series-connectedinductors
1
+
Vo
2
2
2
2
_
L
C
R
Single phase H-bridge, or bridge inverter
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Power Electronics Chapter 6: Convertercircuits20
Differentialconnection to obtain 3inverter
With balanced 3 load,neutral voltage is
Vn= V1+V2+V3
dc source 3ac load
+
V1
13
Phase voltages are
VRn= V1
VnVSn= V2 VnVTn=V3Vn
Control converters such thattheir output voltages containthe same dc biases. This dc
bias will appear at the neutralpoint Vn. It then cancels out,
so phase voltages contain nodc bias.
1 1 g
1+
Vg
Vn++ vSn
22 2 g
+
33 3 g
D3
Converter 2
V =M(D)V
D2
Converter 3
V =M(D)V
Converter 1
V =M(D)V
D
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Power Electronics Chapter 6: Convertercircuits21
3differential connection ofthreebuck converters
3ac load
dcsource +
V1
+
Vg
Vn+
V2
+vSn
+
V3
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Power Electronics Chapter 6: Convertercircuits22
3differential connection ofthreebuck converters
Re-draw for clarity:
dc source 3ac load
+
VnVg
+ vSn
Voltage-source inverter or buck-derived three-phase inverter
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Power Electronics Chapter 6: Convertercircuits23
The 3 current-source inverter
dc source 3ac load
+
VnVg+ v
Exhibits a boost-type conversion characteristic
Sn
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Power Electronics Chapter 6: Convertercircuits24
6.2.A short listofconverters
An infinite number of converters are possible, which contain switchesembedded in a network of inductors and capacitors
Two simple classes of converters are listed here:
switching period is divided into two subintervals. This class containseightconverters.
switching period is divided into two subintervals. Several of the moreinteresting members of this class are listed.
Single-input single-output converters containing a single inductor. The
Single-input single-output converters containing two inductors. The
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Power Electronics Chapter 6: Convertercircuits25
Single-inputsingle-outputconverters
containing one inductor
Use switches to connect inductor between source and load, in onemanner during first subinterval and in another during second subinterval
There are a limited number of ways to do this, so all possiblecombinations can be found
After elimination of degenerate and redundant cases,eightconverters
are found:dc-dc converters
buck boost buck-boost noninverting buck-boost
dc-ac converters
bridge
ac-dc converters
current-fed bridge
Watkins-Johnson
inverse of Watkins-Johnson
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Power Electronics Chapter 6: Convertercircuits26
Converters producinga unipolaroutput voltage
M(D) =D1. BuckM(D)
11
+
+
0.5Vg
Vo
0
D0 0.5 1
M(D) = 1 M(D)
4
2. Boost 1D
2
+ 3
1 2+Vg Vo 1
0 0 0.5 1 D
2
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Power Electronics Chapter 6: Convertercircuits27
Converters producinga unipolaroutput voltage
D0.5M(D) = D
0 13. Buck-boost 0
1D
1+1
2
+
Vg
Vo 3
4
M(D)
M(D) = D4. Noninverting buck-boost M(D)
4
1D
21
+ 3
2+
Vg
1
0
D0 0.5 1
2Vo
2
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Power Electronics Chapter 6: Convertercircuits28
Converters producinga bipolar outputvoltage
suitable asdc-acinverters
M(D) =2D15. BridgeM(D)
1
2
+
Vg + Vo0
1
1
M(D) =2D1 M(D)
1
6. Watkins-JohnsonD
1
+ +or 0
1+
+
VgVo Vg
Vo2 2
3
2
0.5 1 D
12
1
2 0.5 1 D
1
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Power Electronics Chapter 6: Convertercircuits29
Converters producinga bipolar outputvoltage
suitable asac-dcrectifiers
M(D)
21
D1M(D) =
27. Current-fed bridge
1
D0.5 10
1 2
1+
Vg + Vo 21
DD1
1
M(D) =2
or
8. Inverse of Watkins-JohnsonM(D)
21
++ 1
D0.5 1+
Vg 0Vo +
VgVo
2 1
2 2
0.5 1
2
1
2
0.5 1
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Power Electronics Chapter 6: Convertercircuits30
Severalmembersoftheclassoftwo-inductorconverters
M(D) = D D0.5
1. Cuk 0 1
1D 0
1
+2
2 3+
VoVg
4
M(D)
M(D) = D2. SEPIC 1D M(D)
4
+23
+
2VoV 1g1
0
D0 0.5 1
1
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Power Electronics Chapter 6: Convertercircuits31
Severalmembersoftheclassoftwo-inductorconverters
M(D) = D M(D)
4
3. Inverse of SEPIC (ZETA)
11D
+ 3
2+
2Vg
Vo1
0 D0 0.5 1
M(D) =D24. Buck2 M(D)1
1+
2+
VoV 0.5g
1
0
D0 0.5 1
2
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Switch applications
Summary of key points
32PowerElectronics Chapter6:Switchrealization
6.3. SwitchRealization
6.3.1. Single - quadrant switches
6.3.2. Two - quadrant switches.
6.3.3. Four-quadrant switches.
6.3.4. Synchronous rectifiers
6.3.5.
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Buck converter
withSPDTswitch:
SPSTswitch,with
voltageandcurrentpolaritiesdefined
1
i
L1 iL(t)
+
+
Vg
Vo+
v
with two SPSTswitches:
0 Li i(t)A L
++ vA
vB
+devicesfunctionasSPST
B+
V C R V og
iB
2C R
33PowerElectronics Chapter6:Switchrealization
SPST(single-polesingle-throw)switches
switchesbetween their power.terminals
Allpowersemiconductor
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RealizationofSPDTswitchusingtwoSPSTswitches
SPDT switch
It is possible for both SPST switches to be simultaneously ON or OFF
Behavior of converter is then significantly modified
Conducting state of SPST switch may depend on applied voltage or
6PowerElectronics Chapter :Switchrealization34
A nontrivial step: two SPST switches are notexactly equivalent to one
discontinuous conduction modes
current for example: diode
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ua rantso sw tc operat on
1
i Switch A single-quadrant
switch example:
ON-state:i > 0
+
v
OFF-state: v > 00
Switch
off
6PowerElectronics Chapter :Switchrealization35
onstatecurrent
off statevoltage
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Somebasicswitchapplications
on-state
switch ff-state
on-state
quadrantwitchff-state
sw c
Four-
switcholtage
current
so
sw c
on-state
Voltage-
bidirectionaltwo-quadrant witch
ff-state
switch oltage
current
so
switch
Current- current
bidirectional
two-quadrantwitch
oltage
so
switchon-state
Single- currentquadrant
switchitch
off-statevoltagesw
of
36PowerElectronics Chapter6:Switchrealization
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1
i Active switch: Switch state is controlled exclusivelyby a third terminal (control terminal).
Passive
switch:
Switch state is controlled by the
applied current and/or voltage at terminals 1 and 0.
SCR:
A special case turn-on transition is active,while turn-off transition is passive.
+
v
0
Single-quadrant switch: on-state i(t) and off-state v( )
37PowerElectronics Chapter6:Switchrealization
6.3.1. Single-quadrantswitches
are unipolar(not necessarily positive).
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e o e
A passive switch
Single-quadrantswitch:
canconductpositiveon-statecurrent
canblocknegativeoff-
statevoltage
providedthattheintendedon-stateandoff-stateoperatingpointslieonthe
diodei-v characteristic,thenswitchcanberealizedusingadiode
i
1
i
on
+
v
off v
0
Symbol instantaneous i-vcharacteristic
38PowerElectronics Chapter6:Switchrealization
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TheBipolar
Insulated
JunctionTransistor(BJT)andthe
GateBipolarTransistor(IGBT)
An active switch, controlledbyterminalC
Single-quadrantswitch:
canconductpositiveon-statecurrent
canblockpositiveoff-statevoltage
providedthattheintendedon-stateandoff-state
operatingpointslieonthetransistori-v characteristic,
thenswitchcanberealizedusingaBJTorIGBT
1
i
BJT i+
v
C
on
off v0
1
i
IGBT
+
v
C
0 instantaneous i-vcharacteristic
39PowerElectronics Chapter6:Switchrealization
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TheMetal-OxideSemiconductorFieldEffect
Transistor(MOSFET)
An active switch, controlled byterminalC
Normallyoperatedassingle-quadrantswitch:
canconductpositiveon-state
current(canalsoconduct
negativecurrentinsomecircumstances)
canblockpositiveoff-statevoltage
providedthattheintendedon-stateandoff-stateoperatingpointslieontheMOSFETi-vcharacteristic,thenswitchcanberealizedusingaMOSFET
i
1
i
on
+
v
off v C
(reverseconduction)0
Symbol instantaneous i-vcharacteristic
on(reverse
40PowerElectronics Chapter6:Switchrealization
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Realizationofswitchusing
transistorsanddiodes
Buckconverterexample
LiA iL(t)
++ vA
vB
+
+
V C R Vg
Switch A: transistor
SwitchB:diodeiB
iA
SPSTswitchoperatingpoints
Vg
vA
vB
Switch B
SwitchB
on
SwitchB
off
iL
Vg
SwitchA
on iL
SwitchA
off
SwitchA
Vg
iB
41PowerElectronics Chapter6:Switchrealization
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Realizationofbuck converter
using single-quadrantswitches
vAiA L iL(t)+
vL(t)+
Vg
iA
iB
Vg
vA
vB
SwitchB
on
SwitchB
off
iL
Vg
SwitchA
on iL
SwitchA
off
Vg
vB
+
B
+
42PowerElectronics Chapter6:Switchrealization
6 3 2 T d t it h
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Usually an active switch,controlledbyterminalC
Normallyoperatedastwo-quadrantswitch:
negativeon-statecurrent
canblockpositiveoff-statevoltage
providedthattheintendedon-
stateandoff-stateoperating
pointslieonthecompositei-vcharacteristic,thenswitchcan
berealizedasshown
i1
)
+
v
C voff
0
BJT/anti-paralleldioderealization
instantaneous i-v
characteristic
on(transistorconducts
off
on(diodeconducts)
i
43PowerElectronics Chapter6:Switchrealization
Current-bidirectionaltwo-quadrant switches
6.3.2 Twoquadrant switches
canconductpositiveor
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switchon-statecurrent
i
1
i
)
+
v
voffswitchoff-statevoltage
0(diode conducts)
on(transistorconducts
off
on
44PowerElectronics Chapter6:Switchrealization
Twoquadrantswitches
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o y o e
i 1
(transistor conducts)
+
v
Cvoff
(diode conducts)
0
PowerMOSFETcharacteristics
Power MOSFET,anditsintegral
bodydiode
Use of external diodes
topreventconduction
ofbodydiode
on
off
on
i
45PowerElectronics Chapter6:Switchrealization
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Asimpleinverter
iA
+
Q1+
vA v0(t) = (2 1)VgVg D1
iL
++
+
Vg D2 v0C RvB
iB
2
46PowerElectronics Chapter6:Switchrealization
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Inverter:sinusoidal modulationofD
v0(t)=(2 1)Vg
Sinusoidal modulation to
produce ac output:v0
Vg D(t) = 0.5 +Dm sin (t)
D The resulting inductor
current variation is also
sinusoidal:
i(t)=v0(t)=(2D1)
00.5 1
Vg Vg
RL
R
Hence, current-bidirectional
two-quadrant switches are
required.
47PowerElectronics Chapter6:Switchrealization
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Thedc-3acvoltage sourceinverter(VSI)
iR
+
Vg iS
iT
Switches must block dc input voltage, and conduct ac load current.
48PowerElectronics Chapter6:Switchrealization
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Bidirectionalbatterycharger/discharger
D1
+
vbus
spacecraft
mainpowerbus
+
Q1vbatt
Q2
vbus>vbatt
A dc-dc converter with bidirectional power flow.
L
D2
49PowerElectronics Chapter6:Switchrealization
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Usually an active switch,
controlledbyterminalC
Normallyoperatedastwo-quadrantswitch:
canconductpositiveon-statecurrent
canblockpositiveornegativeoff-statevoltage
providedthattheintendedon-stateandoff-stateoperating
pointslieonthecompositei-vcharacteristic,thenswitchcan
berealizedasshown
TheSCRissuchadevice,withoutcontrolledturn-off
i 1i +
vv
C
0
BJT/seriesdioderealization
instantaneous i-v
characteristic
on
off(diode
blocksvoltage)
off(transistor
blocksvoltage)
50PowerElectronics Chapter6:Switchrealization
Voltage-bidirectionaltwo-quadrantswitches
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wo-qua rantsw tc es
1
i switchon-state+
v
i
0v
witchff-stateoltage
1
i +
vC
0
on
off(diodeblocksvoltage)
off(transistorblocksvoltage)
current
sov
51PowerElectronics Chapter6:Switchrealization
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c- ac uc - oost nverter
R+
vab(t)
S
+Vg bc
T
Requires voltage-bidirectional two-quadrant switches.
Another example: boost-type inverter, or current-source inverter (CSI).
+v (t)
iL
52PowerElectronics Chapter6:Switchrealization
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switchon-state
Usually an active switch,controlledbyterminalC
canconductpositiveornegativeon-statecurrent
canblockpositiveornegativeoff-statevoltage
witchoff-statevoltage
current
s
53PowerElectronics Chapter6:Switchrealization
6.3.3. Four-quadrantswitches
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T ree ways to rea ize a our-qua rant switc
1 1 1
i+ + +1
i+
v
v v v
0
0 0 0
ii
54PowerElectronics Chapter6:Switchrealization
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ac- acmatr xconverter
3acinput 3ac output
vRn(t)vSn(t)
vTn(t)
All voltages and currents are ac; hence, four-quadrant switches are required.
Requires nine four-quadrant switches
+
iT
iS
iR
55PowerElectronics Chapter6:Switchrealization
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Replacement of diode with a backwards-connected MOSFET,
to obtain reduced conduction loss
i
1
i
1
i
1
i (reverseconduction)+
v
+
v
+
v
C v
000
idealswitch conventional
dioderectifier
MOSFET as
synchronousrectifier
instantaneous i-v
characteristic
off
on(reverse
on
56PowerElectronics Chapter6:Switchrealization
6.3.4Synchronousrectifier
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uc converterw t sync ronousrect er
MOSFET Q2 is
controlled to turn onwhen diode would
normally conduct
Semiconductor
conduction loss can
be made arbitrarily
small, by reduction
of MOSFET on-
resistances
Useful in low-voltagehigh-current
applications
vAiA L iL(t)+
+Vg
vB
Q1
C
C +
iBQ2
57PowerElectronics Chapter6:Switchrealization
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1. How an SPST ideal switch can be realized using semiconductor devices
depends on the polarity of the voltage which the devices must block in the
off-state, and on the polarity of the current which the devices must conduct
in the on-state.
Single-quadrant SPST switches can be realized using a single transistor or
a single diode, depending on the relative polarities of the off-state voltage
and on-state current.Two-quadrant SPST switches can be realized using a transistor and diode,
connected in series (bidirectional-voltage) or in anti-parallel (bidirectional-
current). Several four-quadrant schemes are also listed here.
A synchronous rectifier is a MOSFET connected to conduct reverse
current, with gate drive control as necessary. This device can be usedwhere a diode would otherwise be required. If a MOSFET with sufficiently
lowRon is used, reduced conduction loss is obtained.
2.
3.
4.
58PowerElectronics Chapter6:Switchrealization
6.5. Summaryofkey points