Converter Circuits

7/25/2019 Converter Circuits

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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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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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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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Interchange power source and load:

Port1

1

Port2L

+

V1

+

V2

Power flow

1D

V1= V2V2=DV1

2


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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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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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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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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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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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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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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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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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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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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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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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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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Conversion ratioM(D),differentially-connected buckconverters

Vo= (2D1)Vg

M(D)1

00.5 1 D

1


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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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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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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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3differential connection ofthreebuck converters

3ac load

dcsource +

V1

+

Vg

Vn+

V2

+vSn

+

V3


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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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The 3 current-source inverter

dc source 3ac load

+

VnVg+ v

Exhibits a boost-type conversion characteristic

Sn


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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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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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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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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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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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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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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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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


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



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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( )


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



39/58

TheBipolar

Insulated

JunctionTransistor(BJT)andthe

GateBipolarTransistor(IGBT)

An active switch, controlledbyterminalC

Single-quadrantswitch:


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



40/58

TheMetal-OxideSemiconductorFieldEffect

Transistor(MOSFET)

An active switch, controlled byterminalC

Normallyoperatedassingle-quadrantswitch:

canconductpositiveon-state

current(canalsoconduct

negativecurrentinsomecircumstances)


providedthattheintendedon-stateandoff-stateoperatingpointslieontheMOSFETi-vcharacteristic,thenswitchcanberealizedusingaMOSFET

i

1

i

on

+

v

off v C

(reverseconduction)0

Symbol instantaneous i-vcharacteristic

on(reverse



41/58

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



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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

+


6 3 2 T d t it h


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Usually an active switch,controlledbyterminalC

Normallyoperatedastwo-quadrantswitch:

negativeon-statecurrent


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


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


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



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Asimpleinverter

iA

+

Q1+

vA v0(t) = (2 1)VgVg D1

iL

++

+

Vg D2 v0C RvB

iB

2



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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.



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Thedc-3acvoltage sourceinverter(VSI)

iR

+

Vg iS

iT

Switches must block dc input voltage, and conduct ac load current.



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Bidirectionalbatterycharger/discharger

D1

+

vbus

spacecraft

mainpowerbus

+

Q1vbatt

Q2

vbus>vbatt

A dc-dc converter with bidirectional power flow.

L

D2



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Usually an active switch,

controlledbyterminalC

Normallyoperatedastwo-quadrantswitch:


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)


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



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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



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switchon-state

Usually an active switch,controlledbyterminalC

canconductpositiveornegativeon-statecurrent

canblockpositiveornegativeoff-statevoltage

witchoff-statevoltage

current

s


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



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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



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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


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



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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.


6.5. Summaryofkey points

Converter Circuits

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