_6_EE362L_DC_DC_Buck_PPT_Spring2009

8/7/2019 _6_EE362L_DC_DC_Buck_PPT_Spring2009

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1

EE362L, Spring 2009DCíDC Buck Converter



2

!

N ote - Helper

From now on this symbol will identify slides in which there is avery important concept that needs to be clearly understood

However, a lack of the symbol in one slide does not imply thatthere is no important material or concept in the slides or thatthe slide does not need to be studied. Slides without thesymbol still need to be studied and could be necessary tosolve problems in exams.



3

Objective ± to efficiently reduce DC voltage

DCíDC BuckConverter

+

Vin

í

+

Vout

í

IoutIin

Lossless objective: P in = P out , which means that V in Iin = Vout Iout and

The DC equivalent of an AC transformer

out

in

in

out

I I

V V !

!



4

Here is an example of an inefficient DCíDCconverter

21

2

RR

RV V inout y

+

Vin

í

+

Vout

í

R1

R2

in

out V

V

RR

R

!! 21

2

L

If Vin = 39V, and V out = 13V, efficiency is only 0.33

Th e load

Unacceptable except in very low power applications



5

Another method ± lossless conversion of 39Vdc to average 13Vdc

If the duty cycle D of the switch is 0.33, then the averagevoltage to the expensive car stereo is 39 0.33 = 13Vdc. Thisis lossless conversion, but is it acceptable?

R stereo+

39Vdc±

Switch state, Stereo voltage

Closed, 39Vdc

Open, 0Vdc

Switch openStereovoltage

39

0

Switch closed

DT

T

Taken from ³Course Overview´ PPT !



6

Convert 39Vdc to 13Vdc, cont.Try adding a large C in parallel with the load to

control ripple. But if the C has 13Vdc, thenwhen the switch closes, the source currentspikes to a huge value and burns out theswitch .

R stereo+

39Vdc±

C

Try adding an L to prevent the hugecurrent spike. But now, if the L hascurrent when the switch attempts toopen, the inductor¶s current momentumand resulting Ldi/dt burns out the switch .

By adding a ³free wheeling´ diode, theswitch can open and the inductor currentcan continue to flow. With high-frequency switching, the load voltageripple can be reduced to a small value.

R stereo+

39Vdc±

C

L

R stereo+

39Vdc±

C

L

A DC-DC Buck Converter

lossless

Taken from ³Course Overview´ PPT



7

C¶s and L¶s operating in periodic steady-state

Examine the current passing through a capacitor that is operatingin periodic steady state. The governing equation is

dt t dv

C t i )(

)( ! which leads to ´!t ot

ot o dt t i

C t vt v )(

1)()(

Since the capacitor is in periodic steady state, then the voltage attime t o is the same as the voltage one period T later, so

),()( oo t vT t v !

The conclusion is that

´!!T ot

ot oo dt t i

C t vT t v )(

10)()(or

0)( !´T

ot

ot

dt t i

the average current through a capacitor operating in periodicsteady state is zero

which means that

Taken from ³Waveforms and Definitions´ PPT !



8

N ow, an inductor

Examine the voltage across an inductor that is operating inperiodic steady state. The governing equation is

dt t di

Lt v)(

)( ! which leads to ´!t ot

ot o dt t v

Lt i t i )(

1)()(

Since the inductor is in periodic steady state, then the voltage attime t o is the same as the voltage one period T later, so

),()( oo t i T t i !

The conclusion is that

´!!T ot

ot oo dt t v

Lt i T t i )(

10)()(or

0)( !´T

ot

ot

dt t v

the average voltage across an inductor operating in periodicsteady state is zero

which means that




9

KVL and KCL in periodic steady-state

,0)(

!§l oopAround

t v

,0)(

!§n odeof O t

t i

0)()()()( 321 !t vt vt vt v N .

S ince KVL and KCL apply at any instance, t h en t h ey must also be validin averages. Consider KVL,

0)()()()( 321 !t i t i t i t i .

0)0(1)(1)(1)(1)(1321 !! ´´´´´ dt

T dt t v

T dt t v

T dt t v

T dt t v

T T o

t

ot

T ot

ot N

T ot

ot

T ot

ot

T ot

ot

.

0321 !Navg avg avg avg V V V V .

Th e same reasoning applies to KCL

0321 !avg avg avg avg I I I I .

KVL applies in the average sense

KCL applies in the average sense




10

Capacitors and Inductors

In capacitors:dt

t dvt i

)()( !

Capacitors tend to keep the voltage constant (voltage ³inertia´). An idealcapacitor with infinite capacitance acts as a constant voltage source.Thus, a capacitor cannot be connected in parallel with a voltage sourceor a switch (otherwise KVL would be violated, i.e. there will be ashort-circuit)

The voltage cannot change instantaneously

In inductors:

Inductors tend to keep the current constant (current ³inertia´). An idealinductor with infinite inductance acts as a constant current source.Thus, an inductor cannot be connected in series with a current sourceor a switch (otherwise KCL would be violated)

The current cannot change instantaneouslydt

t di Lt v

)()( !

!





12

The input/output equation for DC-DC convertersusually comes by examining inductor voltages

Vin

+Vout

±

LC

Ioutiin

+ (V in ± Vout ) ±iL

(iL

± Iout

)

Reverse biased, t h us t h ediode is open

,d t

d iLv LL !

L

V V

d t

d i out inL !,d t

d iLV V L

out in !,out inL V V v !

f or D T seconds

Note ± i f th e switc h stays closed, t h en Vout

= Vin

Switch closed for

DT seconds



13

Vin

+Vout

±

LC

Iout

± Vout +iL

(iL ± Iout )

Switch open for (1 í D)T seconds

iL continues to f low, t h us t h e diode is closed. Th isis t h e assumption o f ³continuous conduction´ in t h einductor w h ich is t h e normal operating condition.

,d t

d iv !

L

V

d t

d i out L !,d t

d iLV L

out !,out V v !

f or (1íD) T seconds



14

Since the average voltage across L is zero

01 !yy! out out inLavg V DV V DV

out out out in V DV V DDV yy!

inout DV V !

From power balance, out out inin I V I V !

D

I I in

out !

, so

The input/output equation becomes

Note ± even t h oug h iin is not constant(i.e., i in h as h armonics), t h e input power is still simply V in Iin because V in h as noh armonics

!



15

Examine the inductor current

S witc h closed,

S witc h open,

L

V V d t

d iV V v out inLout inL !! ,

L

V d t

d iV v out L

out L !! ,

sec/ AL

V V out in

DT (1 í D) T

T

Imax

Imin

Iavg = Iout

From geometry, I avg = Iout is h al f way

between I max and I minsec/ AL

V out

I

iL

Periodic ± finishes

a period where itstarted



16

Effect of raising and lowering I out whileholding V in , Vout , f, and L constant

iL

I

IRaise I out

I

Lower I out

I is unc h anged

Lowering I out (and, t h ere f ore, P out ) moves t h e circuittoward discontinuous operation



17

Effect of raising and lowering f whileholding V in , Vout , Iout , and L constant

iL

Raise f

Lower f

S lopes o f iL are unc h anged

Lowering f increases I and moves t h e circuit towarddiscontinuous operation



18

iL

Effect of raising and lowering L whileholding V in , Vout , Iout and f constant

Raise L

Lower L

Lowering L increases I and moves t h e circuit towarddiscontinuous operation



19

RMS of common periodic waveforms, cont.

T T T

rms t T

V d t t

T

V d t t

T

V

T

V

0

3

3

2

0

2

3

2

0

22

3

1!!¼

½

»¬«!

´´

T

V

0

3

V V rms !

S awtoot h




20

RMS of common periodic waveforms, cont.Using t h e power concept, it is easy to reason t h at t h e f ollowing wave f ormswould all produce t h e same average power to a resistor, and t h us t h eir rmsvalues are identical and equal to t h e previous example

V

0

V

0

V

0

0

-V

V

0

3

V V rms !

V

0

V

0




21

RMS of common periodic waveforms, cont.Now, consider a use f ul example, based upon a wave f orm t h at is o f ten seen inDC-DC converter currents. Decompose t h e wave f orm into its ripple, plus itsminimum value.

minmax I I

0

)(t i(th e ripple

+

0

minI

th e minimum value

)(t imaI

minI =

2

mima I I I avg !

avg I




22


_ a2

m in2

)( I t iA vg I rms ! (

_ a2m inm in

22)(2)( I I t it iAvg I r s y! ((

_ a _ a 2m inm in22 )( 2)( I t iAvg I t iAvg I rms y! ((

2m in

m inmaxm in

2m inmax2

22

3I

I I I

I I I r s y!

2m inm in

22

3I I I

I I PP

PP r s !

m inmax I I I PP !De f ine

Taken from ³Waveforms and Definitions´ PPT



23


2m in PP avg

I I I !

222

223¹º¸©

ª¨¹

º¸©

ª¨! PP

avg PP PP

avg PP

rmsI

I I I

I I

I

423

22

222 PP

PP avg avg PP

PP avg PP

rmsI

I I I I

I I I

I !

222

2

43 avg PP PP

r s I I I

I !

Recognize t h at

12

222 PP avg rms

I I I !

avg I

)(t i

m inmax I I I PP !

2

m inmax I I I avg !

Taken from ³Waveforms and Definitions´ PPT



24

Inductor current rating

22222

12

1

12

1I I I I I out ppavg Lrms (!!

2222

342

12

1out out out Lr s I I I I !! (

M ax impact o f I on t h e rms current occurs at t h e boundary o f continuous/discontinuous conduction, w h ere I =2Iout

out Lr s I I 3

2!

2Iout

0

Iavg = Iout I

iL

Use max



25

Capacitor current and current rating

22222

3

102

12

1out out avg C r s I I I I !!

iL

LC

Iout

(iL ± Iout )

Iout

íI out

0I

M ax rms current occurs at t h e boundary o f continuous/discontinuousconduction, w h ere I =2I

out

3out

rmsI

I !

Use max

iC = (iL ± Iout ) Note ± raising f or L, w h ich lowersI, reduces t h e capacitor current



26

MOSFET and diode currents and current ratingsiL

LC

Iout

(iL ± Iout )

out rms I I 3

2!

Use max

2Iout

0

Iout

iin

2Iout

0

Iout

Take worst case D f or eac h





28

Vin

+Vout

±

iL

LC

iC

Iout

Vin

+Vout

±

iL

LC iC

Ioutiin

Voltage ratings

Diode sees V in

MOS FE T sees V in

C sees Vout

Diode and MOS FE T, use 2V in

Capacitor, use 1. 5 Vout

Switch Closed

Switch Open



29

There is a 3 rd state ± discontinuous

Vin

+Vout

±

LC

Iout

O ccurs f or lig h t loads, or low operating f requencies, w h ereth e inductor current eventually h its zero during t h e switc h -open state

Th e diode opens to prevent backward current f low

Th e small capacitances o f th e MOS FE T and diode, acting inparallel wit h eac h oth er as a net parasitic capacitance,interact wit h L to produce an oscillation

Th e output C is in series wit h th e net parasitic capacitance,but C is so large t h at it can be ignored in t h e oscillationph enomenon

Iout

MOSFE

T

DIO DE

!



30

Inductor voltage showing oscillation duringdiscontinuous current operation

} 65 0kHz. Wit h L = 100µH, t h is correspondsto net parasitic C = 0. 6 nF

vL = (V in ± Vout )

vL = ±V out

Switch open

Switchclosed



31

Onset of the discontinuous state

sec/ AL

V out

f LDV T D

LV I

on se t

out

on se t

out out !y! 112

2Iout

0

Iavg = Iout

iL

(1 í D) T

f I

V L

out

out 2

" guarantees continuous conductionuse max

use min

f I

DV L

out

out on se t 2

1!

Th en, considering t h e worst case (i.e., D 0),

!



32

Impedance matching

out

out l oad I

V R !

equivR

DCíDC BuckConverter

+

Vin

í

+

Vout = DV in

í

Iout = Iin / DIin

+

Vin

í

Iin

22 D

R

DI

V DI

D

V

I V

R l oad

out

out

out

out

in

inequiv !

y!

y!!

Equivalent f romsource perspective

S ource

So, the buck converter makes the loadresistance look larger to the source

!



33

Example of drawing maximum power fromsolar panel

PV Station 13, Bright Sun, Dec. 6 , 2002

0

1

2

3

4

5

6

0 5 10 15 20 25 30 35 40 45

V(panel) - volts

I - amps

Isc

Voc

P ma x is app r o x. 130W (o ccur s at 29 V, 4.5A )

;!! 44.65.4

29A

V Rl oad

For max power frompanels at this solar intensity level, attach

I-V ch aracteristic o f 6 .44 resistor

But as t h e sun conditionsch ange, t h e ³max power resistance´ must alsoch ange



34

Connect a 2 resistor directly, extract only 55W

PV St t Br t S D

0

1

2

3

4

5

6

0 5 10 15 20 25 30 35 40 45

V( ) - t

-m

130W55W

56.044.6

2 ,

2!!!!

equiv

l oad l oad equiv R

RD

D

RR

To draw maximum power (130W), connect a buck converter between t h epanel and t h e load resistor, and use D to modi f y th e equivalent loadresistance seen by t h e source so t h at maximum power is trans f erred

!







37

Comp a ris on s o Ou tpu t Ca p ac itor Rippl e Vol ta g e

Con ve r te r T p e Vol ts p eak-t o -p eak) Bu ck

Cf

I out 4

10A

1500µF 50kHz

0.033V

BUC K DESIG N

Our M (M OSFET). 250V, 20A

Our L. 100µH, 9AOur C. 1500µF, 250V, 5.66A p-p

Our D (Diode). 200V, 16A



38

Minimum Induc t nce Values Needed t Guaran tee Con tinuous Curren t

Conver ter Type For Con tinuousCurren t in th e Inpu t

Induc tor

For Con tinuousCurren t in L2

Buckf I

V Lout

out 2

" ±40V

2A 50kHz

200µH

BUC K DESIG N

Our M (M OSFET). 250V, 20A

Our L. 100µH, 9AOur C. 1500µF, 250V, 5.66A p-p

Our D (Diode). 200V, 16A

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