dc dc buck

8/13/2019 Dc Dc Buck

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EE362L, Fall 2008

DCDC Buck Converter


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Objectiveto efficiently reduce DC voltage

DCDC Buck

Converter

+

Vin

+

Vout

IoutIin

Lossless objective: Pin

= Pout

, which means that Vin

Iin

= Vout

Iout

and

The DC equivalent of an AC transformer

out

in

in

out

I

I

V

V


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3

Here is an example of an inefficient DCDC

converter

21

2

RR

RVV inout

+

Vin

+

Vout

R1

R2

in

out

V

V

RR

R

21

2

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

The load

Unacceptable except in very low power applications


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Another methodlosslessconversion of

39Vdc to average 13Vdc

If the duty cycle D of the switch is 0.33, then the average

voltage to the expensive car stereo is 39 0.33 = 13Vdc. This

is lossless conversion, but is it acceptable?

Rstereo

+

39Vdc

Switch state, Stereo voltage

Closed, 39Vdc

Open, 0Vdc

Switch open

Stereo

voltage

39

0

Switch closed

DT

T


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Convert 39Vdc to 13Vdc, cont.

Try adding a large C in parallel with the load to

control ripple. But if the C has 13Vdc, then

when the switch closes, the source currentspikes to a huge value and burns out the

switch.

Rstereo

+

39Vdc

C

Try adding an L to prevent the huge

current spike. But now, if the L has

current when the switch attempts toopen, the inductors current momentum

and resulting Ldi/dt burns out the switch.

By adding a free wheeling diode, the

switch can open and the inductor current

can continue to flow. With high-

frequency switching, the load voltage

ripple can be reduced to a small value.

Rstereo+39Vdc

C

L

Rstereo

+

39Vdc

C

L

A DC-DC Buck Converter

lossless


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Cs and Ls operating in periodic steady-state

Examine the current passing through a capacitor that is operating

in periodic steady state. The governing equation is

dt

tdvCti )(

)( which leads to totot

o dttiC

tvtv )(1

)()(

Since the capacitor is in periodic steady state, then the voltage at

time tois the same as the voltage one period T later, so

),()( oo tvTtv

The conclusion is that

Totot

oo dttiC

tvTtv )(1

0)()(or

0)( Totot

dtti

the average current through a capacitor operating in periodic

steady state is zero

which means that

Taken from Waveforms and Definitions PPT


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Now, an inductor

Examine the voltage across an inductor that is operating in

periodic steady state. The governing equation is

dt

tdiLtv )(

)( which leads to totot

o dttvL

titi )(1

)()(

Since the inductor is in periodic steady state, then the voltage at

time tois the same as the voltage one period T later, so

),()( oo tiTti

The conclusion is that

Totot

oo dttvL

tiTti )(1

0)()(or

0)( Totot

dttv

the average voltage across an inductor operating in periodic

steady state is zero

which means that



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KVL and KCL in periodic steady-state

,0)(

loopAround

tv

,0)(

nodeofOut

ti

0)()()()( 321 tvtvtvtv N

Since KVL and KCL apply at any instance, then they must also be valid

in averages. Consider KVL,

0)()()()( 321 titititi N

0)0(1

)(1

)(1

)(1

)(1

321

dtT

dttvT

dttvT

dttvT

dttvT

Tot

ot

Tot

ot

N

Tot

ot

Tot

ot

Tot

ot

0321 Navgavgavgavg VVVV

The same reasoning applies to KCL

0321 Navgavgavgavg IIII

KVL applies in the average sense

KCL applies in the average sense



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Vin

+Vout

iL

LC

iC

Ioutiin

Buck converter+ vL

Vin

+Vout

LC

Ioutiin

+ 0 V

What do we learn from inductor voltage and capacitor

current in the average sense?

Iout

0 A

Assume large C so that

Vouthas very low ripple

Since Vouthas very low

ripple, then assume Iout

has very low ripple


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The input/output equation for DC-DC converters

usually comes by examining inductor voltages

Vin

+Vout

LC

Ioutiin

+ (VinVout)iL

(iL Iout)

Reverse biased, thus the

diode is open

,dtdiLv LL

L

VV

dt

di outinL ,dt

diLVV Loutin ,outinL VVv

for DT seconds

Noteif the switch stays closed, then Vout= Vin

Switch closed for

DT seconds


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Vin

+Vout

LC

Iout

Vout+

iL

(iL

Iout

)

Switch open for (1 D)T seconds

iLcontinues to flow, thus the diode is closed. This

is the assumption of continuous conduction in the

inductor which is the normal operating condition.

,dt

diLv LL

L

V

dt

di outL ,dt

diLV Lout,outL Vv

for (1D)T seconds


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Since the average voltage across L is zero

01 outoutinLavg VDVVDV

outoutoutin VDVVDDV

inout DVV

From power balance,outoutinin

IVIV

D

II inout

, so

The input/output equation becomes

Noteeven though iinis not constant

(i.e., iinhas harmonics), the input power

is still simply Vin Iinbecause Vinhas no

harmonics


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Examine the inductor current

Switch closed,

Switch open,

LVV

dtdiVVv outinLoutinL

,

L

V

dt

diVv outLoutL

,

sec/AL

VV outin

DT (1 D)T

T

Imax

Imin

Iavg= Iout

From geometry, Iavg= Ioutis halfway

between Imaxand Iminsec/ALVout

I

iL

Periodicfinishes

a period where itstarted


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Effect of raising and lowering Ioutwhile

holding Vin, Vout, f, and L constant

iL

I

IRaise Iout

I

Lower Iout

I is unchanged

Lowering Iout(and, therefore, Pout) moves the circuit

toward discontinuous operation


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Effect of raising and lowering f while

holding Vin, Vout, Iout, and L constant

iL

Raise f

Lower f

Slopes of iLare unchanged

Lowering f increasesI and moves the circuit toward

discontinuous operation


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iL

Effect of raising and lowering L while

holding Vin, Vout, Ioutand f constant

Raise L

Lower L

Lowering L increasesI and moves the circuit towarddiscontinuous operation


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RMS of common periodic waveforms, cont.

TTT

rms t

T

Vdtt

T

Vdtt

T

V

T

V

0

3

3

2

0

2

3

2

0

22

3

1

T

V

0

3

VVrms

Sawtooth



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Using the power concept, it is easy to reason that the following waveforms

would all produce the same average power to a resistor, and thus their rms

values are identical and equal to the previous example

V

0

V

0

V

0

0

-V

V

0

3

VVrms

V

0

V

0



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RMS of common periodic waveforms, cont.Now, consider a useful example, based upon a waveform that is often seen in

DC-DC converter currents. Decompose the waveform into its ripple, plus its

minimum value.

minmax II

0

)(tithe ripple

+

0

minI

the minimum value

)(ti

maxI

minI=

2

minmax IIIavg

avgI



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2min2 )( ItiAvgIrms

2minmin

22 )(2)( IItitiAvgIrms

2

minmin

22

)(2)( ItiAvgItiAvgIrms

2min

minmaxmin

2minmax2

22

3I

III

IIIrms

2minmin

22

3III

II PP

PPrms

minmax IIIPP Define



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2min

PP

avg

III

222

223

PPavgPP

PPavg

PPrms

III

II

II

423

22222 PPPPavgavg

PPPPavg

PPrms

IIII

III

II

222

2

43 avgPPPP

rms III

I

Recognize that

12

222 PPavgrms

III

avgI

)(ti

minmax IIIPP

2

minmax IIIavg



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Inductor current rating

2222212

1

12

1 IIIII outppavgLrms

2222342

121

outoutoutLrms IIII

Max impact ofI on the rms current occurs at the boundary of

continuous/discontinuous conduction, whereI =2Iout

outLrms II3

2

2Iout

0

Iavg= IoutI

iL

Use max


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Capacitor current and current rating

222223

102

12

1outoutavgCrms IIII

iL

LC

Iout

(iL Iout)

Iout

Iout

0I

Max rms current occurs at the boundary of continuous/discontinuous

conduction, whereI =2Iout

3

outCrms

II

Use max

iC= (iL Iout) Noteraising f or L, which lowersI, reduces the capacitor current


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MOSFET and diode currents and current ratings

iL

LC

Iout

(iL Iout)

outrms II3

2

Use max

2Iout

0

Iout

iin

2Iout

0

Iout

Take worst case D for each


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Worst-case load ripple voltage

Cf

I

C

IT

C

IT

C

QV outout

out

44

22

1

Iout

Iout

0T/2

C charging

iC= (iL Iout)

During the charging period, the C voltage moves from the min to the max.

The area of the triangle shown above gives the peak-to-peak ripple voltage.

Raising f or L reduces the load voltage ripple


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Vin

+Vout

iL

LC

iC

Iout

Vin+

Vout

iL

LC

iC

Ioutiin

Voltage ratings

Diode sees Vin

MOSFET sees Vin

C sees Vout

Diode and MOSFET, use 2Vin

Capacitor, use 1.5Vout

Switch Closed

Switch Open


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There is a 3rdstatediscontinuous

Vin

+Vout

LC

Iout

Occurs for light loads, or low operating frequencies, where

the inductor current eventually hits zero during the switch-open state

The diode opens to prevent backward current flow

The small capacitances of the MOSFET and diode, acting in

parallel with each other as a net parasitic capacitance,

interact with L to produce an oscillation

The output C is in series with the net parasitic capacitance,

but C is so large that it can be ignored in the oscillation

phenomenon

Iout


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Inductor voltage showing oscillation during

discontinuous current operation

650kHz. With L = 100H, this corresponds

to net parasitic C = 0.6nF

vL= (VinVout)

vL=Vout

Switch open

Switch

closed


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Onset of the discontinuous state

sec/AL

Vout

fLDVTD

LVI

onset

out

onset

outout 112

2Iout

0

Iavg= Iout

iL

(1 D)T

fI

VL

out

out

2 guarantees continuous conduction

use max

use min

fI

DVL

out

outonset

2

1

Then, considering the worst case (i.e., D 0),


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Impedance matching

out

outload

I

VR

equivR

DCDC Buck

Converter

+

Vin

+

Vout = DVin

Iout = Iin/ DIin

+

Vin

Iin

22D

R

DI

V

DI

D

V

I

VR load

out

out

out

out

in

inequiv

Equivalent from

source perspective

Source

So, the buck converter

makes the load

resistance look larger

to the source


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Example of drawing maximum power from

solar 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

Pmaxis approx. 130W

(occurs at 29V, 4.5A)

44.65.4

29

A

VRload

For max power frompanels at this solar

intensity level, attach

I-V characteristic of 6.44resistor

But as the sun conditionschange, the max power

resistance must also

change


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Connect a 2resistor directly, extract only 55W

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

130W55W

56.0

44.6

2,

2

equiv

loadloadequiv

R

RD

D

RR

To draw maximum power (130W), connect a buck converter between the

panel and the load resistor, and use D to modify the equivalent load

resistance seen by the source so that maximum power is transferred


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Vpanel

+V

out

iL

L

C iC

Ioutipanel

Buck converter for solar applications

+ vL

Put a capacitor here to provide the

ripple current required by the

opening and closing of the MOSFET

The panel needs a ripple-free current to stay on the max power point.

Wiring inductance reacts to the current switching with large voltage spikes.

In that way, the panel current can be ripple

free and the voltage spikes can be controlled

We use a 10F, 50V, 10A high-frequency bipolar (unpolarized) capacitor


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Worst-Case Component Ratings Comparisons

for DC-DC Converters

ConverterType

Input InductorCurrent(Arms)

OutputCapacitorVoltage

Output CapacitorCurrent (Arms)

Diode andMOSFETVoltage

Diode andMOSFETCurrent(Arms)

BuckoutI3

2

1.5 outV outI3

1

2 inV outI3

2

10A 10A10A 40V 40V

Likely worst-case buck situation

5.66A 200V, 250V 16A, 20AOur components

9A 250V

Our M (MOSFET). 250V, 20A

Our L. 100H, 9A

Our C. 1500F, 250V, 5.66A p-p

Our D (Diode). 200V, 16A

BUCK DESIGN


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Comparisons of Output Capacitor Ripple Voltage

Converter Type Volts (peak-to-peak)

Buck

Cf

Iout

4

10A

1500F 50kHz

0.033V

BUCK DESIGN


Our L. 100H, 9A

Our C. 1500F, 250V, 5.66A p-p



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Minimum Inductance Values Needed toGuarantee Continuous Current

Converter Type For ContinuousCurrent in the Input

Inductor

For ContinuousCurrent in L2

BuckfI

VLout

out2

40V

2A 50kHz

200H

BUCK DESIGN


Our L. 100H, 9A

Our C. 1500F, 250V, 5.66A p-p


dc dc buck

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