1 DC−DC Buck Converter. 2 Objective – to efficiently reduce DC voltage DC−DC Buck Converter +...

1

DC−DC Buck Converter

2

Objective – to efficiently reduce DC voltage


+

Vin

−

+

Vout

−

IoutIin

Lossless objective: Pin = Pout, which means that VinIin = VoutIout and

The DC equivalent of an AC transformer

out

in

in

out

I

I

V

V

!

3

Here is an example of an inefficient DC−DC 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 η is only 0.33

The load

Unacceptable except in very low power applications

4

Another method – lossless conversion 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

Taken from “Course Overview” PPT !

5

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 current spikes 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 to open, the inductor’s 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

Taken from “Course Overview” PPT

6

C’s and L’s 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

tot

oto dtti

Ctvtv )(

1)()(

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

),()( oo tvTtv

The conclusion is that

Tot

otoo dtti

CtvTtv )(

10)()(or

0)( Tot

ot

dtti

the average current through a capacitor operating in periodic steady state is zero

which means that

Taken from “Waveforms and Definitions” PPT !

7

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

tot

oto dttv

Ltiti )(

1)()(

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

),()( oo tiTti

The conclusion is that

Tot

otoo dttv

LtiTti )(

10)()(or

0)( Tot

ot

dttv

the average voltage across an inductor operating in periodic steady state is zero

which means that


8

KVL and KCL in periodic steady-state

,0)(

loopAroundtv

,0)(

nodeofOutti

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

otN

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


9

Capacitors and Inductors

In capacitors:dt

tdvCti

)()(

Capacitors tend to keep the voltage constant (voltage “inertia”). 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 “inertia”). 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

tdiLtv

)()(

!

10

Vin

+ Vout

–

iL

LC iC

Iout iin

Buck converter

+ vL –

Vin

+ Vout

–

LC

Iout iin

+ 0 V –

What do we learn from inductor voltage and capacitor current in the average sense?

Iout

0 A

• Assume large C so that

Vout has very low ripple

• Since Vout has very low

ripple, then assume Iout

has very low ripple

!

11

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

Vin

+ Vout

–

LC

Iout iin + (Vin – Vout) –

iL

(iL – Iout)

Reverse biased, thus the diode is open

,dt

diLv L

L L

VV

dt

di outinL ,

dt

diLVV L

outin ,outinL VVv

for DT seconds

Note – if the switch stays closed, then Vout = Vin

Switch closed for DT seconds

12

Vin

+ Vout

–

LC

Iout – Vout +

iL

(iL – Iout)

Switch open for (1 − D)T seconds

iL continues 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 L

L L

V

dt

di outL ,

dt

diLV L

out ,outL Vv

for (1−D)T seconds

13

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

Note – even though iin is not constant

(i.e., iin has harmonics), the input power is

still simply Vin • Iin because Vin has no

harmonics

!

14

Examine the inductor current

Switch closed,

Switch open,

L

VV

dt

diVVv outinLoutinL

,

L

V

dt

diVv outLoutL

,

sec/ AL

VV outin

DT (1 − D)T

T

Imax

Imin

Iavg = Iout

From geometry, Iavg = Iout is halfway

between Imax and Imin

sec/ AL

Vout

ΔI

iL

Periodic – finishes a period where it started

15

Effect of raising and lowering Iout while

holding Vin, Vout, f, and L constant

iL

ΔI

ΔI

Raise Iout

ΔI

Lower Iout

• ΔI is unchanged

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

toward discontinuous operation

16

Effect of raising and lowering f while holding Vin, Vout, Iout, and L constant

iL

Raise f

Lower f

• Slopes of iL are unchanged

• Lowering f increases ΔI and moves the circuit toward discontinuous operation

17

iL

Effect of raising and lowering L while holding Vin, Vout, Iout and f constant

Raise L

Lower L

• Lowering L increases ΔI and moves the circuit toward discontinuous operation

18

RMS of common periodic waveforms, cont.

TTT

rms tT

Vdtt

T

Vdtt

T

V

TV

0

33

2

0

23

2

0

22

3

1

T

V

0

3

VVrms

Sawtooth


19


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


20


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


21


2min

2 )( ItiAvgIrms

2minmin

22 )(2)( IItitiAvgIrms

2minmin

22 )( 2)( ItiAvgItiAvgIrms

2min

minmaxmin

2minmax2

22

3I

III

IIIrms

2minmin

22

3III

II PP

PPrms

minmax IIIPP Define

Taken from “Waveforms and Definitions” PPT

22


2minPP

avgI

II

222

223

PP

avgPPPP

avgPP

rmsI

III

II

I

423

22

222 PP

PPavgavgPP

PPavgPP

rmsI

IIII

III

I

222

2

43 avgPPPP

rms III

I

Recognize that

12

222 PPavgrms

III

avgI

)(ti

minmax IIIPP

2

minmax IIIavg

Taken from “Waveforms and Definitions” PPT

23

Inductor current rating

22222

12

1

12

1IIIII outppavgLrms

2222

3

42

12

1outoutoutLrms IIII

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

continuous/discontinuous conduction, where ΔI =2Iout

outLrms II3

2

2Iout

0Iavg = Iout ΔI

iL

Use max

24

Capacitor current and current rating

22222

3

102

12

1outoutavgCrms IIII

iL

LC

Iout

(iL – Iout)

Iout

−Iout

0ΔI

Max rms current occurs at the boundary of continuous/discontinuous

conduction, where ΔI =2Iout

3out

CrmsI

I

Use max

iC = (iL – Iout) Note – raising f or L, which lowers ΔI, reduces the capacitor current

25

MOSFET and diode currents and current ratings

iL

LC

Iout

(iL – Iout)

outrms II3

2

Use max

2Iout

0Iout

iin

2Iout

0Iout

Take worst case D for each

26

Worst-case load ripple voltage

Cf

I

C

IT

C

IT

C

QV outout

out

4422

1

Iout

−Iout

0T/2

C chargingiC = (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

!

27

Vin

+ Vout

–

iL

LC iC

Iout

Vin

+ Vout

–

iL

LC iC

Iout iin

Voltage ratings

Diode sees Vin

MOSFET sees Vin

C sees Vout

• Diode and MOSFET, use 2Vin

• Capacitor, use 1.5Vout

Switch Closed

Switch Open

28

There is a 3rd state – discontinuous

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

MOSFET

DIODE

!

29

Inductor voltage showing oscillation during discontinuous current operation

650kHz. With L = 100µH, this corresponds to net parasitic C = 0.6nF

vL = (Vin – Vout)

vL = –Vout

Switch open

Switch closed

30

Onset of the discontinuous state

sec/ AL

Vout

fL

DVTD

L

VI

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),

!

31

Impedance matching

out

outload I

VR

equivR


+

Vin

−

+

Vout = DVin

−

Iout = Iin / DIin

+

Vin

−

Iin

22 D

R

DI

V

DIDV

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

!

32

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 - a

mp

s

Isc

Voc

Pmax is approx. 130W

(occurs at 29V, 4.5A)

44.65.4

29

A

VRload

For max power from panels at this solar intensity level, attach

I-V characteristic of 6.44Ω resistor

But as the sun conditions change, the “max power resistance” must also change

33

Connect a 2Ω resistor 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 - a

mp

s

130W

6.44Ω

resistor

2Ω r

esis

tor

55W

56.044.6

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

!

34

Vpanel

+ Vout

–

iL

LC iC

Iout ipanel

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 10µF, 50V, 10A high-frequency bipolar (unpolarized) capacitor

35

Worst-Case Component Ratings Comparisons for DC-DC Converters

Converter Type

Input Inductor

Current (Arms)

Output Capacitor Voltage

Output Capacitor Current (Arms)

Diode and MOSFET Voltage

Diode and MOSFET Current (Arms)

Buck outI

3

2

1.5 outV outI

3

1

2 inV outI

3

2

10A 10A10A 40V 40V

Likely worst-case buck situation

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

Our components

9A 250V

Our M (MOSFET). 250V, 20A

Our L. 100µH, 9A

Our C. 1500µF, 250V, 5.66A p-p

Our D (Diode). 200V, 16A

BUCK DESIGN

36

Comparisons of Output Capacitor Ripple Voltage

Converter Type Volts (peak-to-peak) Buck

Cf

Iout4

10A

1500µF 50kHz

0.033V

BUCK DESIGN


Our L. 100µH, 9A

Our C. 1500µF, 250V, 5.66A p-p


37

Minimum Inductance Values Needed to Guarantee Continuous Current

Converter Type For Continuous

Current in the Input Inductor

For Continuous Current in L2

Buck

fI

VL

out

out

2

–

40V

2A 50kHz

200µH

BUCK DESIGN


Our L. 100µH, 9A

Our C. 1500µF, 250V, 5.66A p-p


1 DC−DC Buck Converter. 2 Objective – to efficiently reduce DC voltage DC−DC Buck Converter +...

Documents

Transcript of 1 DC−DC Buck Converter. 2 Objective – to efficiently reduce DC voltage DC−DC Buck Converter +...