7-1

DC-DC Switch-Mode Converters

Applications:• Regulated switch mode dc power supplies• dc motor drives

dc-dc Converters:• Step-down (buck) converter• Step-up (boost) converter• Step-down/step-up (buck-boost) converter• Cuk converter• Full-bridge converter

7-2

Functional Block Diagram of DC-DC Converter System

Unregulated dc voltage obtained by rectifying the line voltage, and therefore

will fluctuate with line voltage magnitude

Controlled dc output at a desired voltage level

7-3

Control of DC-DC ConvertersIn a dc-dc converter:• Average output dc voltage must be controlled to equal a desired level.• Utilizes one or more switches to transform dc from one level to another.• The average output voltage is controlled by controlling the switch on and off

durations (ton and toff).• Let’s consider the following switch-mode dc-dc converter:

• Average output dc voltage Vo depends on ton and toff.

• Switching is done at a constant frequency with switching time period Ts.• This method is called pulse-width modulation (PWM) in which the duty ratio D

is varied to control Vo, where D=ton/Ts

7-4

Control of DC-DC Converters (cont’d)

• The switch control signal, which controls the on and off states of the switch, is generated by comparing a signal level control voltage vcontrol with a repetitive waveform.

• The switching frequency is the frequency of the sawtooth waveform with a constant peak.

• The duty ratio D can be expressed as

st

control

s

on

V

vTt

D ^

7-5

Step-Down (Buck) Converter

dds

on

sT

ont

ont

ds

sT

s

DVVTt

dtdtVT

dttvT

V

011

0000

• low-pass filter: to reduce output voltage fluctuations• diode is reversed biased during ON period, input

provides energy to the load and to the inductor• energy is transferred to the load from the inductor

during switch OFF period• in the steady-state, average inductor voltage is zero• in the steady-state, average capacitor current is zero

• converts dc from one level to another• the average output voltage is controlled by the

ON-OFF switch• pulse-width modulation (PWM) switching is

employed• lower average output voltage than the dc input

voltage Vd depending on the duty ratio, D

• D=ton/Ts

• Average output:

Applications:• regulated switch mode dc power supplies• dc motor drives

7-6

Step-Down (Buck) Converter: Continuous current conduction mode

• Inductor current iL flows continuously• Average inductor voltage over a time period

must be zero

Assuming a lossless circuit

ratiodutyDTt

VVor

tTVtVVthereforeequalbemustBandAArea

dtvdtvdtv

s

on

d

onsond

T

tL

t

L

T

L

s

on

ons

0

00

00

,,

0

DVV

IIand

IVIV

d

d

dd

1

0

0

00

Buck converter is like a dc transformer where the turns ratio can be controlledelectronically in a range of 0-1 by controlling D of the switch

7-7

Example…..For a buck converter, R=1 ohm, Vd=40 V, V0=5 V, fs=4 kHz. Find the duty ratio and “on” time of the switch.

7-8

Solution….

D = V0 /Vd = 5/40 = 0.125 = 12.5%

Ts = 1/fs = 0.25 s = 250 s

Ton = DTs = 31.25 s

Toff = Ts – ton = 218.75 s

When the switch is “on”: VL = Vd - V0 = 35 V

When the switch is “off”: VL = -V0 = - 5 V

I0 = IL = V0 / R = 5 A

Id = D I0 = 0.625 A

7-9

Step-Up (Boost) Converter• Output voltage always higher than the

input voltage• When the switch is ON:

diode is reversed biasedoutput circuit is thus isolatedinductor is charged

• When the switch is OFF:the output stage received energy from the inductor as well as from the input

• Filter capacitor is very large to ensure constant output voltage

Applications:• regulated switch mode power supplies• Regenerative braking of dc motors

7-10

Step-Up (Boost) Converter: Continuous current conduction mode

• Inductor current iL flows continuously• Average inductor voltage over a time

period must be zero

Dividing both side by Ts

Assuming a lossless circuit

00 offdond tVVtV

DtT

VV

off

s

d

110

DIIand

IVIV

d

dd

10

00

7-11

Step-Up (Boost) Converter: Effect of parasitic elements

• Parasitic elements are due to the losses associated with the inductor, capacitor, switch and diode

• Figure shows the effect of the parasitic elements on the voltage transfer ratio

• Unlike ideal characteristics, in practice, Vo /Vd declines as duty ratio approaches unity

7-12

Step-Down/Step-Up (Buck-Boost) Converter• This converter can be obtained by the cascade connection

of two converters: the step-down converter and the step-up converter

• The output voltage can be higher or lower than the input voltage

• Used in regulated dc power supplies where a negative polarity output may be desired with respect to the common terminal of the input voltage

• The output to input voltage conversion ratio

• This allows V0 to be higher or lower than Vd

• When the switch is ON:diode is reversed biasedoutput circuit is thus isolatedinductor is charged

• When the switch is OFF:the output stage received energy from the inductor

DD

VV

d

110

7-13

Buck-Boost Converter: Continuous current conduction mode• Inductor current iL flows continuously• Average inductor voltage over a time

period must be zero

Assuming a lossless circuit

• Depending on the duty ratio, the output voltage can be either higher or lower than the input

DD

VV

TDVTDV

d

ssd

1

01

0

0

D

DIIand

IVIV

d

dd

10

00

7-14

Buck-Boost Converter: Effect of parasitic elements

• Parasitic elements are due to the losses associated with the inductor, capacitor, switch and diode

• Parasitic elements have significant impact on the voltage transfer ratio

7-15

Cuk DC-DC Converter

• Named after its inventor• The output voltage can be higher or lower than the input voltage• Provides a negative polarity output voltage with respect to the common terminal

of the input voltage• C1 acts as the primary means of storing and transferring energy from the input to

the output• In the steady-state, average inductor voltages, VL1 and VL2 are zero, therefore,

VC1 = Vd + V0

7-16

Cuk DC-DC Converter

• When the switch is OFF:- iL1 and iL2 flow through the diode

- C1 is charged through the diode by energy from both the input and L1

- energy stored in L2 feeds the output• When the switch is ON:

- Vc1 reverse biases the diode

- iL1 and iL2 flow through the switch

- since Vc1>V0, C1 discharges through the switch, transferring energy to the output and L2

- Therefore, iL2 increases

- Input feeds energy to L1 causing iL1 to increase

7-17

Steady-state current and voltage equations…………..Cuk

DD

II

VV

VD

V

TDVTDVVL

VD

V

TDVVTDVL

d

d

c

ssdc

dc

scdsd

1

101:

11

01:

0

0

01

012

1

11

Vc1 is constant and average voltages across L1 and L2 over a time period must be zero

Equating the above two equations,

7-18

Example 1: Step-down (Buck) converterThe chopper below controls a dc machine with an armature inductance La = 0.2 mH. The armature resistance can be neglected. The armature current is 5 A. fs = 30 kHz. D = 0.8

Vd

vo= Vo

+

voi

-

-

+

id

ioIaLa

ea

The output voltage, Vo, equals 200V. (a) Calculate the input voltage, Vd

(b) Find the ripple in the armature current.(c) Calculate the maximum and the minimum value of the armature current(d) Sketch the armature current, ia(t), and the dc current, id(t).

7-19

Example 2: Step-down (Buck) converter characteristicsA step-down dc-dc converter shown in the following figure is to be analyzed.

The input voltage Vd = 48 V.The output filter inductance L = 0.1 mHSeries resistor (with L) R = 0.2 ΩAssume in all calculations constant voltage over the series resistor R.The output capacitor C is large; assume no ripple in the output voltage.Rated output is 20 V and 25 A

(a) Calculate rated output power.(b) Calculate equivalent load resistance.(c) Calculate duty ratio D for rated output. The voltage across the series resistor R must be taken into consideration.

7-20

Example 3: Step-up (Boost) converter characteristicsA step-up dc-dc converter shown in the following figure is to be analyzed.

The input voltage Vd = 14 V.The output voltage V0 = 42 V.Inductor L = 10 mHOutput resistor R = 1 ΩSwitching frequency fs=10 kHz

(a) Duty ratio, switch on and off time.(b) Plot inductor and diode voltages.

7-21

Example 7-3: Cuk Converter

• The above Cuk converter is operating at 50 Hz, L1=L2=1 mH and C1=5 F• The output capacitor is sufficiently large to yield constant voltage• Vd=10 V and the output V0 is regulated to be constant at 5 V• It is supplying 5 W to a load--------------------------------------------------------------------------------------------------------• Calculate the percentage errors in assuming a constant voltage across C1 or in

assuming constant currents iL1 and iL2.

7-22

Full-Bridge dc-dc Converter

• Four-quadrant operation: magnitude and direction of both v0 and i0 can be controlled

• This converter consists of two legs, A and B. Each leg consists of two switches and their antiparallel diodes

• A reversible flow of power is made possible by connecting diodes in antiparallel with switches

• Applications: dc motor drives and dc-to-ac conversion

7-23

• vAN=Vd (if TA+ is ON and TA- is OFF) :: output current will flow through TA+ if io is positive or it will flow through DA+ if io is negative

• vAN=0 (if TA- is ON and TA+ is OFF) :: output current will flow through TA- if io is negative or it will flow through DA- if io is positive

• The average output voltage of the converter leg A:

where ton and toff are the ON and OFF intervals of TA+, respectively. Output voltage is independent of the direction of io

• One of the two switches in each leg is ON• The output current io will flow continuously

• (TA+ , TB-) and (TA- , TB+) are treated as two switch pairs: switches in each pair are turned ON and OFF simultaneously

Ads

offondAN TofratiodutyV

TttV

V0

7-24

• Similar arguments apply to the converter leg B.• VBN depends on Vd and the duty ratio of the switch TB+:

• VBN is independent of the direction of io

• Output voltage V0 (=VAN-VBN) can be controlled by controlling the switch duty ratios

BdBN TofratiodutyVV

7-25

• (TA+ , TB-) and (TA- , TB+) are two switch pairs: one of the two switch pairs is always ON

• Switching signal is generated by comparing a switching-frequency triangular wave with a control voltage

• If vcontrol>vtri: TA+ and TB- are ON

• If vcontrol<vtri: TA- and TB+ are ON

7-26

controlcontrol

tri

ddddBNAN

AB

BA

tri

control

s

on

son

s

tri

control

s

stritri

kvvV

VVDVDVDVVV

TTDDpairofratioDuty

TTV

vTtDpairofratioDuty

Ttt

T

V

vt

ttat

TtT

tVv

12

,1:2

,121:1

212

4

40

4

1210

11

1

1

1

1

• V0 varies linearly with the input control signal

7-27

Comparison of Converters

• Buck converter: step-down, has one switch, simple, high efficiency greater than 90%, provides one polarity output voltage and unidirectional output current

• Boost converter: step-down, has one switch, simple, high efficiency, provides one polarity output voltage and unidirectional output current, requires a larger filter capacitor and a larger inductor than those of a buck converter

• Buck-boost converter: step-up/step-down, has one switch, simple, high efficiency, provides output voltage polarity reversal

• Cuk converter: step-up/step-down, has one switch, simple, high efficiency, provides output voltage polarity reversal, additional capacitor and inductor needed

• Full-bridge converter: four-quadrant operation, has multiple switches, can be used in regenerative braking

7-28

Conclusions

• In many industrial applications, it is required to convert fixed dc voltage into variable dc voltage

• Various types of dc-to-dc converters• Operation of dc-to-dc converters • The step-down, step-up, buck-boost and Cuk converters are only capable

of transferring energy only in one direction• A full-bridge converter is capable of a bidirectional power flow• Like ac transformers, dc converters can be used to step-up or step-down a

dc voltage source• Applications: electric automobiles, trolley cars, marine hoists, mine

haulers, etc.• Also used in regenerative braking of dc motors to return energy back into

the supply –energy savings for transportation systems with frequent stops