# LECTURE 12 (Ch. 5)

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24 Νοε 2013 (πριν από 4 χρόνια και 7 μήνες)

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LECTURE 12
(Ch.
5)

DC
-
DC CONVERTERS

ECE 452

Power Electronics

1

Introduction

In some industrial applications it is necessary to
convert a fixed
-
voltage dc source to a variable
-
voltage dc source.

A dc
-
dc converter converts directly from dc to
dc and is also known as a dc converter.

A dc converter can be considered as dc
equivalent to an ac transformer with a
continuously variable turns ratio.

2

Introduction

DC converters are used for:

Traction motor control in electric cars

Trolley cars

Marine hoists

Forklift trucks

Mine Haulers

They provide:

Smooth acceleration

High efficiency

Fast dynamic response

3

DC converters can be used in regenerative
braking of dc motors to return energy back into
the supply.

This results in energy savings for transportation
systems with frequent stops.

4

Principle of Step
-
Down Operation

A chopper switch can be implemented by using:

BJTs

MOSFETs

GTOs

IGBTs

These non
-
ideal devices have a voltage drop of
0.5 to 2 V.

5

The principle of step
-
down operation can be
explained with use of the following figure.

6

The average output voltage and currents are:

where
k

is called the duty cycle

The
rms

value of the output voltage is:

R
kV
R
V
I
kV
V
t
f
V
T
t
dt
v
T
V
s
a
a
t
s
s
s
o
a

1
0
1
1
1

kT
s
o
o
V
k
dt
v
T
V
0
2
/
1
2
)
1
(
7

Assuming a lossless converter, the input power
to the converter will be the same as the output
power.

The input resistance seen by the source is:

The duty cycle
k

can be varied from 0 to 1 by
varying t
1

or T.

R
V
k
dt
R
v
T
dt
i
v
T
P
s
kT
o
kT
o
i
2
0
2
0
1
1

k
R
R
kV
V
I
V
R
s
s
a
s
i

/
8

Therefore, the output voltage can be varied
from 0 to Vs by controlling k.

In
constant
-
frequency operation

the chopping
frequency
f

(or T) is kept constant and the on
-
time t
1

is varied.

The width of the pulse is varied and this type of
control is known as
pulse
-
width
-
modulation

(PWM)
control.

9

In
variable
-
frequency operation

the chopping
frequency
f

is varied.

This is called
frequency modulation
, and it would
generate harmonics at unpredictable frequencies.

10

Generation of Duty Cycle

The duty cycle k can be generated by comparing
a dc reference signal
v
cr

with a saw
-
tooth carrier
signal
v
r
.

11

v

The carrier signal is given by:

The carrier signal is equal to the reference signal
at t =
kT
:

Then:

t
T
V
v
r
r

cr
r
v
v

M
V
V
k
V
kT
T
V
V
t
T
V
r
cr
cr
r
cr
kT
t
r

12

Where M is called the modulation index.

By varying the reference signal from 0 to
V
r
, the
modulation index and the duty cycle can be
varied from 0 to 1.

13

Step
-
Down Converter With RL

A converter with an RL load is shown below.

14

The operation of converter can be divided into 2
modes.

15

During mode 1, the converter is switched on
and the current flows from supply to load.

During mode 2, the converter is switched off
and the current continues to flow through the
freewheeling diode.

For large off
-
time, the load current will become
discontinuous.

16

Principle of Step
-
Up Operation

A converter can be used to step
-
up a dc voltage.

17

When the switch is closed for time t
1
, the
inductor current rises and energy is stored in the
inductor L.

If the switch is opened for time t
2
, the energy
stored in the inductor is transferred to load
through diode D
1

and the inductor current falls.

18

When the converter is turned on, the voltage
across the inductor is:

This gives the peak
-
to
-
peak ripple current in the
inductor as:

The average output voltage is:

dt
di
L
v
L

1
t
L
V
I
s

k
V
t
t
V
t
I
L
V
v
s
s
s
o

1
1
)
1
(
2
1
2
19

From the previous equation it can been seen
that the voltage across the load can be stepped
up by increasing the duty cycle.

If a large capacitor is connected across the load,
the output voltage will be continuous and
v
o

would become the average value V
a
.

This can be applied to transfer energy from one
voltage source to another.

20

The analysis of each mode and the equivalent
circuits for the modes of operation follows.

21

For mode 1:

1
1
)
(
I
t
L
V
t
i
dt
di
L
V
s
s

22

For mode 2:

2
2
2
)
(
I
t
L
E
V
t
i
E
dt
di
L
V
s
s

23

The condition for controllable power transfer is:

This equation indicates that the source voltage
should be less than the voltage E.

Note that without the chopping action, V
s

must
be greater than voltage E for transfer of power
from V
s

to E.

E
V
s

0
24