Advanced practical electronics

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A
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E
E
D
D
D



P
P
P
R
R
R
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E
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T
T
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R
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C
S
S
S




F
F
F
R
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R
O
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M
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M



P
P
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O
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W
E
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R
R
R



S
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U
P
P
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P
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T
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I
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P
P
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M
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Preface


Nowadays, electronics has become part of every one daily life. When you are relaxing
you listen to radio
, CD player, or watch DVD, VCR or just TV. When you are going
away you arm the alarm to protect your house, and then you press the immobilizer to
open or start your car. When you go to the bank you use an ATM or the teller use a
computer for your transacti
on. You go to the hospital the physician order the nurse to
connect you to a machine to diagnose the cause of your illness. You want to talk to
somebody in another town you use a phone.


What is common in the above few examples is that they are all electr
onic appliances,
which proves beyond doubt that electronics will always be part of our lives. Hence there
is a dire need for development of expertise in the field. This book is written to help the
reader to get into grips with how to put electronics in pra
ctice. Its emphasis is on
application of electronics in solving our daily problems. So for each device introduced
the author will try to show how it is used in real situation. This will help the reader to be
able to design circuits for different applicatio
ns.


The text is divided into 9 chapters and is organised in such a way that the information is
built up in a logical way. The first chapter is on power supplies. Chapter 2 is on
transducers, chapter 3 is the theory of operational amplifier, chapter 4 is s
ignal
conditioning and interfacing, chapter 5 is filtering, chapter 6 is wave generation and
shaping, chapter 7 is large signal amplification. Chapter 8 is noise, and chapter 9 is
hardware/software interfacing.



Phumzile Malindi, December 2004


1.
POWER
SUPPLIES


1.1


INTORDUCTION


Almost every electronic circuit needs a dc power source to operate. The main function of
the power supply is to take the 220 V ac (mains) voltage and converts it to dc voltage or
voltages that are required to power electronic circu
its. For most electronic applications
the power supply needs to provide dc voltages in the range of 5V for digital electronic
circuits to about 80 V (or more) for large signal (or power) amplifiers, with currents from
few milliamperes to about 5 or more am
peres. In some other applications such as
operational amplifier circuits and power amplifier circuits the power supply needs to
provide both positive and negative voltages to enable both the positive and negative
swings of the output voltages. The latter i
s referred to as dual, dual
-
rail or split supply
since it is providing both positive and negative dc voltages while the former is called a
single
-
rail supply because it is only providing a single voltage, which can be either
positive or negative.


The circ
uit for converting an ac supply to a dc supply involves three main stages: the
stepping
-
down of ac voltage, ac
-
to
-
dc conversion, and voltage regulation

as depicted in
Figure 1.1
.


Stepping-down of ac
voltage
AC-to-dc
conversion
Voltage regulation
RMS
V
220
input
regulated
output



Figure 1.1 Basic power supply

stages


The incomi
ng 220 V
rms

mains voltage is stepped
-
down to a smaller ac voltage, before it is
converted into a dc voltage. The dc voltage is regulated to produce a stable dc voltage.

AC
-
to
-
dc conversion stage involves two processes
:

changing of ac to pulsating dc and
sm
oothening puls
ating dc to produce a steady dc. This has resulted in ac
-
to
-
dc stage
being divided into

two separate stages
, namely

rectification and filtering

as shown in the
following diagram.


Stepping-down
of ac voltage
Rectifier
Filter
Voltage
regulation
regulated
output
RMS
V
220
input

d

c

b

a


d

c

b

a




Figure 1.2 Power

supply





1.2


STEPPI
NG DOWN OF AC VOLTAGE


The stepping down of the incoming 220 V
rms

mains voltage to a smaller ac voltage
involves the use of a transformer as shown in Figure 1.3.










Figure1.3a



Figure 1.3b


Where Figure 1.3a is a normal transformer, which gives
out a single stepped
-
down
output, whereas Figure 1.3b is a center
-
tapped transformer that gives out two stepped
-
down voltages of the same magnitude. For a single
-
rail power supply the normal
transformer is the best candidate but for dual or split supply th
e best transformer to use is
the center
-
tapped in order to generate the two voltages required.


The transformer has two sets of coils: the primary at the input and the secondary at the
output. The primary consists, most of the time, of one coil and the se
condary can have
one or more coils depending on the outputs required. For example, if you are designing a
power supply to provide fixed positive, fixed negative, variable positive, and variable
negative voltages, you will need a transformer that will provi
de four voltages at it
secondary; that is, two center
-
tapped coils on the secondary side of the transformer. The
output voltage of the transformer is determine
d

by the number of turns in both primary
and the secondary or turns ratio of the transformer. Tha
t is,






P
S
P
S
N
N
V
V







(1.1a)







P
P
S
S
V
N
N
V







(1.1b)


Thus, for the transformers shown in Figure 1.3 the output voltages at the secondary will
be 22 V
rms

and two 22 V
rms

for the two transformers, respectively (since the
turns ratio
N
P
:N
S

= 10:1).


1.3


AC
-
TO
-
DC CONVERSION


The function of this stage is to convert the output of the transformer, which is a stepped
-
down ac voltage into a dc voltage. This is accomplished in two stages: rectification and
filtering (or smoothening)
. The first stage called the rectifier converts the ac into a
pulsating dc, which is a dc with an ac component, then the second stage called the filter
Vs
Vs
Vp
Vp
T2
10TO1CT
T1
10TO1
removes the ac component of the pulsating dc to produce a steady dc that has a value
given by










D
pk
S
dc
V
V
V
2
2




=


V
.
V
.
)
pk
(
S
4
1
637
0



(1.2)

Rectification


A rectifier circuit called a full wave bridge rectifier is shown in Figure 1.4. It consists of
four diodes.






D
1


D
2








D
3

D
4












Figure 1.4 Full wave bridge rectifier



T
he way the full
-
wave bridge rectifier works is that only two parallel diodes are
conducting while the other parallel pair is off for each cycle. That is,
during the positive
half
-
cycle diodes
D
2

and
D
3

are conducting while
D
1

and
D
4

are off and for negative half
-
cycle diodes
D
1

and
D
4

are conducting while
D
2

and
D
3

are in the off state. This results in
a series of positive pulses across the output terminals

that has a peak amplitude of






D
)
pk
(
S
)
pk
(
O
V
V
V
2







(1.3)


where
V
s(pk)

is the peak value across the secondary of the transformer and
V
D

is the volt
drop across each diode. Since there are two diodes conducting per cycle, these diodes are
in ser
ies with the input ac voltage hence the volt drop introduced by the rectifier is 2
V
D
,
which is 1.4 V for silicon diodes.


Filtering


The output of the rectifier is a series of positive pulses, which is called pulsating dc, not
genuine dc as required. In or
der to get a genuine dc voltage the output of the rectifier is
filtered or smoothened by a low pass filter to remove the ac component. The most
popular filter circuit used for smoothening is a capacitor that is connected across the
output of the rectifier.

The action of the capacitor filter depends upon the fact that the
capacitor stores energy during the conduction period and delivers it to the load during the
non
-
conduction period. The most commonly used capacitor is a polarized capacitor called
electroly
tic capacitor and its value is chosen so that



in

in

out2

out1

ac

ac





r
load
f
C
R
1







(1.4)


where
f
r

is the ripple frequency, which is twice the mains frequency (i.e. twice 50 Hz in
South Africa and Europe while it is twice 60Hz in America). This makes the time

constant for discharging to be longer than the time between recharging thus ensuring
small ripple. In most instances the value of the load is unknown and it is only the value of
the voltage and the current that are available. Using the available informati
on and the
Ohms law, the value of the capacitor can be determined using







load
r
load
V
f
I
C







(1.5)


At this stage let us put together all the different stages of the power supply covered so far
into one circuit. This power supply is called t
he unregulated power supply and is shown
in Figure 1.5 for both single and dual
-
rail supplies, respectively.

























+

















-



Figure 1.5 Single
-
rail and dual
-
rail (split) unregulated power supplies



1.4


VOLTAG
E REGULATION


Though the output of the filter is a steady dc voltage it is still having some variations or
ripples in it. For general applications this dc voltage is acceptable but for other
applications the voltage needs further processing to remove the v
ariations. This is
accomplished by using a voltage regulator. These voltage regulators are used in most of
the power supplies to provide a dc voltage that almost ripple
-
free. Regulators can be
categorised into linear and switching voltage regulators. Linea
r regulators are the most
commonly used and can be found in almost nearly every regulated power, while
switching regulators are used in dc
-
to
-
dc converters to step up or to convert the polarity
+
C3
Vo
Vo
Vo
+
C2
+
C1
in
in
ac
ac
T2
10TO1CT
T1
10TO1
of the input voltage. The first regulators used discrete compo
nents such as zener diodes
and power transistors to accomplish voltage regulation. However, nowadays complete
voltage regulators are available as inexpensive integrated circuits. The availability of
these IC or monolithic regulators has made the task of de
signing a power supply simple
and the power supply circuit to be more compact.


1.4.1

Linear Voltage Regulators


Linear voltage regulator operates by using a voltage
-
controlled current source to force a
fixed voltage to appear at the output. It has a built
-
in s
ense and control feedback circuitry
that senses the output voltage and adjust the current source so as to hold the output
voltage constant.


The linear IC regulators come as positive and negative, fixed and variable, three
-
terminal,
four
-
terminal and five
-
terminal regulators with different voltage and current ratings. The
three
-
terminal regulators are the most commonly used and they can be classified into
fixed and variable regulators. For the regulator to work properly the input voltage must
be greater tha
t the expected regulated output and for many regulators there is a minimum
difference between the two voltages. This minimum difference is called the dropout
voltage and for the regulator to operate satisfactory the minimum input to an IC regulator
must be

greater than or equals to the expected regulated output plus the dropout voltage.


Fixed Three
-
Terminal Regulators


Three
-
terminal regulators have three connections: input, output, and ground and is
factory
-
trimmed to provide a fixed output, which can eit
her be positive or negative. A
typical example of a positive three
-
terminal regulator is the 78xx, where the output
voltage is specified by the last two digits of the part number and can be any of the
following: 05, 06, 08,10, 15, 18, or 24. The typical ex
ample of a negative version is 79xx,
which is almost the same as the 7800 series except that it works with negative input dc
voltage to produce a negative output. Both the 7800 and 7900 series can provide up to 1
amp load current. Low
-
power versions: 78Lxx

and 79Lxx are also available but they can
provide currents up to 100 mA to the load. The circuit for a fixed regulator is shown in
Figure 1.6 that will provide a 5V at 100 mA to the load. For the regulator to operate
satisfactory the minimum input must be

7 V.










Figure 1.6 Fixed 5 V regulator circuit



Vo
Vin
IN
COM
OUT
78L05
+
C1
1uF

There are other three
-
terminal regulator variants, which are not as popular as 7800/7900
series, which have better performance in regards to volt drop from unregulated input to
regulated output (or
dropout voltage). For an example, the LP2950 is a fixed 5V regulator
just like a 7805, but it regulates with a dropout voltage of 0.4 V, compared with 2 V
dropout for 7805. Except for low
-
dropout other regulators also can deliver higher load
current, for e
xample the LT1085/4/3 series can provide 3 A, 5A, and 7.5 A.


Adjustable Three
-
Terminal Regulators


Adjustable regulators are regulators that are designed in such a way that the user can set
the regulated output. A typical example of an adjustable regulat
or is a LM317 for positive
voltage and LM337 for negative voltage. Unlike the fixed regulators, the adjustable
regulator has adjustment (ADJ) terminal instead of the ground terminal. These 317 and
337 can provide currents up to 1.5 A to the load. The magni
tude of the output voltage can
be set to any value between 1.25 V and 37 V using two additional resistors as shown in
Figure 1.7.












Figure 1.7 Adjustable regulator circuit


Resistor
R
1

is fixed at 240


for 317 and 337 (for other regulators pleas
e consult the
manufacturer data sheets) and R
2

is adjustable to set the required output voltage using the
following equation






2
1
2
1
R
I
R
R
V
V
ADJ
REF
o















(1.6)


With
V
REF

equals 1.25 V and adjustment terminal current is in the range of 50

100

A,
which

is very small, thus making the product
I
ADJ
R
2

in Equation (1.6) negligible small,
the output can be rewritten as






V
R
R
.
V
o










1
2
1
25
1





(1.7)





For adjustable three
-
terminal regulators with higher current ratings, use table 1.1 below.

R2
Vo
Vin
+
C1
1uF
IN
ADJ
OUT
317
R1
240

Table 1
.1 High current adjustable three
-
terminal regulators


Current (A)

Positive Adj. Regulator

Negative Adj. Regulator

3

5

10

LM350

LM338

LM396

LM333




Lifting Regulator above Ground


The fixed regulators provide fixed voltages at only certain values, which

are standard. So
if you want a regulated output, which is not standard, for example 9 V, to emulate a
battery you can use an adjustable regulator with
R
2

set to 1.5 k

. Alternatively you can
still use the standard fixed regulator with its common terminal
lifted above ground by
means of a zener diode that has zener voltage equals to the required output minus the
rated value of the standard regulator. This extends the voltage range by an amount equals
zener voltage. That is,






Z
REG
O
V
V
V







(1.8)


For example to get 9 V from a 5 V regulator you need to use 4 V zener to lift the
common of the regulator above ground as shown in the following circuit.













Figure 1.8 Non
-
standard fixed voltage regulator (with regulator lifted above



ground using a zener diode)



The output voltage is the sum of the regulator voltage and the zener voltage, which in this
case is 5 V + 4 V = 9 V.


External Capacitors and Protection Diodes


A 0.01

F to 25

F capacitor must be c
onnected across the output, as shown in the above
circuits, to eliminate the high frequency noise at the output and to insure stability.

For adjustable regulators the adjustment terminal can be bypassed to ground with a 10

F
capacitor to improve ripple r
ejection by 15 dB to obtain a total ripple rejection of 80 dB
at the output.

D1
Vo
Vin
IN
COM
OUT
78L05
+
C1
1uF
A 0.1

F input bypass capacitor is also recommended for adjustable regulators in order to
compensate for the problems that may arise due to the devices sensitivity when
adjustment

or output capacitors are used.


For the adjustment terminal bypass capacitor and output capacitor it is recommended that
you include safety discharge diodes. These diodes provide discharging paths for these
capacitors in the event of the input or output b
eing shorted. This is very important
especially for higher voltages in order to prevent the capacitors from discharging through
the regulator and damaging it in the event of the input or output being short
-
circuited.


This is shown if Figure 1.9, where ca
pacitor
C
1

is used to eliminate high frequency noise,
diode
D
1

is used to provide a discharging path for
C
1
, and capacitor
C
2

is used to improve
ripple
-
rejection and diode
D
2

is used to provide the discharging path for
C
2
.













Figure 1.9 External

capacitors and safety discharge diodes for regulators


Electronic Shutdown


In other applications such as electronic laboratories, which are used by first year
electronic learners who know little about short circuits, the protection diodes mentioned
above

are not enough to protect your power supply circuit. These diodes only provide
discharging paths when there is a short and do not prevent the excessive current from
damaging the regulator.


Electronic shutdown is a short circuit protection technique that

is used to clamp the
adjustment terminal to ground when an excessive current (due to short circuit) through
the regulator is sensed. This is accomplished by sensing the load current via the volt drop
across resistor
R
S

and switching on transistor
Q
1

when
the current exceeds the set limit.
Once
Q
1

is turned on it extends the input voltage
V
in

to the base of
Q
2

thus making
Q
2

to
also be on and as
Q
2

switches on, adjustable terminal resistor
R
2

is shorted out and the
output voltage drops to
V
ref
, which is 1.2
5 V.





D1
LM317
IN
ADJ
OUT
Vo
Vin
R1
240
R2
C3
0.1uF
+
C2
10uF
+
C1
1uF
D2
D1
Vo
Vin
IN
COM
OUT
78L05
+
C1
1uF














Figure 1.10 Regulator with electronic shutdown


Outboard
-
Pass Transistor for Current
-
Boosting


Most of the regulators covered can deliver a limited current to the load. This current is
sufficient for most applications. However, if y
ou want a current that is more than what
the regulator can deliver, you will need to use an outboard pass transistor, which is an
external pass transistor that can be added to your normal regulator circuit to provide the
extra current. Figure 1.11 shows a
circuit of a regulator with an outboard pass transistor.











Figure 1.11 Regulator with an outboard pass transistor


The circuit uses a 78L05, which is designed to deliver a current of 100 mA to the load.
The value of the series resistor
R
1

is chose
n such that for current less than the maximum
rated current of the regulator, the volt drop across it is less than 0.7 V in order to keep the
outboard transistor
Q
1

in an off state. This will make the regulator to work normal. For
currents greater than the

maximum rated current (which is 100 mA in this case), the volt
drop across
R
1

becomes sufficient to turn the outboard transistor on. When this happens,
the current through the regulator will be limited to the maximum rated current, while the
additional cu
rrent is delivered to the load through the outboard pass transistor.


In some other applications, which need high load currents, one outboard transistor is not
sufficient to provide the required current. In such cases multiple outboard pass transistors
a
re used in parallel to deliver the required high output load currents as shown in Figure
1.12.


Q1
R1
Vo
Vin
IN
COM
OUT
78L05
+
C1
1uF
R4
Rs
Q1
Q2
D2
D1
+
C3
10uF
+
C2
10uF
C1
0.1uF
R2
Vin
Vo
LM317
IN
ADJ
OUT
R1
240













Figure 1.12 Regulator with multiple outboard pass transistors


The operation of the circuit in Figure 1.12 is the same as that of Figure 1.11, exc
ept that
the additional current is shared amongst the three outboard transistors instead of one.
Resistors
R
2
, R
3
, and
R
4

are included for stability and to prevent current swamping.


The problem with the circuit in Figure 1.11 is that, instead of just prov
iding an additional
path for current to pass through, it can amplify the maximum rated current of the
regulator to provide a load current that is equal to beta times the maximum rated current
of the regulator. This current can be high enough to destroy bot
h the transistor and the
load. In order to avoid this from happening, another transistor
Q
2

is connected across the
base
-
emitter junction of the outboard transistor as shown in the following Figure 1.12.










Figure 1.12 Regulator with an outboard pas
s transistor and current
-
limiting circuit


This
Q
2

transistor limits the current through the outboard transistor so that it does not
exceed the stipulated value. This is accomplished by sensing the load current via the volt
drop across resistor
R
sc

and sho
rting out
R
1

when the current causes the volt drop across
base
-
emitter junction of
Q
2

to be 0.7 V. When
R
1

is shorted, the voltage that drives the
outboard will be cut off thereby turning the outboard pass transistor off. The values of the
two resistors a
re given by






ragulator

the

of

current

rated

Max
V
.
O
R
7
1



(1.9)

Q2
Rsc
Q1
R1
Vo
Vin
IN
COM
OUT
78L05
+
C1
1uF
Q3
R4
Q2
R3
R2
R1
+
C1
1uF
IN
COM
OUT
78L05
Vin
Vo
Q1





current

output

quired
Re
V
.
O
R
SC
7




(1.10)


Paralleling Regulators for Higher Current


As an alternative to the use of multiple outboard pass transistor for higher current, two
similar regulators can be connected
in parallel to double the load current or three similar
regulators can be connected in parallel to triple the load current. Figure 1.13 shows a
circuit with two LM338 (10A) regulators, which are connected in parallel. The load
current is the sum of the cur
rents delivered by the two regulators, and since LM338 used
is a 5 A regulator the total current that can be delivered by the circuit to the load is 10 A,
which is twice the current of each regulator. The Opamp ensures that the current is
divided correctly

between the two regulator ICs.





















Figure 1.13 10 A Regulator


1.4.2

Switching Regulators
, DC Voltage Converters

and Isolated Power Supplies


The regulators covered so far are called linear regulators. Though they are easy to use
their e
fficien
cy is not that good. This has resulted in a shift in industry towards the use
of
switching regulators in power supplies more than the linear regulators. This shift can be
attributed to the switching regulator’s efficient transfer of power to the load.
Swit
ching
regulators are used in
switch
-
mode
power supplies
(which are used
by

computers
)
, dc
-
to
-
dc convert
e
rs, and in isolated power supplies.



Unlike linear regulators, switching regulators converts the

input dc voltage to pulses,
which are then stepped up,

rectified and filtered to provide a smooth dc.

A basic
R5
2.7k
+
R4
0.1
R3
0.1
IN
ADJ
OUT
LM338
R1
120
IN
ADJ
OUT
LM338
1.2V to 30 V
Vo
Vin
2.7k
R2
C1
0.1uF
+
C3
10uF
s
witching regulator consists
of a
switching regulator element

(transistor)
, a

reference
voltage
regulator, a voltage divider circuit, an error amplifier and a control circuit (an
oscillator with a pul
se
-
width modulator)
.
Figure 1.1
4

shows a block diagram of a
switching regulator and Figure 1.1
4

shows a block diagram of a
MAX631, which is a
commercial
-
available switching regulator.
Some of the commercially available switching
regulators include
MAX632,
MAX633,
MAX634, MAX635, MAX636,
MAX637,
MAX638
,
MAX639, MAX640,
MAX742,
etc
.


Reference
regulator
Osc
PWM
in
v
Voltage Divider
Error Amp
Power
switch
from regulated
output
out
v



Figure 1.1
4

Block diagram of a switching regulator


Most of the dc
-
to
-
dc converters use switching principle with building blocks such as the
oscillator
, the switching transistor (power MOSFET), the energy
-
storing device
(capacitor or inductor), feedback and smoothening capacitor, hence they are referred to as
switching regulators. The oscillator generates pulses that switch the transistor on and off.
As
the transistor goes into saturation it applies the input dc voltage across the energy
-
storing device for a short interval. During this period the energy (
2
2
LI

or
2
2
CV
) is stored
in the energy
-
storing device and then th
e stored energy is transferred to the capacitor at
the output. The output capacitor smoothes the output and carry the load between charging
pulses. The feedback controls the output by changing the oscillator’s pulse width or
switching frequency in order to

regulate the output. Figure 1.13 shows a block diagram of
a basic switching regulator and Figure 1.14 shows the configurations for both step
-
up and
polarity inversion. However, complete voltage converters are available as integrated
circuits.








Vin
Vo
Q1
L1
Vref
D1
+
R2
R1
Osc






(a)



















(b)


Figure 1.14 Configurations for (a) Step
-
up and (b) Polarity inversion switching regulator





The
dc
converter

is a

circuit that
changes dc

to

another
dc

voltage
. The output dc of the
converter can be either higher or lower th
an the input, and can also be either of the same
or opposite polarity to the input voltage. Since all the regulator circuits covered so far can
provide the stepping down of voltage, voltage converters are commonly used for stepping
up, polarity inversion a
nd provision of isolated supply voltages.


Isolated Power Supply


Galvanic isolation is required for many circuits that are found in medical systems since
there are transducers that are attached to the patient. Some of these circuits also need to
be power
ed by isolated power supplies.


In order to get an isolated power supply you need to use an isolated output voltage
converter. Isolation eliminates any connections between the input and the output ground
and allows the output to float. Unlike ordinary dc
-
t
o
-
dc voltage converter, an isolated
output usually has a transformer to provide isolation for the switching currents and an
optical isolator to isolate the feedback sensing voltage.













Figure 1.15 Simplified isolated dc
-
to
-
dc converter

Vin
Vo
Q1
L1
D1
+
Osc
R1
Vin
-
Vo
Q1
L1
Vref
D1
+
R2
R1
Osc

1.5


POWER SU
PPLY CIRCUITS


















Figure 1.16
Variable dual supply with electronic shut down for short circuit protection









Figure

1.1
7

12 V power supply (load current > regulator’s max rated output current)












Figure 1.18

Isolated

15 V spli
t power supply


+
C7
10uF
+
C10
10uF
D6
D5
R6
240
Rs1
R5
LM337
IN
ADJ
OUT
Vo
R3
C9
0.1uF
Q4
Q3
R1
240
Rs
R4
LM317
IN
ADJ
OUT
Vo
R2
C6
0.1uF
+
C5
10uF
+
C4
10uF
D4
D3
Q2
Q1
+
C3
+
C2
in
ac
T2
10TO1CT
D3
D2
5V
Q1
IN
COM
OUT
78L05
+
C2
1uF
12V
T1
10TO1
ac
in
+
C1
R2
1k
R1
0V
+
C4
1uF
+
C3
1uF
-15V
+15V
D3
Q1
IN
COM
OUT
78L12
+
C2
0.1uF
T1
10TO1
ac
in
+
C1
R2
1k
R1
NMA1215S
Vin
GN
D
+15V
COM
-15V
1.6


INVERTORS


Though this topic is not going to be covered in much detail it is still believed that the
coverage of power supplies would not be complete without the mentioning of inverters.


Assume that you are having a 12 V car battery and

you want to play a TV that can only
use 220 V ac. An inverter, which changes dc to ac, can be a solution. This process of dc
to ac voltage inversion is accomplished by first changing dc to ac using an oscillator and
then stepping up the generated ac signa
l to 220 V ac voltage. In order to meet the power
requirements of the inverter the stepping up is usually preceded by current boosting.


Inverters can be categorized into three basic types: square wave, modified sine wave and
pure sine wave dc to ac invert
ers. Square wave inverters are the simplest
,

cheapest

and
low power quality

of the three, followed by modified sine wave inverters
. Both the square
wave and the modified square wave inverters provide square wave outputs; however, the
difference between the
m is that the former provide a normal square wave while the
modified sine wave inverter provides a square wave with some dead spots between the
half cycles. The sine wave inverter, on the other hand, provides a sine

wave with low
total harmonic distortion
and they are more expensive than the other two inverter types.
Figure 1.19




The dc
-
to
-
ac inversion process is depicted in the following diagram, where the low
-
frequency oscillator is responsible for generating
the required line frequency of
50 Hz
(or
60
Hz)
which is usually a square wave. The output of the oscillator is amplified in order
to get higher current
s

before it is applied to a step
-
up transformer for
stepping up

the
generated
low
ac
voltage to 220 V.


50 Hz
Oscillator
Amplifier
Filter
(optional)
Step-up
Transformer
)
(
dc
i
v
)
(
ac
o
v
220V



Figure 1.
20

Block

diagram of a DC to AC inverter


For generating the ac from a dc source an astable multivibrator is normally used and the
most commonly used astable multivibrator circuits used include the circuits shown in
Figure 1.2
1




1.8 Notes




The transformer used mu
st be able to deliver the required current and voltage



The rectifier diodes (or bridge rectifier) must be capable of passing the high peak
current



Adequate heatsinking must be provided for regulators and outboard pass transistors
and if your high current s
upply is built into a case it is recommended that an extractor
fan must be used for adequate cooling.



The polarity and the voltage rating of the capacitors must be correct since wrong
polarity or exceeded voltage rating can result in the capacitor blowing.



For the regulator to operate satisfactory the minimum input voltage to an IC regulator
must be greater than or equals to the expected regulated output plus the dropout
voltage. If an outboard pass transistor is used, the input voltage must exceed the
outp
ut voltage by the dropout voltage of the regulator plus a
V
BE

drop.



Use a positive regulator with a positive input and a negative regulator with a negative
input.



Make sure that the protection diodes are connected correctly (that is, they are reverse
biase
d), to avoid shorting out the device to which they are connected across.


References


Boylestad, R. and L. Nashelsky.
Electronic Devices and Circuit Theory, 5
th

edition
.
Prentice Hall, New Jersey, 1992.

Horrowitz, P. and W. Hill.
The Art of Electronics, 2
n
d

edition
. Cambridge, New York,
1994.

Ibrahim, K.F.
Electronic Systems and Techniques, 2
nd

edition
. Longman Scientific and
Technical, Essex, 1994.

Mathews, T. Switching Regulators Demystified. National Semiconductors.

Millman, J. and A. Grabel.
Micro
-
elec
tronics, 2
nd

edition
. McGraw
-
Hill, New York,
1987.

Newport Components. Product data disk.

SGS
-
Thomson Microelectronics. LM138/238/338 Three
-
Terminal 5
-
A Adjustable
Voltage Regulators Datasheet, 1994.

Simpson, S. Linear and Switching Voltage Regulator Funda
mentals. National
Semiconductors.

http://www.mitedu.freeserve.co.uk/Ciruits/Power/boosting.htm

http://www
.mitedu.freeserve.co.uk/Ciruits/Power/1230psu.htm












2.

TRANSDUCERS


2.1


INTRODUCTION


A transducer can be defined as a device that can be used to convert energy from one form
to another form. In electronics a transducer enables the electronic system t
o communicate
with the outside world by converting physical quantity such as pressure, motion,
temperature, or light into an electrical quantity, or vice versa (i.e. converts electrical
quantity into physical quantity). This enables the use of electronics
to control and log
process.


Transducers that are responsible for converting from physical to electrical are referred to
as sensors while those that convert from electrical to physical are called actuators. Some
few transducers can be used interchangeable
as sensors and as actuator. One such
transducer is an antenna (aerial) that is used in transceiver systems such as two
-
way radio
and mobile (cellular) phones. A transceiver system has one antenna, which is used as an
actuator to convert modulated carrier i
nto waves when transmitting and as a sensor to
intercept waves and covert them to electrical signals when receiving.


Transducers can be further classified as passive and active transducers. Active
transducers are those that need to be powered in order to
work, whereas the passive
transducers operate without being powered.


2.2


SENSORS


Sensors are input transducers that transform energy from one form, which is not electric,
into electric energy. They are used in electronics to acquire data about their surroun
dings
and convert that into an electrical quantity for further processing. Sensors are classified
according to the major forms of energy they detect, hence there are acoustic sensors,
temperature sensors, light sensors, pressure sensors, etc. and they conv
ert energy from
one form into electrical quantity that can be voltage, resistance, capacitance, current, or
inductance.


2.2.1

ACOUSTIC SENSORS


Acoustic sensor converts sound or acoustic energy into electrical signal. A microphone is
a typical example of an aco
ustic sensor that changes the sound waves into electrical
energy, which may then be amplified, transmitted, or recorded. Microphones come in
different types, which include moving coil (or dynamic), carbon, electret, piezoelectric
(or crystal), and capacito
r (or condenser) type. Carbon is a very low quality microphone,
moving coil, capacitor and electret types are good quality microphones, and crystal type
has a performance that is somewhere between carbon and moving coil type.




2.2.2

TEMPERATURE SENSORS


Temper
ature sensors convert temperature changes into electrical quantity. There are four
main types of temperature sensors: thermocouples, resistive temperature detectors
(RTDs), thermistors and IC temperature sensors.


Thermocouples


Thermocouple consists of t
wo dissimilar metal conductors, which are connected at one
end to form a joint. Due to Seebeck effect, the two wires would produce a small open
-
circuited voltage, called Seebeck voltage when the junction is heated. This voltage, which
is in millivolts, is
proportional to the temperature of the junction. Thermocouple can
operate over a wide range of temperatures.


Resistive Temperature Detectors (RTDs)


A resistance temperature detector (RTD) is a device whose resistance increases with
temperature. They are
more stable and more accurate than other temperature sensors.
RTDs are available in materials such as platinum, nickel, copper, and tungsten, which
have different temperature range and resistance coefficient,

. Table 2.1 shows the linear
temperature range

and resistance coefficient for these RTDs. Since RTD is a resistive
device, you must pass current through it to produce voltage that can be conditioned by an
amplifier circuit. The disadvantage of RTDs is that they are more expensive and self
-
heating.


Ta
ble 2.1 linear temperature range and resistance coefficient of RTDs


RTD type

Temperature range (
0
C)

Resistance coefficient,


Platinum

-
184 to 815

0.0039

/
o
C

Copper

-
51 to 149

0.0042

/
o
C

Tungsten

-
73 to 276

0.0045

/
o
C

Nickel

-
73 to 149

0.0067

/
o
C



The temperature coefficient shown in Table2.1 is the amount of resistance change that
can be expected for each degree Celsius of change in temperature. The amount of
resistance change per
o
C (

r
) can be obtained by multiplying the temperature coefficien
t
(

) by the nominal resistance of the RTD at 0
0
C (
R
0
). That is,






0
R
r









(2.1)


If the temperature changes to
T
x
, the new resistance would change by a value equals to
the product of

r

and new temperature, hence the new resistance

of the RTD at
temperature
T
x

will be






0
R
rT
R
x
x








(2.2)


For platinum RTDs, which have nominal resistance of 100


at 0
0
C and resistance
coefficient of 0.0039

/
o
C the amount of resistance change per
o
C is


C
/
.
C
/
.
R
r
0
0
0
39
0
100
0039
0














If the temperature changes to 100
0
C, the new resistance would change by a value equals
to the product of

r

and new temperature, hence the new resistance of the RTD at
temperature 100
0
C will be
















139
100
100
39
0
0
0
0
100
100
C
C
/
.
R
rT
R


The temperature ranges shown in
Table 2.1 can be extended, but at the expense of
linearity in the extended range.


The most popular type of RTD is made of platinum, which has a nominal resistance of
100


at 0
0
C. The reason for this is that platinum is stable, it resists corrosion and
o
xidation, has a high melting point and a high degree of resistivity.



Thermistors


Thermistors is a contracted name for thermally sensitive resistors, which have a very high
negative temperature coefficient; that is, their resistances decrease as temperat
ure
increases. Thermistors are more sensitive and faster reacting to temperature changes than
thermocouples and RTDs but they are not linear and they are self
-
heating like RTDs. The
characteristic temperature
-
resistance relationship is in the form






T
/
b
T
e
R
R


0





(2.3)


where
T

is temperature in Kelvin’s,
R
0

is resistance at 0
0
C

and
b

is a constant for a
specific thermistor.


IC Temperature Detectors


IC temperature sensors convert temperature into voltage or current. They are very small,
w
hich allows them to be placed in PCB. They are the most linear of the temperature
sensors and they are inexpensive. However, their disadvantages include their temperature
range, which is less than 200
0
C, they are slow to react to changes in temperature, an
d
they are self
-
heating. Typical examples of IC temperature sensors include LM35, which
provides voltage, and AD590, which produces current.





2.2.3

LIGHT/OPTICAL SENSORS


Light sensors convert light into an electrical quantity. Light or optical sensors includ
e
devices such as light dependant resistor (LDR), photodiode, phototransistor, and
photovoltaic cell.


Light Dependant Resistor (LDR)


Light dependant resistor is a device that has a resistance that decreases with an increase
in the amount of light. That i
s, it converts light into resistance, and it is also known as
photoconductive cell or photoresistive device.


Photodiode and Phototransistor


Photodiodes and phototransistors are devices that are used to convert light into current.
Photodiodes are designed

for high speed, high efficiency and low noise than the
phototransistor. However, phototransistors have more output current than photodiode, but
at the expense of speed.


Photovoltaic Cell


A photovoltaic or solar cell converts light into electrical energy


2.2.4

PRESSURE SENSORS


Pressure sensors convert pressure into electrical quantity. Since pressure and force are
interrelated, pressure sensors can also used to detect other various form of energy such as
weight, and force. Pressure can be defined as the amoun
t of force applied to an area.
Force, on the other hand, may be defined as a push or a pull. Weight is a force exerted on
a mass of an object by a gravitational field. Other terms related to force and pressure are
strain and stress, where strain is a force

to make a change on an object and stress is
pressure or tension exerted on an object. One of the most commonly used pressure
sensors is a strain gauge.


Strain Gauge


The most common strain gauge consists of a grid of very fine foil or wire whose
resistan
ce varies linearly with the strain applied to the device. When using a strain gauge,
you bond the strain gauge to the device under test, apply force, and then measure the
strain by detecting the changes in resistance. Strain gauges are also used in sensor
that
detect force or other derived parameters, such as acceleration, weight and vibration.


Load Cell


Load cell is a sensor, which uses strain gauges that are mounted in specific patterns to
provide a meaningful value of change in pressure or weight. Sinc
e load cell is made by
combining a number of strain gauges in a common sensor, it will give out resistance that
will depend on the amount of pressure applied.


Capacitance Pressure Sensors


Capacitance pressure sensors use capacitance and reluctance to con
vert pressure to
voltage. One plate is kept stationary and the other one is connected to a diaphragm so that
when the diaphragm moves due to applied pressure, the plate will move and the amount
of capacitance will change. In most cases the dielectric betwe
en the two plates is a
silicone oil filing


2.2.5

LEVEL SENSORS


Level sensors are used to convert the amount of a product in a container to an electrical
quantity. Level sensors can be classified into point
-
contact and continuous level sensors.


Point
-
Contact
Level Sensors


Point
-
contact level sensor determines the level at a single set point. Most of them include
a switch that is activated when the level reaches a specific point. Point
-
contact level
sensors include float
-
level sensor, multiple float
-
level sens
or, displacer
-
level sensor,
paddlewheel
-
level sensor, beam
-
breaker level sensor, two
-
wire conductance
-
level sensor,
and thermistor
-
level sensor.


Continuous Level Sensors


Continuous level sensors provide continuous level readings from the minimum to the
m
aximum level. They are more expensive than point
-
contact level sensors and they
provide analogue current or voltage. They include RF admittance (capacitance), the
sonic, and the conductive type.


2.2.6

POSITION SENSORS


Position or displacement sensors are used

to convert position or distance moved into
electrical quantity.


Linear Potentiometer and Rotary Potentiometer


Linear potentiometer and rotary potentiometer sensors are basically variable resistors. As
you move the slider or the wiper (the adjustable ter
minal) the value of the resistance is
changed and this change is directly proportional to the movement of the slide. Linear
potentiometers are used for linear measurements to convert linear motion into resistance,
and rotary potentiometers are used to conv
ert rotary motion into resistance.




Linear Variable Differential Transformers (LVDTs)


Linear variable differential transformer position sensor uses a primary transformer
winding and two identical secondary windings that are wound around a hollow tube,
w
hich provides a cavity for a movable core that is attached to the system whose position
is being measured. When ac voltage is applied to the primary of the transformer, there
will be an induced voltage at the secondary, which is determined by the turns rat
io and
the core. As the core move in and out the amount of the induced voltage will increase and
decrease.


2.2.7

BIOMEDICAL SENSORS


Our nervous system uses the flow of ions to communicate. The communication activity
of the nervous system can be measured on the

surface of the skin using electromechanical
sensors, which are called microelectrodes or just electrodes. The signals that are detected
are referred to as electrophysiological signals and they include gross electrical activities
of the brain nerve cells,
gross electrical activities of the heart, muscle movement, and
summation of receptor potentials in the retina due to light stimulation. Some of these
signals are listed in Table 2.2 below. Most of them have frequencies between dc (0 Hz)
and 3 000 Hz and am
plitudes ranging between 10 microvolts and 10 milli
-
volts (
Plonsey,
1996)
.


Table 2.2 Electrophysiological signals and sensors


Signal

Biological source

Average amplitude

Frequency


Electrocardiogram (ECG)

Heart

1
-
5 mV

0.05
-
100 Hz

Electroencephalogram (E
EG)

Brain

10
-
50

V

0
-
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There are two properties that make Ag
-
AgCl a good choice for an electrode. It is non
-
polarizable, which means that current flows freely across the electrode junction, and
secondly, it generates less than 10

V of noise.

In other medical appl
ications, especially in the incubators, it is also required to measure
the temperature and the amount of oxygen. For temperature one RTD or IC temperature
sensor can be used, and for oxygen a fuel cell, which converts the percentage of oxygen
into voltage,

can be used.



2.3


ACTUATORS


Actuators are output transducers that transform energy from electric into another form,
which can be temperature, light, sound, or movement. Like sensors, actuator can be
classified according to the major forms of energy they pr
oduce.


2.3.1

ACOUSTIC ACTUATORS


Acoustic sensor converts electrical energy into sound. Loudspeaker, headphones, and
earpieces are acoustic actuators. A microphone is a typical example of an acoustic sensor
that changes the sound waves into electrical energy, w
hich may then be amplified,
transmitted, or recorded.


2.3.2

TEMPERATURE ACTUATORS


Temperature actuator converts electrical energy into temperature. An element is a typical
example of a temperature actuator. It is fitted in geyser, kettles, irons and cooking
ap
pliances to provide heat when current is passed through.


2.3.3

LIGHT ACTUATORS


Light actuators are used to convert electricity into light. Examples of light actuators
include a light bulb, light emitting diode (LED), laser diode, liquid crystal display (LCD),

and LED display, cathode ray tube (CRT). LCD and CRT are used in computer monitors,
video monitors, oscilloscopes and television.


2.3.4

MOTION ACTUATORS


Motion actuator converts electrical energy into motion. A typical example is an electric
motor, which con
verts electrical energy into motion and a relay converts electrical into
movement.


2.4


Notes




When choosing a sensor make sure you know its output, its range and other
characteristics such as accuracy, sensitivity, response time, and linearity. This is
impor
tant since most of the sensors will need additional electronics to condition their
raw outputs



For sensors that are giving out resistance a Wheatstone bridge is recommended for
converting resistance into voltage.



For Sensors that are giving out current a c
urrent to voltage conversion is required
(check chapter 4).



For sensors that are attached to human beings (biomedical sensors) include some
form of isolation in conditioning circuits.



To drive actuators some form of interfacing is needed. Interfacing will
be covered
later in the text.

References


Barney, G.C.
Intelligent Instrumentation
. Prentice Hall, New Jersey, 1988.

Boylestad, R. and L. Nashelsky.
Electronic Devices and Circuit Theory, 5
th

edition
.
Prentice Hall, New Jersey, 1992.

Duncan, T.
Electronic
s for today and tomorrow
. John Murray, London, 1985.

Horrowitz, P. and W. Hill. The Art of Electronics, 2
nd

edition. Cambridge, New York,
1994.

Kissell, T.E.
Industrial Electronics
. Prentice Hall, New Jersey, 1997

Mancini, R. (editor in chief). Op Amps For

Everyone: Design Reference. Texas
Instruments, Advanced Analog Products (SLOD006B), August 2002.

National Instruments. Signal Conditioning Tutorial. www.natinst.com

Plonsey, R.
Electronic Engineer Handbook,

4
th

edition

-

Electrocardiography and
Biopotenti
als. McGraw
-
Hill, 1996.

Temperature Controls (Pty) Ltd. Thermocouple & Resistance Temperature Detectors.

Tompkins, W.J., editor.
Biomedical Digital Signal Processing
. Prentice Hall, 1995.


Tompkins, W.J. and J.G.
Webster, editors. In
terfacing sensors to the IBM PC
. Prentice
-
Hall, 1988.

Webster, J.G.
Medical Instrumentation
-

application and design
. Houghton Mifflin, 1978.

























3.

OPERATIONAL AMPLIFIE
RS (OPAMPS)


3.1 INTRODUCTION


Operational amplifier (Opamp) is monoli
thic amplifying device with a differential input
stage, which consists of many [BJT or FET] transistors, resistors and capacitors
connected as multistage transistor amplifiers that are integrated together into one
package. These multistage amplifiers are d
irect coupled to allow the operational amplifier
to be used for both dc and ac signals. Operational amplifiers come in packages that are
having one, two (dual), or four (quad) identical Opamp units on a single chip.


An Opamp is basically a differential am
plifier with the following properties:


(a)

High open
-
loop gain
A
o

of about 10
5

at 0 Hz (dc) and low frequencies, which
decreases as the frequency increases

(b)

Very high input impedance, which is greater or equal to 1 M


(c)

Very low output impedance

(d)

The output is th
e amplified version of the difference of the two input signals


Due to the first property, any input to the Opamp will result in a very high output.
However, the output can not be greater than the supply voltage, hence the output will be
limited to the sup
ply voltage (or a value that is about supply voltage minus 2 V for most
of the Opamps). Due to the second property, the current into the input of the Opamp is
assumed to be zero. This assumption is almost true in FET Opamps where the current is
about 1 pA
or less, but not always true in BJT Opamps where the current can be as high
as tens of

A.


Since an Opamp is a differential amplifier it has two inputs: the inverting input and the
non
-
inverting input as shown in Figure 3.1 below. Most of the time the su
pply voltage
terminals are omitted as shown on the right.











Figure 3.1 Basic operational amplifiers





The inverting input is marked


and the non
-
inverting input is denoted by a + mark. If an
input is applied to the non
-
inverting (+) input the
output will be in
-
phase with the input,
but if the input is applied to the inverting (
-
) input the output will be 180
0

out
-
of
-
phase
with respect to the input (i.e. the output will be inverted).

output
output
input
input
input
input
-Vs
+Vs
+
3.2 NEGATIVE FEEDBACK AND CLOSED LOOP OPERATION


To control th
e gain of the Opamp so that the output does not go into saturation, a negative
feedback is used. This is accomplished by including a negative feeding back, where some
of the output is fed back to the inverting input. This makes the gain of the Opamp to be
controllable, and it also reduces the output voltage. The inclusion of the negative
feedback changes the gain from being open
-
loop
A
o

to close
-
loop gain
A
c
.


When the Opamp is having a negative feedback, it is said to be operated in a close
-
loop
mode. The

advantage of operating the Opamp in this mode is that, unlike in the open
-
loop operation, the gain of the Opamp is predictable, and controllable so as to avoid
distortion, which is caused by Opamp operating in the saturation region that is not linear.


3
.3 BASIC OPAMP CIRCUITS


3.3.1 CLOSED
-
LOOP OPERATION


Amplifier


One of the most commonly used Opamp circuit is a constant
-
gain amplifier. A constant
-
gain multiplier is used to amplify the incoming signal, which is fed to one of the input of
the Opamp. The
re are two versions of this circuit: the inverting and the non
-
inverting
amplifier. For the inverting amplifier, the input is applied to the inverting input via an
input resistor
R
i
, and there is also a feedback resistor
R
f

to control the gain of the
ampli
fier as shown in Figure 3.2.










Figure 3.2 Inverting amplifier


The gain and the output voltage are given by






i
f
i
o
v
R
R
V
V
A








(3.1)

and





i
v
i
i
f
o
V
A
V
R
R
V








(3.2)


where the minus (
-
) indicates that the output is inverted
.


For the non
-
inverting amplifier, the input is applied to the non
-
inverting input. It also has
a feedback resistor
R
f
, and resistor
R
i

connected between the inverting input and ground
Vi
Rf
Ri
Vo
to control the gain as shown in Figure 3.3. Unlike the inverting ampli
fier, the non
-
inverting amplifier has an output that is in
-
phase with the input.














Figure 3.3 Non
-
inverting amplifier


The gain and the output voltage of the non
-
inverting amplifier are given by






i
f
i
o
v
R
R
V
V
A



1





(3.3)

and





i
v
i
i
f
o
V
A
V
R
R
V











1




(3.4)


Voltage
-
follower


If the value of resistor
Ri

in Figure 3.3 is increased towards infinity and the feedback
resistor
R
f

towards zero, then
R
i

will be like an open circuit and equations (3.3) and (3.4)
will become






1
0
1
1







i
f
i
o
v
R
R
V
V
A




(3.5)

and





i
i
v
i
i
f
o
V
V
A
V
R
R
V












1




(3.6)


The circuit will also change to be like the one in Figure 3.4, which is referred to as a
voltage
-
follower. It is used as a buffer amplifier to provide isolation properties (high
input imp
edance, low output impedance), hence it is also known as unity
-
gain buffer or
just as a buffer.









Figure 3.4 Voltage
-
follower


Vi
Rf
Ri
Vo
Vi
Vo
Summing (Adding) Amplifier


A summing amplifier provides algebraically addition to the voltages that are fed to one of
the

inputs, with each voltage multiplied by a constant
-
gain factor, which is determined by
the respective input resistances and feedback resistor. Figure 3.5 shows a circuit of a
summing amplifier with four input voltages and the output is given by



















4
4
3
3
2
2
1
1
V
R
R
V
R
R
V
R
R
V
R
R
V
f
f
f
f
o


(3.7)














Figure 3.5 Summing amplifier


Where voltages
V
1

through
V
4

are input voltages that are going to be added and resistors
R
1

through
R
4

are input resistors. If we make the input resistors to be of the same value,
that i
s,
R
1

= R
2

= R
3

= R
4

= R
i
, then equation (3.7) becomes








4
3
2
1
V
V
V
V
R
R
V
i
f
o









(3.8)


Integrator


The integrator circuit is almost the same as the inverting amplifier, but the feedback
resistor is replaced by a capacitor as shown in Figure 3.6.











Figure 3.6 Integrator


Since the Opamp has high input impedance, it draws negligible current, which results in
the current flowing through the input resistor to be the same as the current flowing
through the feedback capacitor. That is,

R1
V1
R2
V2
R3
V3
V4
Vo
Rf
R4
C
Vi
Vo
Ri




dt
dV
C
R
V
o
i
i








(3.9)


Integrating and re
-
arranging gives an output voltage






dt
V
C
R
V
i
i
o



1






(3.10)


Differential (Subtractor) Amplifier


The differential amplifier has two input signals: one to the inverting input and another to
th
e non
-
inverting input. These input voltage signals are fed to the Opamp inputs via input
resistors
R
i
s

and there is also a feedback resistor
R
f

to control the gain and another resistor
R
g

(equal to
R
f
) between non
-
inverting input and ground to improve comm
on
-
mode
rejection ratio, as shown in Figure 3.7.


















Figure 3.7 Differential amplifier


The output is equal to the amplified difference of the two input signals. That is,










1
2
2
1
V
V
R
R
V
V
R
R
V
i
f
i
f
o








(3.11)


ac Amplifier


The amplifier circ
uits shown in Figures 3.2 and 3.3 are general
-
purpose amplifiers and
they can amplify both ac and dc signals. However, by adding a capacitor between resistor
R
i

and ground to the non
-
inverting amplifier in Figure 3.3 the operation of the circuit can
be com
pletely changed for dc inputs. At dc the capacitor will have a very high
impedance, which will be infinite, and it will act as an open circuit. This will make the
gain of the amplifier at dc to be






1
1




f
v
R
A



Rg
Ri
V2
V1
Vo
Rf
Ri
As the frequency starts incr
easing above 0 Hz (dc), the impedance of the capacitor will
decrease, thus resulting in the gain increasing. At a certain frequency, which is
determined by the capacitor and resistor
R
i
, the gain will be 70.7% of the maximum gain
of the amplifier. This poi
nt is known as the cut
-
off, half
-
power, or low
-
frequency 3dB
point. The gain and the frequency at this point is given by





)
MAX
(
v
)
dB
(
v
A
.
A
707
0
3





(3.12)

And





i
i
c
C
R
f

2
1







(3.13)


At high frequencies the capacitor’s impedance become
s very small and can be neglected.
Thus making the gain to be






i
f
v
R
R
A


1




which is the maximum gain
A
v(MAX
)

of the ac amplifier. The ac amplifier circuits are
shown in Figure 8 for dual
-
rail and a single
-
rail supply.
















(a
)






(b)



Figure 8 ac amplifier circuits (a) with a split supply, and (b) with a single supply


For the ac amplifier in Figure 8 (b), which uses a single
-
rail supply the reference voltage
of the input has to be raised to a value that is above zero so as

to allow both positive and
negative swings of the output voltage. This is achieved by using two resistors,
R
1

and
R
2
,
which set the reference to a value that is equal to
cc
V
2
1
. During amplification this
reference voltage is not amplified

since it is dc but ac is amplified and since the reference
is above zero both the positive and negative swings will appear at the output of the
amplifier. Coupling capacitor
C
c

at the input and at the output of the amplifier are used to
confine the introd
uced reference voltage to the ac amplifier so that it does not interfere
with the circuits that are connected to the input or output of the amplifier. Their values
are chosen such that they offer little impedance to the signal of interest.

Vi
Vo
+
20V
Cc
Ci
Cc
Ri
1.527k
Rf
270k
R2
100k
R1
100k
-10V
Vi
Vo
+
10V
Ci
Ri
1.527k
Rf
270k
3.3.2 OPEN
-
LOOP
OPERATION


Comparator


The Opamp circuits covered so far operate in a closed loop mode; hence their gain is
predictable and controllable. The comparator, on the other hand, operates in an open
-
loop
mode; that is, there is no negative feedback to control th
e gain. The absence of gain
-

control drives the output into [negative or positive] saturation. If the inverting input is
greater than the non
-
inverting input, the output will go to negative saturation, but when
the non
-
inverting input is greater than the i
nverting input, the output will go to positive
saturation. In most comparator applications one input is held constant at value called
V
ref
,
which can be zero, greater than zero or less than zero, and the input voltage is only
applied to one of the comparat
or input. Like in amplifiers, comparator circuits come in
both inverting and non
-
inverting versions, where the inverting comparator introduces a
phase
-
shift of 180
0

with respect to the input signal. Some comparator circuits are shown
in Figure 3.9, where (
a) and (b) depict the non
-
inverting and inverting comparators with a
reference voltage of zero (zero
-
crossing detectors), respectively, and (c) and (d) depict
non
-
inverting comparators with positive (
V
ref

> 0) and negative (
V
ref

< 0) reference
voltages, re
spectively.








(a)











(b)



(c)




(d)


Figure 3.9 Comparators: (a) non
-
inverting, (b) inverting, (c) V
ref

> 0, and (d) V
ref

< 0


There are special IC such as LM311, LM339, LM306, LM393, NE521, NE527, and
TLC372, which are specifical
ly designed for use as comparators. Though an ordinary
Opamp can be used in many comparator circuits, the above
-
mentioned comparator ICs
have some advantages over ordinary Opamps. Firstly, they have a fast response than
ordinary Opamps, and secondly a pull
-
up resistor connected between output and supply
voltage can enable the output to swing from the supply voltage to ground, whereas in
ordinary Opamps the output can swing between the supply voltages minus 2 V.


The configuration of a comparator using a co
mparator IC is the same as that of ordinary
Opamps (Figure 3.9), but it also includes a pull
-
up resistor, which is not present when
using ordinary Opamp. This is shown in Figure 3.10 below, where resistor
R
1

is the pull
-
up resistor.





Vo
Vi
5V
R2
1k
R1
1k
Vo
Vi
-5V
R2
1k
R1
1k
Vo
Vi
Vo
Vi










Figure 3
.10 A comparator circuit using a comparator IC


Schmitt trigger


A Schmitt trigger is a comparator with a positive feedback resistor. The inclusion of the
positive feedback resistor ensures a rapid output transition, regardless of the speed of the
input wa
veform. It also widens the threshold by making the circuit to have two trip points
(TPs): upper threshold point (UTP) and lower threshold point (LTP). Figure 3.11 shows
the threshold for an ordinary comparator and a comparator with a positive feedback
(Sch
mitt trigger), where the Schmitt trigger has a wider threshold than the ordinary
comparator.




V
sat







V
sat
















UTP


TP







LTP



-
V
sat






-
V
sat




(a)







(b)



Figure 3.11 Threshold for an ordinary comparator and a Schmitt trigger


For noisy input signals the thin threshold in ordinary comparator will result in an erratic
output that jumps back and forth

between its low and high states when the input is near
the trip point (TP). The widened threshold in the Schmitt trigger minimises multiple
triggering, which results when a noisy input is near the threshold as shown in Figure 3.12.











Figure 3.12 Output waveforms of a comparator and a Schmitt trigger for a noisy input.

R1
1k
5V
Vo
Vi
V
SAT

V
SAT

TP

-
V
SAT

-
V
SAT

UTP

LTP

Input

Input

Output

Output

Some basic Schmitt trigger circuits of Schmitt triggers are shown in Figure 3.13, below.














(a)





(b)




(c)



F
igure 3.13 Schmitt trigger circuits: (a) Non
-
inverting, (b) & (c) inverting


The output voltage of the Schmitt trigger depends both on the input voltage and on its
recent history. That is, the output voltage will remain in a given state until the input
exc
eeds the reference voltage for that state.


For non
-
inverting Schmitt trigger:






sat
V
R
R
UTP
2
1







(3.14)

and







sat
V
R
R
LTP


2
1





(3.15)


Assume the output is negatively saturated. The feedback will result in a LTP at the non
-
inve
rting input. Since LTP is less than the voltage at the inverting input (which is zero),
the output will remain negatively saturated until the input is positive enough to make the
error voltage positive. When this happens, the output switches to positive sa
turation and
the voltage at the non
-
inverting input switches to UTP. The output remains until the input
is negative enough to make an error voltage negative, and when it does the output
changes to negative saturation and the non
-
inverting input changes to
LTP. This
phenomenon can be illustrated by a graph of output voltage versus input voltage as
shown in Figure 3.14.








V
o










LTP


UTP


V
in





Figure 3.14 Graph of output voltage versus input voltage

Vin
Vo
-15V
15V
+
R2
R1
+
Vin
Vo
-15V
15V
R2
R1
R3
+
Vin
Vo
5V
R2
R1

For inverting Schm
itt trigger:






sat
V
R
R
R
UTP
2
1
1







(3.16)

and







sat
V
R
R
R
LTP



2
1
1




(3.17)


Assume the output is positively saturated. The feedback will result in a UTP at the non
-
inverting input. The output will remain positively saturated until the
input is more than
UTP. When this happens, the output switches to negative saturation and the voltage at the
non
-
inverting input switches to LTP. The output remains low until the input is more
negative than LTP, and when it does the output changes to posit
ive saturation and the
non
-
inverting input changes to UTP. This phenomenon can be illustrated by a graph of
output voltage versus input voltage as shown in Figure 3.15.








V
o










LTP


UTP


V
in





Figure 3.15 Graph of o
utput voltage versus input voltage


The output voltage versus input voltage graphs shown in Figures 3.14 and 3.15 show that
the positive feedback causes the hysteresis. This hysteresis is equal to the difference
between the trip points. That is,










LTP
UTP
H







(3.18)


The hysteresis makes Schmitt trigger to be more immune to false triggering than ordinary
comparator. That is, it prevents noisy inputs from causing false triggering when the input
is near the threshold. However, for hyste
resis to be effective the peak
-
to
-
peak noise
voltage must be less than hysteresis.


Window
-
Comparator


A window comparator is an electronic circuit that consists of two comparators in parallel.
Each of the comparators has its own reference, which is comple
tely different from the
other. Unlike the ordinary comparator covered previously, a window comparator operates
as a window detector. The circuit for a window comparator is shown in Figure 3.16.






















Figure 3.16 Window comparators


3.3.3
OTHER OPAMP CIRCUITS


Constant current source


An external transistor can be connected at the output of an Opamp to make a current
source, as shown in Figure 3.17.

















Figure 3.17 Current source


Resistors
R
1

and
R
2

set the input voltage to
CC
in
V
R
R
R
V
2
1
2


. The feedback forces a
voltage equals supply voltage minus input voltage across resistor
R
3
, thus giving a
collector current that is equal to


Load
Vcc
R3
R2
R1
Q1
Vo2
Vo1
Vin
R1
390
R2
1k
R3
4k
R4
1k
A2
Vref2
A1
Vref1
5V
5V
Vo
Vin
A2
Vref2
A1
Vref1
5V
5V
R1
390
R2
1k
R3
4k
R4
1k




3
R
V
V
I
in
CC
C







(3.19)


which is almost the same to the emitter or load cu
rrent.


As an improvement to the current source circuit shown above, resistor
R
2

is replaced by a
zener diode to produce a stable reference voltage that is used as input voltage
V
in
.

Another output power transistor, mounted on a heatsink, is also added to

the existing
external transistor to form a Darlington pair that will provide more current to the load, as
shown in Figure 3.18.
















Figure 3.18 Improved current source suitable for high currents


The feedback forces a voltage equals reference (
zener or input) voltage across resistor
R
3
,
thus giving an emitter current that is equal to






3