Theme 2: Electronics Technology

Department of Electrical-Electronics Technology

This MODULE is prepared

for
Electronics and Communication Technology exit exam
examinees

Theme-2: Electronics Technology

2023/2024
ADDIS ABABA
ETHIOPIA

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Contents
I. Learning Objective.................................................................................................................................... 4
Chapter-1: Electronic Device and Their Application.......................................................................................... 5
1.1 Introduction ............................................................................................................................................. 5
1.2 Semiconductor and Diodes ..................................................................................................................... 5
1.3 Diode circuits (Applications) ................................................................................................................ 16
1.4 Op-amp................................................................................................................................................... 30
1.5 Tuning circuit ........................................................................................................................................ 41
Activities and Exercises .............................................................................................................................. 47
1.6 Multivibrator circuits ........................................................................................................................... 55
1.7 Assessments ............................................................................................................................................ 64
1.8 Summaries and Reviews ....................................................................................................................... 65
1.9 Resources and References .................................................................................................................... 66
Chapter- 2: Digital Electronics ...................................................................................................................... 67
2.1 Introduction ........................................................................................................................................... 67
2.2 Number Systems .................................................................................................................................... 73
Activities and Exercises .............................................................................................................................. 89
2.3 Binary coding schemes .......................................................................................................................... 90
Activities and Exercises .............................................................................................................................. 93
2.4 Logic gates.............................................................................................................................................. 93
2.5 Combinational logic gates and families ............................................................................................... 97
2.6 Boolean Expression for Logic Circuits .............................................................................................. 102
2.7 Assessments .......................................................................................................................................... 115
2.8 Summaries and Reviews ..................................................................................................................... 116
2.9 Resources and References .................................................................................................................. 117
Chapter -3: Power Electronics ..................................................................................................................... 118
3.1 Introduction ......................................................................................................................................... 118
3.2 Power electronic semiconductors ....................................................................................................... 125
3.3 The construction, working principles of Thyristors: SCR, IGBT, MOSFET... ............................ 127
3.4 Types of rectifiers ................................................................................................................................ 150
Activities and Exercises ............................................................................................................................ 158
3.5 Types of inverters ................................................................................................................................ 158
Activities and Exercises ............................................................................................................................ 159
3.6 Assessments .......................................................................................................................................... 163

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3.7 Summaries and Reviews ..................................................................................................................... 164

3.8 Resources and References .................................................................................................................. 165
II. Conclusions .................................................................................................................................. 166

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I. Learning Objective
Welcome, aspiring electronics & communication technology, to the Electronics and communication
Exit Exam Preparation Module! As you near the result of your academic journey in electronics &
communication, this module is designed to provide you with a comprehensive review of key concepts,
principles, and skills essential for success in your exit exam.

The primary objective of this module is to equip you with the knowledge, skills, and confidence
necessary to excel in your exit exam. Through focused study and practice, you will:

 Understand the operational principle of Semiconductor devices (Diodes, BJT and op-amp).
• Identify type of semiconductors diode
• Apply diode to different circuits
 Understand amplifiers and wave shaping.
• Distinguish Application of op-amp
• Apply tuning circuit
• Analyse multivibrator circuits
 Understand the basic and derived logic gates, Boolean algebra, digital logic circuits
(including combinational and sequential logic circuits).
• Compute the Number System Conversions (convert between decimal, binary, octal
and hexadecimal number systems).
• Discuss the different binary coding schemes
• Recall the different types of Logic Gates and their characteristics
• Apply Boolean operation and expression to simplify logic circuits
 Analyse the characteristics of power semiconductor devices.
• Explain the principles of operation of power electronic semiconductors
• Define the construction, working principles of SCR, IGBT and MOSFET
 Explain the principle of power converter device and know their applications.
• Differentiate types of rectifiers
• Use types of inverters

As you embark on this journey through the Electronics & communication Exit Exam Preparation
Module, remember that your dedication, perseverance, and commitment to excellence will be key to
your success. Stay focused, stay curious, and embrace the learning process with interest and
determination. Together, let us embark on this final leg of your academic adventure, as you prepare
to demonstrate your mastery of electronics & communication technology and embark on the next
phase of your professional journey.

Best wishes for a fruitful and rewarding learning experience!

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Chapter-1: Electronic Device and Their Application

1.1 Introduction
Definition: The branch of engineering which deals with current conduction through a Vacuum or
Gas or Semiconductor is known as Electronics.

An electronic device is any system or any other device that in which current flows through a vacuum
or gas or semiconductor.

Applications of Electronics:

Audio Systems, Video Systems, TV (Television), Computer, Laptop, Digital Camera, DVD Players,
Home and Kitchen Appliances, GPS, Mobiles Phones etc

 Conductors
 Insulators
 Semi-Conductors

Elements of an Atom

All matter is made up atoms. Atoms have a nucleus with electrons in motion around it. The
nucleus is composed of protons and neutrons (not shown). Electrons have a negative charge (-).
Protons have a positive charge (+). Neutrons are neutral. In the normal state of an atom, the number
of electrons is equal to the number of protons and the negative charge of the electrons is balanced by
the positive charge of the protons.

1.2 Semiconductor and Diodes

Classification of semiconductor materials
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 INTRINSIC &
 EXTRINSIC SEMICONDUCTOR

Depending upon the type of impurity added extrinsic semiconductors are classified into:

 N-type Semiconductor
 P-type Semiconductor

Intrinsic & Extrinsic Semiconductor

Intrinsic Semiconductor

A semiconductor in an extremely pure form is known as an intrinsic semiconductor.

When electric field is applied across an intrinsic semiconductor, the current conduction takes place
by two processes, namely: by free electrons and holes as shown in Figure below:

The total current inside the semiconductor is the sum of currents due to free electrons and holes.

The free electrons are produced due to the breaking up of some covalent bonds by thermal energy.
At the same time, holes are created in the covalent bonds.

Diagram showing the electronic bonds in an intrinsic semiconductor (Si)

Extrinsic Semiconductor

It is a semiconductor doped by addition of small amount impurity which is able to change its
electrical properties (conduction), making it suitable for electronic applications.
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This is achieved by adding a small amount of suitable impurity (having 3 or 5 valence electron) to a
semiconductor (having 4 valence electron).

It is then called impurity or extrinsic semiconductor.

The process of adding impurities to a semiconductor is known as doping.

If a pentavalent impurity (having 5 valence electrons) is added to the semiconductor, a large number
of free electrons are produced in the semiconductor.

If a trivalent impurity (having 3 valence electrons) is added to the semiconductor, large number of
holes are produced in the semiconductor crystal.

Depending upon the type of impurity added, extrinsic semiconductors are classified into:

i. n-type semiconductor
ii. p-type semiconductor

(i) n-type semiconductor

When a small amount of pentavalent impurity is added to a pure semiconductor, it is known as n-

type.

The addition of pentavalent impurity provides a large number of free electrons in the semiconductor
crystal.

Electrons are said to be the majority carriers whereas holes are the minority carriers.

Such impurities which produce n-type semiconductor are known as donor impurities because they
donate or provide free electrons to the semiconductor crystal.

Schematic representation of electronic bonds in a Silicon crystal doped with Phosphorus P (n

doping)

(ii) p-type Semiconductor

When a small amount of trivalent impurity is added to a pure semiconductor, it is called p-type

The addition of trivalent impurity provides a large number of holes in the semiconductor.

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Such impurities which produce p-type semiconductor are known as acceptor impurities because the
holes created can accept the electrons.

Electrons are said to be the minority carriers whereas holes are the majority carriers.

Schematic representation of a Si crystal doped with boron (P doping)

Semiconductor Diode

A diode is a 2 lead semiconductor that acts as a one way gate to electron flow. It allows current to
pass in only one direction.

A PN-junction diode is formed by joining together N-type and P-type silicon.

How Diode Works

When a diode is connected to a battery as shown, electrons from the n-side and holes from the p-side
are forced toward the center by the electrical field supplied by the battery.

The electrons and holes combine causing the current to pass through the diode.

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When a diode is arranged in this way, it is said to be forward biased.

Forward-biased (“open door”)

(a) (b)

(a) Forward bias diode (b) I-V Characteristics

How it doesn’t work

When a diode is connected to a battery as shown, holes in the N-side are forced to the left while
electrons in the P-side are forced to the right.

It results in an empty zone around the PN- junction that is free of charge carries creating a depletion
region.
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This depletion region acts as an insulator preventing current from flowing through the diode.

When a diode is arranged in this way, it is said to be reverse biased.

Reverse-biased

The following graph shows the state of diode conduction in forward and reverse biased conditions.

During the reverse bias, current produced through minority carriers exist known as “Reverse
current”. As the reverse voltage increases, this reverse current increases and it suddenly breaks down
at a point, resulting in the permanent destruction of the junction.

Diode Analysis
Ideal versus Practical Diodes

Definition of Diode Current and Voltage

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Diode specifications ratings and parameters

 Semiconductor material
 Diode type
 Forward voltage drop
 Peak Inverse Voltage
 Maximum forward current
 Junction operating temperature
 Leakage current
 Junction capacitance

Load-Line Analysis

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The point where the load line and the characteristic curve intersect is the Q-point, which identifies
ID and VD for a particular diode in a given circuit.

DIODE CONFIGURATIONS
 Series Diode Configurations
 Parallel Diode Configurations

Series Diode Configurations

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Example 2.4

For the series diode configuration of Fig. 2.13, determine VD, VR, and ID.

Solution: Since the applied voltage establishes a current in the clockwise direction to match the
arrow of the symbol and the diode is in the “on” state,

Repeat Example 2.4 with the diode reversed.

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Solution: Removing the diode, we find that the direction of I is opposite to the arrow in the diode
symbol and the diode equivalent is the open circuit. The result is the network of Fig. 2.14, where
ID= 0 A due to the open circuit. Since VR= IRR, we have VR = (0) R = 0 V. Applying Kirchhoff’s
voltage law around the closed loop yields

Parallel Diode Configurations

The methods applied in Section 2.3 can be extended to the analysis of parallel and series– parallel
configurations. For each area of application, simply match the sequential series of steps applied to
series diode configurations.

EXAMPLE 2.10

Determine Vo, I1, ID1, and ID2 for the parallel diode configuration of Fig. below.

EXAMPLE 2.13

Determine the currents I1, I2, and ID2 for the network of Fig. 2.37
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Solution:

The applied voltage is such as to turn both diodes on, as indicated by the resulting current directions
in the network of Fig. 2.38. The solution is obtained through an application of techniques applied to
dc series–parallel networks.

Applying Kirchhoff’s voltage law around the indicated loop in the clockwise direction yields

At the bottom node a

Diode Equivalent Circuits

An equivalent circuit is a combination of elements (like R, L, C etc.) properly chosen to best

represent the actual characteristics of device in a particular operating region.

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3 types of diode equivalent ckt

 ideal equivalent circuit

 piecwise-linear equivalent circuit
 constant voltage drop or simplified equivalent circuit

Types of diodes

There are many types of diodes depending upon many factors such as the frequency used, their
working and construction, their applications etc.

Junction diodes

The junction diodes are the normal PN junction diodes but differ in construction. There are three
types of junction diodes, as shown in the following figure.

1.3 Diode circuits (Applications)

Practical Applications

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Rectifier Diode
Rectification is the process of turning an alternating current waveform into a direct current
waveform, i.e., creating a new signal that has only a single polarity. In this respect it's reminiscent of
the common definition of the word, for example where “to rectify the situation” means “to set
something straight”. Before continuing, remember that a DC voltage or current does not have to
exhibit a constant value (like a battery). All it means is that the polarity of the signal never changes.
To distinguish between a fixed DC value and one that varies in amplitude in a regular fashion, the
latter is sometimes referred to as pulsating DC.

The concept of rectification is crucial to the operation of modern electronic circuits. Most electronic
devices such as a TV or computer require a fixed, unchanging DC voltage to power their internal
circuitry. In contrast, residential and commercial power distribution is normally AC. Consequently,
some form of AC to DC conversion is required. This is where the asymmetry of the diode comes in.

Half-wave Rectification

To understand the operation of a single diode in an AC circuit, consider the diagram of Figure 1.16.
If an alternating voltage is applied across a diode in series with a load, a pulsating voltage will
appear across the load only during the half cycles of the ac input during which the diode is forward
biased. Such rectifier circuit, as shown in Figure 1.20, is called a half-wave rectifier. The secondary
of a transformer supplies the desired ac voltage across terminals A and B. When the voltage at A is
positive, the diode is forward biased and it conducts. When A is negative, the diode is reverse-biased
and it does not conduct. The reverse saturation current of a diode is negligible and can be considered
equal to zero for practical purposes. (The reverse breakdown voltage of the diode must be
sufficiently higher than the peak ac voltage at the secondary of the transformer to protect the diode
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from reverse breakdown.) Therefore, in the positive half-cycle of ac there is a current through the
load resistor RL and we get an output voltage, as shown in Figure 1.20(b), whereas there is no
current in the negative half cycle. In the next positive half-cycle, again we get the output voltage.
Thus, the output voltage, though still varying, is restricted to only one direction and is said to be
rectified. Since the rectified output of this circuit is only for half of the input ac wave it is called as
half-wave rectifier.

Figure 1.20. (a) Half-wave rectifier circuit, (b) Input ac voltage and output voltage waveforms from
the rectifier circuit. [1]

The resulting signal seen across the load resistor is a pulsating DC waveform. We have effectively
removed the negative half of the waveform leaving just the positive portion. Because only half of the
input waveform makes it to the load, this is referred to as half-wave rectification.

It is worth noting that if the AC peak input voltage is not particularly large; there can be an obvious
discrepancy between the peak levels of the input and load signals. For example, if the peak input
voltage is in the range of three or four volts and a silicon diode is used, the resulting waveforms
would look more like Figure 1.21.

The effect of using a silicon diode with VK =0.7V

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Figure 1.21. Half-wave rectification waveforms including forward diode drop.[2]

In this case the 0.7 volt forward drop cannot be ignored as it represents a sizable percentage of the
input peak. The positive pulses are also slightly narrowed as current will not begin to flow at
reasonable levels until the input voltage reaches 0.6 to 0.7 volts.

If the diode was oriented in reverse, it would block the positive portion of the input and allow only
the negative portion through.

Smoothing (Filtering) the Output The second issue we have is smoothing and leveling the pulsating
DC. The most straightforward method to achieve this is to add a capacitor in parallel with the load.
The capacitor will charge up during the conduction phase, thus storing energy. When the diode turns
off, the capacitor will begin to discharge, thus transferring its stored energy into the load.

The larger the capacitor, the greater its storage capacity and the smoother the load voltage will be. It
turns out that there is a down side to large capacitors, as we shall see. Consequently, the goal will not
be to use as large of a capacitor as possible but rather to use an optimal size for a given application.
A half-wave rectifier with transformer and capacitor is shown in Figure 1.22.

Figure 1.22. Half-wave rectifier with transformer and filter capacitor. [2]

Full-wave Rectification

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An improvement on half-wave rectification is full-wave rectification. Half-wave rectification is

inefficient because it essentially throws away the negative portion of the input. In contrast, full-wave
rectification makes use of the negative portion by inverting or flipping its polarity. The resulting
circuit is modestly larger and more complicated but results in large performance improvements. For
example, filter capacitor size is greatly reduced.

There are two popular methods to achieve full-wave rectification. The first method uses a pair of
diodes with a center-tapped (i.e., split) secondary. The second method uses a four diode bridge
network. The diode bridge form is also capable of producing a bipolar output (i.e., a positive output
along with a negative output, typically of the same magnitude).

The two diode center-tapped secondary circuit is shown in Figure 1.22. This schematic also includes
the filter capacitor.

Figure 1.22. Full-wave center-tapped rectifier with capacitor. [2]

The operation is as follows. During the positive half of the source voltage diode D1 is forward-
biased while D2 is reverse-biased. Therefore the upper half of the secondary behaves like a simple
half-wave rectifier allowing current to flow through D1 and into the load. Due to the reverse-bias on
D2, the lower half presents an open circuit and is effectively removed. In mirror fashion, when the
applied potential switches polarity D1 will be reverse-biased while D2 becomes forward-biased.
Current is now free to flow through D2 into the load.

Thus, both halves of the input waveform are used. The resulting waveforms are illustrated in Figure
1.23. For clarity, the filtering effect of the capacitor is not shown and Vin represents one half of the
total secondary voltage.
Full-wave: Vdc = 0.636Vm

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Figure 1.23. Full-wave rectifier waveforms. [2]

An important point to remember about this configuration is that the load only “sees” half of the
secondary at any given time. Therefore, the load voltage will only be half of the total secondary
voltage (minus one forward diode drop). For example, if the transformer has a 10:1 turns ratio and is
being fed from a standard 120 volt source, the secondary will produce 12 volts RMS. Ignoring the
diode drop, the load would see half of this, or 6 volts RMS (about 8.5 volts peak). Typically,
transformers are rated by their total secondary voltage so this transformer would be referred to as
having a “12 volt center-tapped secondary”.

A four-diode bridge rectifier is shown in Figure 1.24. A filter capacitor is included. Also, note the
usage of a standard non center-tapped secondary. As this is a very common configuration, the four-
diode bridge is available as a single four-lead part in a variety of sizes and current capacities.

Figure 1.24. Full-wave bridge rectifier with capacitor. [2]

The operation of this circuit is illustrated in Figure 1.25 for the positive portion of the input. First,
current flows from the top of the secondary to the D1/D2 junction. Only D2 offers a forward-bias
path so current flows through D2 to the junction with D4 and the load. As D4 presents a reverse-bias
path, current must flow down through the load. From ground, current continues to the D1/D3
junction. Although at first glance it appears that current could flow through either diode, remember
that the cathode of D1 is tied to the high side of the secondary.

Therefore, its potential must be higher than the anode side, making it reverse-biased. Consequently,
the current flows down through D3. A similar situation occurs at D4 and current is directed back to
the low side of the secondary. In short, D2 and D3 are forward-biased while D1 and D4 are reverse-
biased. The load sees the entire secondary voltage minus two forward diode drops.

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Figure 1.25. Full-wave bridge rectifier analysis, positive input. [2]

During the negative polarity portion of the input the situation is reversed as illustrated in Figure 1.26.
Current will flow from the bottom of the secondary through D4, down through the load, and finally
back to the top of the secondary via D1. Thus, D1 and D4 are forward-biased while D2 and D3 are
reverse-biased. The important thing is that in both cases, the current flows down through the load,
top to bottom, resulting in a positive output voltage.

Figure 1.26. Full-wave bridge rectifier analysis, negative input. [2]

Example 1.3

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Design a rectifier/filter that will produce an output voltage of approximately 30 volts with a
maximum current draw of 300 milliamps. It is to be fed from a 120 VAC RMS source. The ripple
voltage should be less than 10% of the nominal output voltage at full load.

For this design we shall focus on using common off-the-shelf parts. As we have seen, the full-wave
rectifiers are more efficient at converting AC to DC so we shall go that route, specifically, a four
diode bridge arrangement. We will use the circuit of Figure 1.22 as a guide.

The first item to consider is the size of the transformer. A 30 volt output would require a peak
secondary voltage of at least 32 volts as we must add in two forward diode drops. The equivalent
RMS value is 32/√2 or 22.6 volts. At full load the filtered output voltage will droop somewhat so a
somewhat larger value is called for. A standard 24 volt secondary should suffice. Given the 300
milliamp load current rating, the transformer must be at least 0.3 amps * 24 volts or 7.2 VA.

As far as the capacitor is concerned, it must be rated for the peak voltage. The peak equivalent is 24
VAC RMS * √2 or 34 volts. Although a 35 volt rated capacitor might be tried, a standard 50 volt
rating would leave a generous safety margin and increase reliability. To find the capacitance value
we must first find the effective worst case load impedance.

This is apparent by noting how far the output voltage has dropped by midway through the off portion
of the cycle. Consequently, we will need a larger time constant, perhaps by a factor of two. That puts
us at 200 milliseconds.

Clipper and Clamper Circuits

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Wave shaping circuits are the electronic circuits, which produce the desired shape at the output
from the applied input wave form. These circuits perform two functions −

 Attenuate the applied wave

 Alter the dc level of the applied wave.
There are two types of waves shaping circuits: Clippers and Clampers.

Clippers

A clipper is an electronic circuit that produces an output by removing a part of the input above or
below a reference value. That means, the output of a clipper will be same as that of the input for
other than the clipped part. Due to this, the peak to peak amplitude of the output of a clipper will be
always less than that of the input.

The main advantage of clippers is that they eliminate the unwanted noise present in the
amplitude of an ac signal.

Clippers can be classified into the following two types based on the clipping portion of the input.
 Positive Clipper
 Negative Clipper
Clipper circuits, also called limiter circuits, are used to eliminate portion of a signal that are above
or below a specified level – clip value.

The purpose of the diode is that when it is turn on, it provides the clip value

Clip value = V’. To find V’, use KVL at L1

The equation is: V’ – VB - V = 0  V’ = VB + V

(a) (b)

Figure 3.12.

Then, set the conditions

If Vi> V’, what happens? diode conducts, hence Vo = V’
If Vi < V’, what happens? diode off, open circuit, no current flow, Vo = Vi

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Single Diode Clipper

Figure 3.13.

Figure 3.14. Clipper circuit

Application:

Limit input voltage to an electronic circuit to prevent component damage.

Parallel Based Clippers

The shunt clipper contains a diode that is in parallel with the load.

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Figure 3.15. Shunt Clipper

 Positive and negative clipping can be performed simultaneously by using a double limiter or a
parallel-based clipper.

Figure 3.16.

Figure 3.17.

 The parallel-based clipper is designed with two diodes and two voltage sources oriented in
opposite directions.
 This circuit is to allow clipping to occur during both cycles; negative and positive
Clipper – Diode in Series
As shown in Figure below, the series clipper contains a diode that is in series with the load.

Figure 3.18.

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The series clipper is a familiar circuit. The half-wave rectifier is nothing more than a series clipper.
When the diode in the series clipper is conducting, the load waveform resembles the input
waveform. When the diode is not conducting, the output is approximately 0 V. The direction of the
diode determines the polarity of the output waveform. If the diode symbol (in the schematic
diagram) points toward the source, the circuit is a positive series clipper, meaning that it clips the
positive alternation of the input. If the diode symbol points toward the load, the circuit is a negative
series clipper, meaning that it clips the negative alternation of the input.

Ideally, a series clipper has an output of when the diode is conducting (ignoring the voltage
across the diode). When the diode is not conducting, the input voltage is dropped across the diode,
and .

Clampers (DC Restorer)

A clamper is a circuit that is designed to shift a waveform above or below a dc reference voltage
without altering the shape of the waveform. This results in a change in the dc average of the
waveform. Both of these statements are illustrated in Figure below (The clamper has changed the dc
average of the input waveform from 0 V to +5 V without altering its shape.)

Figure 3.19. A clamper with its input and (ideal) output waveforms.

A clamper is an electronic circuit that produces an output, which is similar to the input but with a
shift in the DC level. In other words, the output of a clamper is an exact replica of the input. Hence,
the peak-to-peak amplitude of the output of a clamper will be always equal to that of the input.

Clampers are used to introduce or restore the DC level of input signal at the output. There are two
types of op-amp based clampers based on the DC shift of the input.

 Positive Clamper
 Negative Clamper
Clamping shifts the entire signal voltage by a DC level.

 Consider, the sinusoidal input voltage signal, vI.

 1st 900, the capacitor is charged up to the peak value of Vi which is VM.
 Then, as Vi moves towards the –ve cycle,
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 the diode is reverse biased.

 Ideally, capacitor cannot discharge, hence Vc = VM
 By KVL, we get
VO = -VC + VI = -VM + VM sint

Figure 3.20.

NOTE: The input signal is shifted by a dc level; and that the peak-to-peak value is the same

A clamping circuit that includes an independent voltage source VB.

Figure 3.21.
STEP 1: Knowing what value that the capacitor is charged to. And from the polarity of the diode,
we know that it is charged during positive cycle. Using KVL,

VC + VB – VS = 0  VC = VM – VB

STEP 2: When the diode is reversed biased and VC is already a constant value

VO – VS + VC = 0  VO = VS – VC.

Example

What is Vo if the diode is non-ideal?

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The diode is a non-ideal with V = 0.7V

(a) (b)

Figure 3.22.

Step 1: VC + V - VB – Vi = 0  VC = 10 + 5 – 0.7 = 14.3V

Step 2: VO – Vi + VC = 0  VO = Vi – Vc=10-14.3= -4.3

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1.4 Op-amp
Typical functions of amplifiers in electronic systems:

An amplifier is used to increase the amplitude of a signal waveform, without changing other
parameters of the waveform such as frequency or wave shape. They are one of the most commonly
used circuits in electronics and perform a variety of functions in a great many electronic systems.
The general symbol for an amplifier is shown in Figure 2.1. The symbol gives no detail of the type
of amplifier described, but the direction of signal flow can be assumed (as flowing from left to right
of the diagram). Amplifiers of different types are also often described in system or block diagrams
by name.

Figure 2.1. Amplifier general symbol, used in system diagrams. [3]

o Operational Amplifiers (usually called ‘op amps’) were originally made from discrete
components, being designed to solve mathematical equations electronically, by performing
operations such as addition and division in analogue computers.
o Now op amps are produced in integrated-circuit (IC) form.
o Op amps have many uses, with one of the most important being as a high gain d.c. and a.c.
voltage amplifier.
o Op amp is a high-gain DC-coupled amplifier with a differential input and single ended
output.
o In nearly all amplifier applications, the op-amp is used with negative feedback (“closed-
loop”),
o The closed-loop gain of the amplifier depends primarily on the feedback network
components, and not on the op-amp itself.
o It is widely used as a basic building block in electronic designs.

Operational Amplifier - An operational amplifier (op amp) is a high gain differential amplifier with
nearly ideal external characteristics. Internally the op amp is constructed using many transistors.

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Figure 2.2. Op-amp symbol. [3]

Terminologies:

V+ = non-inverting input voltage

V- = inverting input voltage

Vo = output voltage

Io = output current

I+ = non-inverting input current

I- = inverting input current

±VDC = positive and negative DC supply voltages used to power the op amp (typically ±5V to
±30V)

ΔV = V+ - V- = difference voltage

The main properties of an op amp include:

i. A very high open-loop voltage gain Ao of around 105 for d.c. and low frequency a.c., which
decreases with frequency increase.
ii. Very high input impedance, typically 106 W to 1012 W such that current drawn from the
device, or the circuit supplying it, is very small and the input voltage is passed on to the op
amp with little loss.
iii. A very low output impedance, around 50-75W, such that its output voltage is transferred
efficiently to any load greater than a few kilo ohms.
iv. The operation of an op amp is most convenient from a dual balanced d.c. power supply ± VS
(i.e. +VS, 0, -VS); the centre point of the supply, i.e. 0 V, is common to the input and output
circuits and is taken as their voltage reference level.
v. The power supply connections are not usually shown in a circuit diagram.
vi. An op amp is basically a differential voltage amplifier.

Typical Values of an OP AMP

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Property Ideal Real

Voltage gain ∞ 105 - 109
Input resistance ∞Ω 106Ω
Input current 0A 10-12 – 10-8A
Output resistance 0Ω 100-1000 Ω
Bandwidth Very wide Narrow
Table: Values of an Op-am

Op-Amps configuration

 Op-Amps can be configured in many different ways using resistors and other components.
 Most configurations use feedback.

Applications of Op-Amps

 Amplifiers provide gains in voltage or current.

 Op-Amps can convert current to voltage.
 Op-Amps can provide a buffer between two circuits.
 Op-Amps can be used to implement integrators and differentiators.
 Op-Amps can be used to implement Adder or Summing and Subtractor or Differential
 Active filters:-Low pass and band pass filters.

Basic Op-Amp circuits

The Golden rules for Op-Amp circuit analysis

(V+) + (V-) = 0

(I+) = (I-) = 0

Figure 2.7. Op-amp circuit. [3]

The voltage between both inputs of the Op amp is forced to be 0.

There is no short circuit between both inputs because the current is also 0.

The circuit between both inputs is called virtual-short-circuit: v = 0; I = 0.

Gain is so high (~ 106) that a few μV at the input will swing the output over its full range, so any
feedback control of Vout attempts to do whatever is necessary to make the voltage difference
between the inputs zero. The input impedance of Op-Amps is very high so it draws very little input
current (0.08 μA for the 741; picoamps for FET-input types). Thus the input current is negligible.
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Types of Feedback

The process of injecting a fraction of output energy to the input of any device is called feedback

Figure 2.11. Negative and positive feedbacks. [3]

Negative Feedback

As information is fed back, the output becomes more stable. Output tends to stay in the desired
range.

Examples: cruise control, heating/cooling systems

Positive Feedback

As information is fed back, the output destabilizes. The Op-Amp will saturate.

Examples: Oscillator

Op-Amp Circuits use Negative Feedback

Negative feedback is the process whereby a portion of the output voltage of an amplifier is returned
to the input with a phase angle that opposes (subtract form) the input signal.

This lowers the amplifier’s gain, but improves:

Freedom from distortion and nonlinearity

Flatness of frequency response or conformity to some desired frequency response

Stability and Predictability

Insensitivity to variation in Aol

Amplifiers with negative feedback depend less and less on the open-loop gain and finally depend
only on the properties of the feedback network itself.

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Figure 2.12. Op-amp circuit use negative feedback. [3]

Op-amp types

Operational amplifiers can be connected using external resistors or capacitors in a number of

different ways to form basic "Building Block" circuits such as, Inverting, Non- Inverting, Voltage
Follower, Summing, Differential, Integrator and Differentiator type amplifiers. There are a very
large number of operational amplifier IC's available to suit every possible application.

The most commonly available and used of all operational amplifiers is the industry standard 741
type IC.

Figure 2.21. Industry standard 741 type IC. [3]

Inverting and Non-inverting amplifiers

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Figure 2.28. Inverting and Non inverting amplifiers. [3]

Inverting Amplifier

Signal and feedback resistor, connected to inverting (-) input.

v+ = v- connected to ground or v- is virtual ground.

Figure 2.29. Inverting amplifier. [3]

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iS  iF  iin  0
i S  i F
vS  v  vout  v 
 
RS RF
vS  0 v 0
  out
RS RF
RF
vout   vS
RS

vout R
Gain   F
vS RS  
v+ grounded, so: v  v  0

Example

Find the closed loop gain of the following inverting amplifier circuit.

Figure 2.30. Closed loop inverting amplifier circuit. [3]

Gain (Av) = Vout/Vin = - Rf/Rin

Substitute the values of the resistors in the circuit as follows, Rin =10kΩ and Rƒ = 100kΩ, and the
gain of the circuit is calculated as:

A = -Rƒ/Rin = 100k/10k = -10.

Adder or Summing:

Sum of all the i/p signals appear at the o/p as shown in Figure 2.58.

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Figure 2.58.

Summing Op-amp

Summing amplifier can be used to add ac or dc signals.

When an op amp is connected as a multi-input inverting amplifier, the output signal is given by:
𝑣1 𝑣2 𝑣3
𝑣0 = −𝑅𝑓 [ + + ]
𝑅1 𝑅2 𝑅3

If R 1 = R2 = R 3 = Rf

Then, Vout = - [V1 + V2 + V3]

Or

If it is assumed that the inverting (-) terminal of the op amp draws no input current, all of it passing
through Rf, then:

I = I1 + I2 + I3

Since X is a virtual earth (i.e. at 0 V), it follows that:

𝑣0 𝑣1 𝑣2 𝑣3
− =[ + + ]
𝑅𝑓 𝑅1 𝑅2 𝑅3

𝑣1 𝑣2 𝑣3
𝑣0 = −𝑅𝑓 [ + + ]
𝑅1 𝑅2 𝑅3

Such circuits may be used as ‘mixers’ in audio systems to combine the outputs of microphones
electric guitars, pick-ups, etc.

One of the advantages of inverting op-amp mixers is that there is no interaction between the inputs.

The virtual GND (inverting input) prevents one input signal from appearing at the other inputs.

They are also used to perform mathematical process of addition in analogue computing.

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Subtractor or Differential:

Op-amp can be used in subtracting mode.

It is a circuit that can provide the difference between the two inputs.

With all resistors equal the output is given by:

Vout = V2 – V1 for Rf = R1 = R2 = R3

Figure 2.59.

Integrator:

The feedback occurs via a capacitor C, rather than via a resistor in an inverting amplifier.

Integration is a process of continuous addition.

The current through resistor R is supplied by charging the feedback capacitor.

Figure 2.60.

Op-amp Integrator

For a constant input signal the charging current of capacitor is constant.

Hence the voltage across capacitor increases as a linear function of time and a negative ramp appears
at the output.

Integrator is widely used for voltage to frequency convertor.

The output voltage is given by:

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1
𝑣0 = − ∫ 𝑣𝑖 ⅆ𝑡
𝐶𝑅
Since X is a virtual earth in the above figure, i.e. at 0V, the voltage across R is Vi and that across C
is Vo.

Assuming again that none of the input current I enters the op-amp inverting (-) input, then all of
current I flows through C and charges it up.

If Vi is constant, I - will be a constant value given by:

I = Vi/R

Capacitor C therefore charges at a constant rate and the potential of the output side of C charges so
that the feedback path absorbs I.

If Q is the charge on C at time t and the p.d. across it (i.e. the output voltage) changes from 0 to Vo
in that time then:

Q = -VoC =It

i.e. –VoC = (Vi/R)t and

Vo = -(1/CR)Vit

This result is the same as would be obtained from

1
𝑣0 = − 𝐶𝑅 ∫ 𝑣𝑖 ⅆ𝑡. If:

Vi is a constant value.

e.g., if the input voltage Vi = -2V and, say CR =1S then

Vo = -(-2)t =2t

A graph of Vo/t will be a ramp function as shown in Figure 2.61.

(Vo = 2t is of the straight line form y =mx + c; in this case y=Vo and x=t, gradient, m=2 and vertical
axis intercept c = 0).

Vo rises steadily by +2V/s in figure below, and if the power supply is, say,
+ 9V, then Vo reaches +9V after 4.5s when the op-amp saturates.

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Figure 2.61.

The voltage waveform of the integrator of the above example

Differentiator:

Differentiator is an op-amp circuit that has an output voltage proportional to the instantaneous rate of
change of the input voltage.

The differentiator gives an output voltage that is proportional to the rate of change (slope) of the
input voltage.

To prevent magnifying high ‐ frequency noise, series resistance R is included in the circuit as shown
in Figure 2.62. (a).

(b)

Figure 2.62.

A differentiator circuit

ⅆ𝑄 ⅆ𝑣
𝐼= =𝐶
𝑡 ⅆ𝑡
The current is converted to a voltage

ⅆ𝑉𝑖𝑛
𝑣𝑜𝑢𝑡 = −𝑖𝑅𝑓 = −𝑅𝑓 𝑐𝑖
ⅆ𝑡
An amplifier can utilize the relation between charge and current.

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1.5 Tuning circuit

TUNED AMPLIFIERS
Amplifiers which amplify a specific frequency or narrow band of frequencies are called Tuned
Amplifiers.

Tuned amplifiers are mostly used for the amplification of high or radio frequencies. It is because radio
frequencies are generally single and the tuned circuit permits their selection and efficient
amplification. However, such amplifiers are not suitable for the amplification of audio frequencies as
they are mixture of frequencies from 20 Hz to 20 kHz and not single. Tuned amplifiers are widely
used in radio and television circuits where they are called upon to handle radio frequencies.

Figure 2.38. Tuned circuit. [4]

Figure 2.39 shows the circuit of a simple transistor tuned amplifier. Here, instead of load resistor, we
have a parallel tuned circuit in the collector. The impedance of this tuned circuit strongly depends
upon frequency. It offers a very high impedance at resonant frequency and very small impedance at
all other frequencies. If the signal has the same frequency as the resonant frequency of LC circuit,
large amplification will result due to high impedance of LC circuit at this frequency. When signals of
many frequencies are present at the input of tuned amplifier, it will select and strongly amplify the
signals of resonant frequency while rejecting all others (For all other frequencies, the impedance of LC
circuit will be very small. Consequently, little amplification will occur for these frequencies). Therefore, such
amplifiers are very useful in radio receivers to select the signal from one particular broadcasting station
when signals of many other frequencies are present at the receiving aerial.

Figure 2.39. A simple transistor tuned amplifier [4]

Bandwidth of Amplifier
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Frequency Response of Tuned Amplifier

The voltage gain of an amplifier depends upon β, input impedance and effective collector load. In a
tuned amplifier, tuned circuit is used in the collector. Therefore, voltage gain of such an amplifier is
given by:

Voltage gain = βZc/Zin

Where ZC = effective collector load

Zin = input impedance of the amplifier

The value of ZC and hence gain strongly depends upon frequency in the tuned amplifier. As ZC is
maximum at resonant frequency, therefore, voltage gain will be maximum at this frequency. The
value of ZC and gain decrease as the frequency is varied above and below the resonant frequency.
Figure 2.28 shows the frequency response of a tuned amplifier. It is clear that voltage gain is
maximum at resonant frequency and falls off as the frequency is varied in either direction from
resonance.

Bandwidth: The range of frequencies at which the voltage gain of the tuned amplifier falls to 70.7
% of the maximum gain is called its bandwidth. Referring to Figure 2.40, the bandwidth of tuned
amplifier is f1 − f2. The amplifier will amplify nicely any signal in this frequency range. The
bandwidth of tuned amplifier depends upon the value of Q of LC circuit i.e. upon the sharpness of
the frequency response. The greater the value of Q of tuned circuit, the lesser is the bandwidth of the
amplifier and vice-versa. In practice, the value of Q of LC circuit is made such so as to permit the
amplification of desired narrow band of high frequencies. The practical importance of bandwidth of
tuned amplifiers is found in communication system. In radio and TV transmission, a very high
frequency wave, called carrier wave is used to carry the audio or picture signal. In radio
transmission, the audio signal has a frequency range of 10 kHz. If the carrier wave frequency is 710
kHz, then the resultant radio wave has a frequency range between (710 –5) kHz and (710 +5) kHz.
Consequently, the tuned amplifier must have a bandwidth of 705 kHz to 715 kHz (i.e. 10 kHz). The
Q of the tuned circuit should be such that bandwidth of the amplifier lies in this range.

Figure 2.40. Frequency response of a tuned amplifier. [4]

Distinction between Tuned Amplifiers and other Amplifiers

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We have seen that amplifiers (e.g., voltage amplifier, power amplifier etc.) provide the constant gain
over a limited band of frequencies i.e., from lower cut-off frequency f1 to upper cut-off frequency f2.
Now bandwidth of the amplifier is, BW = f2 − f1. The difference between tuned and other amplifiers
is that tuned amplifiers are designed to have specific, usually narrow bandwidth. This point is
illustrated in in Figure 2.41.(a). Note that BWS is the bandwidth of standard frequency response
while BWT is the bandwidth of the tuned amplifier. In many applications, the narrower the bandwidth
of a tuned amplifier, the better it is.

(a) (b)

Figure 2.41. Tuned and un-tuned amplifier. [4]

Consider a tuned amplifier that is designed to amplify only those frequencies that are within ± 20
kHz of the central frequency of 1000 kHz (i.e., fr = 1000 kHz ). Here [See Fig. 2.41.(b)], f1 = 980
kHz, fr = 1000 kHz, f2 = 1020 kHz, BW = 40 kHz This means that so long as the input signal is
within the range of 980 – 1020 kHz, it will be amplified. If the frequency of input signal goes out of
this range, amplification will be drastically reduced.

Parallel and Series Resonance in an Amplifier

Analysis of Parallel Tuned Circuit
A parallel tuned circuit consists of a capacitor C and inductor L in parallel as shown in Figure 2.30
(i). In practice, some resistance R is always present with the coil. If an alternating voltage is applied
across this parallel circuit, the frequency of oscillations will be that of the applied voltage. However,
if the frequency of applied voltage is equal to the natural or resonant frequency of LC circuit, then
electrical resonance will occur. Under such conditions, the impedance of the tuned circuit becomes
maxiimum and the line current is minimum. The circuit then draws just enough energy from a.c.
supply necessary to overcome the losses in the resistance R.

Parallel resonance: A parallel circuit containing reactive elements (L and C) is resonant (In an a.c.
circuit if applied voltage and supply current are in phase (i.e., in step with), resonance is said to occur. If this
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happens in a parallel a.c. circuit, it is called parallel resonance.) when the circuit power factor is unity
i.e. applied voltage and the supply current are in phase. The phasor diagram of the parallel circuit is
shown in Figure 2.42 (ii). The coil current IL has two rectangular components that is to say active
component IL cos φL and reactive component IL sin φL. This parallel circuit will resonate when the
circuit power factor is unity. This is possible only when the net reactive component of the circuit
current is zero i.e.

Figure 2.42. Phasor diagram of the parallel circuit. [4]

IC - IL sin φL = 0

or IC = IL sin φL

Resonance in parallel circuit can be obtained by changing the supply frequency. At some frequency
fr (called resonant frequency), IC = IL sin φL and resonance occurs.

Resonant frequency: The frequency at which parallel resonance occurs (i.e. reactive component of
circuit current becomes zero) is called the resonant frequency fr.

At parallel resonance, we have, IC = IL sin φL

Now I L = V/ZL ; sin  L = X L /ZL and IC = V/X C

Therefore, V/X C =V/ZL * X L /ZL
or X L X C =ZL 2
L
or  Z L 2  R 2  X L 2 ................................(i )
C
L
or  R 2  (2 f r L) 2
C
L
or (2 f r L) 2   R 2
C
L
or 2 f r L   R2
C
1 L
or fr   R2
2 L C
1 1 R2
Therefore, Re sonantfrequency, f r   2 ..................(ii )
2 LC L
If the coil resis tan ce R is small (as is generally the case), then,
1
fr  ....................................(iii )
2 LC
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L
or 2 f r L   R2
C
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or fr  2
R
2 L C
1 1 R2
Therefore, Re sonantfrequency, f r   ..................(ii )
2 LC L2
If the coil resis tan ce R is small (as is generally the case), then,
1
fr  ....................................(iii )
2 LC

The resonant frequency will be in Hz if R, L and C are in ohms, henry and farad respectively. Note.
If in the problem, the value of R is given, then eq. (ii) should be used to find fr. However, if R is not
given, then eq. (iii) may be used to find fr.

Characteristics of Parallel Resonant Circuit

It is now desirable to discuss some important characteristics of parallel resonant circuit.

(i) Impedance of tuned circuit. The impedance offered by the parallel LC circuit is given by the
supply voltage divided by the line current i.e., V/I. Since at resonance line current is minimum,
therefore, impedance is maximum at resonant frequency. This fact is shown by the impedance
frequency curve of Figure 2.43. It is clear from impedance-frequency curve that impedance rises
to a steep peak at resonant frequency fr. However, the impedance of the circuit decreases rapidly
when the frequency is changed above or below the resonant frequency. This characteristic of
parallel tuned circuit provides it the selective properties i.e. to select the resonant frequency and
reject all others.

Figure 2.43. Impedance frequency curve. [4]

Line current I  I L COSL
V V R
or  *
Zr ZL ZL
1 R
or 
Zr ZL2
1 R CR
or  
Zr L/C L
L
[QZ L 2  from eq.(i )]
C
L
Therefore, circuit impedance, Z r 
CR

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Thus, at parallel resonance, the circuit impedance is equal to L/CR. It may be noted that Zr will be in
ohms if R, L and C are measured in ohms, henry and farad respectively. Hence, from the ratio L/RC
two things are worth noting. First, Zr (= L/CR) is a pure resistance because there is no frequency
term present. Secondly, the value of Zr is very high because the ratio L/C is very large at parallel
resonance.

(ii) Circuit Current. At parallel resonance, the circuit or line current I is given by the applied
voltage divided by the circuit impedance Zr i.e.,
V L
Line current , I  where, Z r 
Zr CR
Because Zr is very high, the line current I will be very small.
(ii) Quality factor Q. It is desired that resonance curve of a parallel tuned circuit should be as sharp
as possible in order to provide selectivity. The sharp resonance curve means that impedance
falls rapidly as the frequency is varied from the resonant frequency. The smaller the resistance
of coil, the sharper the resonance curve is. This is due to the fact that a small resistance consumes
less power and draws a relatively small line current. The ratio of inductive reactance and
resistance of the coil at resonance, therefore, becomes a measure of the quality of the tuned
circuit. This is called quality factor and may be defined as under: The ratio of inductive
reactance of the coil at resonance to its resistance is known as quality factor Q i.e.,

X L 2 f r L
Q 
R R
The quality factor Q of a parallel tuned circuit is very important because the sharpness of
resonance curve and hence selectivity of the circuit depends upon it. The higher the value of
Q, the more selective is the tuned circuit. Fig. 2.44 shows the effect of resistance R of the coil
on the sharpness of the resonance curve. It is clear that when the resistance is small, the
resonance curve is very sharp. However, if the coil has large resistance, the resonance curve is
less sharp. It may be emphasized that where high selectivity is desired, the value of Q should
be very large.

 Strictly speaking, the Q of a tank circuit is defined as the ratio of the energy stored in the
circuit to the energy lost in the circuit i.e.,

Energy stored Re active Power I L 2 X L X

Q   2 or Q  L
Energy lost Re sistive Power IL R R

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Figure 2.44. Effect of resistance ‘R’ of the coil on the sharpness of the resonance curve [4]

Activities and Exercises

Example. A parallel resonant circuit has a capacitor of 250pF in one branch and inductance of
1.25m H plus a resistance of 10Ω in the parallel branch. Find

(i) resonant frequency

(ii) impedance of the circuit at resonance
(iii) Q-factor of the circuit.
Solution.

R = 10Ω ; L = 1.25 * 10-3H; C = 250 * 10-12 F

(i) Resonant frequency of the circuit is

1 1 R2
fr   2
2 LC L
1 1012 102
  Hz
2 1.25*103 *  250 (1.25*103 ) 2
 284.7 *103 Hz  284.7kHz
(iii) Impedance of the circuit at resonance is
L 1.25*103
Zr   12
 500*103 
CR 250*10 *10
 500k 
1. Quality factor of the circuit is

2 frL 2 (284.7*103 )*1.25*103

Q   223.6
R 10

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Example 2.2. A parallel resonant circuit has a capacitor of 100pF in one branch and inductance of
100µH plus a resistance of 10 Ω in parallel branch. If the supply voltage is 10 V,
calculate

(i) Resonant frequency

(ii) Impedance of the circuit and line current at resonance
Solution:

R = 10, L = 100 x 10-6 H x 10-12F

(i) Resonant frequency of the circuit is

1 𝑅2
𝑓𝑟 = √ −
𝐿𝑐 𝐿2

1012 102
√ −
100 ∗ 10−6 ∗ 100 (100 ∗ 10−6 )2

1592.28 x 103 Hz = 1592.28 KHz

(ii) Impedance of the circuit at resonance is

𝐿 𝐿 1 100 × 10−6 1
𝑧𝑟 = = × = ×
𝐶𝑅 𝑐 𝑅 100 × 10−12 𝑅

= 106 x 1/R = 106 x 1/10 = 105 =0.1M

Note that the circuit impedance Zr is very high at resonance. It is because the ratio L/C is very large
at resonance.

Line current at resonance is

I = V/Zr 10V/105 = 100A

* Impedance of parallel resonant circuit at ressonance is called dynamic impedance.

Advantages of Tuned Amplifiers

In high frequency applications, it is generally required to amplify a single frequency, rejecting all
other frequencies present. For such purposes, tuned amplifiers are used. These amplifiers use tuned
parallel circuit as the collector load and offer the following advantages:

(i) Small power loss: A tuned parallel circuit employs reactive components L and C. Consequently,
the power loss in such a circuit is quite low. On the other hand, if a resistive load is used in the

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collector circuit, there will be considerable loss of power. Therefore, tuned amplifiers are highly
efficient.

(ii) High selectivity: A tuned circuit has the property of selectivity i.e. it can select the desired
frequency for amplification out of a large number of frequencies simultaneously impressed upon it.
For instance, if a mixture of frequencies including fr is fed to the input of a tuned amplifier, then
maximum amplification occurs for fr. For all other frequencies, the tuned circuit offers very low
impedance and hence these are amplified to a little extent and may be thought as rejected by the
circuit. On the other hand, if we use resistive load in the collector, all the frequencies will be
amplified equally well i.e. the circuit will not have the ability to select the desired frequency.

(iii) Smaller collector supply voltage: Because of little resistance in the parallel tuned circuit, it
requires small collector supply voltage VCC. On the other hand, if a high load resistance is used in the
collector for amplifying even one frequency, it would mean large voltage drop across it due to zero
signal collector current. Consequently, a higher collector supply will be needed.

Relation between Q and Bandwidth

The quality factor Q of a tuned amplifier is equal to the ratio of resonant frequency (fr) to bandwidth
(BW) i.e.,

fr
Q
BW
The Q of an amplifier is determined by the circuit component values. It may be noted here that Q of
a tuned amplifier is generally greater than 10. When this condition is met, the resonant frequency at
parallel resonance is approximately given by:

1
fr 
2 LC

Example .The Q of a tuned amplifier is 60. If the resonant frequency for the amplifier is 1200 kHz,
find:

(i) Bandwidth and

(ii) Cut-off frequencies.

Solution:

(i) BW = fr/Q 1200 KHz/60 = 20 KHz

(ii) Lower cut-off frequency, f1 = 1200 – 10 =1190 KHz

Upper cut-off frequency, f2 = 1200 + 10 = 1210 KHz

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Single and Double Tuned Amplifiers

Single Tuned Amplifier
A single tuned amplifier consists of a transistor amplifier containing a parallel tuned circuit as the
collector load. The values of capacitance and inductance of the tuned circuit are so selected that its
resonant frequency is equal to the frequency to be amplified. The output from a single tuned
amplifier can be obtained either: (a) by a coupling capacitor CC as shown in Figure 2.33 (i). or (b) by
a secondary coil as shown in Figure 2.45 (ii).

Figure 2.45. Single tuned amplifier. [4]

Operation: The high frequency signal to be amplified is given to the input of the amplifier. The
resonant frequency of parallel tuned circuit is made equal to the frequency of the signal by changing
the value of C. Under such conditions, the tuned circuit will offer very high impedance to the signal
frequency. Hence a large output appears across the tuned circuit. In case the input signal is complex
containing many frequencies, only that frequency which corresponds to the resonant frequency of
the tuned circuit will be amplified. All other frequencies will be rejected by the tuned circuit. In this
way, a tuned amplifier selects and amplifies the desired frequency. Note: The fundamental
difference between AF and tuned (RF) amplifiers is the bandwidth they are expected to amplify. The
AF amplifiers amplify a major portion of AF spectrum (20 Hz to 20 kHz) equally well throughout.
The tuned amplifiers amplify a relatively narrow portion of RF spectrum, rejecting all other
frequencies.

Figure 2.46.

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At the resonant frequency, the impedance of the parallel resonant circuit is very high and is purely
resistive. Therefore, when the circuit is tuned to resonant frequency, the voltage across RL is
maximum. In other words, the voltage gain is maximum at fr. However, above and below the
resonant frequency, the voltage gain decreases rapidly. The higher the Q of the circuit, the faster the
gain drops off on either side of resonance [See Figure 2.46 (ii)].

A.C. Equivalent Circuit of Tuned Amplifier

Figure 2.35 (i) shows the ac equivalent circuit of the tuned amplifier. Note the tank circuit
components are not shorted. In order to completely understand the operation of this circuit, we shall
see its behaviour at three frequency conditions viz.,

(i) fin = fr (ii) fin < fr (iii) fin > fr

(i) When input frequency equals fr (i.e., fin = fr). When the frequency of the input signal is equal
to fr, the parallel LC circuit offers a very high impedance i.e., it acts as an open. Since RL
represents the only path to ground in the collector circuit, all the ac collector current flows
through RL. Therefore, voltage across RL is maximum i.e., the voltage gain is maximum as shown
in Figure 2.47 (ii).
(ii) When input frequency is less than fr (i.e., fin < fr ). When the input signal frequency is less than
fr, the circuit is effectively* inductive. As the frequency decreases from fr, a point is reached
when XC − XL = RL. When this happens, the voltage gain of the amplifier falls by 3 db. In other
words, the lower cut-off frequency f1 for the circuit occurs when XC − XL = RL.
(iii) When input frequency is greater than fr (i.e., fin > fr). When the input signal frequency is
greater than fr, the circuit is effectively capacitive. As fin is increased beyond fr, a point is reached
when XL − XC = RL. When this happens, the voltage gain of the amplifier will again fall by 3db.
In other words, the upper cut-off frequency for the circuit will occur when XL − XC = RL.

Figure 2.47.
Example. For the tuned amplifier shown in Figure 2.48, determine:

(i) The resonant frequency

(ii) The Q of tank circuit and
(iii) Bandwidth of the amplifier.
* At frequencies below fr, XC > XL or IL > IC. Therefore, the circuit will be inductive.
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Figure 2.48.
Solution:
1 1
(i) Resonant frequency, 𝑓𝑟 = =
2𝜋√𝐿𝑐 2𝜋√33∗10−3 𝑥 0.1𝑥10−6

= 2.77 x 103 Hz = 2.77 KHz

(ii) XL = 2frL = 2 x (2.77 x 103 ) x 33 x 10-3 =574
 Q = XL/R = 574/25 = 23
(iii) BW = fr/Q = 2.77 KHz/23 = 120 Hz
a. Double Tuned Amplifier
Figure 2.49 shows the circuit of a double tuned amplifier. It consists of a transistor amplifier
containing two tuned circuits; one (L1C1) in the collector and the other (L2C2) in the output as shown.
The high frequency signal to be amplified is applied to the input terminals of the amplifier. The
resonant frequency of tuned circuit L1C1 is made equal to the signal frequency. Under such
conditions, the tuned circuit offers very high impedance to the signal frequency. Consequently, large
output appears across the tuned circuit L1C1. The output from this tuned circuit is transferred to the
second tuned circuit L2C2 through mutual induction. Double tuned circuits are extensively used for
coupling the various circuits of radio and television receivers.

Figure 2.49

Frequency response: The frequency response of a double tuned circuit depends upon the degree of
coupling i.e. upon the amount of mutual inductance between the two tuned circuits. When coil L2 is

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coupled to coil L1 [See Figure 2.50 (i)], a portion of load resistance is coupled into the primary tank
circuit L1C1 and affects the primary circuit in exactly the same manner as though a resistor had been
added in series with the primary coil L1.

Figure 2.50.
When the coils are spaced apart, all the primary coil L1 flux will not link the secondary coil L2. The
coils are said to have loose coupling. Under such conditions, the resistance reflected from the load
(i.e. secondary circuit) is small. The resonance curve will be sharp and the circuit Q is high as shown
in Fig. 2.50 (ii). When the primary and secondary coils are very close together, they are said to have
tight coupling. Under such conditions, the reflected resistance will be large and the circuit Q is
lower. Two positions of gain maxima, one above and the other below the resonant frequency, are
obtained.

Bandwidth of Double–Tuned Circuit

If you refer to the frequency response of double-tuned circuit shown in Figure 2.50 (ii), it is clear
that bandwidth increases with the degree of coupling. Obviously, the determining factor in a double
tuned circuit is not Q but the coupling. For a given frequency, the tighter the coupling, the greater is
the bandwidth.

BWdt = k fr

The subscript dt is used to indicate double-tuned circuit. Here k is coefficient of coupling.

Example. It is desired to obtain a bandwidth of 200 kHz at an operating frequency of 10 MHz using
a double tuned circuit. What value of co-efficient of coupling should be used?

Solution:

BWdt = k fr

Therefore, Co-efficient of coupling,

BWdt 200kHz
k   0.02
fr 10*103 kHz

Practical Application of Double Tuned Amplifier

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Double tuned amplifiers are used for amplifying radio-frequency (RF) signals. One such application
is in the radio receiver as shown in Figure 2.51. This is the IF stage using double tuned resonant
circuits. Each resonant circuit is tuned to 455 kHz. The critical coupling occurs when the coefficient
of coupling is

1
kcritical 
QQ
1 2

Where Q1 = quality factor of primary resonant circuit (L1 C1)

Q2 = quality factor of secondary resonant circuit (L2 C2)

Figure 2.51 Figure 2.52

When two resonant circuits are critically coupled, the frequency response becomes flat over a
considerable range of frequencies as shown in Figure 2.52. In other words, the double tuned circuit
has better frequency response as compared to that of a single tuned circuit. The use of double tuned
circuit offers the following advantages:

(i) Bandwidth is increased.

(ii) Sensitivity (i.e. ability to receive weak signals) is increased.
(iii) Selectivity (i.e. ability to discriminate against signals in adjacent bands) is increased.

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1.6 Multivibrator circuits

INTRODUCTION

The process of shaping pulses is very important, since the shape of pulses can affect the operation of
many devices, ranging from radar system to microprocessor. The process by which nonsinusoidal
waveforms are altered in passing through the circuit element (such as diodes, resistors, inductors and
capacitors) is called wave shaping. The wave shaping is used to perform any one of the following
functions.

 To generate one wave from the other.

 To limit the voltage level of the waveform to some preset value and suppressing all other volt
age levels in excess of the preset level.
 To cut-off the positive and negative portions of the input waveform.
 To hold the waveform to a particular D.C. level.
The wave shaping is important in most of the signal process systems and is performed by the circuits
known as differentiators, integrators, limiters, clippers and clampers.

Classification of wave shaping circuits:

Figure 3.1.
Types of wave shaping Circuits:

Linear wave shaping circuits:

 The circuits, which make use of only linear circuit elements such as the inductors capacitors a
nd resistors are known as linear wave shaping circuits.
 Such circuits are used to perform functions of differentiation and integration.
Non-Linear wave shaping circuits:
 The circuits, which (in addition to linear circuit elements) make use of nonlinear circuit eleme
nts such as Diodes and Transistors are known as nonlinear wave shaping circuits.
 Such circuits are used to perform functions of amplitude limiting, clipping and clamping.
Multivibrator
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A multivibrator circuit is nothing but a switching circuit. It generates non-sinusoidal waves such as
Square waves, Rectangular waves and Saw tooth waves etc. Multivibrators are used as frequency
generators, frequency dividers and generators of time delays and also as memory elements in
computers etc.

According to the definition, A Multivibrator is a two-stage resistance coupled amplifier with positive
feedback from the output of one amplifier to the input of the other. Two transistors are connected in
feedback so that one controls the state of the other. Hence the ON and OFF states of the whole
circuit, and the time periods for which the transistors are driven into saturation or cut off are
controlled by the conditions of the circuit.

The following figure shows the block diagram of a Multivibrator.

Figure 3.29.
Types of Multivibrators

There are two possible states of a Multivibrator. In first stage, the transistor Q1 turns ON while the
transistor Q2 turns OFF. In second stage, the transistor Q1 turns OFF while the transistor Q2 turns
ON. These two states are interchanged for certain time periods depending upon the circuit
conditions.

Depending upon the manner in which these two states are interchanged, the Multivibrators are
classified into three types. They are Astable multivibrator, Monostable multivibrator and
Bistable multivibrator

Figure 3.30.

Astable Multivibrator

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An Astable Multivibrator is such a circuit that it automatically switches between the two states
continuously without the application of any external pulse for its operation. As this produces a
continuous square wave output, it is called as a Free-running Multivibrator. The dc power source
is a common requirement.

An astable multivibrator has no stable states. Once the Multivibrator is ON, it just changes its states
on its own after a certain time period which is determined by the RC time constants. A dc power
supply or Vcc is given to the circuit for its operation.

Construction of Astable Multivibrator

Two transistors named Q1 and Q2 are connected in feedback to one another. The collector of
transistor Q1 is connected to the base of transistor Q2 through the capacitor C1 and vice versa. The
emitters of both the transistors are connected to the ground. The collector load resistors R1 and
R4 and the biasing resistors R2 and R3 are of equal values. The capacitors C1 and C2 are of equal
values.

The following figure shows the circuit diagram for Astable Multivibrator.

Figure 3.31.

Operation of Astable Multivibrator

When Vcc is applied, the collector current of the transistors increase. As the collector current depends
upon the base current, Ic=βIB

As no transistor characteristics are alike, one of the two transistors say Q1 has its collector current
increase and thus conducts. The collector of Q1 is applied to the base of Q2 through C1. This
connection lets the increased negative voltage at the collector of Q1 to get applied at the base of
Q2 and its collector current decreases. This continuous action makes the collector current of Q2 to
decrease further. This current when applied to the base of Q1 makes it more negative and with the
cumulative actions Q1 gets into saturation and Q2 to cut off. Thus the output voltage of Q1 will be
VCE (sat) and Q2 will be equal to VCC.

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The capacitor C1 charges through R1 and when the voltage across C1 reaches 0.7v, this is enough to
turn the transistor Q2 to saturation. As this voltage is applied to the base of Q2, it gets into saturation,
decreasing its collector current. This reduction of voltage at point A is applied to the base of
transistor Q1 through C2 which makes the Q1 reverse bias. A series of these actions turn the transistor
Q1 to cut off and transistor Q2 to saturation. Now point B has the potential VCC. The capacitor
C2 charges through R2. The voltage across this capacitor C2 when gets to 0.7v, turns on the transistor
Q1 to saturation.

Hence the output voltage and the output waveform are formed by the alternate switching of the
transistors Q1 and Q2. The time period of these ON/OFF states depends upon the values of biasing
resistors and capacitors used, i.e., on the RC values used. As both the transistors are operated
alternately, the output is a square waveform, with the peak amplitude of VCC.

Waveforms

The output waveforms at the collectors of Q1 and Q2 are shown in the following figures.

Figure 3.32.

Frequency of Oscillations
The ON time of transistor Q1 or the OFF time of transistor Q2 is given by
t1 = 0.69R2C1

Similarly, the OFF time of transistor Q1 or ON time of transistor Q2 is given by

t2 = 0.69R3C2

Hence, total time period of square wave

t = t1 + t2 = 0.69(R2C1 + R3C2)

As R2 = R3 = R and C1 = C2 = C, the frequency of square wave will be

f=1/t=1/1.38RC=0.7RC

Advantages

The advantages of using an astable multivibrator are as follows −

• No external triggering required.
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• Circuit design is simple

• Inexpensive
• Can function continuously
Disadvantages

The drawbacks of using an astable multivibrator are as follows −

• Energy absorption is more within the circuit.

• Output signal is of low energy.
• Duty cycle less than or equal to 50% can’t be achieved.
Applications

Astable Multivibrators are used in many applications such as amateur radio equipment, Morse code
generators, timer circuits, analog circuits, and TV systems.

Monostable Multivibrator

A Monostable Multivibrator has a stable state and a quasi-stable state. This has a trigger input to
one transistor. So, one transistor changes its state automatically, while the other one needs a trigger
input to change its state.

As this Multivibrator produces a single output for each trigger pulse, this is known as One-shot
Multivibrator. This Multivibrator cannot stay in quasi-stable state for a longer period while it stays
in stable state until the trigger pulse is received.

Construction of Monostable Multivibrator

Two transistors Q1 and Q2 are connected in feedback to one another. The collector of transistor Q1 is
connected to the base of transistor Q2 through the capacitor C1. The base Q1 is connected to the
collector of Q2 through the resistor R2 and capacitor C. Another dc supply voltage –VBB is given to
the base of transistor Q1 through the resistor R3. The trigger pulse is given to the base of Q1 through
the capacitor C2 to change its state. RL1 and RL2 are the load resistors of Q1 and Q2.

One of the transistors, when gets into a stable state, an external trigger pulse is given to change its
state. After changing its state, the transistor remains in this quasi-stable state for a specific time
period, which is determined by the values of RC time constants and gets back to the previous stable
state.

The following figure shows the circuit diagram of a Monostable Multivibrator.

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Figure 3.23.

Operation of Monostable Multivibrator

Firstly, when the circuit is switched ON, transistor Q1 will be in OFF state and Q2 will be in ON
state. This is the stable state. As Q1 is OFF, the collector voltage will be VCC at point A and hence
C1 gets charged. A positive trigger pulse applied at the base of the transistor Q1 turns the transistor
ON. This decreases the collector voltage, which turns OFF the transistor Q2. The capacitor C1 starts
discharging at this point of time. As the positive voltage from the collector of transistor Q2 gets
applied to transistor Q1, it remains in ON state. This is the quasi-stable state.

The transistor Q2 remains in OFF state, until the capacitor C1 discharges completely. After this, the
transistor Q2 turns ON with the voltage applied through the capacitor discharge. This turn ON the
transistor Q1, which is the previous stable state.

Output Waveforms

The output waveforms at the collectors of Q1 and Q2 along with the trigger input given at the base of
Q1 are shown in the following figures.

Figure 3.34.

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Output Waveforms

The width of this output pulse depends upon the RC time constant. Hence it depends on the values of
R1C1. The duration of pulse is given by T=0.69R1C1

The trigger input given will be of very short duration, just to initiate the action. This triggers the
circuit to change its state from Stable state to Quasi-stable or Semi-stable state, in which the circuit
remains for a short duration. There will be one output pulse for one trigger pulse.

Advantages

The advantages of Monostable Multivibrator are as follows −

• One trigger pulse is enough.

• Circuit design is simple
• Inexpensive
Disadvantages

The major drawback of using a monostable multivibrator is that the time between the applications of
trigger pulse T has to be greater than the RC time constant of the circuit.

Applications

Monostable Multivibrators are used in applications such as television circuits and control system
circuits.

Bistable Multivibrator

A Bistable Multivibrator has both the two states stable. It requires two trigger pulses to be applied
to change the states. Until the trigger input is given, this Multivibrator cannot change its state. It’s
also known as flip-flop multivibrator. As the trigger pulse sets or resets the output, and as some
data, i.e., either high or low is stored until it is disturbed, this Multivibrator can be called as a Flip-
flop.

Construction of Bistable Multivibrator

Two similar transistors Q1 and Q2 with load resistors RL1 and RL2 are connected in feedback to one
another. The base resistors R3 and R4 are joined to a common source –VBB. The feedback resistors
R1 and R2 are shunted by capacitors C1 and C2 known as Commutating Capacitors. The transistor
Q1 is given a trigger input at the base through the capacitor C3 and the transistor Q2 is given a trigger
input at its base through the capacitor C4.

The capacitors C1 and C2 are also known as Speed-up Capacitors, as they reduce the transition
time, which means the time taken for the transfer of conduction from one transistor to the other.

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The following figure shows the circuit diagram of a self-biased Bistable Multivibrator.

Figure 3.35.

Operation of Bistable Multivibrator

When the circuit is switched ON, due to some circuit imbalances as in Astable, one of the transistors,
say Q1 gets switched ON, while the transistor Q2 gets switched OFF. This is a stable state of the
Bistable Multivibrator.

By applying a negative trigger at the base of transistor Q1 or by applying a positive trigger pulse at
the base of transistor Q2, this stable state is unaltered. So, let us understand this by considering a
negative pulse at the base of transistor Q1. As a result, the collector voltage increases, which forward
biases the transistor Q2. The collector current of Q2 as applied at the base of Q1, reverse biases
Q1 and this cumulative action, makes the transistor Q1 OFF and transistor Q2 ON. This is another
stable state of the Multivibrator.

Now, if this stable state has to be changed again, then either a negative trigger pulse at transistor
Q2 or a positive trigger pulse at transistor Q1 is applied.

Output Waveforms

The output waveforms at the collectors of Q1 and Q2 along with the trigger inputs given at the bases
of Q1 and Q2 are shown in the following figures.

Figure 3.36.

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Advantages

The advantages of using a Bistable Multivibrator are as follows −

• Stores the previous output unless disturbed.
• Circuit design is simple
Disadvantages

The drawbacks of a Bistable Multivibrator are as follows −

• Two kinds of trigger pulses are required.
• A bit costlier than other Multivibrators.
Applications

Bistable Multivibrators are used in applications such as pulse generation and digital operations like
counting and storing of binary information.

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1.7 Assessments
1. Mention at least two functions of wave shaping circuit in electronics device applications.
2. Differentiate clippers from clampers.
3. Which circuits are called multivubrators?
4. Which are the various types of multivibrators? And their applications.
5. Explain at least three advantage of double tuned circuit amplifier
6. Mention the applications of operational amplifier (op-amp)
7. Define the following terms
a. Common mode rejection ratio
b. Negative feed back
c. Slew Rate (SR)
d. Saturation voltage
e. Bandwidth
f. Quality factor
8. List 3 types of diode equivalent circuits
9. What are the characteristics of Ideal diode and practical diode?
10. What do you understand by rectification? Give the classifications

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1.8 Summaries and Reviews

Over the last 70 years, semiconductors became a crucial element in the manufacturing of electronics.
Since the invention of the Transistor, the world of electronics has always been on an exponential curve
in terms of research, development, manufacturing, bringing up new devices and technologies.
Electronic Devices are all about handling information i.e. high-speed transmission, acquisition and
processing in fields of industries and manufacturing, communications, arts, medicine and even in
warfare. But all these can be dialed back to the heart of modern electronics and its manufacturing:
Semiconductor Devices. Even though an electronic system is manufactured with the help of metals,
insulators and semiconductors (more about these later), the semiconductors are considered the
backbone of electronics.

Overall, semiconductors and diodes are foundational elements in electronics, enabling the technology
that powers our modern world. Their continuous improvement drives innovation and pushes the
boundaries of what is possible in the realm of electronics.

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1.9 Resources and References

[1] Principle of electronics-v.k. Mehta, Rohit Mehta, S. Chand

[2] Electronics for Industrial Electricians, Stephen L. Herman, Delmar Publishers, Inc., latest edition

[3] Somanathan Nair B, “Electronic Devices and Applications”, PHI, 2006.

[4] Jacob Millman, Christos C Halkias, Satyabrata Jit, “Electron Devices and Circuits”, Tata
McGraw Hill, 2010.

[5] David A Bell, “Fundamentals of Electronic Devices and Circuits”, Oxford Press, 2009.

[6] Thomas L. Floyd, ELECTRONIC DEVICE, Library of Congress Cataloging-in Publication

Data, 9th edition

[7] Theraja.B.L, Sedha.R.S, “Principles of Electronic Devices and Circuits”, Chand. S, 2004

[8] Robert L. Boylestad and Louis Nashelsky, “Electronic Devices and Circuit Theory”, Pearson
Education, 9th Edition, 2009.

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Chapter- 2: Digital Electronics

2.1 Introduction
In science, technology, business, and, in fact, most other fields of endeavor, we are constantly
dealing with quantities.

Quantities are measured, monitored, recorded, manipulated arithmetically, observed, or in some

other way utilized in most physical systems.

It is important when dealing with various quantities that we can be able to represent their values
efficiently and accurately.

There are basically two ways of representing the numerical value of quantities: analog and digital.

Digital versus Analog systems

Analog Representation:

In analog representation a quantity is represented by a voltage, current, or meter movement that is

proportional to the value of that quantity.

Analog quantities such as those cited above have an important characteristic: they can vary over a
continuous range of values.

Analog voltage vs time

5

3
Voltage(V)

-1 2 4 6 8 10 12 14 16 18 20

-3

-5
Time (s)

Digital Representation:
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In digital representation the quantities are represented not by proportional quantities but by symbols
called digits.

As an example, consider the digital watch, which provides the time of day in the form of decimal
digits which represent hours and minutes (and sometimes seconds).

As we know, the time of day changes continuously, but the digital watch reading does not change
continuously; rather, it changes in steps of one per minute (or per second).

In other words, this digital representation of the time of day changes in discrete steps, as compared
with the representation of time provided by an analog watch, where the dial reading changes
continuously.

Digital voltage vs time

5

3
Voltage(V)

-1 2 4 6 8 10 12 14 16 18 20

-3

-5
Time (s)

The major difference between analog and digital quantities is

Analog  Continuous

Digital  Discrete

Advantages and Limitations of Digital Techniques

Advantages

Digital systems are easier to design.

The switching circuits in which there are only two voltage levels, HIGH and LOW, are easier to
design. The exact numerical values of voltages are not important because they have only logical
significance; only the range in which they fall is important.

Information storage is easy.

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There are many types of semiconductor and magnetic memories of large capacity which can store
data for periods as long as necessary.

Accuracy and precision are greater.

Digital systems arc much more accurate and precise than analog systems, because digital systems
can be easily expanded to handle more digits by adding more switching circuits. Analog systems will
be quite complex and costly for the same accuracy and precision.

Digital systems are more versatile.

It is fairly easy to design digital systems whose operation is controlled by a set of stored instructions
called the program. Any time the system operation is to be changed, it can easily be accomplished by
modifying the program

Digital circuits are less affected by noise.

Unwanted electrical signals are called noise. Noise is unavoidable in any system. Since in analog
systems the exact values of voltages are important and in digital systems only the range of values is
important, the effect of noise is more severe in analog systems. In digital systems, noise is not
critical as long as it is not large enough to prevent us from distinguishing a HIGH from a LOW.

Limitation

There is really only one major drawback when using digital techniques:
“ The real world is mainly analog

To take advantage of digital techniques when dealing with analog inputs and outputs, three steps
must be followed:

Convert the real-world analog inputs to digital form. (ADC)

Process (operate on) the digital information.

Convert the digital outputs back to real-world analog form. (DAC)

The following diagram shows a temperature control system that requires analog/digital
conversions in order to allow the use of digital processing techniques.

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(Analog) (Digital)
Temperature
(analog) Measuring Analog-to-Digital Digital
Device Converter (ADC) Processing

Digital-to- Analog Adjust

Controller
Converter (DAC) temperature
(Digital) (Analog)

Fig 3.1: Block diagram of a typical temperature control system.

Binary logic Gates

The general public as being magical sometimes looks upon computers, calculators, and other digital
devices.

Actually, digital electronic devices are extremely logical in their operation.

The basic building block of any digital circuit is a logic gate.

The logic gates we will use operate with binary numbers, hence the term binary logic gates.

Logic gates are the building blocks for even the most complex computers.

Logic gates can be constructed by using simple switches, relays, transistors and diodes, or lCs.

Because of their availability, wide use, and low cost, ICs will be used to construct digital circuits.

A variety of logic gates are available in all logic families including TTL and CMOS.

Digital Signals

Digital systems use the binary number system.

Therefore, two-state devices are used to represent the two binary digits 1 and 0 by two different
voltage levels, called HIGH and LOW.

If the HIGH voltage level is used to represent 1 and the LOW voltage level to represent 0, the system
is called the positive logic system.

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HIGH

Leading Trailing
edge edge

LOW

a) Positive pulse

On the other hand, if the HIGH voltage level represents 0 and the LOW voltage level represents 1,
the system is called the negative logic system.

HIGH
Leading
Trailing
edge
edge
LOW

b) Negative pulse

Normally, the binary 0 and 1 are represented by the logic voltage levels 0V and +5 V.

So, in positive logic system, 1 is represented by + 5 V (HIGH) and 0 is represented by 0 V (LOW);

and in a negative logic system, 0 is represented by + 5 V (HIGH) and l is represented by 0 V (
LOW).

Both positive and negative logics are used in digital systems, but the positive logic is more common.

In reality, because of circuit variations, the 0 and 1 would be represented by voltage ranges instead
of particular voltage levels.

Example of Voltages Level in TTL family

Waveform Characteristics
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Most waveforms encountered in digital systems are composed of series of pulses, sometimes called
pulse trains, and can be classified as either periodic or non-periodic.

A periodic pulse waveform is one that repeats itself at a fixed interval, called a period (T). The
frequency (f) is the rate at which it repeats itself and is measured in hertz (Hz).

A non-periodic pulse waveform, of course, does not repeat itself at fixed intervals and may be
composed of pulses of randomly differing pulse widths and/or randomly differing time intervals
between the pulses. An example of each type is shown in Figure.

The frequency (f) of a pulse (digital) waveform is the reciprocal of the period. The relationship
between frequency and period is expressed as follows:

An important characteristic of a periodic digital waveform is its duty cycle. The duty cycle is the
ratio of the pulse width (tW) to the period (T) and can be expressed as a percentage

T1 T2 T3

Period = T1 = T2 =T3 =…=Tn

Frequency=1/T

Periodic pulse-train

Non-Periodic pulse-train

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Tw

T
Duty cycle = 50%

Tw

T
Duty cycle = 75%

2.2 Number Systems

This part introduces some basic number system concepts and those useful in electrical, electronics,
and computer engineering. A number system is nothing more than a code that uses symbols to refer
to a number of items. The binary number system and digital codes are fundamental to computers and
to digital electronics in general. Number system is commonly used to count any activity or articles.
In practical life, we are using decimal number system. In decimal number system, 10 digits
(0,1,2,3,4,5,6,7,8,9) are used. But in digital electronics, we use ‘1’ and ‘0’. Computers,
microprocessor, and digital electronic devices do not process decimal numbers. Instead, they work
with binary number, which use only the two digits ‘0’ and’1’.

People do not like working with binary numbers, owing to their very lengthy combinations of digits,
while representing larger decimal values. As a result, octal and hexadecimal numbers are widely
used to compress long strings of binary numbers. Some number systems are discussed below.

A. Decimal Number System

In childhood, people are often taught the fundamentals of counting by using their fingers. Counting
from one to ten is one of many milestones a child achieves on their way to becoming educated
members of society. We will review these basic facts on our way to gaining an understanding of
alternate number systems. The child is taught that the fingers and thumbs can be used to count from
one to ten. Extending one finger represents a count of one; two fingers represents a count of two, and
so on up to a maximum count of ten. No fingers (or thumbs) refers to a count of zero. The child is
later taught that there are certain symbols called digits that can be used to represent these counts.
These digits are, of course: 0, 1, 2, 3, 4, 5, 6, 7, 8, 𝑎𝑛ⅆ 9.

Radix: The radix, or base of a counting system is defined as the number of unique digits in a given
number system. Back to our elementary example. We know that our hypothetical child can count
from zero to ten using their fingers and thumbs. There are ten unique digits in this counting system,
therefore the radix of our elementary counting system is ten. We represent the radix of our counting

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system by putting the radix in subscript to the right of the digits. For example, 310, representing 3 in
decimal (base 10).

Positional values
(weight)
103 102 101 100 10-1 10-2 10-3

2 7 4 5 . 2 1 4

MSD Decimal points LSD

(2*10 3)+(7*10 2)+(4*10 1)+(5*100)+(2*10 –1)+(1*10 –2)+(4*10 –3)

Our special case (ten) illustrates a fundamental rule of our number system that was not readily
apparent - what happens when the count exceeds the highest digit? Obviously, a new digit is added,
to the left of our original digit which is "worth more", or has a higher weight than our original digit.
(In reality, there *always* are digits to the left; we simply choose not to write those digits to the left
of the first nonzero.)

1010 = 01010 = 0001010 = 00000000000000000000001010 ≠ 0010010

When our count exceeds the highest digit available, the next digit to the left is incremented and the
original digit is reset to zero. For example: 910 + 110 = 1010

Because we are dealing with a base -10 system, each digit to the left of another digit is weighted ten
times higher. Using exponential notation, we can imagine the number 10 as representing:

10110 = 1𝑥102 + 0𝑥101 + 1𝑥100

4892 = 4𝑥103 + 8𝑥102 + 9𝑥101 + 2𝑥100

Binary Number System

It is widely believed that the decimal system that we find so natural to use is a direct consequence of
a human being's ten fingers and thumbs being used for counting purposes. One could easily imagine
that a race of intelligent, six-fingered beings could quite possibly have developed a base-six counting
system. From this perspective, consider the hypothesis: the most intuitive number system for an
entity is that for which some natural means of counting exists. Since our focus is electronic and
computer systems, we must narrow our focus from the human hand to the switch, arguably the most
fundamental structure that can be used to represent a count. The switch can represent one of two
states; either open or closed. If we return to our original definition of a digit, how many digits are
required to represent the possible states of our switch? Clearly, the answer is 2. We use the binary
digits zero and one to represent the open and closed states of the switch.

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Counting in Binary

Counting in binary like base 10 can be accomplished with your fingers with some differences. In
decimal base 10 each finger represents a number in the first digit 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. When
you consider that each digit in binary is worth 2 times more than the previous (right to left always)
then it makes sense. Let’s compare number lines.

o Binary: 128, 64, 32, 16, 8, 4, 2, 1

o Decimal: 1, 2 ,3 ,4 ,5 ,6 ,7 ,8 ,9 ,10 ,11 ,12 ,13 ,14 ,15 ,16 ,17 ,18 ,19 ,20 , …

From our earlier definition of radix, the binary system has a radix of two. We use the radix in the
subscript much like we do with decimals: 01012

Similar to decimals, binary digits are weighted. Each bit is weighted twice as much as the bit to the
right of it: 01012 = 0𝑥23 + 1𝑥22 + 0𝑥21 + 1𝑥20

Counting from zero to nine (base 10) in binary yields:

00002, 00012, 00102, 00112, 01002, 01012, 01102, 01112, 10002, 10012

Let us use 4 bit binary numbers to illustrate the method for counting in binary. The sequence (shown
on the right side) begins with all bits at 0, this is called the Zero count.

For each successive count the units (20) position toggles; that is, it changes from one binary value to
the other.

Each time the units bits changes from a 1 to 0, the twos (21) position will toggle (change states).

Each time the twos position changes from 1 to 0, the fours (22) position will toggle (change states).

Likewise, each time the fours position goes from 1to 0, the eights (23) position toggles.

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Weights 23=8 22=4 21=2 20=1 Decimal Equivalent

0 0 0 0 0

0 0 0 1 1

0 0 1 0 2

0 0 1 1 3

0 1 0 0 4

0 1 0 1 5

0 1 1 0 6

0 1 1 1 7

1 0 0 0 8

1 0 0 1 9

1 0 1 0 10

1 0 1 1 11

1 1 0 0 12

1 1 0 1 13

1 1 1 0 14

1 1 1 1 15

Basic Binary Arithmetic

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Binary addition, subtraction, multiplication and division operations work essentially the same as they
do for decimals. For addition, you add equally weighted bits, much like decimal addition (where
you add equally weighted digits) and carry as required to the left.

01002 + 01112 ⟹ 01002

+ 01112
100112
As you can see, a carry is generated in the 23 column which increments the 23 column.

Subtraction works just like decimal arithmetic, using borrowing as required.

10112 + 01112 ⟹ 10112

− 01112
01002
Here, a borrow is required, reducing the 23 column to 0 − 0 = 0 and changing the 22 column to 2 − 1
= 1.

Multiplication is straight forward also:

10112 x 01112 ⟹ 1011

X 0111
1011
10110
101100
= 1001101
N.B> Division is left as an exercise to the student [hint: use long division]

Hexadecimal Number Systems

The hexadecimal system uses base 16.

Thus, it has 16 possible digit symbols.

It uses the digits

0 through 9 plus

The letters A, B, C, D, E and F as the 16 digit symbols.

In table below the relationships among hexadecimal, decimal and binary is shown.

Note that each hexadecimal digit represents a group of four binary digits.

It is important to remember that hex (abbreviation for hexadecimal) digits A through F are
equivalent to the decimal values 10 through 15.

Counting in Hexadecimal

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When counting in hex, each digit position can be incremented (increase by 1) from 0 to F.

Once a digit position reaches the value F, it is reset to 0 and the next digit position is incremented.

This is illustrated in the following hex counting sequences.

Decimal Binary Hexadecimal

0 0000 0

1 0001 1

2 0010 2

3 0011 3

4 0100 4

5 0101 5

6 0110 6

7 0111 7

8 1000 8

9 1001 9

10 1010 A

11 1011 B

12 1100 C

13 1101 D

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14 1110 E

15 1111 F

16 10000 10

17 10001 11

The most commonly used number system in computer systems is the hexadecimal, or more simply
hex, system. It has a radix of 16, and uses the numbers zero through nine, as well as A through F as
its digits:

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 𝐴, 𝐵, 𝐶, 𝐷, 𝐸, 𝐹

Hex numbers can have the subscript 16, but more often have a leading *0x* to indicate their type.
0𝑥0𝐵49

Counting: Counting from zero to twenty (base 10) in hex yields:

0x0, 0x1, 0x2, 0x3, 0x4, 0x5, 0x6, 0x7, 0x8, 0x9, 0xA, 0xB, 0xC, 0xD, 0xE, 0xF, 0x10, 0x11, 0x12,
0x13, 0x14

Or

0016, 0116, 0216, 0316, 0416, 0516, 0616, 0716, 0816, 0916, 0𝐴16, 0𝐵16, 0𝐶16, 0𝐷16, 0𝐸16, 1016, 1216, 1316,
1416.

Hexa-decimal Arithmetic

Hex arithmetic, yet again, follows the same rules and patterns of decimal arithmetic. As an exercise,
verify the following:

3216 x 5616 = 8816

3216 x 5616 = 10CC16

4A16 / 2516 = 216

Octal Number System

The octal number system is very important in digital Computer work.

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The octal number system has a base of eight, meaning that it has eight possible digits: 0,1,2,3,4,5,6
and 7.

Thus, each digit of an octal number can have any value from 0 to 7.

The advantage of the octal system is its usefulness in converting directly from a 3 bit binary number.

The digit positions in an octal number have weights as follows.

84 83 82 81 80 8-1 8-2 8-3 8-4 8-5

Octal points

The equivalent binary and octal representations for decimal numbers 0 through 17 is shown below

Decimal Binary Octal

0 000 0

1 001 1

2 010 2

3 011 3

4 100 4

5 101 5

6 110 6

7 111 7

8 001 000 10

9 001 001 11

10 001 010 12

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11 001 011 13

12 001 100 14

13 001 101 15

14 001 110 16

15 001 111 17

16 010 000 20

17 010 001 21

The name octal implies eight, if you consider that an octagon has eight sides. Octal has a radix of
eight, and uses the following octal digits: 0, 1, 2, 3, 4, 5, 6, 7

Counting: Counting from one to ten (base 10) in octal yields:

018, 028, 038, 048, 058, 068, 078, 108, 118, 128,

Counting in Octal

The largest octal digit is 7, so that in counting in octal, a digit position is incremented up ward form
0 to 7.

Once it reaches 7, it recycles to 0 on the next count and causes the next higher digit position to be
incremented.

For example:

Octal Arithmetic: octal arithmetic, like binary arithmetic, follows the same rules and patterns of
decimal arithmetic. As an exercise, verify the following:

328 + 568 = 1108 328 x 568 = 22548 528 / 258 = 28

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Conversion of one Number System to Another

Conversion of binary number from one number format to another number format can be performed
by adapting some rules and regulations. Some of the important conversion processes are explained
below. For the conversion of integer and fractional number, separate conversion methods are used.

Binary-to-decimal Conversions:

Any binary number can be converted to its decimal equivalent simply by summing together the
weights of the various positions in the binary number, which contain a 1.

For Example

Note that the procedure is to find the weights (i.e. powers of 2) for each bit position that contains a 1,
and then to add them up.

Also note that the MSB has a weight of 27 even though it is the eighth bit this is because the LSB is
the first bit and has a weight of 20.

Decimal – to – Binary conversions

There are two ways to convert a decimal whole number to its equivalent binary system
representation.

The 1st method (Sum-of-Weights)

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The decimal number is simply expressed as a sum of power of 2 and then 1s and 0s are written in the
appropriate bit positions.

The 2nd method (‘’Repeated Division’’)

This method uses repeated division by 2.

Requires repeatedly dividing the decimal number by 2 and writing down the remainder after division
until the quotient of 0 is obtained.

Note that the binary result is obtained by writing the first remainder as the LSB and the last
remainder as the MSB.

Examples

Flow chart for Repeated Division

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Hex –to- decimal Conversion

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A hex number can be converted to its decimal equivalent by using the fact that each hex digit
position has a weight that is a power of 16.

The LSD has a weight of 160 = 1, the next higher digit position has a weight of 161 = 16, and the
next has a weight of 162 = 256, and so on.

Decimal-to-Hex conversion

Recall that we did decimal –to- binary conversion using repeated division by 2. Likewise decimal-
to-hex conversion can be done using repeated division by 16.

Examples

Hex-to-Binary conversion

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The Hexadecimal number system is used primarily as a ‘’Shorthand’’ method for representing
binary numbers.

It is a relatively simple method to convert a hex number to binary.

Each hex digit is converted to its 4 bit binary equivalent. (See table ‘’Hexadecimal Number
system’’).

Binary-to- Hex conversion

Conversion from binary to hex is just the reverse of the above process.

The binary number is grouped in to groups of four bits, and each group is converted to its equivalent
hex digit.

Zeros are added, as needed, to complete a 4-bit group.

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Octal to decimal Conversion

An octal number, can easily be converted to its decimal equivalent by multiplying each octal digit by
its positional weight i.e. a power of 8.

Octal to Binary Conversion

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Binary to Octal Conversion

Converting from binary to octal integers is simply the reverse of the foregoing process.

The bits of the binary number are grouped into groups of three bits starting at the LSB.

The each group is converted to its octal equivalent.

Fractions

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As far as fractions are concerned, you multiply by 2 and record a carry in the integer position.

The carries taken in forward order are the binary fraction.

Activities and Exercises

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2.3 Binary coding schemes

All digital circuits operate with only two states namely, High and Low or ON and OFF or 1 and 0. In
binary number system, the number of bits required goes on increasing as the numbers become larger
and larger. So, some special binary codes are required to represent alphabets and special characters.
Based on these points, different types of binary code have been developed.

Binary Coded Decimal

The Binary Coded Decimal (BCD) uses 4 bits to represent the decimal numbers through and these
are shown in the Table 1.1 along with other coding types.

As it can be observed from the table, only ten of the sixteen (24) possible combinations are used in
BCD; the remaining six combinations 1010, 1011, 1100, 1101, 1110, and 1111are invalid in BCD.

Since in BCD we require four bits to represent a single decimal character, a decimal number
between 10 and 99 must be represented with 8 bits, a decimal number between 100 and 999 will
require 12 bits in BCD, and so on. In general, a decimal number with n digits in BCD must be
represented by 4n bits.

Excess – three code

The Excess-3 code also uses 4 bits to represent the decimal numbers 0 through 9 and these are
shown in the Table 1.1. The Excess-3 Code derives its name from the fact that each decimal
representation in Excess-3 code is larger than the BCD code by three. The advantage of the Excess-3
code over the BCD code is that the Excess-3 code is a self-complementing code as illustrated in the
table.

Gray-code

In Gray Code only a single bit changes between successive numbers. This is very desirable in certain
applications such as optical or mechanical shaft position encoders, and digital-to-analog conversion.

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To generate this code, we start with all zeros and subsequently change the lsb that will produce a
new value. Gray code is an unweight code which not suitable for arithmetic operations. Only one bit
in the code group changes when going from one step to the next.

Table 1.1. Showing the decimal equivalent of BCD, Excess-3 and Gray in one table.

The American Standard Code for Information Interchange (ASCII) Code

Digital computers use alphanumeric codes, that is, codes consisting of both alphabetic and numeric
characters. The ASCII code is the most widely accepted. It was proposed by the American National
Standards Institute (ANSI). The table that is shown below is referred to as seven-bit ASCII and
represents 128 (27) characters assigned to numbers, letters, punctuation marks, and the most special
characters. The standard 7-bit character representation with the high-order bit and the low-order bit is
shown in table below.

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Figure 2.7. ASCII table (source: google image).

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Activities and Exercises

2.4 Logic gates

BASIC

Gates are the fundamental building blocks of digital logic circuitry. These devices function by
“opening” or “closing” to admit or reject the passage of a logical signal. From only a handful of
basic gate types (AND, OR, XOR, and NOT), a vast array of gating functions can be created.

"Vcc" stands for the constant voltage supplied to the collector of a bipolar junction transistor circuit,
in reference to ground. Those points in a gate circuit marked by the label "Vcc" are all connected to
the same point, and that point is the positive terminal of a DC voltage source, usually 5 volts (+ 5V).

There are quite a few different types of logic gates, most of which have multiple input terminals for
accepting more than one signal. The output of any gate is dependent on the state of its input(s) and
its logical function.

One common way to express the particular function of a gate circuit is called a truth table. Truth
tables show all combinations of input conditions in terms of logic level states (either "high" or "low,"
"1" or "0" for each input terminal of the gate), along with the corresponding output logic level, either
"high" or "low." For the inverter, or NOT, circuit just illustrated, the truth table is very simple
indeed:

 In digital circuits, binary bit values of 0 and 1 are represented by voltage signals measured in
reference to a common circuit point called ground. An absence of voltage represents a binary
"0" and the presence of full DC supply voltage represents a binary "1."

 A logic gate, or simply gate, is a special form of amplifier circuit designed to input and
output logic level voltages (voltages intended to represent binary bits). Gate circuits are most
commonly represented in a schematic by their own unique symbols rather than by their
constituent transistors and resistors.

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 Just as with operational amplifiers, the power supply connections to gates are often omitted
in schematic diagrams for the sake of simplicity.

 A truth table is a standard way of representing the input/output relationships of a gate circuit,
listing all the possible input logic level combinations with their respective output logic levels.

Negation (NOT gate)

An even simpler gate is the NOT gate. It has only one input and one output. The output is always the
opposite (or negation) of the input. It is used change “1” level to “0” or vice versa.

NOT gate

Truth Table for NOT Gate

0 1

1 0

Pulse Operation of NOT gate

The AND Gate

A basic AND gate consists of two inputs and an output. If the two inputs are A and B, the output
(often called Q) is “on” only if both A and B are also “on.” In digital electronics, the on state is often
represented by a 1 and the off state by a 0. The relationship between the input signals and the output
signals is often summarized in a truth table, which is a tabulation of all possible inputs and the
resulting outputs. For the AND gate, there are four possible combinations of input states: A=0, B=0;
A=0, B=1; A=1, B=0; and A=1, B=1. AND gate performs logical multiplication. Q = A.B

AND gate

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In the following truth table, these are listed in the left and middle columns. The AND gate output is
listed in the right column.

Truth Table for AND Gate

A B Q

0 0 0

1 0 0

0 1 0

1 1 1

Pulse operation of AND gate

The OR Gate

The OR gate is also a two-input, single-output gate. Unlike the AND gate, the output is 1 when one
input, or the other, or both are 1. The OR gate output is 0 only when both inputs are 0. Q = A+B

OR gate

Truth Table for OR Gate

A B Q

0 0 0

1 0 1

0 1 1

1 1 1

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Pulse operation of OR gate

The XOR (Exclusive OR) Gate

A related gate is the XOR, or exclusive OR gate, in which the output is 1 when one of the inputs is 1.
In other words, the XOR output is 1 if the inputs are different (Two inputs are at opposite logic
levels). Q  A  B

XOR gate

Truth Table for XOR Gate

A B Q

0 0 0

1 0 1

0 1 1

1 1 0

Pulse operation of OR gate

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The XOR (Exclusive OR) Gate

A related gate is the XOR, or exclusive OR gate, in which the output is 1 when one of the inputs is 1.
In other words, the XOR output is 1 if the inputs are different (Two inputs are at opposite logic
levels). Q  A  B

XOR gate

Truth Table for XOR Gate

A B Q

0 0 0

1 0 1

0 1 1

1 1 0

Pulse operation of NOR gate

2.5 Combinational logic gates and families

The NAND, NOR, and NXOR Gates

Negation is quite useful. In addition to the three two-input gates already discussed (AND, OR, and
XOR), three more are commonly available. These are identical to AND, OR, and XOR, except that
the gate output has been negated. These gates are called the NAND (“not AND”), NOR (“not OR”),
and NXOR (“not exclusive OR”) gates. Their symbols are just the symbols of the nonnegative gate
with a small circle drawn at the output:

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From the above figures

Building Gates from Other Gates

Given a handful of NAND gates, you can reproduce all other basic logic gates. For example, you can
form the NOT gate by connecting both NAND input terminals to the same input:

Similarly, you can easily build an AND gate from two NAND gates:

An OR gate requires three NAND gates:

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Gates with More than Two Inputs

Although the note includes all the basic two-input gates, you may require more inputs. For example,
the AND truth table below can be generalized to three inputs where Q = A AND B AND C:

A B C Q

0 0 0 0

0 0 1 0

0 1 0 0

0 1 1 0

1 0 0 0

1 0 1 0

1 1 0 0

1 1 1 1

From a pair of two-input AND gates, you can easily build the three-input AND:

Logic Gate Families

- The two most commonly used family of ICs are TTL & CMOS

TTL (Transistor-Transistor Logic)

- It is a circuit technology that makes use of BJT (Bipolar Junction Transistor) to construct
gates at the chips level.

- It consists of a series of logic circuits. The different series differs in their performance
characteristics such as propagation delay time, power dissipation and fan out (the number of
logic gate )

Table: TTL series logic gates

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TTL Prefix Examples of device

designation

Stranded TTL 54 or 74 (No 7400 (Quad NAND gate)

letter)

Low-power TTL 54L or 74L 74L00 (Quad NAND gate)

Schottky TTL 54S or 74S 74S00 (Quad NAND gate)

Low-power Schottky TTL 54LS or 74LS 74LS00 (Quad NAND gate)

Advanced Low-power Schottky TTL 54ALS or 74ALS 74ALS00 (Quad NAND

gate)

Advanced Schottky TTL 54AS or 74AS 74AS00 (Quad NAND

gate)

CMOS (Complementary Metal Oxide Semiconductor)

The CMOS family of integrated circuits differs from TTL by using an entirely different type of
transistor as its basic building block. The TTL family uses bipolar transistor (NPN and PNP).
CMOS (Complementary Metal Oxide Semiconductor) uses complementary pairs of transistors (N
type and P type) called MOSFETs (Metal Oxide Semiconductor Field Effect Transistors)

 Some of the more common low-voltage families are identified by the following suffixes

LV – Low voltage HCMOS (H=speed)

LVC – Low voltage CMOS

LVT – Low voltage technology

ALVC – Advanced Low Voltage CMOS

HLL – High-speed low power low voltage

Advantages of CMOS

 Very low power dissipation

 Good noise immunity

 Can operate from a wide range of power supply (2-15V)

Disadvantages of CMOS

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 High propagation delay

 Low output current capability

BOOLEAN ALGEBRA

Rules & Laws of Boolean Algebra

Laws

1. Commutative Law

A + B = B + A; AB = BA

2. Associative Law

A + (B + C) = (A + B) + C

A (BC) = (AB) C

3. Distributive Law

A (B+C) = AB + AC

Basic Rules

1. A + 0 = A

2. A + 1 = 1

3. A  0  0

4. A 1  1
5. A + A = A

6. A  A  1

7. A  A  A

8. A  A  0

9. A  A
10. A + AB = A

11. A  AB  A  B
12. (A + B) . (A + C) = A + BC

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De Morgan’s Theorem

 The complement of sum is equal to the product of the complement

A  B  ....  N  AB...N

Two variables A  B  AB  OR-NOT (NOR) to AND NOT (NAND)

 The complement of a product is equal to the sum of the complement

ABC...N  A  B  C  ...  N

Two variables AB  A  B  NAND to OR-NOT (NOR)

2.6 Boolean Expression for Logic Circuits

F (A, B, C . . .) refers to Boolean expression, Boolean equation or Logic function.

Problem statement  Drive Boolean expression  Simplify Boolean equation  Draw logic circuit

We have two-basic forms of Boolean expression

 Sop (Sum of product)

 Pos (Product of sum)

SOP Form

- In Sop form the Boolean expression is two or more AND functions ORed together

Examples; AB + BCD, ABC  D E , etc

- The sop expression a single bar cannot extend over more than one variable in a term, although more
than one variable in a term can have a bar over it.

Example; AB  BCD ()

AB  BCD ()

- The Sop form is more commonly employed because it can be converted easily to truth table (TT) and
because it tends itself well to simplification techniques.

 The output of a Sop expression is equal to “1” whenever any one of the product is “1”.

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Example; Implement the Sop expression F  AB  BC D  EFG with logic gates

Any logic expression can be changed into Sop form by applying Boolean algebra techniques.

Example; Convert the following to Sop form

( A  B)  C

Solution: Applying De Morgan’s theorem we have

( A  B)  C  ( A  B).C

 ( A  B).C

 AC  BC

Pos Form

- It is the AND of two or more OR functions

Examples; ( A  B)(C  D)

( B  C  D)(C  E  F )

- It can contain a single variable term, as in

A( B  C )(B  C  D)

Examples; Implement the Pos expression for F  ( A  B)(B  C  D) with logic gates.

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Conversion from Sop to Pos

Steps 1. Simplify the Sop expression if possible

2. Invert the Sop form

3. Multiply out and simplify the inverse expression

4. Invert the result

Examples; Convert the Sop expression F  ABC  ABC into Pos form

Solution: F  ABC  ABC

F  ABC  ABC

F  ( ABC )  ( ABC )

F  ( A  B  C)  ( A  B  C)

F  ( A  B  C)  ( A  B  C)

F  AA  AB  AC  AB  B B  BC  AC  BC  C C

F  AB  AC  AB  BC  AC  BC

F  F  AB  AC  AB  BC  AC  BC

      
F  AB  AC  AB  BC  AC  BC

F  A  B  A  C  A  B  B  C  A  C  B  C 

    
F   A  B  A  C  A  B  B  C  A  C  B  C 

Simplification Using Boolean algebra

Example: Simplify the following Boolean expression.

1. [ AB(C  BD)  AB]C

2. ABC  ABC  ABC  ABC  ABC

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3. [( A  BC  CD)  ( BC]

Solutions

Q1. = [ AB(C  BD)  AB]C

= [ ABC  ABBD  AB]C ………………. [Distributive law]

= [ ABC  AB]C …………………………. [Rule 8 since BB  0 then ABCD  0 ]

= ABCC  ABC ………………………… [Distributive law]

= A BC  A BC …………………………… [Rule 7]

= BC[ A  A] ……………………………… [Factor out BC ]

= BC  1 …………………………………… [Rule 6]

= BC ……………………………………… [Rule 4]

Implementation of example 1 before simplification

Implementation of example 1 after simplification

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Q2. = ABC  ABC  ABC  ABC  ABC

= ABC  ABC  ABC  ABC  ABC

= ABC  ABC  ABC  BC ( A  A)

= BC( A  A)  ABC  BC

= BC  A BC  BC

= C ( B  AB)  BC

= C ( A  B)  BC

= AC  BC  BC

Q3. = [( A  BC  CD)  ( BC]

= [( A  BC  CD)  BC ………… De Morgan’s theorem

= ( A  BC  CD)  BC

= ABC  (C  D)  BC

= ABC  ABC D  BC

= ABC (1  D)  BC

= ABC  BC

= B( AC  C)

= B( A  C ) ……….. [Simplified Pos]

= AB  BC ……… . [Simplified Sop]

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Simplification Using the Karnaugh Map (K-map)

Simplifying Boolean expression using Boolean algebra is lengthy & error-prone. A better method of
simplification is using Karnaugh-Map (K-map).

A K-map is a convenient method of simplifying Boolean equations in which the function to be simplified is
displayed diagrammatically on a set of squares or cells. Each cell maps one term of the function. The number
of cells in the map is equal to 2n, where n is the number of variables in the equation to be simplified. The cells
are arranged so that there is only a single variable change between any adjacent cells.

Examples

Plotting Sop Expression

One concept Sop expressions on the K-map by placing a “1” in each cell corresponding to a term in the Sop
expression and zeros in other cells.

Example: Consider the four variable expression

F  ABC D  ABCD  ABC D  ABCD

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A Sop expression may not have a complete set of variables in each of its terms. For example the expression
AB  ABC  ABC contains a term that doesn’t include the variable C or C (missing variables). Such Sop
expressions must be rewritten to include the missing variable before it is plotted on the K-map. This is done
by expanding the shortened form.

For the above given example

AB  ABC  ABC

 AB(C  C )  ABC  ABC

 ABC  ABC  ABC  ABC [Canonicalform]

Now we can plot the above expression on the K-map.

Grouping Cells for Simplification

You can group “1”s that are in adjacent cells according to the following drawing a loop around those cells.

1. Adjacent cells are cells that differ by only a single variable (for eg. ABCD & ABC D are adjacent)

 Cells that are side by side in the horizontal and vertical direction (but not diagonal)

 The outer (extreme left & extreme right) cells in each row, and the top & bottom cells in
column

 The four corners in a four variables map

2. The “1”s in adjacent cells must be combined in groups of 2, 4, 8, 16 and so on.

3. Each group of “1”s should be maximized to include the largest number of adjacent cells as much as
possible in accordance with rule 2.

4. Every 1 on the map must be included in at least one group. There can be overlapping groups if they
include non-common “1”s.

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Simplifying the Expression

When all the 1s representing terms in the original Boolean expression are grouped, the mapped expression is
ready for simplification. The following rules will apply to the simplification.

1. Each group of 1s creates a product term composed of all variables that appear in only one form (either
uncomplemented or complemented) with in the group. Variables that appear both uncomplemented &
complemented with in the group are illuminated. These are contradictory.

2. The fixed simplified expression is formed by summing (ORing) the product terms of all the groups.

Examples: Reduce the following expressions to its minimized Sop form

1. F  ABC  ABC  ABC  ABC  ABC

Fm  B  AC Minimized form

Using Boolean algebra

F  ABC  ABC  ABC  ABC  ABC

F  ABC  ABC  ABC  ABC  ABC

F  AB(C  C )  AB(C  C )  ABC

F  AB  AB  ABC

F  B( A  A)  ABC

F  B  ABC

F  B  AC

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2. F  ABC D  ABC D  ABC D  ABC D  ABCD  ABCD  ABC D  ABC D  ABC D  ABC D

Fm  D  BC

3. F  ABC D  ABC D  ABC D  ACD  ABC D

Solution: F  ABC D  ABC D  ABC D  ACD( B  B)  ABC D

F  ABC D  ABC D  ABC D  ABCD  ABCD  ABC D

Fm  B D  ACD

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K-map Plotting from a Truth Table

A logic function can be stated in a truth table format. The truth table gives the output of a specified logic
function for all possible input combinations. From the truth table we first find the Boolean terms for each
combinations of input variables for which the output is 1. Then we can plot them directly on the K-map.

Example: Reduce the logic function specified by the following truth table to its minimized Sop form.

A B C D F(A,B,C,D)

0 0 0 0 1 A BC D

0 0 0 1 1 A BC D

0 0 1 0 1 ABC D

0 0 1 1 1 A BCD

0 1 0 0 1 ABC D

0 1 0 1 0

0 1 1 0 1 ABC D

0 1 1 1 1 ABCD

1 0 0 0 0

1 0 0 1 0

1 0 1 0 0

1 0 1 1 0

1 1 0 0 1 ABC D

1 1 0 1 0

1 1 1 0 1 ABC D

1 1 1 1 0

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Fm  AB  B D  AC

Plotting Pos Equations

The following method can be employed to plot Boolean equations in Pos form on the K-map.

 Convert each term in a product by changing all ANDs signs to OR and all OR signs to AND, and also
complementing each variable, and inter a “0” into the corresponding cells in the map. This means that

i. A term such as A + B must be read as A B &

ii. A term such as A + B read as AB . This is shown in the map below.

 Enter 1s into all the remaining cells

 Loop the zero cells

 Read the group of 0 cells with the complements of each term and with AND

 Sign interchanged

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Example 1

Reduce the following Pos equation to its simplified (minimum) form

F  ( A  B  C)  ( A  B  C)  ( A  B  C)  ( A  B  C)

Fm ( A, B, C )  ( A  B)  ( B  C )

Example 2

Reduce the logic function represented by the following truth table into minimum Pos form.

[It is shown on the next table]

A B C D F(A,B,C,D)

0 0 0 0 1

0 0 0 1 0

0 0 1 0 1

0 0 1 1 1

0 1 0 0 1

0 1 0 1 0

0 1 1 0 1

0 1 1 1 1

1 0 0 0 1

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1 0 0 1 0

1 0 1 0 1

1 0 1 1 1

1 1 0 0 0

1 1 0 1 0

1 1 1 0 0

1 1 1 1 0

Canonical Form

The canonical form of a Boolean equation is one in which each of the input variables once only.
Examples: Write the following Boolean equation in their canonical form

1. AB  C B

Solution: AB  C B

 AB(C  C )  ( A  A) BC

 ABC  ABC  ABC  ABC

 ABC  ABC  ABC Canonical form

2. ( A  B)  (C  B)

 ( A  B  C)  ( A  B  C)  ( A  C  B)  ( A  C  B)

 ( A  B  C )  ( A  B  C )  ( A  B  C ) Canonical form

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2.7 Assessments
1. Identify each of these logic gates by name, and complete their respective truth tables:

2. Draw the circuit diagram for x = [D + (A + B) C)].E:

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2.8 Summaries and Reviews

Digital electronics is a branch of electronics that deals with digital signals rather than analog signals. It involves
the use of digital circuits to process, store, and transmit information in binary format, where data is represented
using combinations of 0s and 1s. Digital electronics encompasses various components and devices, including
logic gates, flip-flops, counters, and microprocessors. It plays a fundamental role in modern technology,
powering computers, smartphones, digital cameras, and countless other electronic devices.

Digital electronics has revolutionized the way information is processed and communicated, ushering in the
digital age. Its reliance on binary representation enables efficient storage, transmission, and manipulation of
data, leading to advancements in computing power, speed, and reliability. Digital circuits are highly versatile
and can perform complex operations with precision, making them indispensable in applications ranging from
telecommunications to entertainment.

One of the key advantages of digital electronics is its immunity to noise and distortion, ensuring accurate
transmission and reception of signals over long distances. Additionally, digital systems offer flexibility and
scalability, allowing for easy integration of new features and functionalities without the need for extensive
hardware modifications.

Despite its many benefits, digital electronics also presents challenges such as power consumption and heat
dissipation, especially as electronic devices become smaller and more powerful. However, ongoing research
and innovation continue to address these issues, driving progress in digital design methodologies,
semiconductor technologies, and system architectures.

In conclusion, digital electronics has transformed the world by enabling the development of sophisticated
computing systems and electronic devices. Its impact is felt across industries, shaping how we work,
communicate, and interact with technology. As digital technology continues to evolve, the future promises even
more exciting possibilities for innovation and advancement.

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2.9 Resources and References

[1] Rowe, Jim. "Circuit Logic – Why and How". December, 1966. Electronics Australia

[2] Thomas L Floyd. Digital fundamentals. Harlow: Pearson Education, 2015.

[3] https://babbage.cs.qc.cuny.edu/

[4] http://www.wiley.com/

[5] https://sandbox.mc.edu

[6] Robert K. Dueck. Digital Design with CPLD Applications and VHDL. Delmar Pub, 2001.

[7] Giorgio Rizzoni. Principles and Applications of Electrical Engineering. 5th Edition.

McGraw-Hill Education, 2005.

[8] Randy H. Katz, Contemporary Logic Design, Benjamin-Cummings, 1994

[9] https://vlab.amrita.edu/

[10] https://www.electronicshub.org/

[11] https://www.vssut.ac.in/

[12] https://www.teachmint.com/

[13] Digital Electronics, Tokheim, Tata-McGraw Hill, 4th Edition.

[14] Digital Design, M. Morris Mano, Pearson Education, 3rd Edition.

[15] R. J. Tocci, N Widmer, and G. L. Moss, “Digital Systems, Principles and Applications”,

Pearson, 10th Edition, 2013.

[16] Mano, M. M., “Digital Logic and Computer Design”, PHI, 1989, 3rd Edition.

[17] Millman, and Grabel, A., “Microelectronics”, New York: Mc Graw Hill, 2nd Edition, 2010.

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Chapter -3: Power Electronics

3.1 Introduction
Power electronics belongs to Power and Electronic Engineering.

The era of modern power electronics began with the invention of silicon-controlled-rectifier (SCR) by Bell
Laboratory in 1956. Its prototype was introduced by GEC (General Engineering Consultant) in 1956.
Subsequently, GEC introduced SCR-based systems commercially in 1958.Since then, there has been
emergence of many new power semiconductor devices.

Power engineering deals with generation, transmission, distribution and utilization of electric energy at high
efficiency.

Electronic Engineering on the other hand deals with the design, fabrication and operation of circuits,
electronic devices, and systems and it is also transmission and reception of data and signal of very low power
level.

Power Electronics is the subject that concerns the application of Electronic principles at a power level than a
signal level.

In this regard the main field of Power Electronics is to process and control the flow of electric power by
supplying voltages and currents in a form that is optimally suited for user loads.

Fig 3.1: Basic block diagram

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Requirement

To convert electrical energy from one form to another, i.e. from the source to load with:

– Highest efficiency,

– Highest availability

– Highest reliability

– Lowest cost,

– Smallest size

– Least weight.

Power Electronics versus Linear Electronics

Example: Linear voltage Regulator.

Fig 3.2: Linear voltage Regulator

Linear Electronics operates on the linear region (active) of the characteristic curve. Series transistor is thus
used as an adjustable resistor. Thus Linear electronics

Low Efficiency

Heavy and bulky

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Fig 3.3: SMPS

In power Electronics

Transistor is used as a switch

High Efficiency

High-Frequency Transformer (light weight)

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Why PE & high efficiency?

Energy scenario

 Need to reduce dependence on fossil fuel as:

 Coal, natural gas, oil, and nuclear power resource
 Depletion of these sources is expected.
 Tap renewable energy resources as:
 Solar, wind, fuel-cell, ocean-wave
 Energy saving by PE applications. Examples:
 Variable speed compressor air-conditioning system:
30% savings compared to thermostat-controlled system.
 Lighting using electronics ballast boost efficiency of Fluorescent lamp by 20%.

Environment issues

• Nuclear safety.

 Nuclear plants remain radioactive for thousands of years.

• Burning of fossil fuel

 Emits gases such as CO2, CO (oil burning), SO2, NOx (coal burning) etc.

– Creates global warming (greenhouse effect), acid rain and urban pollution from smokes.

• Possible Solutions by application of PE. Examples:

– Renewable energy resources.

– Centralization of power stations to remote non-urban area. (Mitigation).

– Electric vehicles.

Scope and Applications of Power Electronics

The expanded market demand for power electronics has been due to several factors discussed below.

1. Switch mode power supplies and uninterruptible power supply.

- All electronics devices need regulated power supply

2. Energy Conservation.

- Increasing energy cost and the concern for environment have combined to make energy conservation
a priority.

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3. Process control and Factory automation.

- Adjustable-speed-drive

- Robotics servo drive (adjustable and position drive)

4. Transportation

- Electric train

-Electric cars

5. Electro-technical application.

- Welding, electroplating and induction heating

6. Utility-related application.

- HVDC

- Supplementary energy sources (solar and wind)

Power Electronic Applications:

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Application Example in Adjustable Speed Drives

Fig 3.4: Energy Conservation: (a) conservational drive, (b) adjustable speed drive.

Conventional drive wastes energy across the throttling valve to adjust flow rate

Using power electronics, motor-pump speed is adjusted efficiently to deliver the required flow rate

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Drive Application: Air-Conditioning System

Fig 3.5: Air-Conditioning System

Power semiconductor devices (Power switches)

Power switches:

Work-horses of PE systems.

Operates in two states:

1. Fully on, i.e. switch closed.

– Conducting state

2. Fully off, i.e. switch opened.

– Blocking state

NB: Power switch never operates in linear mode

Can be categorized into three groups:

– Uncontrolled: Diode:

– Semi-controlled: Thyristor (SCR).

– Fully controlled: Power transistors:

E.g. BJT (bipolar junction transistor), MOSFET (metal oxide semiconductor field effect transistor), IGBT
(insulated-gate bipolar transistor), GTO (gate turn off thyristor), IGCT (integrated gate commuted thyristor)

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Power Electronics Converters

Fig 3.5: Power Electronics Converters

3.2 Power electronic semiconductors

Power semiconductor diodes

Power semiconductor diodes play a significant role in power electronics circuits. A diode acts as a switch to
perform various functions, such as switches in rectifi ers, freewheeling in switching regulators, charge reversal
of capacitor and energy transfer between components, voltage isolation, energy feedback from the load to the
power source, and trapped energy recovery.

Power diodes can be assumed as ideal switches for most applications but practical diodes differ from the ideal
characteristics and have certain limitations. The power diodes are similar to pn-junction signal diodes. However,
the power diodes have larger power-, voltage-, and current-handling capabilities than that of ordinary signal
diodes. The frequency response (or switching speed) is low compared to signal diodes.

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DIODE CHARACTERISTICS

A power diode is a two-terminal pn-junction device and a pn-junction is normally formed by alloying, diffusion,
and epitaxial growth. The modern control tech niques in diffusion and epitaxial processes permit the desired
device characteris tics. Figure 2-1 shows the sectional view of a pn-junction and diode symbol.

When the anode potential is positive with respect to the cathode, the diode is said to be forward biased and the
diode conducts. A conducting diode has a relatively small forward voltage drop across it; and the magnitude of
this drop would depend on the manufacturing process and junction temperature. When the cathode potential is
positive with respect to the anode, the diode is said to be reverse biased. Under reverse-biased conditions, a
small reverse current (also known as leakage current) in the range of micro- or milliampere flows and this
leakage current increases slowly in magnitude with the reverse voltage until the avalanche or zener voltage is
reached. Figure 2-2a shows the steady-state v—i characteristics of a diode. For most practical purposes, a diode
can be regarded as an ideal switch, whose characteristics are shown in Fig. 2-2b.

The v—i characteristics shown in Fig. 2-2a can be expressed by an equation known as Schockley diode
equation, and it is given by.

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3.3 The construction, working principles of Thyristors: SCR, IGBT, MOSFET...

Thyristors

A thyristor is one of the most important types of power semiconductor devices.Thyristors are used extensively
in power electronic circuits. They are operated as bistable switches, operating from nonconducting state to
conducting state. Thyristors can be assumed as ideal switches for many applications, but the practical thyristors
exhibit certain characteristics and limitations.

SCR

The basic structure and circuit symbol of SCR is shown below. It is a four layer three terminal device in which
the end P-layer acts as anode the end N-layer acts as cathode and P-layer nearer to cathode acts as a gate. As
leakage current in silicon is very small compared to Germanium SCRs are made of silicon and not Germanium

Identification:

When the leads of the SCR are in the same plane but evenly spaced the central lead is the Gate, left side of the
gate is Anode and the other is Cathode.

Specifications:

The following is a list of some important SCR specifications:

1. Latching Current (IL):

Latching current is the minimum current required to latch or trigger the device from its OFF-state to its ON-
state.

2. Holding Current (IH):

Holding current is the minimum value of current to hold the device in ON-state. For turning the device OFF,
the anode current should be lowered below IH by increasing the external circuit resistance.

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3. Gate Current (Ig):

Gate current is the current applied to the gate of the device for control purposes. The minimum gate current is
the minimum value of current required at the gate for triggering the device the maximum gate current is the
maximum value of current applied to the device without damaging the gate. Move the gate current earlier is the
triggering of the device and vice versa.

Voltage safety factor (Vf) voltage safety factor Vf is a ratio which is related to the PIV, the RMS value of the
normal operating voltage.

Testing:

• The SCR should be switched on and voltage measured between anode and cathode, which should be
approximately volt and the voltage between gate and cathode should be 0.7 volt.

• An ohmmeter can also be used to test SCR the gate –cathode of a thyristor has a similar characteristic to a
diode with the gate positive with respect to the cathode, a low resistance (typically below 100Ω) should be
indicated on the other hand with the gate negative with respect to the cathode a high resistance (greater than
100kΩ) will be indicated. A high resistance is indicated in either direction for the anode to cathode connections.

Applications:

These are used in power control applications such as lamp dimmers motor speed control, temperature control
and invertors. They are also employed for over voltage protection in DC power supplies.

THYRISTOR CHARACTERISTICS

A thyristor is a four-layer semiconductor device of pnpn structure with three pn junctions. It has three terminals:
anode, cathode, and gate. The following fig shows the thyristor symbol and the sectional view of three pn-
junctions. Thyristors are manufactured by diffusion. When the anode voltage is made positive with respect to
the cathode, the junctions J and J are forward biased. The junction J is reverse biased, and only a small leakage
current flows from anode to cathode. The thyristor is then said to be in the forward blocking or off-state
condition and the leakage current is known as off-state current ‘D If the anode-to-cathode voltage VAK is
increased to a sufficiently large value, the reverse-biased junction J will break. This is known as avalanche
breakdown and the corresponding voltage is called forward break down voltage VBO. Since the other junctions
J and J are already forward biased, there will be free movement of carriers across all three junctions, resulting
in a large forward anode current. The device will then be in a conducting state or on- state. The voltage drop
would be due to the ohmic drop in the four layers and it is small, typically, 1 V. In the on-state, the anode current
is limited by an external impedance or a resistance, RL, as shown in Fig. 4-2a. The anode current must be more
than a value known as latching current ‘L, in order to maintain the required amount of carrier flow across the
junction; otherwise, the device will revert to the blocking condition as the anode-to-cathode voltage is reduced.
Latching current ‘L is the minimum anode current required to maintain the thyristor in the on-state immediately
after a thyristor has been turned on and the gate signal has been removed. A typical v—i characteristic of a
thyristor is shown in Fig. 4-2b.

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Once a thyristor conducts, it behaves like a conducting diode and there is no control over the device. The device
will continue to conduct because there is no depletion layer on the junction J due to free movements of carriers.
However, if the forward anode current is reduced below a level known as the holding current ‘H, a depletion
region will develop around junction J due to the reduced number of carriers and the thyristor will be in the
blocking state. The holding current is in the order of milliamperes and is less than the latching current ‘L That
is, ‘L > ‘H. Holding current ‘H is the minimum anode current to maintain the thyristor in the on-state. The
holding current is less than the latching current.

When the cathode voltage is positive with respect to the anode, the junction J is forward biased, but junctions J
and J are reverse biased. This is like two series-connected diodes with reverse voltage across them. The thyristor
will be in the reverse blocking state and a reverse leakage current known as reverse current, ‘R, would flow
through the device.

A thyristor can be turned on by increasing the forward voltage VAK beyond VBO, but such a turn-on could be
destructive. In practice, the forward voltage is maintained below VBO and the thyristor is turned on by applying
a positive voltage between its gate and cathode. This is shown in Fig. 4-2b by dashed lines. Once a thyristor is
turned on by a gating signal and its anode current is greater than the holding current, the device continues to
conduct due to positive feedback, even if the gating signal is removed. A thyristor is a latching device.

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Two-Transistor Model of an SCR

The proper name for the SCR is the reverse blocking triode thyristor. The name is derived from the fact that the
SCR is a four-layer thyristor made of PNPN material. Fig. 4-3a shows the four-layer PNPN material. Fig. 4-3b
shows the PNPN material split apart as two transistors, a PNP and an NPN. Fig. 4-3c shows the SCR as two
transistors. These figures will help you understand how the operation of the SCR can be explained by the four-
layer (two-transistor) model. The anode is at the emitter of the PNP transistor (T2), and the cathode is at the
emitter of the NPN transistor (Ti). The gate is connected to the base of the NPN transistor. Since the anode is
the emitter of the PNP, it must have a positive voltage to operate, and since the cathode is the emitter of the
NPN transistor, it must be negative to operate. When a positive pulse is applied to the gate, it will cause collector
current I to flow through the NPN transistor (Ti). This current will provide bias voltage to the base of the PNP
transistor (T2). When the bias voltage is applied to the base of the PNP transistor, it will begin to conduct I
which will replace the bias voltage on the base that the gate signal originally supplied. This allows the gate
signal to be a pulse, which is then removed since the current through the SCR anode to cathode will flow and
replace the base bias on transistor Ti. Since the SCR is the equivalent of the two-transistor model, you can see
that it will block reverse current just like a junction diode. If reverse voltage is applied to the anode—cathode
circuit, both of the transistors will fail to conduct.

The point in the ac sine wave where the SCR is triggered into conduction is called the firing angle. You should
notice that the smaller the firing angle for ti SCR, the earlier it will turn on during the ac sine wave. This means
that the will start into conduction earlier and, therefore, conduct more current. Since ti SCR has commutation

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at exactly the same point in the ac sine wave (at the 18. point), the amount of current the SCR will conduct is
determined by how early il the ac sine wave the SCR is triggered.

The amount of time the SCR is conducting current is also expressed in de (0) and it is called the conduction
angle. This means that the firing angle and t conduction angle are the complement of each other, since their
total is always 18001 when the SCR is used in an ac circuit. For example, if the SCR has a firing an of 450, it
would turn on at the 45° point and remain in conduction for the remainder of the 1800, which is three-fourths
of the sine wave. This means the conduction angle would be 135°. You must be very careful when the SCR is
being discussed to determine if its operation is described in terms of the firing angle or the conduction angle.

Waveforms of the SCR and the Load

Confusion with waveforms may also arise when you use an oscilloscope to display the waveforms across the
SCR and the load resistor. Since the SCR will exhibit characteristics like a switch, the voltage will be measured
across the SCR when it is off, and the voltage will be measured across the load when the SCR is in conduction.
This means that the oscilloscope will show the waveform of the firing angle when it is across the SCR, and it
will show the conduction angle when it is across the load. Fig. 4-’6 shows these two waveforms.

Methods of Turning on an SCR

The SCR is normally turned on by a pulse to its gate. It can also be turned on by three alternative methods that
include exceeding the forward breakover voltage, by excessive heat that allows leakage current, or by exceeding
the dv/dt level (allowable voltage change per time change) across the junction. The three alternative methods
of turning on an SCR generally cause conditions which should be controlled to prevent the SCR from being
turned on when this is not wanted.

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Turning on an SCR by Exceeding the Forward Breakover Voltage • Each SCR has a forward-bias volt age level
that should never be exceeded because it will immediately go into conduction, even when a gate signal is not
applied. If this forward voltage level is exceeded, it is called forward breakover voltage (VBO). When excessive
forward voltage is applied, the SCR goes into conduction and the current that flows through the anode will latch
the SCR in conduction even if the excessive forward voltage returns to normal levels. This means that a sudden
uncon trolled pulse of excessive forward voltage could turn the SCR on and it would remain on until it was
commutated. SCRs must be sized so that the V rating is sufficiently larger than the circuit voltage it will be
controlling to prevent uncontrolled turn- on. In some circuits additional solid-state devices such as varistors are
used to prevent any undesirable forward-voltage spikes that may exceed the forward breakover level. The
varistor will shunt the excess voltage to prevent it from turning on the SCR

Turning on an SCR by Leakage Current • the junction of the SCR is generally subjected to a buildup of heat. If
this heat is not dissipated or controlled, it will allow the temperature of the junction to increase to a point where
it will allow leakage current to flow through the junction. If the leakage current reaches a sufficient level, the
SCR will turn on and allow forward conduction. This also allows the forward current to latch the SCR in
conduction until it is commutated. The maximum junction temperature will be identified in the SCR
specifications by the term (max). The temperature of the SCR junction is controlled by providing methods of
moving the heat away from the SCR. This can be accomplished by providing heat sinks or fans to move the
heat.

Turning on the SCR by Gate Triggering

When a positive pulse is applied to the gate of the SCR, it must be large enough to provide sufficient current to
the first junction (the base terminal of transistor Ti in the two-transistor model in Fig. 4-3). If the current level
of the pulse is sufficient, the first junction will go into conduction and the current flow through it will cause the
second junction (transistor T2) to go into conduction. The current through the second junction will be sufficient
to latch up the SCR by supplying an alternative source for the gate current. This means that the current to the
gate can be removed and the SCR will remain in conduction. The SCR will commutate when the power supply
it is connected to returns to the zero voltage level at 180° or when ac voltage is in reverse polarity (181° to
360°). If the pulse of current to the gate is too small or is not long enough in duration, the SCR will not turn on.
If you look at the SCR as a three-part device (anode, cathode, and gate), the positive pulse of gate current is
applied to the gate terminal and it will flow through the cathode where it leaves the device. The timing of the
pulse is very critical if the SCR is being used to control the current proportionally. Since the current is being
controlled from zero to maximum, the amount of resolution will be determined by the accuracy of the gate pulse
timing.

Characteristics of the SCR Gate Signal

Since the most common way to turn on an SCR is through a positive pulse, it is important to understand the
characteristics of this signal. The gate pulse must be positive in respect to the cathode and its current should be
0.1—50 mA. The minimum from zero to maximum, the amount of resolution will be determined by the accuracy
of the gate pulse timing.

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Basic Gate Circuit

Fig. 4-8 shows a simple circuit that provides a gate pulse during each positive half-cyvle

of the ac sine wave. The fixed resistor and the adjustable resistor provide a voltage drop that sets the amount of
gate voltage. Fig. 4-9 shows two sets of diagrams of the ac sine wave, the gate signal, the waveform across the
SCR, and the waveform across the load. The minimum gate current ‘UT is shown as a dotted line in the diagram
of the gate signal. In Fig. 4-9a the gate current becomes strong enough at the peak of the ac cycle at the 90°
point. The waveform for the SCR and the load shows the SCR turning on at the 90° point and staying on to the
180° point where the ac reverses its polarity. In Fig. 4-9b, the variable resistor has been adjusted so that the
amount of voltage for the gate signal has increased significantly. This increase in voltage provides an increase
in gate current so that the minimum gate current ‘UT is exceeded at the 30° point. This means that the SCR is
in conduction for 150° (30° to 180°). This method of gate control is rather simplistic since it depends on the
gate current exceeding the minimum current requirement to turn on the SCR.

Methods of Commutating SCRs

Once an SCR is turned on, it will continue to conduct until it is commutated (turned off). Commutation will
occur in an SCR only if the overall current gain drops below unity (1). This means that the current in the anode—
cathode circuit must drop below the minimum (near zero) or a current of reverse polarity must be applied to the
anode-cathode. Since the ac sine wave provides both of these conditions near the 1800 point in the wave, the
main method to commutate an SCR is to use ac voltage as the supply voltage.

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In an ac circuit, the voltage will drop to zero and cross over to the reverse direction at the 1800 point during
each sine wave. This means that if the supply voltage is 60 Hz, this will happen every 16 msec. Each time the
SCR is commutated, it can be triggered at a different point along the firing angle, which will provide the ability
of the SCR to control the ac power between 00 and 1800. The main problem with using ac voltage to commutate
the SCR arises when higher-frequency voltages are used as the supply voltage. You should keep in mind the
SCR requires approximately 3—4 i to turn off; therefore, the maximum frequency is dependent on the turn-off
time.

If the SCR is used in a dc voltage circuit, similar commutation methods can be achieved if the supply voltage
is pulsing dc that returns to near 0 volts at the end of each cycle. Pulsing dc voltage would be available from
rectified ac voltage before it is filtered. In some cases, the SCR is used to rectify the ac voltage instead of
junction diodes, which would provide the ability to control current as well as rectify the voltage.

If the SCR is used in a pure dc voltage circuit, a means of commutating it must be devised. Fig. 4-11 shows
several of these types of commutation circuits. In Fig. 4-ha the SCR is in a dc circuit and a switch is placed in
series with the anode—cathode circuit. This may seem redundant since the SCR acts like a switch, but you
should remember that the SCR has the ability to turn on in such a way to prevent contact bounce or arcing at
contacts. In this circuit, the switch is only used to turn off the SCR. This type of circuit is usable in a simple
alarm circuit. The SCR acts like a relay in that the anode—cathode circuit will provide the function of the
contacts, and the gate will provide the function of the coil. Since the circuit operates well with dc voltage, it can
be used in battery-operated systems when the power is interrupted in the factory. The SCR could control a horn
for the alarm, or it could switch on emergency lights. When the alarm is acknowledged, the switch would be
opened and the SCR would turn off. The switch would need to remain open for 0.1 msec for the hold in current
to drop below the minimum.

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The circuit in Fig. 4-lib shows an LC commutation method. In this circuit

An inductor and capacitor are connected in series with the SCR and load. When the SCR is triggered and current
begins to flow, the LC circuit will become active. The time it takes to charge the capacitor will be a function of
the resonant cycle. When the capacitor is fully charged at the halfway point in the resonant cycle, it will begin
to reverse the current to the anode, which will commutate the SCR. This means the SCR conduction cycle will
be half the resonant cycle. The capacitor and inductor can be sized to set the resonant cycle.

Fig. 4-lic shows a parallel resonant circuit. In this circuit, the LC circuit is connected in parallel with the SCR.
In this circuit, the capacitor is charged as soon as power is applied. When the SCR is turned on, it provides a
path for the capacitor to discharge. When the capacitor becomes fully discharged, it will begin to charge again.
Since the SCR is still in conduction, the current charging the capacitor will be reverse biased to the current in
the SCR. As soon as the current in the capacitor is larger than that flowing in the SCR, the SCR will be
commutated. This means commutation will take place after approximately half the resonant cycle.

The SCR is a current-operated semiconductor device and requires a certain value of positive gate current to
switch it into a conducting state. The amount of gate current re quired to switch the device on is called the gate
trigger current, ‘GT’ and is required for only a brief instant to switch on an SCR. Typically, the gate current
required to trigger an SCR is between 0.1 and 100 mA. Because there is a silicon pn junction between the gate
and cathode, the voltage between these two terminals must be slightly above 0.7 V.

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SCR PHASE-ANGLE CONTROL

There are two basic methods of commutation: forced and natural. In the previous section, it was shown how an
SCR could be switched off by physically interrupting the flow of current by using a switching mechanism.
When SCRs are used in AC circuits, the negative- going alternation of the sine wave will naturally commutate
the SCR. Remember, in order for an SCR to conduct, it must be properly biased. When an AC sine wave crosses
the zero axis, the voltage at the anode become negative with respect to the cathode. This reversal of voltage will
commutate the SCR, and the device will remain off until the gate is pulsed and the proper bias voltage is
connected across the anode and cathode terminals.

SCRs are primarily used in industrial electronic circuits to vary the amount of current supplied to a load, such
as an AC motor. Unlike the transistor, the SCR does not act like a valve. That is, it cannot gradually turn on or
off. Instead, the SCR is either fully conducting or it is completely off, like a switch. In order to vary the amount
of current supplied to a load, the SCR is switched on and off at specific intervals. The longer the SCR is on, the
more current supplied to the load. Consider the waveforms shown in Figure 4-11. The voltage waveform in
Figure 4—11(a) represents the load voltage for 1800 of the conducting cycle. The peak voltage for this
waveform is 200 V. The waveform shown in Figure 4-11(b) also has a peak voltage of 200 V but does not begin
conducting until the 90° point. If a voltmeter were connected across the load in Figure 4-11(b), it would read
one-half of the voltage for the waveform shown in Figure 4-11(a). Since the waveform in Figure 4-11(a)
conducts for twice as long as that of Figure 4-11(b), the voltage reading would double.

A simple SCR circuit that rectifies and controls the amount of current supplied to a load is shown in Figure 4-
1 2 In this circuit, the gate relies on the positive-going alter nation of the input sine wave to trigger the SCR.
Diode D is a steering diode that is used to ensure that only positive current is applied to the gate. All SCRs are
sensitive to reverse gate current and are easily if a n is applied. The AC input waveform is shown in Figure 4-
12(b). As the AC input voltage increases, the SCR is forward-biased but will not conduct until ‘GT is reached.
When the SCR is triggered, max imum current flows through the circuit, and the output voltage is approximately
equal to the input voltage, as shown in Figure 4-12(c). The SCR remains latched on until the input voltage
decreases to the point where the load current falls below the rated holding current for the SCR. At this point,
the SCR is naturally commutated and remains off until 1 is reached again.

Resistor R is a variable resistor that is used to control the current in the gate circuit. If R is increased, it will take
a greater value of gate voltage to produce ‘GT• If R is de creased, a lower value of gate voltage will produce
‘GT• by varying R we are controlling the phase angle of the load voltage. However, the phase angle can only
be effectively controlled between 0° and 90° for the circuit of Figure 4-12(a). When the AC input goes neg
ative, the SCR does not conduct because it is reverse-biased. Consequently, the entire neg ative input waveform
cannot be utilized in this type of circuit.

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To calculate the average output voltage for the circuit of Figure 4-12, the following equation is used:

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Applications of SCRs

SCRs are used in a wide variety of industrial applications that include large currents up to 2000 A at 4000 volts
as well as a variety of low-current applications. The larger SCRs are usually packaged as modules so that they
can fit compactly into motor frequency drives and other types of power supplies. Fig. 4-12 shows an example
of SCRs in modular packages. From this diagram you can see that the terminals for these devices are larger
because the current for the device is larger. Since these SCRs are in a package, their temperature is much easier
to control and replacement of the complete assembly is also easier.

Some applications such as rectifier circuits may use SCRs in place of diodes. Fig. 4-13 shows a variety of
combinations of SCRs that provide single-phase and three-phase half-wave and full-wave rectifier bridges.

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These circuits provide a means of combining the rectification part of the SCR with its ability to control the
amount of current that flows in the circuit. You should also notice that one combination of two SCRs that are
connected in inverse parallel is called an ac switch. The two SCRs are specifically chosen as a matched set and
are mounted in the package together. Since the package is encapsulated in plastic like the ones shown in the
previous figure, you do not have to worry about a mismatch of current or voltage characteristics between the
SCRs. This type of package for the SCR is commonly used in motor drive circuits, welding, and power supply
circuits that use larger currents where a large triac is not available. You will see later in this chapter that the
triac is essentially two SCRs connected inverse and parallel to each other. The second set of diagrams shows a
combination of SCRs and diodes to provide a variety of circuits such as doublers, common cathode devices,
common anode devices, and a three-phase full-wave bridge made from a combination of SCRs and diodes. The
diode is used for part of the circuit because it is less expensive than the SCR, yet it will provide rectification
like the SCR. Since the bridge rectifier is basically a series circuit for the SCR and diode, only one device needs
to have the ability to control the amount of current flow in the circuit.

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The SCRs provide the ability to convert the three-phase voltage that is the input for the circuit to pulsing dc
voltage. Since SCRs are used in the rectifier section instead of diodes, the input voltage can be controlled as
well as rectified.

SCRs are also used in this circuit in the inverter section where the dc voltage is turned back into ac voltage.
Since the devices must provide both the positive and the negative half-cycles, a diode is connected in inverse
parallel to a diode to provide the hybrid ac switch. This combination of devices is not used as often in newer
drives because a variety of larger triacs and power transistors is available that can do the job better. This type
of circuit was very popular in the mid-1980s.

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Since a TRIAC is a bidirectional device, its terminals cannot be designated as anode and cathode. If terminal
MT is positive with respect to terminal MT the TRIAC can be turned on by applying a positive gate signal
between gate G and terminal MT If terminal MT is negative with respect to terminal MT it is turned on by
applying negative gate signal between gate G and terminal MT It is not necessary to have both polarities of gate
signals and a TRIAC can be turned on with either a positive or negative gate signal. In practice, the sensitivities
vary from one quadrant to another, and the TRIACs are normally operated in quadrant I (positive gate voltage
and gate current) or quadrant 111 (negative gate voltage and gate current).

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DIACS

The DIAC is a full-wave or bi-directional semiconductor switch that can be turned on in both forward and
reverse polarities. The DIACgains its name from the contraction of the words DIode Alternating Current. The
DIAC is widely used to assist even triggering of a TRIAC when used in AC switches.

The diac is a two-terminal thyristor that is used as a type of voltage-controlled switch. Fig ure 4—31(a) shows
the equivalent circuit for a diac. When a voltage is applied across the diac, it will not conduct readily because
one of the pn junctions are reverse-biased. However, if the voltage rises to a certain value, the Zener point of
the diac is reached and the diac begins to conduct. The amount of voltage required to switch a diac into a
conducting state is called the breakover voltage. The diac is a bilateral device, which means it will function with
either a positive or negative voltage applied across its terminals. Once the diac is conducting, the only way to
switch it off is to reduce the current flow below the rated holding current of the device. Diacs are primarily used
as triggering devices in phase-control circuits for light dimming, universal motor-speed control, heat control,
and similar applications. The schematic symbol for a diac is shown in Figure 4—31(b), and the current versus
voltage characteristic curve is shown in Figure 4—31(c).

Figure 4—32(a) shows a diac in a simple light dimmer circuit. This type of circuit can control lighting loads in
excess of 1, 000 W and operates on the principle of phase-angle control. The amount of light produced by the
lighting load is directly related to the output waveshape. The longer the triac is commutated, the lower the output
current, and the lower the power delivered to the load. The advantage of using a diac in this type of circuit is
that it prevents the capacitor voltage from triggering the triac until the diac breakover voltage is reached.

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Application of Diac

It can be used mainly in the triac triggering circuit. The diac is connected in the gate terminal of the triac. When
the voltage across the gate decreases below a predetermined value, the gate voltage will be zero and hence the
triac will be turned off. The main applications are-

 It can be used in the lamp dimmer circuit.

 It is used in the heat control circuit.
 It is used in the speed control of a universal motor

UJT

Identification:

UJT is a three terminal semiconductor switching device. As it has only one PN junction and three leads it is
commonly called as uni- junction transistors.

The basic structure of UJT is as shown below.

Picture

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Specifications :( For UJT 2N2646)

 Peak emitter current (Ip) = 2A

 Continuous emitter current (IE) = 50mA
 Inter Base Voltage (VBB) = 35V
 Emitter Base Reverse Voltage (VEB2) = -30V
 Power dissipation at 25°C = 300mW

Testing:

 In case of UJT, emitter to base, (cont1) and emitter to base2 (confg2) should be exhibit a typical diode
characteristics except that the diode resistance in forward and reverse cases is different for the two
configurations.
 The resistance across base1 to base2 should be fixed resistance in either direction.

Applications:

UJT can be used as relaxation oscillator and phase control circuit.

Power MOSFET –

The metal-oxide semiconductor field effect transistor has a gate, source and drain just like JFET. Like a JFET,
the drain current in a MOSFET is controlled by the gate-source voltage VGS. There are two basic types of
MOSFETs. The enhancement type and depletion type. The enhancement type MOSFET is usually referred to
as an E-MOSFET and the depletion type MOSFET is referred to as a D-MOSFET.

Power MOSFETs are the most popular device for SMPS, lighting ballast type of application where high
switching frequencies and low operating voltages are desired.

The construction of a power MOSFET

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Being a voltage fed, majority carrier device (resistive behavior) with a typically rectangular Safe Operating
Area, it can be conveniently utilized.

The resistive characteristics of its main terminals permit easy paralleling externally also.

Utilizing shared manufacturing processes, comparative costs of MOSFETs are attractive.

The circuit symbol of an n-channel MOSFET and its steady-state i-v characteristics are shown

The key difference between JFETs and MOSFETs is that the gate terminal in a MOSFET is insulated from the
channel. Because of this, MOSFETs are sometimes referred to as insulated gate FETs or IGFETs. Because of
the insulated gate, the input impedance of a MOSFET is many times higher t that of a JFET.

Types of MOSFET’S:

 1. n-channel D- MOSFET (b) P-channel D-MOSFET

 2. n-channel E-MOSFET (d) p-channel E-MOSFET

Specifications:

A typical MOSFET is the 3N200 made by BEL. It has two independent gates against only one in a common
MOSFET. Its specifications are drain to source voltage VDS= 0.2V to 20 V. Gate 1 to source voltage V G1S
= 0.6 V to +3 V

Gate 2 to source voltage V G2S = 0.6 V to +6 V Drain to gate 2 voltage VDG2 = +20V

Drain current ID = 50 mA

Transistor dissipation PT = 330 mw Derating = 2.2 m2/0C

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Testing:

1. In case of MOSFET, drain to source should be a fixed resistance in either direction

2. Gate to drain or gate to source should be an open circuit or a very high resistance (greater than FET).

The device under test in the given circuit is a depletion type N- channel JFET, with the gate circuit kept open,
the magnitude of the drain current is sufficient to make the ID R2 drop large enough. So that the BJT is
forward biased and driven into its ON state. Therefore the lamp glows. The switch SW is now closed. The
bias on the FET gate then causes depletion of its channel.

This lowers the IDR2 drop to the point where conduction through the BJT output circuit fails to keep the bulb
glowing. All this will happen if the FET is in good condition. On the other hand, a short circuited FET will
deep the lamp ON in either position of switch SW, while an open FET will fail to switch the indicator lamp
ON. Burst commercially near the end 70’s. First successful modern ICs power devices

Its voltage drive capability and a higher gain, the ease of its paralleling and most importantly the much higher
operating frequencies reaching up to a few MHz enabled it replacing the BJT at the sub-10 KW range mainly
for SMPS type of applications.

Also extension of VLSI manufacturing facilities for the MOSFET reduced its price vis-à-vis the Bipolar.

However, being a majority carrier device its on-state voltage is dictated by the RDS (ON) of the device, which
in turn is proportional to about VDSS2.3 rating of the MOSFET.

Consequently, high-voltage MOSFETS are not commercially viable.

Gate-turn-off (GTO) thyristor-

Improvements were being tried out on the SCR regarding its turn-off capability mostly by reducing the turn-on
gain.

Different versions of the GTOs were proposed by various manufacturers - each advocating their own symbol
for the device.

The requirement for an extremely high turn-off control current via the gate and the comparatively higher cost
of the device restricted its application only to inverters rated above a few hundred KVA.

Like the thyristor, the GTO can be turned on by a short-duration gate current pulse, and once in the on-state,
the GTO may stay on without any further gate current.

However, unlike the thyristor, the GTO can be turned off by applying a negative gate-cathode voltage that cause
a sufficient negative gate current to flow.

Hence there is no need for an external commutation circuit to turn it off like SCR.

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The reverse gate current amplitude is large and dependent on the anode current to be turned off (typically as
large as one-third the anode current being turned off).

Because turn-off is provided by bypassing carriers directly to the gate circuit, its turn-off time is short, thus
giving it more capability for high frequency operation than thyristors.

The circuit symbol for the GTO and its steady-state i-v characteristics are shown

Application

The on-state voltage (2-3V) of GTO is slightly higher than those of thyristors.

The GTO switching speeds are in the range of a few microseconds to 25 μs.

Because of their capability to handle large voltages (up to 5 KV) and large currents (up to 4KA), the GTO is
used when a switch is needed for high voltages and large currents in a switching frequency range of a few
hundred hertz to 1 KHz.

Consequently it has replaced the forced commutated inverter grade thyristor in all DC to AC and DC to DC
converter circuits.

GTOs have the I2t withstand capability and hence can be protected only by semiconductor fuses.

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Insulated Gate Bipolar Transistor (IGBT)-

The lookout for a more efficient, cheap, fast and robust turn-off-able device proceeded in different directions
with MOS drives for both the basic thyristor and the Bipolar.

IGBT basically a MOSFET driven Bipolar from its terminal characteristics has been a successful proposition
with devices being made available at about 4 KV and 4 KA.

Its switching frequency of about 25 KHz and ease of connection and drive ensured it totally removing the
Bipolar from practically all applications.

It is a voltage controlled four-layer device with the advantages of the MOSFET driver and the Bipolar Main
terminal.

IGBTs can be classified based on their structure as

 Punch-through (PT)
 Non-punch-through (NPT)

In the PT IGBT, a better trade-off between the forward voltage drop and turn-off time can be achieved.

They are available up to about 1200 V.

NPT IGBTs of up to about 1.2A/4.5 KV available and they are more robust than PT IGBTs particularly under
short circuit conditions.

However they have a higher forward voltage drop than the PT IGBTs.

The IGBT has also pushed up the GTO to applications above 2-5 MVA.

Its switching times can be controlled by suitably shaping the drive signal. This gives the IGBT a number of
advantages:

It does not require protective circuits, it can be connected in parallel without difficulty, and series connection is
possible without dv/dt snubbers.

The IGBT is presently one of the most popular device in view of its wide ratings, switching speed of about 100
KHz an easy voltage drive and a square Safe Operating Area devoid of a Second Breakdown region.

Advantages and ratings of IGBTs

The IGBTs have some of the advantages of the MOSFET, the BJT and the GTO combined.

Similar to MOSFET, the IGBT has a high impedance gate, which requires only a small amount of energy to
switch the device.

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Like the BJT, the IGBT has a small on-state voltage even in devices with large blocking voltage ratings (for
example, Von is 2-3 V in a 1000-V device).

IGBTs have turn-on and turn-off times on the order of 1 microseconds and are available in module ratings as
large as 4500V and 1200 A.

The IGBT can switch at moderately high frequency (<20 kHZ) and in this range is likely to replace the BJTs in
all medium to high power applications.

The circuit symbol for the IGBT and its steady-state i-v characteristics are shown

Industrially, only the MOSFET has been able to continue in the sub – 10 KVA range primarily because of its
high switching frequency.

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Summary of power scr devices capabilities in 80’s

Fig.3.7

3.4 Types of rectifiers

Controlled Rectifiers:

We have seen previously that diode rectifiers provide a fixed output voltage only. To obtain controlled output
voltages, phase control thyristors are used instead of diodes. The output voltage of thyristor rectifiers is varied
by control ling the delay or firing angle of thyristors. A phase-control thyristor is turned on by applying a
short pulse to its gate and turned off due to natural or line commuta tion; and in case of a highly inductive
load, it is turned off by firing another thyristor of the rectifier during the negative half-cycle of input voltage.

These phase-controlled rectifiers are simple and less expensive; and the efficiency of these rectifiers is, in
general, above 95%. Since these rectifiers con vert from ac to dc, these controlled rectifiers are also called
ac—dc converters and are used extensively in industrial applications, especially in variable-speed drives,
ranging from fractional horsepower to megawatt power level.

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The phase-control converters can be classified into two types, depending on the input supply: (1) single-phase
converters, and (2) three-phase converters. Each type can be subdivided into (a) semiconverter, (b) full
converter, and (c) dual converter. A semiconverter is a one-quadrant converter and it has one polarity of
output voltage and current. A full converter is a two-quadrant converter and the polarity of its output voltage
can be either positive or negative. However, the output current of full converter has one polarity only. A dual
converter can operate in four quadrants; and both the output voltage and current can be either positive or
negative. In some applications, converters are connected in series to operate at higher voltages and to improve
the input power factor.

The method of Fourier series similar to that of diode rectifiers can be applied to analyze the performances of
phase-controlled converters with RL loads. However, to simplify the analysis, the load inductance can be
assumed sufficiently high so that the load current is continuous and has negligible ripple.

Let us consider the circuit in Fig. 5-la with a resistive load. During the positive half-cycle of input voltage, the
thyristor anode is positive with respect to its cathode and the thyristor is said to be forward biased. When
thyristor T is fired at c = a, thyristor T conducts and the input voltage appears across the load. When the input
voltage starts to be negative at cot = , the thyristor anode is negative with respect to its cathode and thyristor T
is said to be reverse biased; and it is turned off. The time after the input voltage starts to go positive until the
thyristor is fired at cot = a is called the delay or firing angle a.

Figure 5-lb shows the region of converter operation, where the output volt age and current have one polarity.
Figure 5-ic shows the waveforms for input voltage, output voltage, load current, and voltage across T This
converter is not normally used in industrial applications because its output has high ripple content and low
ripple frequency. If f is the frequency of input supply, the lowest frequency of output ripple voltage is fs.

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Activities and Exercises

1. What Are The Advantage Of Free Wheeling Diode In A Full Wave Rectifier?
It reduces the harmonics and it also reduces sparking and arching across the mechanical switch so that
it reduces the voltage spike seen in a inductive load.
2. What Is Natural Commutation?
The process of the current flowing through the thyristor goes through a natural zero and enable the
thyristor to turn off is called as natural commutation.
3. A single-phase semi-converter is operated from a 240 V, 60 Hz, AC source. It is fired at an angle of
45°. Find the value of average output voltage.
For a semi-converter, the output voltage Vo = √2Vs (1+cosα)/π = 184 V
4. A single phase full converter has average & peak voltage values of 133 V and 325 V respectively.
Find the value of the firing angle.
Vm = 325V
Vo = 2Vm/π cosα = 133 V = 50°

3.5 Types of inverters

DEFINITION: Converts DC to AC power by switching the DC input voltage (or current) in a pre-determined
sequence so as to generate AC voltage (or current) output.

General block diagram

TYPICAL APPLICATIONS:

 Adjustable speed drives (ASDs),

 Uninterruptible power supplies (UPS),
 Power conversion from PV array and fuel cell
 HVDC transmission, etc

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For sinusoidal ac outputs, the magnitude, frequency, and phase should be controllable.

According to the type of the load nature, Inverter topologies can be considered as

1. Voltage source inverters (VSIs)

2. Current source inverters (CSIs) – used with capacitive load where di/dt spikes become very high.

NB: VSI structures are the most widely used because they naturally behave as voltage sources as
required by many industrial applications, such as adjustable speed drives (ASDs), which are the most popular
application of inverters;

Activities and Exercises

Example: 3.5

Solution

Voltage source inverter. Current source inverter.

Single-phase half-bridge VSI

Inductive load is connected between point 'a' and the center point '0' of a split capacitor power supply.

Q1 and Q2 are closed alternately for angle to generate square wave output voltage.

Vao oscillates between +0.5Vd and -0.5Vd.

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AC Waveform Generation (Single phase Full-bridge VSI Inverter)

S1, S2 ON; S3, S4 OFF for t1< t <t2

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S3, S4 ON; S1, S2 OFF for t2< t <t3

Harmonics Filtering

Output of the inverter is “chopped AC voltage with zero DC component”. It contain harmonics.

• An LC section low-pass filter is normally fitted at the inverter output to reduce the high frequency
harmonics.

• In some applications such as UPS, “high purity” sine wave output is required. Good filtering is a must.

• In some applications such as AC motor drive, filtering is not required.

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Variable Voltage Variable Frequency Capability

Output voltage frequency can be varied by “period” of the square-wave pulse.

• Output voltage amplitude can be varied by varying the “magnitude” of the DC input voltage.

• Very useful: e.g. variable speed induction motor drive

Three Phase bridge inverters:

Three phase inverters are more popular in industrial drives to provide variable frequency supply.

A three phase inverter consists of six thyristors, each gated at regular intervals of 600 in the proper sequence.

Transistor devices (such as IGBT) are preferred for Inverters as they do not require commutation circuit.

For high power rating, SCRs are used and they require commutation circuit and it increases the complexity in
the inverter.

Whatever devices are used, the operation remains same, but device turn ON and turn OFF method is different.

There are two possible patterns in controlling the inverter.

 In one pattern, each SCR conducts for 1800 and

 In the other, each SCR conducts for 1200.

Three phase 1800 mode VSI

In this mode, each SCR conduct for 1800 of a cycle. There are three arms (or legs). Each arm SCR is made to
conduct for 1800.

Three phase 1200 mode VSI

In this mode, each SCR conduct for 1200 in each cycle. At every 600, one SCR is fired. In this mode, at any
time only two SCRs will be in conduction.

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3.6 Assessments
1. Construction, working principle and current voltage characteristics of :
A. Diode
B. BJT transistor
C. MOSFET
D. IGBT
E. DIAC
F. SCR
G. TRIAC
H. Triggering ckt
11. Circuit diagram and wave form of:
A. Single phase half wave with R, RL, and RL with FWD
B. Single phase full wave with large and small L/R ratio
12. Give an Expression for Average Voltage of Single Phase half-wave control?
13. What Are The Applications Of An Inverter?

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3.7 Summaries and Reviews

Power electronics is a specialized branch of electronics that deals with the conversion, control, and regulation
of electrical power. It involves the design and implementation of circuits and systems to efficiently convert
electrical energy from one form to another, such as AC to DC, DC to AC, DC to DC, and AC to AC. Power
electronic devices such as diodes, transistors, thyristors, and power converters play a crucial role in various
applications, including power supplies, motor drives, renewable energy systems, electric vehicles, and industrial
automation.

Power electronics has become increasingly important in today's world as the demand for energy-efficient and
reliable electrical systems continues to rise. Its applications span a wide range of industries, from consumer
electronics to transportation and renewable energy. Power electronic converters enable the efficient control and
distribution of electrical power, improving energy conversion efficiency and reducing losses in electrical
systems.

One of the key advantages of power electronics is its ability to regulate voltage, current, and frequency with
high precision, enabling optimal performance and operation of electrical devices and systems. For example, in
electric vehicle propulsion systems, power electronic converters manage the flow of electrical energy between
the battery, motor, and other components, maximizing efficiency and extending battery life.

Power electronics also plays a critical role in renewable energy systems, such as solar and wind power plants,
by enabling the integration of renewable energy sources into the electrical grid. Power converters help smooth
out fluctuations in power generation and ensure compatibility between renewable energy sources and the
existing grid infrastructure.

However, power electronics also presents challenges, including heat dissipation, electromagnetic interference,
and reliability issues. Designing efficient and reliable power electronic systems requires careful consideration
of factors such as component selection, thermal management, and electromagnetic compatibility.

Overall, power electronics continues to drive innovation and advancement in electrical engineering, enabling
the development of energy-efficient and sustainable technologies. As the demand for clean energy and
electrification grows, the importance of power electronics in shaping the future of energy systems cannot be
overstated.

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3.8 Resources and References

[1] B. R. Pelly, Thyristor Phase-Controlled Converters and Cycloconverters, Wiley, NewYork, 1971

[2] C. Lander, Power Electronics, Second Edition, McGraw Hill, England, 1987

[3] B. K. Bose, Power Electronics and Ac Drives, Prentice-Hall, New Jersey, 1986

[4] H. Li, B.Ozpineci and B.K.Bose, “A Soft-Switched High Frequency Non-Resonant Link

Integral Pulse Modulated DC-DC Converter for AC Motor Drive”, Conference

Proceedings of IEEE-IECON, Aachen/Germany, 1998, vol. 2, pp 726-732

[5] B. Ozpineci, B.K. Bose, “A Soft-Switched Performance Enhanced High Frequency NonResonant

Link Phase-Controlled Converter for AC Motor Drive”, Conference Proceedings of IEEE-IECON,

Aachen/Germany, 1998, vol. 2, pp 733-739

[6] Power Electronics – by VedamSubramanyam, New Age International (P) Limited,P

[7] Power Electronics - by V.R.Murthy , 1st edition -2005, OXFORD University Press

[8] Power Electronics-by P.C.Sen,TataMcGraw-Hill Publishing.

[9] Thyristorised Power Controllers – by G. K. Dubey, S. R. Doradra, A. Joshi and R. M. K. Sinha, New Age
International (P) Limited Publishers, 1996

[10] Power Electronics by P.C. Sen Tata McGraw Hill. New Delhi

[11] Power Electronics by P.S. Bhimbhra, Khanna Publishers, New Delhi

[12] Power Electronics by M.S. Berde, Khanna Publishers, New Delhi.

[13] Industrial Electronics and Control by SK Bhattacharya and S. Chatterji, New Age

[14] Power Electronics by S Rama Reddy, Narosa Publishing House Pvt. Ltd.,

[15] Power Electronics – Principles and Applications by J Michael Jacob, Vikas PublishingHouse, New Delhi

[16] Principle of electronics-v.k. Mehta, Rohit Mehta, S. Chand

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II. Conclusions
Overall
This module has been designed to comprehensively prepare electrical-electronics students for their upcoming
exit exam, equipping them with the knowledge, skills, and confidence needed to succeed. Throughout the
course, students have delved deep into the principles and applications of electronics, covering topics ranging
from basic electronic components to advanced circuit design and analysis.

By systematically reviewing key concepts such as semiconductor and diode theory, and digital logic and power
electronics, students have gained a solid understanding of the fundamental principles that underpin electronic
systems. They have honed their analytical and problem-solving skills through hands-on exercises, practical
demonstrations, and simulated experiments, allowing them to apply theoretical knowledge to real-world
scenarios.

Moreover, this module has emphasized the importance of critical thinking, attention to detail, and effective
communication in the field of electronics. Students have been encouraged to approach problems systematically,
break them down into manageable steps, and articulate their solutions clearly and concisely. These skills are
essential not only for success in the exit exam but also for future academic and professional endeavors.

As students prepare to take their exit exam, it is important for them to remain focused, disciplined, and confident
in their abilities. They should continue to review and reinforce key concepts, practice solving sample problems,
and seek clarification on any areas of uncertainty. Additionally, they should make use of resources such as
textbooks, online tutorials, and peer support to supplement their learning and address any gaps in understanding.

Finally, as students embark on the next phase of their academic or professional journey, they should remember
that learning is a lifelong process. The knowledge and skills acquired in this module are just the beginning of
their journey in the field of electronics. By staying curious, adaptable, and open to new challenges, they will
continue to grow and succeed in this dynamic and ever-evolving field.

We wish all students the best of luck in their exit exam and future endeavors in the
exciting world of electronics!"

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