Basic idea about Electronics
Definition of electronics:
A branch of physics that deals with the study of flow and
control of electrons (electricity) and the study of their behavior
and effects in vacuums, gases, and semiconductors, and with
devices using such electrons.
Difference between Electrical and Electronics:
• Electronics deals with flow of charge (electron) through non-
metal conductors (semiconductors).
• Electrical deals with the flow of charge through metal
conductors.
1
2
Basic idea about Electronics
Electrical Device
[Transformer, Induction Motor
etc.]
Electronic Device
[Transistor, Diode,
Microprocessor etc.]
3
Importance of Electronics
• Rectification
• Amplification
• Control
• Generation
• Conversion of light into electricity
• Conversion of electricity into light
Bohr’s Atomic Model
(i) An atom consists of a positively charged
nucleus around which negatively charged
electrons revolve in different circular orbits.
(ii) The electrons can revolve around the
nucleus only in certain permitted orbits i.e.
orbits of certain radii are allowed.
(iii) The electrons in each permitted orbit have
a certain fixed amount of energy. The larger the
orbit (i.e. larger radius), the greater is the
energy of electrons.
(iv) If an electron is given additional energy
(e.g. heat, light etc.), it is lifted to the higher
orbit. The atom is said to be in a state of
excitation.
5
Energy Levels
Fig. 1 Fig. 2
6
Energy Bands
Fig. 3
The range of energies possessed by an electron in a solid is
known as energy band. Band structure of a material defines the
band of energy levels that an electron can occupy.
7
Energy Bands
Fig. 4
1. Valence band: Valance band is the
range of electron energy where
the electron remain bended to the
atom and do not contribute to the
electric current.
2. Conduction band: Conduction
bend is the range of electron
energies higher than valance band
where electrons are free to
accelerate under the influence of
external voltage source resulting
in the flow of charge.
3. Forbidden energy gap: The separation
between conduction band and valence
band on the energy level diagram is
known as forbidden energy gap.
8
Energy Bands
Glass, wood Germanium, silicon Copper, Aluminum
9
Semiconductor Materials
Materials commonly used in the development of
semiconductor devices
• Silicon (Si)
• Germanium (Ge)
• Gallium Arsenide (GaAs)
10
Semiconductor Materials
11
Semiconductor Materials
Intrinsic Semiconductor:
A pure form of semiconductors is called as intrinsic semiconductor.
Conduction in intrinsic semiconductor is either due to thermal excitation or
crystal defects. Si and Ge are the two most important semiconductors used.
Other examples include Gallium arsenide GaAs, Indium Antimonide (InSb)
etc.
Extrinsic Semiconductor:
Intrinsic semiconductor has very limited applications as they conduct very
small amounts of current at room temperature. The current conduction
capability of intrinsic semiconductor can be increased significantly by adding
a small amounts impurity to the intrinsic semiconductor. By adding impurities
it becomes impure or extrinsic semiconductor. This process of adding
impurities is called as doping. The amount of impurity added is 1 part in 10^6
atoms.
12
Intrinsic Semiconductor:
For Silicon/ Germenium, there are four electrons
in the outermost shell, which are referred to as
valence electrons.
In a pure silicon or germanium crystal the four
valence electrons of one atom form a bonding
arrangement with four adjoining atoms.
Although the covalent bond will result in a
stronger bond between the valence electrons
and their parent atom, it is still possible for the
valence electrons to absorb sufficient kinetic
energy from external natural causes to break
the covalent bond and assume the “free” state.
The free electrons in a material due only to
external causes are referred to as intrinsic
carriers.
13
Doping
• The electrical characteristics of silicon and germanium are
improved by doping.
• There are just two types of doped semiconductor materials
 n-type
 p-type
• n-type materials contain an excess of conduction band
electrons. Example of n-type materials are Antimony,
Phosphorus, Bismuth , Arsenic etc.
• p-type materials contain an excess of valence band holes.
Example p-type materials : Boron, Indium, Gallium etc.
14
Extrinsic Materials (1/2)
• n-Type Material: If the added impurity is a pentavalent atom
then the resultant semiconductor is called N-type semiconductor.
• Examples of pentavalent impurities are Phosphorus, Arsenic,
Bismuth, Antimony etc.
15
Extrinsic Materials (1/2)
A pentavalent impurity has five valance electrons. The
fifth electron is loosely bound to the impurity atom.
This loosely bound electron can be easily excited from
the valance band to the conduction band by the
application of electric field or increasing the thermal
energy.
The addition of pentavalent impurity provides a large
number of free electrons in the semiconductor crystal.
Such impurities which produce n-type semiconductor
are known as donor impurities because they donate or
provide free electrons to the semiconductor crystal.
Consider the pure silicon crystal which has four valence electrons. When small
amount of pentavalent impurity like Antimony (Sb) is added to Si crystal, a large
number of free electrons become available in the crystal. The reason is that Sb
atom fits in the Si crystal in such a way that its four valence electrons form covalent
bonds with four Si atoms. The fifth valence electron of Sb atom finds no place in
covalent bonds and is thus free.
16
Extrinsic Materials (1/2)
At room temperature almost all the fifth electrons from the
donor impurity atom are raised to conduction band and hence
the number of electrons in the conduction band increases
significantly.
In the N-type semiconductor the no. of electrons increases and
the no. of holes decreases compared to those available in an
intrinsic semiconductor.
Thus current in N type semiconductor is dominated by
electrons which are referred to as majority carriers. Holes are
the minority carriers in N type semiconductor.
17
Extrinsic Materials (2/2)
• p-Type Material: If the added impurity is a trivalent
atom then the resultant semiconductor is called P-type
semiconductor.
• Examples of trivalent impurities are Boron, Gallium,
indium etc.
18
Extrinsic Materials (2/2)
The crystal structure of p type semiconductor is shown in
the figure. The three valance electrons of the impurity
(Boron) forms three covalent bonds with the neighboring
atoms (Si) and a vacancy exists in the fourth bond giving
rise to the holes. The hole is ready to accept an electron
from the neighboring atoms. Each trivalent atom
contributes to one hole generation and thus introduces a
large no. of holes in the valance band. At the same time
the no. electrons are decreased compared to those
available in intrinsic semiconductor because of increased
recombination due to creation of additional holes.
Thus in P type semiconductor, holes are majority carriers and electrons are
minority carriers. Since each trivalent impurity atoms are capable accepting an
electron, these are called as acceptor atoms.
19
Electron versus Hole Flow
20
Majority and Minority Carriers
• Majority Carriers
The majority carriers in n-type materials are electrons.
The majority carriers in p-type materials are holes.
• Minority Carriers
The minority carriers in n-type materials are holes.
The minority carriers in p-type materials are electrons.
21
p-n Junctions (1/2)
• When a p-type semiconductor is suitably joined to
n-type semiconductor, the contact surface is called
p-n junction.
• One end of a silicon or germanium crystal can be
doped as a p-type material and the other end as an
n-type material.
• The result is a p-n junction.
22
p-n Junctions (2/2)
• At the p-n junction, the excess
conduction-band electrons on the n-
type side are attracted to the valence-
band holes on the p-type side.
• The electrons in the n-type material
migrate across the junction to the p-
type material (electron flow).
• The electron migration results in a
negative charge on the p-type side of
the junction and a positive charge on
the n-type side of the junction.
The result is the formation of a
depletion region around the
junction.
Depletion layer is formed due to diffusion force of majority carriers of p and
n type materials.
24
Diodes
25
Diode
When both n-type and p-type materials are available,
we can construct out first solid-state electronic device:
The semiconductor diode.
It is a two-terminal device that conducts current only in
one direction.
A diode has three operating conditions
• No bias
• Forward Bias
• Reverse Bias
26
Diode Operating Conditions - No Bias
•
27
Diode Operating Conditions - Forward Bias
• A forward-bias or “on” condition is established by applying the positive
potential to the p-type material and the negative potential to the n-type
material.
• If the p-n junction diode is forward biased with approximately 0.7 volts for
silicon diode or 0.3 volts for germanium diode, the p-n junction diode starts
allowing the electric current.
28
Diode Operating Conditions - Forward Bias
•
29
Diode Operating Conditions - Reverse Bias
• The positive terminal of the battery is connected to the
n-type semiconductor and the negative terminal of the
battery is connected to the p-type semiconductor.
• The holes from the p-side are attracted towards the negative
terminal whereas free electrons from the n-side are attracted
towards the positive terminal.
• The free electrons begin their journey at the negative terminal
whereas holes begin their journey at the positive terminal.
• Free electrons, which begin their journey at the negative
terminal, find large number of holes at the p-type
semiconductor and fill them with electrons. On the other hand,
holes or positive charges, which begin their journey at the
positive terminal, find large of free electrons at the n-type
semiconductor and replace the electrons position with holes.
• This increases the width of depletion region.
• The wide depletion region of the p-n junction diode
completely blocks the majority charge carriers. Hence,
majority charge carriers cannot carry the electric current.
30
Diodes
The diode is a 2-terminal device.
A diode ideally conducts in only one direction.
• The ideal diode, therefore, is a short circuit for the region of
conduction.
• The ideal diode, therefore, is an open circuit in the region of
no conduction.
31
Ideal Diode Characteristics
 Forward Biasing  Reverse Biasing
32
Actual Diode Characteristics, or I-V
Characteristics
 Note the regions
for no bias,
reverse bias, and
forward bias
conditions.
 Carefully note the
scale for each of
these conditions.
33
Forward Bias Voltage
• The point at which the diode changes from no-bias
condition to forward-bias condition occurs when the
electrons and holes are given sufficient energy to cross the
p-n junction. This energy comes from the external voltage
applied across the diode.
• The forward bias voltage required for a
Gallium Arsenide diode ≥ 1.2 V
Silicon diode ≥ 0.7 V
Germanium diode ≥ 0.3 V
34
Si, Ge, GaAS
35
Ideal vs Actual Diode Characteristics
36
Ideal vs Actual Diode Characteristics
• A diode is said to be an Ideal
Diode when it is forward biased
and acts like a perfect conductor.
• Similarly, when the diode is
reversed biased, it acts as a
perfect insulator with zero
current through it.
• An Ideal diode also acts like a
switch. When the diode is
forward biased it acts like a
closed switch.
• Whereas, if the diode is reversed
biased, it acts like an open
switch.
37
Ideal vs Actual Diode Characteristics
•
38
Ideal vs Actual Diode Characteristics
Ideal diodes Actual diodes
Ideal diodes act as perfect
conductor and perfect insulator.
Practical diodes cannot act as
perfect conductor and perfect
insulator.
Ideal diode draws no current
when reverse biased.
Practical diode draws very low
current when reverse biased.
Ideal diode offers infinite
resistance when reverse biased.
Practical diode offers very high
resistance when reverse biased.
It cannot be manufactured. It can be manufactured.
It has zero cut-in voltage. It has very low cut-in voltage.
Ideal diode has zero voltage
drops across its junction when
forward biased.
It has very low voltage drop
across it, when forward biased.
40
Diode Equivalent Circuit
Simplified equivalent circuit for the silicon semiconductor diode.
Components of the piecewise-linear equivalent circuit.
41
Diode Equivalent Circuit
Ideal diode and its characteristics.
42
Semiconductor diode notation
43
Problem Analysis
• For the series diode configuration, determine VD,
VR, and ID.
Repeat the problem with the diode reversed.
44
45
VI=5 v
46
Example for Practice
Ref. Book- “Electronic Devices and Circuit Theory”
by Louis Nashelsky and Robert Boylestad, 12th
Edition.
Example: 2.1, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9, 2.10, 2.11, 2.12
47
Various types of junction diodes
48
Zener Diode
• A Zener is a diode operated in reverse bias at the
Zener voltage (VZ).
• Common Zener voltages are between 1.8 V and 200
V
49
Zener Region
• The Zener region is in the diode’s
reverse-bias region.
• At some point the reverse bias
voltage is so large that the diode
breaks down and the reverse current
increases dramatically
• The maximum reverse-bias potential
that can be applied before entering
the Zener region is called the peak
inverse voltage (referred to simply as
the PIV rating) or the peak reverse
voltage (denoted by PRV rating).
• The voltage that causes a diode to
enter the zener region of operation is
called the zener voltage (VZ).
50
Zener Diode
The Zener diode is a special type of diode that is designed to operate in the
reverse breakdown region.
51
Zener Diode
52
Zener Diode
53
Problem Analysis:
• Ref. Book- “Electronic Devices and Circuit Theory” by
Louis Nashelsky and Robert Boylestad, 11th
Edition.
Example: 2.1, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9, 2.10, 2.11, 2.12, 2.13,
2.16, 2.17, 2.26, 2.27.
• Ref. Book: “Principles of Electronics” by V. K. Mehta.
Example: 6.4, 6.5, 6.6, 6.8

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EEE 2187.......................... .pptx

  • 1. Basic idea about Electronics Definition of electronics: A branch of physics that deals with the study of flow and control of electrons (electricity) and the study of their behavior and effects in vacuums, gases, and semiconductors, and with devices using such electrons. Difference between Electrical and Electronics: • Electronics deals with flow of charge (electron) through non- metal conductors (semiconductors). • Electrical deals with the flow of charge through metal conductors. 1
  • 2. 2 Basic idea about Electronics Electrical Device [Transformer, Induction Motor etc.] Electronic Device [Transistor, Diode, Microprocessor etc.]
  • 3. 3 Importance of Electronics • Rectification • Amplification • Control • Generation • Conversion of light into electricity • Conversion of electricity into light
  • 4. Bohr’s Atomic Model (i) An atom consists of a positively charged nucleus around which negatively charged electrons revolve in different circular orbits. (ii) The electrons can revolve around the nucleus only in certain permitted orbits i.e. orbits of certain radii are allowed. (iii) The electrons in each permitted orbit have a certain fixed amount of energy. The larger the orbit (i.e. larger radius), the greater is the energy of electrons. (iv) If an electron is given additional energy (e.g. heat, light etc.), it is lifted to the higher orbit. The atom is said to be in a state of excitation.
  • 6. 6 Energy Bands Fig. 3 The range of energies possessed by an electron in a solid is known as energy band. Band structure of a material defines the band of energy levels that an electron can occupy.
  • 7. 7 Energy Bands Fig. 4 1. Valence band: Valance band is the range of electron energy where the electron remain bended to the atom and do not contribute to the electric current. 2. Conduction band: Conduction bend is the range of electron energies higher than valance band where electrons are free to accelerate under the influence of external voltage source resulting in the flow of charge. 3. Forbidden energy gap: The separation between conduction band and valence band on the energy level diagram is known as forbidden energy gap.
  • 8. 8 Energy Bands Glass, wood Germanium, silicon Copper, Aluminum
  • 9. 9 Semiconductor Materials Materials commonly used in the development of semiconductor devices • Silicon (Si) • Germanium (Ge) • Gallium Arsenide (GaAs)
  • 11. 11 Semiconductor Materials Intrinsic Semiconductor: A pure form of semiconductors is called as intrinsic semiconductor. Conduction in intrinsic semiconductor is either due to thermal excitation or crystal defects. Si and Ge are the two most important semiconductors used. Other examples include Gallium arsenide GaAs, Indium Antimonide (InSb) etc. Extrinsic Semiconductor: Intrinsic semiconductor has very limited applications as they conduct very small amounts of current at room temperature. The current conduction capability of intrinsic semiconductor can be increased significantly by adding a small amounts impurity to the intrinsic semiconductor. By adding impurities it becomes impure or extrinsic semiconductor. This process of adding impurities is called as doping. The amount of impurity added is 1 part in 10^6 atoms.
  • 12. 12 Intrinsic Semiconductor: For Silicon/ Germenium, there are four electrons in the outermost shell, which are referred to as valence electrons. In a pure silicon or germanium crystal the four valence electrons of one atom form a bonding arrangement with four adjoining atoms. Although the covalent bond will result in a stronger bond between the valence electrons and their parent atom, it is still possible for the valence electrons to absorb sufficient kinetic energy from external natural causes to break the covalent bond and assume the “free” state. The free electrons in a material due only to external causes are referred to as intrinsic carriers.
  • 13. 13 Doping • The electrical characteristics of silicon and germanium are improved by doping. • There are just two types of doped semiconductor materials  n-type  p-type • n-type materials contain an excess of conduction band electrons. Example of n-type materials are Antimony, Phosphorus, Bismuth , Arsenic etc. • p-type materials contain an excess of valence band holes. Example p-type materials : Boron, Indium, Gallium etc.
  • 14. 14 Extrinsic Materials (1/2) • n-Type Material: If the added impurity is a pentavalent atom then the resultant semiconductor is called N-type semiconductor. • Examples of pentavalent impurities are Phosphorus, Arsenic, Bismuth, Antimony etc.
  • 15. 15 Extrinsic Materials (1/2) A pentavalent impurity has five valance electrons. The fifth electron is loosely bound to the impurity atom. This loosely bound electron can be easily excited from the valance band to the conduction band by the application of electric field or increasing the thermal energy. The addition of pentavalent impurity provides a large number of free electrons in the semiconductor crystal. Such impurities which produce n-type semiconductor are known as donor impurities because they donate or provide free electrons to the semiconductor crystal. Consider the pure silicon crystal which has four valence electrons. When small amount of pentavalent impurity like Antimony (Sb) is added to Si crystal, a large number of free electrons become available in the crystal. The reason is that Sb atom fits in the Si crystal in such a way that its four valence electrons form covalent bonds with four Si atoms. The fifth valence electron of Sb atom finds no place in covalent bonds and is thus free.
  • 16. 16 Extrinsic Materials (1/2) At room temperature almost all the fifth electrons from the donor impurity atom are raised to conduction band and hence the number of electrons in the conduction band increases significantly. In the N-type semiconductor the no. of electrons increases and the no. of holes decreases compared to those available in an intrinsic semiconductor. Thus current in N type semiconductor is dominated by electrons which are referred to as majority carriers. Holes are the minority carriers in N type semiconductor.
  • 17. 17 Extrinsic Materials (2/2) • p-Type Material: If the added impurity is a trivalent atom then the resultant semiconductor is called P-type semiconductor. • Examples of trivalent impurities are Boron, Gallium, indium etc.
  • 18. 18 Extrinsic Materials (2/2) The crystal structure of p type semiconductor is shown in the figure. The three valance electrons of the impurity (Boron) forms three covalent bonds with the neighboring atoms (Si) and a vacancy exists in the fourth bond giving rise to the holes. The hole is ready to accept an electron from the neighboring atoms. Each trivalent atom contributes to one hole generation and thus introduces a large no. of holes in the valance band. At the same time the no. electrons are decreased compared to those available in intrinsic semiconductor because of increased recombination due to creation of additional holes. Thus in P type semiconductor, holes are majority carriers and electrons are minority carriers. Since each trivalent impurity atoms are capable accepting an electron, these are called as acceptor atoms.
  • 20. 20 Majority and Minority Carriers • Majority Carriers The majority carriers in n-type materials are electrons. The majority carriers in p-type materials are holes. • Minority Carriers The minority carriers in n-type materials are holes. The minority carriers in p-type materials are electrons.
  • 21. 21 p-n Junctions (1/2) • When a p-type semiconductor is suitably joined to n-type semiconductor, the contact surface is called p-n junction. • One end of a silicon or germanium crystal can be doped as a p-type material and the other end as an n-type material. • The result is a p-n junction.
  • 22. 22 p-n Junctions (2/2) • At the p-n junction, the excess conduction-band electrons on the n- type side are attracted to the valence- band holes on the p-type side. • The electrons in the n-type material migrate across the junction to the p- type material (electron flow). • The electron migration results in a negative charge on the p-type side of the junction and a positive charge on the n-type side of the junction. The result is the formation of a depletion region around the junction.
  • 23. Depletion layer is formed due to diffusion force of majority carriers of p and n type materials.
  • 25. 25 Diode When both n-type and p-type materials are available, we can construct out first solid-state electronic device: The semiconductor diode. It is a two-terminal device that conducts current only in one direction. A diode has three operating conditions • No bias • Forward Bias • Reverse Bias
  • 27. 27 Diode Operating Conditions - Forward Bias • A forward-bias or “on” condition is established by applying the positive potential to the p-type material and the negative potential to the n-type material. • If the p-n junction diode is forward biased with approximately 0.7 volts for silicon diode or 0.3 volts for germanium diode, the p-n junction diode starts allowing the electric current.
  • 28. 28 Diode Operating Conditions - Forward Bias •
  • 29. 29 Diode Operating Conditions - Reverse Bias • The positive terminal of the battery is connected to the n-type semiconductor and the negative terminal of the battery is connected to the p-type semiconductor. • The holes from the p-side are attracted towards the negative terminal whereas free electrons from the n-side are attracted towards the positive terminal. • The free electrons begin their journey at the negative terminal whereas holes begin their journey at the positive terminal. • Free electrons, which begin their journey at the negative terminal, find large number of holes at the p-type semiconductor and fill them with electrons. On the other hand, holes or positive charges, which begin their journey at the positive terminal, find large of free electrons at the n-type semiconductor and replace the electrons position with holes. • This increases the width of depletion region. • The wide depletion region of the p-n junction diode completely blocks the majority charge carriers. Hence, majority charge carriers cannot carry the electric current.
  • 30. 30 Diodes The diode is a 2-terminal device. A diode ideally conducts in only one direction. • The ideal diode, therefore, is a short circuit for the region of conduction. • The ideal diode, therefore, is an open circuit in the region of no conduction.
  • 31. 31 Ideal Diode Characteristics  Forward Biasing  Reverse Biasing
  • 32. 32 Actual Diode Characteristics, or I-V Characteristics  Note the regions for no bias, reverse bias, and forward bias conditions.  Carefully note the scale for each of these conditions.
  • 33. 33 Forward Bias Voltage • The point at which the diode changes from no-bias condition to forward-bias condition occurs when the electrons and holes are given sufficient energy to cross the p-n junction. This energy comes from the external voltage applied across the diode. • The forward bias voltage required for a Gallium Arsenide diode ≥ 1.2 V Silicon diode ≥ 0.7 V Germanium diode ≥ 0.3 V
  • 35. 35 Ideal vs Actual Diode Characteristics
  • 36. 36 Ideal vs Actual Diode Characteristics • A diode is said to be an Ideal Diode when it is forward biased and acts like a perfect conductor. • Similarly, when the diode is reversed biased, it acts as a perfect insulator with zero current through it. • An Ideal diode also acts like a switch. When the diode is forward biased it acts like a closed switch. • Whereas, if the diode is reversed biased, it acts like an open switch.
  • 37. 37 Ideal vs Actual Diode Characteristics •
  • 38. 38 Ideal vs Actual Diode Characteristics Ideal diodes Actual diodes Ideal diodes act as perfect conductor and perfect insulator. Practical diodes cannot act as perfect conductor and perfect insulator. Ideal diode draws no current when reverse biased. Practical diode draws very low current when reverse biased. Ideal diode offers infinite resistance when reverse biased. Practical diode offers very high resistance when reverse biased. It cannot be manufactured. It can be manufactured. It has zero cut-in voltage. It has very low cut-in voltage. Ideal diode has zero voltage drops across its junction when forward biased. It has very low voltage drop across it, when forward biased.
  • 39. 40 Diode Equivalent Circuit Simplified equivalent circuit for the silicon semiconductor diode. Components of the piecewise-linear equivalent circuit.
  • 40. 41 Diode Equivalent Circuit Ideal diode and its characteristics.
  • 42. 43 Problem Analysis • For the series diode configuration, determine VD, VR, and ID. Repeat the problem with the diode reversed.
  • 43. 44
  • 45. 46 Example for Practice Ref. Book- “Electronic Devices and Circuit Theory” by Louis Nashelsky and Robert Boylestad, 12th Edition. Example: 2.1, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9, 2.10, 2.11, 2.12
  • 46. 47 Various types of junction diodes
  • 47. 48 Zener Diode • A Zener is a diode operated in reverse bias at the Zener voltage (VZ). • Common Zener voltages are between 1.8 V and 200 V
  • 48. 49 Zener Region • The Zener region is in the diode’s reverse-bias region. • At some point the reverse bias voltage is so large that the diode breaks down and the reverse current increases dramatically • The maximum reverse-bias potential that can be applied before entering the Zener region is called the peak inverse voltage (referred to simply as the PIV rating) or the peak reverse voltage (denoted by PRV rating). • The voltage that causes a diode to enter the zener region of operation is called the zener voltage (VZ).
  • 49. 50 Zener Diode The Zener diode is a special type of diode that is designed to operate in the reverse breakdown region.
  • 52. 53 Problem Analysis: • Ref. Book- “Electronic Devices and Circuit Theory” by Louis Nashelsky and Robert Boylestad, 11th Edition. Example: 2.1, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9, 2.10, 2.11, 2.12, 2.13, 2.16, 2.17, 2.26, 2.27. • Ref. Book: “Principles of Electronics” by V. K. Mehta. Example: 6.4, 6.5, 6.6, 6.8