Electrical and Electronic Fundamental

CHAPTER 5

FUNDAMENTAL OF SOLID STATE PRINCIPLES

Introduction

Learning Objectives
The objectives of this chapter are to:
1. Explain the basic structure of atoms.
2. Explain the difference of insulators, conductors and semiconductors.
3. Describe how current is produced in semiconductor.
4. Describe the properties of n-type and p-type of semiconductor.

5.1 Atomic Theory
The atom is the smallest particle of an element that retains the original

characteristics of that element. The simplest atomic model, called the Bohr
model, represents the atom as a central core (called the nucleus) and one
or more orbiting electrons as depicted in Figure 5.1. The nucleus contains
neutrons (which are electrically neutral) and protons. Protons are positively
charged particles. The orbiting electrons are negatively charged particles.
In their natural state, atoms contain an equal number of protons (+) and
electrons (-), resulting in a net charge of zero.

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Orbital shells

Orbiting electron M
L
Nucleus K
(proton and neutron)

Figure 5.1: Bohr model of the atom

A given element can be classified as a conductor, semiconductor,
or insulator, depending on the number of electrons in its valence
(outermost) orbital shell. Generally, any element with:

• One valence electron is referred to as a conductor.

• Four valence electrons is referred to as a semiconductor.

• Eight valence electrons is referred to as an insulator.

Conductors have low resistivity ratings. Insulators have extremely high
resistivity ratings. Semiconductors have resistivity ratings that fall about
halfway between those of a conductor and those of an insulator. Under
specific circumstances, the resistance of a semiconductor can be varied
between that of a conductor and that of an insulator.

The three most commonly used semiconductor materials are silicon,
germanium, and carbon as shown in Figure 5.2. Silicon (Si) and germanium
(Ge) are typically used in the production of solid-state devices, whereas
carbon (C) is typically used in the production of basic resistors and
potentiometers.

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Silicon Germanium Carbon

Figure 5.2: Semiconductor atom

5.1.1 Charge and Conduction

The space that exists between two orbital shells is referred to as an
energy gap. Figure 5.3 shows the energy gap and level for the silicon. When
an electron absorbs enough energy to overcome the energy gap between
two orbital shells, the electron jumps from the lower energy shell to the
higher energy shell. In this case, the electron is said to be in its excited state.
Eventually, an excited electron gives up the energy it absorbed and returns
to a lower energy shell. The energy given up by the electron is in the form
of light or heat.

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Conduction band Energy e4 = 1.8eV
Energy gap
Valence e3 = 0.7eV
band e2
e1

Figure 5.3: Silicon energy gap and level

5.1.2 Covalent Bonding
The valence shell of an atom is said to be complete when it contains

eight electrons. In a covalent bond, atoms complete their valence shells by
sharing valence electrons with surrounding atoms. Silicon covalen bonding
is shown in Figure 5.4. The results of the bond are:

• The atoms are held together, forming a solid.
• The atoms act as insulators.

Si Si
Si Si

Figure 5.4: Silicon covalent bonding
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5.1.3 Conduction

When an electron absorbs sufficient energy, it can break free from its
parent atom, leaving a gap, or hole, in the covalent bond (Figure 5.5). Note
that every conduction band electron in a pure semiconductor material has
a matching valence band hole. Eventually, the electron gives up its energy
(in the form of light or heat) and falls back into a valence band hole. This
recombination generally happens within a few microseconds.

Energy Conduction band

Si Valence band
Si

Si
Si

Figure 5.5: Generation of electron-hole pair

At room temperature, thermal energy (heat) causes a constant
creation of electron-hole pairs (and the subsequent recombination). If
temperature decreases, the number of free electrons generated also
decreases. If temperature increases, so does the number of free electrons
generated. This is why conduction through a semiconductor increases as
the material warms up.

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5.2 Doping
Pure (intrinsic) semiconductors have very low conductivity as a result

of covalent bonding (and other factors). Doping is the process of adding
impurity atoms to intrinsic silicon or germanium to improve the conductivity
of the material. The term impurity is used to describe the doping element
because the semiconductor is no longer pure once the doping occurs.
Two types of elements are used for doping:

• Trivalent elements are made up of atoms with 3 valence electrons.
• Pentavalent elements are made up of atoms with 5 valence

electrons.
When a trivalent impurity is added to an intrinsic semiconductor, the
resulting material is referred to as a p-type material. When a pentavalent
impurity is added to an intrinsic semiconductor, the resulting material is
referred to as an n-type material.

N-type Materials
When a pentavalent atom bonds with four silicon (or germanium)

atoms, the bond contains an excess electron that is not a part of the bond
(Figure 5.6). Since the excess electron is not part of the covalent bond, little
energy is required to force it into the conduction band. On a larger scale,
millions of pentavalent atoms added to an intrinsic semiconductor result in
a material with millions of electrons that are not part of the covalent bonds
(Figure 5.7). These electrons can be forced to flow through the material with
little difficulty.

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Si Excess covalent
bond electron
Si
As
Si

Si

Figure 5.6: n-type material

Energy Conduction band

Electrons
(majority carriers)

Valence band

Holes
(manority carriers)

Figure 5.7: Energy diagram (n-type material)

Since the conduction band electrons in an n-type material
outnumber the valence band holes, the electrons are referred to as
majority carriers and the holes are referred to as minority carriers. Even
though the electrons outnumber the valence band holes, the n-type
material is still electrically neutral. This is due to the fact that the numbers of
electrons (-) and protons (+) within the material are still equal.

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P-type Materials

When a trivalent atom bonds with four silicon (or germanium) atoms,
the bond contains an excess hole (Figure 5.8). On a larger scale, millions of
trivalent atoms added to an intrinsic semiconductor result in a material with
millions of gaps in the covalent bonds (Figure 1.9). These holes greatly
outnumber the conduction band electrons generated by thermal energy.

Si

Si Covalent bond
Al hole

Si

Si

Figure 5.8: p-type material

Energy Conduction band

Electrons
(manority carriers)

Valence band

Holes
(majority carriers)

Figure 5.9: Energy diagram (p-type material)
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Since the valence band holes in a p-type material outnumber the
conduction band electrons, the holes are referred to as majority carriers
and the electrons are referred to as minority carriers. Even though the holes
outnumber the conduction band electrons, the p-type material is still
electrically neutral. This is due to the fact that the numbers of electrons (-)
and protons (+) within the material are still equal. The characteristics of p-
type and n-type materials are summarized in Table 5.1.

Table 5.1: Characteristics of p-type and n-type materials

Material n-type p-type

Bonding Si
diagram
Si
Excess Si
As covalent
bond Si Hole in
Si electron Al the
Si covalent
Si bond

Si

Doping Pentavalent (donor atoms) Trivalent (acceptor atom)
element Conduction-band electrons Valence-band holes
Valence-band holes Conduction-band electrons
Majority Neutral Neutral
carriers

Minority
carriers

Material
charge

5.3 The PN Junction
P-type and n-type materials become extremely useful when they are

joined together to form a pn junction. When a pn junction is formed:
• Free electrons in the n-type material diffuse (wander) across the
junction and fall into the excess holes in the p-type material.

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• The n-type and p-type materials at the junction lose charge carriers
(electrons and holes, respectively) as a result of the diffusion. As a
result, the area around both sides of the junction is depleted of
charge carriers. This area is referred to as the depletion layer or
depletion region (Figure 5.10).

np np

Depletion layer

Energy
Energy

(a) (b)

Figure 5.10: The forming of the depletion layer.

Since the n-type material near the junction loses electrons, it has an
overall positive charge. Since the p-type material near the junction gains
electrons, it has an overall negative charge. As a result, a natural difference
of potential (voltage) exists across the junction. This voltage is referred to as
the barrier potential. The barrier potentials for silicon and germanium are
approximately 0.7 V and 0.3 V, respectively.

The atoms in the n-type material that lose electrons are referred to as
donor atoms. The atoms in the p-type material that gain electrons are
referred to as acceptor atoms.

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5.4 Bias

Bias is a potential used to control the width of a depletion layer, and
thus its resistance. As the width of a depletion layer increases, its resistance
increases. As the width of a depletion layer decreases, its resistance
decreases. The relationship between the width of the depletion layer and
the junction current is summarized in Table 5.2.

Table 5.2: Relationship between the width of the depletion layer and the
junction current

Depletion layer width Junction resistance Junction current

Minimum Minimum Maximum

Maximum Maximum Minimum

5.4.1 Forward bias

Forward bias is a potential that reduces the size (and resistance) of a
depletion layer. A pn junction is forward biased when the applied potential
causes the n-type material to be more negative than the p-type material
(Figure 1.14). When a forward voltage (VF) is applied to a pn junction, the
depletion layer is reduced to its minimum width, provided that exceeds the
barrier potential of the junction. The voltage across a forward biased pn
junction is approximately equal to its barrier potential.

When forward biased, a pn junction provides little opposition to
current. The forward resistance of the n-type and p-type materials is
referred to as bulk resistance.

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Figure 5.11: The effects of forward bias
A pn junction can be forward biased by:

• Applying a potential to the n-type material that is more negative
than the potential applied to the p-type material

• Applying a potential to the p-type material that is more positive than
the potential applied to the n-type material (Figure 5.12)

+V -V

pn
np

(a) (b)

Figure 5.12: Some forward-biased pn junctions.
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5.4.2 Reverse Bias
Reverse bias is a potential that increases the size (and resistance) of

a depletion layer. A pn junction is reverse biased when the applied
potential causes the n-type material to be more positive than the p-type
material (Figure 5.13). When a reverse voltage (VR) is applied to a pn
junction, the width of the depletion layer increases. The overall effect of
widening the depletion layer is that the resistance of the junction is
drastically increased and conduction drops to nearly zero.

Figure 5.13: The effects of reverse bias

A pn junction can be reverse biased by:
• Applying a potential to the n-type material that is more positive than
the potential applied to the p-type material
• Applying a potential to the p-type material that is more negative
than the potential applied to the n-type material.
Note that a pn junction with no biasing potential applied is

considered to be reverse biased. Figure 1.18 summarizes the characteristics
of forward and reverse biased pn junctions.

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Table 5.3: Characteristics of forward and reverse biased pn junctions

Bias Forward bias Reverse bias

Bias +V -V +V -V
polarities

p nn p
n pp n

Depletion (a) (b) (a) (b)
layer width Minimum Maximum
Minimum Maximum
Device Maximum Minimum
resistance

Device
current

Exercise
1. What is the maximum number of electrons that can exist in the 3rd

shell of an atom?
2. A certain atom has four valence electrons. What type of atom is it?
3. Describe the process of doping.
4. What type of impurity added to intrinsic semiconductor to produce P

and N type semiconductor?
5. Distinguish between P and N type material.
6. What is the majority carrier for P and N type semiconductor?

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7. How PN junction is formed?

Summary
1. A semiconductor element is one that neither a conductor nor an

insulator, but rather, lies halfway between the two. Under certain
circumstances, the resistive properties of a semiconductor material
can be varied between those of a conductor and those of an
insulator.
2. The outermost orbital shell of an atom is referred to as the valence
shell. This shell is important because it determines the conductivity of
the atom.
a. Element with one valence shell electron are conductors.
b. Element with eight valence shell electrons are insulators.
c. Semiconductor elements have four valence shell electrons.
3. The most commonly used semiconductor elements are carbon,
silicon, and germanium.
a. Silicon and germanium are commonly used in the production

of solid-state components
b. Carbon is used primaruly in the production of resistors and

potentiometer
4. Covalent bonding is the method by which atoms complete their

valence shells when they “share” electrons with other atoms.
5. The result of covalent bonding are:

a. Atoms are held together, forming a solid substance

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b. The atoms are electrically stable, because their valence shells
are complete

c. The complete valence shells cause intrinsic (pure) silicon or
germanium to act as an insulator

6. Silicon is a better insulator than germanium at room temperature. This
desirable characteristic is one of the reasons that most solid-state
components are made using silicon.

7. Conductivity in semiconductor is directly proportional to
temperature.

8. Because of their poor conductivity, intrinsic silicon and germanium
are of little use.

9. Doping is the process of adding impurities to semiconductor element
to improve their conductivity ratings. An impurity (in this case) is an
element other than silicon or germanium.

10. Trivalent and pentavalent elements are commonly used as doping
elements.

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CHAPTER 6

DIODES

Introduction
Diode is one of the simplest structures from the semiconductor

devices family. It is created from a combination of N-type and P-type of
semiconductor materials. The characteristics and behaviors of the diode
are actually due to its semiconductor materials. Diode is a device that
allows current to flow in one direction. There are several different types of
diode which are designed for specific applications such as pn diode
(diode), Zener diode, LED diode and seven segment display.

Learning Objectives
By the end of the lesson, students should be able to:
1. Draw the basic construction of the diode and its symbol.
2. Explain the I-V characteristic of the PN diode and zener diode.
3. Identify the diode terminals.
4. Explain forward biased and reverse biased connection.
5. Differentiate types of the diodes and its application

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6.1 Introduction to PN Junction Diode

A diode is a single pn junction device with conductive contacts and
wire leads connected to each region. The n region is called the cathode;
p region is called the anode. The arrow in the symbol points in the direction
of conventional current flow (opposite to electron flow) as shown in Figure
6.1.

pn junction Metal contacts anode cathode
and wire leads
pn

Basic diode structure Schematic symbol

Figure 6.1: Diode structure and schematic symbol

Forward bias is the condition that allows current through the pn
junction as shown in Figure 6.2. The negative side of DC supply is connected
to the n region of the diode and positive side is connected to the p region.
The bias voltage must be greater than the barrier potential. The resistor limits
the current to a value that will not damage the pn structure. Reverse bias is
the condition that essentially prevents current through the diode. The
external bias voltage, is connected that the positive side of is connected to
the n region of the diode and the negative side is connected to the p
region. The depletion region is much wider than in forward bias.

110

+ VF _ _ VF
IF +

R IF = 0A
VBIAS
VBIAS
+_ _+

Forward bias Reverse bias

Figure 6.2: Forward bias and reverse bias connections

6.1.1 Voltage Current Characteristic of a Diode

When a forward biased connection is applied to a diode, forward
current will through the diode. This current is called forward current, IF. Figure
6.3 shows the I-V characteristics curve for a forward-biased diode.

IF (mA)

C

A B knee
VF (V)

0.7V

Figure 6.3: IV characteristics curve for a forward-biased diode.

From the graph, with 0V across the diode, there is no forward current.
The forward current increases gradually as you increase the forward-bias
voltage shown from point A to B. When the forward bias voltage is

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increased to a value where the voltage across the diode reaches
approximately 0.7V, the forward current begins to increase slowly, as shown
at the knee of the curve. At this point, forward voltage remains at
approximately 0.7V but IF increases rapidly. This is due to the voltage drop
across the internal dynamic resistance.

Point A - corresponds to a zero-bias condition
Point B - the VF is less than the barrier potential of 0.7V
Point C - the VF approximately equals the barrier potential and IF
increase rapidly.

For the reverse biased, when a reverse voltage is applied across the
diode, there is only an extremely small reverse current, IR through pn
junction. With 0V across the diode, there is no reverse current. As the reverse
voltage increases gradually, there is a very small reverse current and the
voltage across the diode increases. When the applied bias voltage is
increased to a value where the reverse voltage across the diode, VR
reaches the break-down value, VBR the reverse current begins to increase
rapidly. As you continue to increase the bias voltage, the current continues
to increase very rapidly but the voltage across the diode increases very little
above VBR. Remember that reverse bias prevents current as long as the
reverse bias voltage does not equal or exceed the breakdown voltage of
the junction.

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VR (V) VBR
B knee
A

C

IR (μA)

Figure 6.4: IV characteristics curve for a reverse-biased diode

From Figure 6.4:
Point A - corresponds to a zero-bias condition.
Point B - there is a very small IR as the reverse voltage, VR increases.
Point C - the VR reaches the VBR and IR begins to increase rapidly
until the diode damage.

Figure 6.5 is the complete IV characteristic curve for a diode by
combining the curves for both forward bias and reverse bias. Notice that
the IF scale is in mA compared to the IR scale is µA. For both forward and
reverse currents, as the temperature is increased, both currents will also
increase.

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IF (mA)

Forward
bias

VBR knee
knee
VR (V) 0 0.7V VF (V)

Reverse
bias

IR
(μA)

Figure 6.5: Complete IV characteristics curve

6.2 Ideal and Practical Diode

Figure 6.6 shows how the forward-biased and reverse-biased are
connected. Notice about the positive terminal and negative terminal
connected to the anode and cathode. When the diode is forward biased,
it acts like a closed (on) switch and for reverse biased it acts like an open
(off) switch as figures below. Figure 6.6 also shows the ideal I-V characteristic
curve graphically depicts the ideal operation.

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Ideal diode model Ideal diode model

AC AC

IF IF = 0
VBIAS
RLIMIT RLIMIT

VBIAS

IF (mA)

Forward bias Reverse bias

VR (V) VF (V)

IR (μA)
Ideal characteristic curve

Figure 6.6: The ideal model of a diode where VBP = 0

But for practical diode model, we add the barrier potential to the
ideal switch model. When the diode is forward-biased, it is equivalent to a
closed switch in a series with a small equivalent voltage source equal to the
barrier potential (0.7V) with the positive side toward the anode. (Note: The
typical barrier potential is approximately 0.7 V for silicon and 0.3 V for
germanium at 25o C as shown in Figure 6.7 for IV characteristics for practical
silicon and germanium diode. When the diode is reverse-biased, it is
equivalent to an open switch just in the ideal model.

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Practical diode model Practical diode model

AC AC

IF IF = 0
VBIAS
RLIMIT RLIMIT

VBIAS

Forward bias Reverse bias
IF (mA) IF (mA)

VR (V) VF (V) VR (V) VF (V)

0.7V 0.3V

Characteristic curve (silicon) Characteristic curve (germanium)

Figure 6.7: The practical model of a diode for silicon and germanium

Example 6.1
By assuming the diode is ideal and practical, calculate the load

current, load voltage and load power consumption of the following circuit

IN4001

E R1
10V 1kΩ

By assuming the diode is an ideal diode:
Load current = Diode current

E 10
ID = R1 = 1k = 10mA

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Load voltage
VL = IDR1 = (10m)(1k) = 10V

Load power consumption
P = IDVL = (10m)(10) = 100mW

By assuming the diode is a practical diode:
Load current = Diode current

E - 0.7 10 - 0.7
ID = R1 = 1k = 9.3mA

Load voltage
= 1 = (9.3 )(1 ) = 9.3

Load power consumption
= = (9.3 )(9.3) = 86.5

6.3 Zener Diode

A zener diode is a silicon pn junction device that differs from the
precious diodes because it is designed for operation in the reverse-
breakdown region. There is some modification of the construction of the
semiconductor material. The zener diode symbol is shown in Figure 6.8.

anode cathode

Figure 6.8: Symbol of Zener diode
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The IV characteristic of the zener diode is quite similar with the pn
diode. The main different is at the reverse biased region. For the zener diode
the breakdown region occurred at the lower reverse voltage based on the
zener diode operating voltage design. When a diode reaches reverse
breakdown, its voltage remains almost constant even though the current
changes drastically. The characteristic curve for zener diode is shown in
Figure 6.9.

IF (mA)

Breakdown Forward -bias
region
VR (V) VZ
VF (V)
0

Reverse
Breakdown
region

Reverse-bias
region

IR
(μA)

Figure 6.9: General characteristic curve for zener diode

Refer to Figure 6.10, as the zener reverse voltage, VZ increased, the
zener reverse current, IZ remains extremely small up to the knee of the curve.
At this point, the breakdown effect begins. The zener breakdown voltage,
VZ remains essentially constant although it increases slightly as the zener
current IZ increases.

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VZ (V) VZT

(VZT,IZT) IZK(Zener knee current)
IZT(Zener test current)

IZM(Zener maximum current)

IZ
(mA)

Figure 6.10: Reverse characteristic of zener diode

The ability to keep the reverse voltage across its terminal essentially
constant is the key feature of the zener diode. A zener diode operating in
breakdown acts as a voltage regulator because it maintains a nearly
constant voltage across its terminals over a specified range of reverse-
current values.

A minimum value of reverse current, IZK must be maintained in order
to keep the diode in breakdown for voltage regulation. A maximum
current, IZM is the maximum current which the diode may be damaged due
to excessive power dissipation. So, the zener diode maintains a nearly
constant voltage across its terminal for values of reverse current ranging
from IZK to IZM. IZT is a zener test current. Figure 6.11 shows the ideal and
practical model of zener diode in reverse breakdown respectively.

∆VZ

VR (V)

IZK

VZ ZZ = ∆VZ ∆IZ
∆IZ

IZM

IR (mA)

Figure 6.11: Ideal and Practical zener diode and its characteristic curve
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Example 6.2
Determine whether the zener diode is connected in a right biasing

manner or not. Determine the VO and IZ in the circuit below with a given E
values below. Assume the zener diode voltage is 10V.

R1
2kΩ

E

a. E = 8V
b. E = 12V

Solution:
a. When the E ≤ VZ the circuit is open or zener diode if in off condition

Vz = 0A and VO = E=10V

b. When the E≥VZ the circuit is close or zener diode if in on condition

Zener current;

IZ = E - VZ 12 - 10 = 2mA
R1 = 1k

Output voltage;

Vo = VZ = 10V

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6.4 Light Emitting Diode
A light-emitting diode (LED) is a semiconductor light source. It is

based on the semiconductor diode. LEDs are used as indicator lamps in
many devices and are increasingly used for lighting. In early years, LEDs
emitted low-intensity red light, but modern versions are available across the
visible, ultraviolet and infrared wavelengths, with very high brightness.

When a diode is forward biased (switched on), electron cross the p-
n junction from n-type material and recombines with holes in p-type
material. A large exposed surface area on one layer of the semi conductive
materials permits the photons to be emitted as visible light. This process is
called electroluminescence.

Figure 6.12: LED and its symbol

LEDs are made of gallium arsenide (GaAs), gallium arsenide
phosphide (AsP) or gallium phosphide (GaP). The voltage drop across the
LED typically ranges from 1.8V-4V. Silicon and germanium are not used
because they essentially heat-producing materials and very poor at
producing light.

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6.5 Series and Parallel Diode

Before we go to some other typical applications using diode as one
of the main component, we should understand the concept and behavior
of the diode electrical characteristics in series and parallel configuration.
Some circuits may use more than one diode in the circuit as shown in Figure
6.13.

R1 D1 I1 I2
1kΩ
I3
E D2
10V R2
1kΩ

Figure 6.13: Series configuration circuit

The analysis of this circuit may have a bit different compare to the
common resistive loop circuit. From the above circuit, we try to understand
the current and voltage characteristics toward diode. By assuming the
diodes are from silicon semiconductor mater, the diode have 0.7 voltage
drop across it.

Applying KVL I1 current can be calculated by

-E + VR1 + VD1 + VD2 = 0

I1 current can be calculated by;

I1 = E - VD1 - VD2 = 10 - 0.7 - 0.7 = 8.6mA
R1 1k

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Voltage across R2 resistor is equal to the voltage drop across D2 diode which
is 0.7V

Thus, the I2 current can be determined by;

I2 = VD2 = 0.7 = 0.7mA
R2 1k

Applying KCL, the I3 current can be calculated by;
I3 = I1 + I2 = 8.6m - 0.7m = 7.9mA

Base on this analysis, we can say that majority of the current will flow
through D2 diode because its offer less resistance.

6.6 Half wave rectifier

The half wave rectifier converts the AC sinusoidal input waveform into
a pulsating dc voltage with one output pulse occurring for each cycle. As
refer to the block diagram and circuit diagram below, a diode is
connected to an ac source and a load resistor forming a half wave rectifier
circuit.

Vin Vout
0V
Half-wave 0V
rectifier

Figure 6.14: Block diagram for half-wave rectifier

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RL

Figure 6.15: Circuit diagram for half-wave rectifier

a. During the first-half cycle (positive cycle):
The analysis of the half wave rectifier operation can be divided into

two cycles which is half positive and negative cycle. Basic operation for
half-wave rectifier for positive cycle is shown in Figure 6.16 below:

Vin +_ Vout
+ I

0V RL 0V to t1
to t1 t2 _

Figure 6.16: Half-wave rectifier in the first-half cycle (positive cycle)

• When the sinusoidal input voltage, VIN goes positive, the diode is
forward-biased and conducts current through the load resistor, RL.

• The current produces an output voltage across the RL, producing the
same shape as the positive half-cycle of the VIN.

• But when we use the practical diode model, we have to consider the
barrier potential of 0.7V.

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• During the positive half-cycle, the input voltage must overcome the
barrier potential before the diode becomes forward biased.

• This resulting the half-wave output, VP(OUT) with a peak value that is
0.7V less than the peak value of the input, VP(IN).

• Thus, the output for the first-half cycle is VP(out) = VP(in) = 0.7V

b. During the second-half cycle (negative cycle):
• When the input voltage goes negative during second half-cycle, the

diode is reverse-biased, so there is no current.
• The net result is that only the positive half-cycles of the ac input

voltage appear across the RL.
• Thus, the output for the second-half cycle is VP(out) = 0V

The resultant wave form by the half-wave rectifier is called half-wave
pulsating direct voltage. Peak inverse voltage, PIV equals the peak value
of the input voltage which occurs at the peak of each negative alternation
of the input voltage when the diode is reverse-biased. PIV = VP(in)

With continuation of positive and negative cycle of the input supply
applied to the half wave rectifier, the output as shown in Figure 6.17 will be
produced. Thus, a half wave rectifier (ideal) allows conduction for only 180°
or half of a complete cycle. The output frequency of the output voltage is
the same as the input. The direct current or average output, VDC of the
pulsating half wave rectifier can be calculated by using this relation, VDC =

VOP
π

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Vin +_ Vout
I=0
_
0V t1 t2 RL 0V to t1
to
+

Figure 6.17: Half-wave rectifier in the second-half cycle (negative cycle)

Example 6.3
Draw the circuit diagram of the negative half wave rectifier and its output.

Solution:

Vin _+
I
0V t1 _ RL 0V to t1
to t2 -Vout

+

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6.7 Full wave rectifier

A transformer is often used to couple the ac input voltage from
source to the full-wave rectifier. Transformer coupling provides two
advantages:

a. Allows the source voltage to be stepped up or stepped down.

b. The ac source is isolated from the rectifier, thus preventing a shock
hazard in secondary circuit.

Full wave rectifier allows unidirectional (one-way) current through the
load during the entire 360o of the input cycle as in the Figure 6.18. The
number of positive alternations that make up the full-wave rectified voltage
is twice that of the half-wave voltage for the same interval. The full wave
rectifier coverts an ac sinusoidal input voltage into a pulsating dc voltage
with two output pulses occurring for each input cycle.

Vin Vout
0V
Full-wave 0V
rectifier

Figure 6.18: Block diagram for full-wave rectifier

There are two type of full wave rectifier circuit known as Center
tapped Full Wave Rectifier and Full Wave Bridge Rectifier.

127

6.7.1 Center tapped Full Wave

A Center tapped Full Wave rectifier consist of center tapped
transformer, 2 diode and 1 output resistor or load in a circuit as shown in
Figure 6.19

D1

Vsec
Vin 2

0V t1 t2 Vsec RL
to 2

D2

Figure 6.19: Circuit diagram for center-tapped full-wave rectifier

Similar to the half-wave rectifier, since the ac voltage has two cycle;
positive and negative cycle, therefore we can also divide the full-wave
rectifier basic operation into two cycles.

6.7.1.1 Basic operation for full-wave rectifier:

a. During the first-half cycle (positive cycle):

F + D1 _ + Vout

Vin +
0V _
+
_ RL 0V
_
_+
D2

Figure 6.20: Full-wave rectifier in the first-half cycle (positive cycle)
128

For a positive half-cycle of the input voltage, the diode D1 is in
forward-bias condition and D2 is in reverse-bias, so the current path is
through D1 and the load resistor, RL.

Thus, the output for the first-half cycle is VP(out) = VP(sec) - 0.7
2

b. During the second-half cycle (negative cycle):

F _ D1
+

Vin _ + Vout
0V +_
+
RL 0V
+_ _
D2

Figure 6.21: Full-wave rectifier in the second-half cycle (negative cycle)

For the negative half-cycle of the input voltage, the D1 is reverse bias
and D2 is forward bias, so the current path is through D2 and RL. And as the
output current during both positive and negative portions of the input cycle
is in the same direction through the load, the output voltage across the load
resistor is a full-wave rectified DC voltage.

Thus, the output for the second-half cycle is VP(out) = VP(sec) - 0.7
2

Peak inverse voltage, PIV for full-wave rectifier, 2VP(out) + 0.7

Related formulae for full-wave rectifier:

1. Peak secondary output voltage, VP(sec) = nVP(pri)

2. Transformer turn ratio, n = N2
N1

129

The continues process positive and negative ac input cycle convert

to the dc pulsating waveform The direct current or average output, VDC of

the pulsating full wave rectifier can be calculated by using this relation,

VDC = 2VOP
π

6.7.2 Full Wave Bridge rectifier

The full-wave bridge rectifier takes advantage of the full output of the
secondary winding. The circuit employs a transformer with four diodes and
a load. The four diodes arranged such that current flows in the direction
through the load during each half of the cycle. Figure 6.22 shows the circuit
diagram for full-wave bridge rectifier.

F + + + _0.7V
Vp(sec) _ PIV
+ _ +
Vp Vp(pri) +
0.7V _ +
_ _ PIV RL

Vp(out)

_

Figure 6.22: Circuit diagram for full-wave bridge rectifier

Basic operation for full-wave bridge rectifier can be analyzed into
positive and negative cycles:

130

F

I D3 D1
++

Vin +
__

D2 D4 RL V(out)
_0

Figure 6.23: Full-wave bridge rectifier in the first-half cycle (positive cycle)

During the first-half cycle (positive cycle), as shown in Figure 6.23

• The diode D1 and D2 is in forward biased condition meanwhile diode
D3 and D4 in reverse bias condition.

• The current will pass through from the positive voltage of the
secondary transformer to the D1 diode, load Resistor and D2 diode
before completing the cycle to negative input transformer.

• Thus, the output for the first-half cycle is, VOP = V2P - VD1 - VD2 = V2P - 1.4

During the second-half cycle (negative cycle)

F

I D3 D1
__

Vin +

++ D2 RL V(out)
_0
D4

Figure 6.24: Full-wave bridge rectifier in the second-half cycle (negative
cycle)

131

• Assuming the polarity of the secondary transformer output is change
as shown in the above figure. Base on this condition, the diode D3 and
D4 is in forward biased condition meanwhile diode D1 and D2 in reverse
bias condition.

• The current will pass through from the negative voltage of the
secondary transformer to the D4 diode, load Resistor and D3 diode
before completing the cycle to negative input transformer.

• Thus, the output for the first-half cycle is, VOP = V2P - VD3 - VD4 = V2P - 1.4
• The direction of the current pass through the resistive load is similar

polarity either positive or negative cycle. Thus, producing similar
pulsating waveform output.

Continuing to the processes, the full wave bridge rectifier producing
continues pulsating DC waveform. The DC voltage calculation is similar with
the center tap rectifier. In additional, the similar concept applied to the
negative pulsating full wave rectifier by inverting the polarity or
arrangement of the diodes.

132

Example 6.4 D1
Base on the circuit below;

4:1

110 Vrms RL
1kΩ

D2
a. name the rectifier below?
b. what is the total peak secondary voltage?
c. find the peak voltage across each half of the secondary.
d. sketch the voltage waveform across RL.
e. Calculate the average voltage across the RL
f. Calculate the DC current across the RL

Solution:
a. Center tapped full wave rectifier
b. Secondary peak voltage is output at the secondary coils of the

transformer:
Convert the 110Vrms in peak voltage;

V1P = �2Vrms = 155.6V
Secondary peak voltage,

133

V2P = N2 × V1P = 1 × 155.6 = 38.9V
N1 4

c. Output peak voltage across the load resistor

VOP = V2P - VD= 38.9 - 0.7 = 38.2V

d.

Vp
38.2V

e.

VDC = 2VOP = 2(38.2) = 24.3V
π π

IDC = VDC = 24.3 = 24.3mA
RL 1k

6.8 Power supply

The DC power supply converts the standard 240VAC 50Hz available
at wall outlets into a constant DC voltage. The basic power supply block
diagram consists of the rectifier, filter, regulator and finally end up to the
load. Sometime the transformer is needed prior to the rectifier to step up or
step down the input ac supply.

0V 0V 0V 0V 0V

Transformer Rectifier Filter Regulator

Figure 6.25: DC power supply block diagram
134

The rectifiers either half wave rectifier or full wave rectifier is to convert
the ac input voltage to a pulsating DC voltage as shown in previous topics.
The filters will remove or eliminate the fluctuations in the rectified voltage
and produce a relatively smooth DC voltage. The main component in the
filter is capacitor. The capacitor-input filter will charge and discharge such
that it fills in the “gaps” between each peak. This reduces variations of
voltage. This voltage variation is called ripple voltage. Figure 6.26 shows the
charging and discharging activities in the filter from the half wave rectifier.

0 t0 +_ + +
_ RL
+
Vin t0 _

_

Initial charging of capacitor happen when the power is turned on (when
diode is forward biased)

0 _+ + +
t0 t1 _ RL
_
Vin t0 t1 t2 _

t2 +

The capacitor discharge throughout RL, after peak of positive attenuation
when the diode is reverse biased. This discharging occurs during the portion
of the input voltage indicated by the solid blue curve.

_+ + +
RL
0 t0 t1 + _ t0 t1 t2
Vin _

t2 _

The capacitor charges back to peak of the input when the diode becomes
forward biased. This charging occurs during the portion of the input voltage
indicated by the solid blue color.

Figure 6.26: Charging and discharging process for filtering

135

The advantage of a full-wave rectifier over a half-wave is shown in
Figure 6.27. The capacitor can more effectively reduce the ripple when the
time between peaks is shorter.

ripple Same slope (capacitor
discharge rate)

(a) Half-wave

(b) Full-wave

Figure 6.27: Half wave and Full wave rectifier filtering output

The ripple voltage output from the filter can be determined by,

Vr(pp) = �1� VP(rec).

fRLC

where

Vr(pp) is voltage ripple peak to peak

f is frequency

R is resistor

C is capacitor

136

Output DC voltage from the filter can be find by,

VDC = �1 - 1 � VP(rec)
2fRL
C

Regulation is the last step in eliminating the remaining ripple and
maintaining the output voltage to a specified value. Regulators will
maintain a constant DC voltage. Typically, this regulation is performed by
an integrated circuit regulator. There are many different types used based
on the voltage and current requirements. Figure 6.28 shows a complete DC
power supply circuit.

F

On-off + + D1
switch
110 Vac 12.6 Vac
D3
_ _
7805 + +5.0V

D2 D4 + C2

RL _ C1 _1μF
1000μF

D1 – D4 are IN4001 rectifier diodes

Figure 6.28: complete DC power supply circuit.

137

Example 6.5
Base on the Figure 6.28. Draw the block diagram to represent the power
supply.

Solution:

Example 6.6
Briefly explain the function of each block diagram in Example 6.5.

Solution:
Input power supply: AC incoming or input supply
Transformer: To step down incoming voltage to a suitable voltage for

rectifier
Full wave bridge rectifier: To convert AC voltage supply to a pulsating

DC supply
Filter: To remove or eliminate the fluctuations in the rectified voltage
and produce a relatively smooth DC voltage.
Regulator: to maintains an essentially constant output voltage
138

6.9 Clipper

Clippers or Diode limiters are used to clip off portions of signal voltage
from exceeding some particular limit, either negative or positive. Limiter can
be divided into two types of limiting:

a. Limit the negative or positive alternation without biasing

b. Limit the positive or positive alternation with biasing

Vin Vout
0V
Clipper 0V

Figure 6.29: Block diagram for clipper
R1
RL

Figure 6.30: Circuit diagram for clipper

6.9.1 Limiter without Biasing
6.9.1.1 Limit the Negative Alternation without biasing

We divide the diode limiter for negative alternation limiting basic
operation into two cycles; first-half cycle and second-half cycle. Basic
operation for negative alternation limiting:

139

a. During the first-half cycle (positive cycle):

R1

Vin Vout

0V to t1 t2 + RL to t1
_

Figure 6.31: Limiter for negative limiting in the first-half cycle (positive
cycle)

When the input voltage goes positive, the diode reverse-biases and
acts as an open circuit. All currents flow through the load resistor, RL. The
output voltage determined by the voltage divider formed by R1 and RL,

VP(out) = �RL R+LR1� VP(in)

b. During the second-half cycle (negative cycle):

R1

Vin Vout

0V to t1 t2 _ RL to t1 t2
+

-0.7V

Figure 6.32: Limiter for negative limiting in the second-half cycle (positive
cycle)

When the input voltage goes below -0.7V, the diode is still in reverse-
bias condition and acts as an open circuit. Therefore, -0.7V flow through

140

load resistor, RL. However, when the input goes above -0.7V, the diode forward-
biases and acts as a closed circuit. Therefore, currents flow through the diode.

The output voltage at RL, VP(out) = -0.7V

6.9.1.2 Limit the Positive Alternation without biasing

a. During the first-half cycle (positive cycle):

R1

Vin Vout

0V to t1 t2 + +0.7V
_
RL 0V to t1

Figure 6.33: Limiter for positive limiting in the first-half cycle (positive cycle)

When the input voltage goes below 0.7V, the diode is in reverse-bias
condition and acts as an open circuit. Therefore, 0.7V flow through load
resistor, RL. However, when the input goes above 0.7V, the diode forward-
biases and acts as a closed circuit. Therefore, currents flow through the
diode.

The output voltage at RL, VP(out) = 0.7V

141

b. During the second-half cycle (negative cycle):

R1

Vin Vout

0V to t1 t2 _ +0.7V t2
+
RL 0V to t1

Figure 6.34: Limiter for positive limiting in the second-half cycle (positive
cycle)

When the input voltage goes negative, the diode reverse-biases and
acts as an open circuit. All currents flow through the load resistor, RL. The
output voltage determined by the voltage divider formed by R1 and RL.

VP(out) = �RL RL R1 � VP(in)
+

6.9.2 Limiter with Voltage Biasing

The level to which an ac voltage is limited can be adjusted by adding
a bias voltage,VBIAS , in series with the diode. Limiter with voltage biasing
can also be divided into two types of limiting:

a. Limiter with voltage biasing which limits the negative alternation

b. Limiter with voltage biasing which limits the positive alternation

6.9.2.1 Limiter with voltage biasing which limits the negative alternation

We divide the diode limiter with voltage biasing for negative
alternation limiting basic operation into two cycles; first-half cycle and
second-half cycle. Basic operation for negative alternation limiting:

142