CHAPTER ONE

Basic Semiconductor Theory

 1, Atomic theory
Structure of matter
• Here are a few basic scientific terms that are often
used in the study of chemistry. They are also very
important in the study of electronics.
• First, matter is anything that occupies space and
that has weight. Matter can be a solid, a liquid, or
a gaseous material. Solid matter includes things as
metal and wood; liquid matter is exemplified by
water and gasoline; and gaseous matter includes
such things as oxygen and hydrogen.
• Matter changes state when the particles of which
they are made are heated.
Contd…
• As they are heated, the particles move and strike one
another, causing them to move farther apart.
• Ice is converted into a liquid by adding heat.
• If heated to a high temperature, water becomes a gas
(steam).
• Some materials require more heat than others to
become a liquid or a gas.
• All materials can be made to change from a solid to a
liquid or from a liquid to a gas if enough heat is
added.
• Similarly these materials can change into liquids or
solids if heat is taken from them.
 element
• The next important term in the study of the
structure of matter is the element.
• An element is considered to be the basic material
that makes up all matter.
• elements such as hydrogen, aluminum, copper,
iron, and iodine are a few of the over 100 elements
known to exist.
• Some elements exist in nature and some are
manufactured.
• Everything around us is made up of elements.
Contd…
• There are many more materials in our world than
there are elements.
• Other materials are made by combining
elements.
• A combination of two or more elements is called a
compound. For example, water is a compound
made from the elements hydrogen and oxygen.
• Salt is made from sodium and chlorine.
• Another important term is molecule.
• A molecule is believed to be the smallest particle
that a compound can be reduced to before being
broken down into its basic elements.
Contd…
• For example, one molecule of water has two
hydrogen atoms and one oxygen atom.
• An atom is considered to be the smallest particles
to which an element can be reduced.
• The smallest particles that are found in all atoms
are called electrons, protons, and neutrons.
• The relationship of matter, elements, compounds,
molecules, atoms, electrons, protons, and neutrons
is shown in Figure 1-1.
 Contd…

Figure1.1: Structure of Matter

 Contd…
• The number of protons that each atom has is called its
atomic number.
• The nucleus of an atom contains protons (+) and neutrons
(N).
• Since neutrons have no charge and protons have positive
charges, the nucleus of an atom has a positive charge. The
mass, or weight, of a proton is over 1800 times that of an
electron, whose mass is about 9x10–28 g.
• Electrons move easily in their orbits around the nucleus of
an atom. It is the movement of electrons that causes
electrical energy to exist.
• Atoms consist of a dense, positively charged nucleus
surrounded by a series of orbits that occupy energy levels,
which are commonly called shells. The shell that has highest
energy is known as the valence shell, and the electrons in it
are known as valence electrons.
 2, Semiconductor materials and their
types
• Electrons each carry a single unit of negative
electric charge while; protons each exhibit a single
unit of positive charge. Since atoms normally
contain an equal number of electrons and
protons; the net charge present will be zero.
Electrons are in constant motion as they orbit
around the nucleus of the atom.
• The maximum number of electrons present in the
first shell is 2, in the second shell 8, and in the
third, fourth and fifth shells it is 18, 32 and 50,
respectively. In electronics, only the outer most
shell is important.
Contd…
• If the valence shell contains the maximum number
of electrons possible; the electrons are rigidly
bonded together and the material has the
properties of an insulator. If, however, the valence
shell does not have its full complement of
electrons; the electrons can be easily loosened
from their orbital bonds, and the material has the
properties associated with an electrical conductor.
• A silicon atom contains four electrons in its
valence shell.
• When silicon atoms combine to form a solid
crystal, the valence shells overlap from one atom
to another.
Contd…
• Each individual valence electron is shared by two
atoms as shown in Fig. 1.2. By sharing the
electrons between four adjacent atoms each
individual silicon atom appears to have eight
electrons in its valence shell. This sharing of
valence electrons is called covalent bonding.
Contd…

Figure 1.2 Silicon Lattice showing covalent bonding

 Contd…
• Regardless of whether the impurity element produces surplus
electrons or holes;
• The material will no longer behave as an insulator or a
metallic conductor. Instead, we call the material a
semiconductor.
• The term simply indicates that the substance is no longer a
good insulator or a good conductor but is somewhere in
between.
• Conductor is a material that will support a generous flow of
charge when a voltage source is applied across its terminals.
• An insulator is a material that offers a very low level of
conductivity for an applied voltage source.
• A semiconductor, therefore, is a material that has a
conductivity level somewhere between the extremes of an
insulator and a conductor.
Contd…

Fig. 1.3. conductivity of materials

Contd…
• A semiconductor material is one those electrical
properties lie in between those of insulators and
good conductors. Examples are : germanium and
silicon.
• In terms of energy bands, semiconductors can be
defined as those materials which have almost an
empty conduction band and almost filled valence
band with a very narrow energy gap (of the order
of 1 eV) separating the two.
• At 00K, there are no electrons in the conduction
band and the valence band is completely filled
 Contd…
• With increase in temperature, width of the
forbidden energy bands is decreased so that
some of the electrons are liberated into the
conduction band.
Moreover, such departing
electrons leave behind
positive holes in the
valence band (Fig. 1.4).
Hence, semiconductor
current is the sum of
electron and hole currents
flowing in opposite Fig 1.4. Energy band
 3. Semiconductor materials types
A. Intrinsic Semiconductor :An intrinsic semiconductor is one
which is made of the semiconductor material in its extremely
pure form. Common examples of such semiconductors are :
pure germanium and silicon which have forbidden energy
gaps of 0.72eV and 1.1eV respectively.
 The energy gap is so small that even at ordinary room
temperature, there are many electrons which possess
sufficient energy to jump across the small energy gap
between the valence and the conduction bands.
 When an electric field is applied to an intrinsic semiconductor
at a temperature greater than 00K, conduction electrons move
to the anode and the holes in the valence band move to the
cathode. Hence semiconductor current consists of movement
of electrons and holes in opposite directions.
 Electron current is due to movement of electrons in the conduction band
whereas hole current is within the valence band as a result of the holes
‘jumping’ from one atom to another.
Contd…
• The number of such charge carriers per unit
volume (i.e. intrinsic carrier density) is given by

• where N is constant for a given semiconductor, Eg

is the band gap energy in joules, k is Boltzmann’s
constant and T is the temperature in 0K.
• Note : an intrinsic semiconductor may be defined
as one in which the number of conduction
electrons is equal to the number of holes.
Contd…
B. Extrinsic Semiconductor:
• When extremely small amounts (about 1 part in 108) impurity or
doping agent or dopant is added to intrinsic semiconductor is called
extrinsic or impurity semiconductors. The usual doping agents are :
1. pentavalent atoms having five valence electrons (arsenic, antimony,
phosphorus) . Pentavalent doping atom is known as donor atom
because it donates or contributes one electron to the conduction band
of pure germanium.
2.trivalent atoms having three valence electrons (gallium, indium,
aluminum, boron). The trivalent atom, on the other hand, is called
acceptor atom because it accepts one electron from the germanium
atom.
Depending on the type of doping material used, extrinsic semiconductors
can be sub-divided into two classes :
(i) N-type semiconductors and
(ii) P-type semiconductors.
 Contd…
• The process of introducing an atom of another
(impurity) element into the lattice of another pure
material is called doping.
• When the pure material is doped with an impurity with
five electrons in its valence shell (i.e. a pentavalent
impurity) . it will become an N-type material.
• If, however, the pure material is doped with an impurity
having three electrons in its valence shell (i.e. a
trivalent impurity) it will become P-type material.
• N-type semiconductor material contains an excess of
negative charge carriers, and
• P-type material contains an excess of positive charge
carriers.
 N-type Extrinsic Semiconductor
• This type of semiconductor is obtained when a
pentavalent material like antimony(Sb) is added to pure
Silicon crystal.
• In its pure state, silicon is an insulator because the
covalent bonding rigidly holds all of the electrons
• no free (easily loosened) electrons to conduct current.
If, however, an atom of a different element (i.e. an
impurity) is introduced that has five electrons in its
valence shell, a surplus electron will be present, as
shown in Fig. 1.5. These free electrons become
available for use as charge carriers and;
• They can be made to move through the lattice by
applying an external potential difference to the
material.
 Contd…

Figure 1.5: Free negative charge carriers (electrons)

produced by introducing a pentavalent impurity
Contd…
• The effect of such impurity elements is indicated in Fig.
1.6 (using antimony as the impurity in a silicon
base).Note that the four covalent bonds are still
present. The additional fifth electron due to the
impurity atom is unassociated with any particular
covalent bond.
• This remaining electron, loosely bound to its parent
(antimony) atom, is relatively free to move within the
newly formed n-type material.
• Since the inserted impurity atom has donated a
relatively “free” electron to the structure:
• Diffused impurities with five valence electrons are
called donor atoms.
Contd…

• Figure 1.6 Antimony impurity in n-type material

P-type Extrinsic Semiconductor
• This type of semiconductor is obtained when traces of a
trivalent like boron (B) are added to a pure germanium
crystal. In this case, the three valence electrons of boron
atom form covalent bonds with four surrounding germanium
atoms but one bond is left incomplete and gives rise to a hole
as shown in Fig. 1.7 . Thus, boron which is called an acceptor
impurity causes as many positive holes in a germanium
crystal as there are boron atoms thereby producing a P-type
(P for positive) extrinsic semiconductor.
• Similarly, if the impurity element introduced into the pure
silicon lattice has three electrons in its valence shell,
• The absence of the fourth electron needed for proper
covalent bonding will produce gaps into which electrons can
fit, as shown in Fig. 1.7.
• These gaps are referred to as holes.
Contd…

• Figure 1.7 Holes produced by introducing a trivalent

impurity
 P-Type Material
• The p-type material is formed by doping a pure
germanium or silicon crystal with impurity atoms
having three valence electrons.
• The elements most frequently used for this
purpose are boron, gallium, and indium.
• The effect of one of these elements, boron, on a
base of silicon is indicated in Fig. 1.8.
Contd…

• Figure 1.8 Boron impurity in p-type material

Contd…
• Note that there is now an insufficient number of
electrons to complete the covalent bonds of the
newly formed lattice.
• The resulting vacancy is called a hole and is
represented by a small circle or positive sign due to
the absence of a negative charge.
• Since the resulting vacancy will readily accept a
“free” electron:
• The diffused impurities with three valence electrons
are called acceptor atoms.
 Majority and Minority Carriers
• In an n-type material (Fig.1.9a) the electron is called
the majority carrier and the hole the minority
carrier. For the p-type material the number of holes
far outweighs the number of electrons, as shown in
Fig.1.9b. In a p-type material the hole is the
majority carrier and the electron is the minority
carrier.
Contd…
• When the fifth electron of a donor atom leaves the
parent atom;
– the atom remaining acquires a net positive charge:
– hence the positive sign in the donor-ion representation.
• For similar reasons, the negative sign appears in
the acceptor ion.
• The n- and p-type materials represent the basic
building blocks of semiconductor devices.
 Contd…

• Figure 1.9a (a) n-type material; (b) p-type material

 CHAPTER TWO

Semiconductor diodes and

their applications
 1.PN Junction Formation(1)
 P-N junction is formed by joining n-type and p-type
semiconductor materials
 It is a two terminal device that allows electric current
in one direction and blocks electric current in
another direction.

Figure2. 1. How
is PN Junction
Formed
 PN Junction Formation (2)
 The concentration difference between electrons and holes appears
at their junction.
 Due to the difference in the concentration of free electrons and
holes, some electrons will diffuse from the N-type region to the P-
type region, and some holes will diffuse from the P-type region to
the N-type region.
 As a result of their diffusion, the P region loses holes, leaving
negatively charged impurity ions, and the N region loses electrons,
leaving positively charged impurity ions.
 The ions in the semiconductor cannot move arbitrarily in an open
circuit, so they do not participate in conduction.
 These immovable charged particles form a space charge zone near
the interface between the P and N zones. The thickness of the
space charge zone is related to the concentration of dopants.
 PN Junction Formation (3)
 After the space charge region is formed, due to the
interaction between the positive and negative charges,
an internal electric field is formed in the space charge
region.
 The direction of this electric field is opposite to the
direction of carrier diffusion, which used to prevent
diffusion.
 On the other hand, this electric field will cause the
minority carrier holes in the N region to drift to the P
region, and the minority carrier electrons in the P
region to drift to the N region. The direction of the drift
movement is just opposite to the diffusion movement.
 PN Junction Formation (4)
The holes drifting from the N region to the P
region supplement the holes lost in the P-
region on the original interface, and the
electrons drifting from the P region to the N
region supplement the electrons lost in the N
region on the original interface, which makes
the electric charge is reduced and the internal
electric field is weakened.

Figure 2.2. PN Junction

Depletion Region
 2. Semiconductor diodes
When a junction is formed between N-type and
P–type semiconductor materials,
the resulting device is called a diode.
• This component offers an extremely low
resistance to current flow in one direction and an
extremely high resistance to current flow in the
other.
• An ideal diode would pass an infinite current in
one direction and no current at all in the other
direction.
Contd…
• In addition, the diode would start to conduct
current when the smallest of voltage is present.
• a small voltage must be applied before conduction
takes place. Furthermore a small leakage current
will flow in the reverse direction.
• This leakage current is usually a very small fraction
of the current that flows in the forward direction.
• If the P-type semiconductor material is made
positive relative to the N-type material by an
amount greater than its forward threshold voltage,
– the diode will freely pass current.
Contd…
Diode Representation

Figure 2.3 A P-N junction diode representation

Contd…
Forward and Reverse Biasing of Diode

• Figure 2.4 (a) shows a diode in which the anode is

made positive with respect to the cathode.
• In this forward-biased condition, the diode freely
passes current.
• Figure 2.4 (b) shows a diode with the cathode made
positive with respect to the cathode.
• In this reverse-biased condition, the diode passes a
negligible amount of current.
• In the forward biased state, the diode acts like a
closed switch.
• In the reverse biased state, the diode acts like an open
switch.
Contd…

• Figure 2.4 Forward and reverse biased P-N junction

Forward biased diode
• If a positive voltage is applied to the P-type material, the
free positive charge carriers will be repelled and they will
move away from the positive potential towards the junction.
Likewise, the negative potential applied to the N-type
material .It will cause the free negative charge carriers to
move away from the negative potential towards the
junction.
• When the positive and negative charge carriers arrive at
the junction, they will attract one another and combine. As
each negative and positive charge carrier combine at the
junction; a new negative and positive charge carrier will
be introduced to the semiconductor material from the
voltage source.
• As stated earlier, the applied voltage must exceed the
forward threshold voltage before the diode conducts.
Contd…
• The applied voltage must be high enough to
completely remove the depletion layer and force
charge carriers to move across the junction.
• The forward voltage causes the
depletion region to narrow.
• The electrons and holes are
pushed toward the p-n
junction.
• The electrons and holes have
sufficient energy to cross the p-
n junction.
• With silicon diodes, this forward threshold voltage
is approximately 0.6 V to 0.7 V.
• With germanium diodes, the forward threshold
voltage is approximately 0.2 V to 0.3 V.
Reverse biased diode
• The P-type material is negatively biased relative to
the N-type material. In this case, the negative
potential applied to the P-type material attracts
the positive charge carriers, drawing them away
from the junction. Likewise, the positive potential
applied to the N-type material attracts the
negative charge carriers away from the junction.
• This leaves the junction area depleted;
– virtually no charge carriers exist.
Contd…
• Therefore, the junction area becomes an insulator,
and current flow is inhibited. The reverse bias
potential may be increased to the reverse
breakdown voltage for which the particular diode is
rated. As in the case of the maximum forward
current rating, the reverse breakdown voltage is
specified by the manufacturer.
The reverse breakdown
voltage is usually very
much higher than the
forward threshold voltage.
Contd…
• A typical general-purpose diode may be specified
as having a forward threshold voltage of 0.6 V and
a reverse breakdown voltage of 200 V.
• If the reverse biased voltage exceeds the reverse
breakdown voltage ; the diode may suffer
irreversible damage.
• Through the use of solid-state physics , the general
characteristics of a semiconductor diode can be
defined by the following equation,
– referred to as Shockley’s equation,
 Contd…
• for both the forward- and reverse-bias regions:

The voltage VT is called the thermal voltage and is determined

by
Contd…

Figure 2.5 Typical diode characteristics

Temperature Effect

Fig 2.6.Temperature effect on the diode V-I characteristic

3,Characteristics of diodes
Resistance of an Ideal diode
• One of the important parameters for the diode is
the resistance at the point or region of operation.
• If we consider the conduction region defined by the
direction of ID and polarity of VD in Fig. 2.7a (upper-
right quadrant of Fig. 2.7b);
• The value of the forward resistance, RF, as defined
by Ohm’s law is
 Contd…
• Where: VF is the forward voltage across the diode and
IF is the forward current through the diode. The ideal
diode, therefore, is a short circuit for the region of
conduction. Consider the region of negatively applied
potential (third quadrant) of Fig. 2.4b

Where: VR is reverse biased voltage across the diode

and IR is reverse current in the diode.
The ideal diode, therefore, is an open circuit in the region of non conduction.

Diode symbol
Contd…

Figure 2.7 Ideal and actual characteristics of

diode
Contd…
Resistance of actual diode
• As the operating point of a diode moves from one
region to another;
– the resistance of the diode will also change due to the
nonlinear shape of the characteristic curve.
• The type of applied voltage or signal will define the
resistance level of interest.
Contd…
Example 2.1
• The characteristic shown in Fig. 2.8 refers to a
germanium diode. Determine the resistance of the
diode when (a) the forward current is 2.5 mA and (b)
when the forward voltage is 0.65 V.

Figure 2.8: Example 2.1

Contd…
Solution
• When IF = 2.5 mA the corresponding value of VF can be read
from the graph. This shows that VF = 0.43 V.
• The resistance of the diode at this point on the
characteristic will be given by:

• When VF = 0.65 V the corresponding value of IF can be read

from the graph. This shows that IF = 7.4 mA. The resistance
of the diode at this point on the characteristic will be given
by:
 DC or Static Resistance
• The application of a dc voltage to a circuit
containing a semiconductor diode will result; an
operating point on the characteristic curve that
will not change with time.
• The resistance of the diode at the operating point
can be found; simply by finding the corresponding
levels of VD and ID
Contd…
• The dc resistance levels at the knee and below
will be greater than the resistance levels obtained
for the vertical rise section of the characteristics.
• The resistance levels in the reverse-bias region will
naturally be quite high.

Figure 2.9 Determining the

dc resistance of a diode at
a particular operating point
 AC or Dynamic Resistance

• If a sinusoidal input is applied, the situation will

change completely.
• The varying input will move the instantaneous
operating point up and down in the region of the
characteristics
• With no applied varying signal, the point of
operation would be the Q-point appearing on Fig.
2.10 determined by the applied dc levels.
• The designation Q-point is derived from the word
quiescent, which means “still or unvarying.”
Contd…

Where ∆ signifies a finite change in

the quantity

Figure 2.10 Defining the dynamic or ac resistance

 Average AC Resistance
• If the input signal is sufficiently large to produce a
broad swing such as indicated in Fig. 2.13;
– the resistance associated with the device for this region
is called the average ac resistance.
• It is the resistance determined by a straight line
drawn between the two intersections established
by the maximum and minimum values of input
voltage.
Contd…

Figure 2.13 Determining the average ac resistance between

indicated limits
Contd…
 3, Analysis of diode Circuits
Diode Equivalent Circuits
• An equivalent circuit is a combination of elements
properly chosen to best;
– represent the actual terminal characteristics of a
device, in a particular operating region.
• Since a silicon diode does not reach the conduction
state until VD reaches 0.7 V with a forward bias (as
shown in Fig. 2.14),
• a battery VT opposing the conduction direction
must appear in the equivalent circuit as shown in
Fig. 2.15
Contd…

Figure 2.14 An equivalent circuit using straight-line

segments to approximate the characteristic curve
Contd…
• When conduction is established the resistance
of the diode will be the specified value of rav.

Figure 2.15 Components of the piecewise-linear

equivalent circuit
 Simplified Equivalent Circuit
• For most applications, the resistance rav is sufficiently
small in comparison to the other elements of the network
and can be ignored.
• under dc conditions a silicon diode has a drop of 0.7 V
across it in the conduction state at any level of diode
current (within rated values).

Figure 2.16 Simplified equivalent circuit for the silicon semiconductor diode
 4, Diode types
• Diodes are often divided into signal or rectifier types
according to their application.
• Signal diodes are small size diodes that require low
forward current rating and low forward voltage drop.
Signal diodes are mostly used in lower voltage/lower
current electronic circuits.
– Usually used in high frequency applications or in
clipping and switching applications with short-duration
pulse waveforms.
– Rectifier diodes : large in size and can withstand high
values of reverse voltage and large values of forward
current;
– Rectifier diodes are used in power supplies circuits(like
rectifiers).
Contd…
• Zener diode: is a special highly doped diode
• A zener diode is a type of diode that permits current not
only in the forward direction like normal diode. but also in
the reverse direction, if the voltage is larger than the
breakdown voltage known as Zener knee voltage or Zener
voltage.
• When a Zener diode is applied with the zener voltage; the
voltage appearing across it will remain constant (equal to
the nominal Zener voltage) regardless of the current
flowing.
• This property makes the Zener diode ideal for use as a
voltage regulator.
Contd…
Contd…
• Light emitting diodes(LED):
• It emits photons when it is forward biased.
• These can be in the infrared or visible spectrum.
• It’s purpose is for indication and displays.
• Various impurities are added during the doping process to
vary the color output. LEDs are current-dependent devices
and therefore, need to be protected from excessive current.
• It is protected from excessive supply voltage and current by
adding a series resistor in the circuit
• The forward bias voltage of LED is usually in the range of 2 V
to 3 V.
Contd…
• The value of the resistor may be calculated as:

• Where VF is the forward voltage drop produced by the LED

and V is the applied voltage. Note that it is usually safe to
assume that VF will be 2 V and choose the nearest
preferred value for R.

Figure 2.21 Use of a current

limiting resistor with an LED
 Load-Line Analysis

• Load line analysis is used to determine the operating

point of a diode in a circuit.
• The applied load have an important impact on the
point or region of operation of a diode.
• The load line plots all possible combinations of
diode current (ID) and voltage (VD) for a given
circuit
 Series Diode Configurations
forward-bias region
• Applying Kirchhoff’s voltage law to the series circuit
of Fig. 2.23a

• The maximum ID equals E/R, and the maximum VD

equals E.
Contd…

Figure 2.23 Series diode configuration: (a) circuit

Contd…
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.

Figure 2.23 Series diode

configuration: (b)
characteristics
Contd…
• if we simply employs the fact that anywhere on the
horizontal axis ID = 0 A and
• anywhere on the vertical axis VD = 0 V.
• If we set VD = 0 V in the above equation, and solve
for ID, we have the magnitude of ID on the vertical
axis.
• Therefore, with VD = 0 V, the equation becomes as;
Contd…
• A straight line drawn between the two points will
define the load line.

• Change in the level of R (the load) alters the

intersection of the load line on the vertical.

• The result will be a change in the slope of the load

line and;

• a different point of intersection between the load

line and the different diode operating point.
Contd…
• The point of intersection between the two is the
point of operation for this circuit.

• By simply drawing a line down to the horizontal axis

the diode voltage VDQ can be determined,

• whereas a horizontal line from the point of

intersection to the vertical axis will provide the level
of IDQ.
Contd…
• The current ID is actually the current through the
entire series configuration of Fig. 2.23a.

• The point of operation is usually called the

quiescent point (abbreviated “Q-pt.”) to reflect its
“still, unmoving” qualities as defined by a dc
network.
Contd…

Figure 2.24 Drawing the load line and finding

the point of operation
5: Applications of diode circuits

Sinusoidal Inputs; Half-Wave Rectification

Figure 2.27 Half-wave rectifier

Contd…
• The diode only conducts when it is forward biased,
• therefore only half of the AC cycle passes through
the diode to the output.

Figure 2.28 Conduction region (0 → T/2)

Contd…

Non conduction région (T/2 to T).

Contd…

Figure 2.29 Half-wave

rectified signal

•The process of removing one-half the input

signal to establish a dc level is called half-wave
rectification.
 Half wave rectifier(practical diode)
• The effect of using a silicon diode with VT = 0.7 V is
demonstrated in Fig. 2.30 for the forward-bias
region.
• The applied signal must now be at least 0.7 V
before the diode can turn “on.”
• For levels of vi less than 0.7 V, the diode is still in an
open circuit state and Vo = 0 V
• When conducting, the difference between vo and vi
is a fixed level of VT = 0.7 V and vo= vi - VT
Contd…
• The net effect is a reduction in area above the
axis, which naturally reduces the resulting dc
voltage level.
Vm >>VT,
• The equation below can be applied to determine
the average value with a relatively high level of
accuracy.
Contd…

Figure 2.30 Effect of VT on half-wave rectified signal

 PIV (PRV)
• Because the diode is only forward biased for one-
half of the AC cycle, it is also reverse biased for
one-half cycle.

• It is important that the reverse breakdown

voltage rating of the diode be high enough to
withstand the peak, reverse-biasing AC voltage.
–PIV (or PRV) > Vm
• PIV = Peak inverse voltage
• PRV = Peak reverse voltage
• Vm = Peak AC voltage
 FULL-WAVE RECTIFICATION
1, Bridge Rectifier

• The dc level obtained from a sinusoidal input can be

improved using a process called full-wave
rectification.
• During the period t = 0 to T/2 the polarity of the
input is as shown in Fig. 2.34.
• D2 and D3 are conducting while D1 and D4 are in
the “off” state.
• Since the diodes are ideal the load voltage is vo = vi
Contd…

Figure 2.33 Full-wave bridge rectifier

Contd…

Figure 2.34 Network of Fig. 2.33 for the period 0 →

T/2 of the input voltage vi
Contd…

Figure 2.35 Conduction path for the positive region of vi

Contd…
• For the negative region of the input the conducting
diodes are D1 and D4, resulting in the configuration
of Fig. 2.36.
• The important result is that the polarity across the
load resistor R is the same as in Fig. 2.34,
• So that establishing a second positive pulse, as
shown in Fig. 2.36.
• Over one full cycle the input and output voltages
will appear as shown in Fig. 2.37.
Contd….

Figure 2.36 Conduction path for the negative region of vi

Contd…

Figure 2.37 Input and output waveforms for a full-wave

rectifier
• Since the area above the axis for one full cycle is now
twice that obtained for a half-wave system,

•the dc level has also been doubled and

Vdc = 2(0.318Vm)
 2, Center-Tapped Transformer

• A second popular full-wave rectifier appears in Fig.

2.40.

• It has only two diodes

• During the positive portion of vi applied to the

primary of the transformer;
– the network appears as shown in Fig. 2.41.
Contd…
• D1 assumes the short-circuit equivalent and D2
the open-circuit equivalent.

• It is determined by the secondary voltages and

the resulting current directions.

• The output voltage appears as shown in Fig. 2.41.

Contd…

Figure 2.40 Center-tapped transformer full-wave rectifier

Contd…

Figure 2.41 Network conditions for the positive region of vi

Contd…
• During the negative portion of the input the
network appears as shown in Fig. 2.42,
• It reverses the roles of the diodes but maintaining
the same polarity for the voltage across the load
resistor R.
• The net effect is the same output as that appearing
in Fig. 2.37 with the same dc levels.
Contd….

Figure 2.42 Network conditions for the negative region of vi

 CLIPPERS
• Clipper is a circuit that has the ability to “clip” off a
portion of the input signal without distorting the
remaining part of the alternating waveform.

• The half-wave rectifier is an example of the

simplest form of diode clipper one resistor and
diode.

• Depending on the orientation of the diode, the

positive or negative region of the input signal is
“clipped” off.
Contd…
• There are two general categories of clippers:

series and parallel.

• The series configuration is defined as one where the

diode is in series with the load,
• while the parallel variety has the diode in a branch
parallel to the load.
 Series Configuration

Figure 2.44 Series clipper

 Parallel Configuration

Figure 2.46 Response to a parallel clipper

Summary of Clipper Circuits
Summary of Clipper Circuits
 CLAMPERS
• A clamper is a network constructed of a diode, a
resistor, and a capacitor
• It shifts a waveform to a different dc level without
changing the appearance of the applied signal.
• Additional shifts can also be obtained by
introducing a dc supply to the basic structure.
• The chosen resistor and capacitor of the network
must be chosen such that;
– the time constant determined by τ= RC is sufficiently
large
Contd…

• This ensures that the voltage across the capacitor

does not discharge significantly during the
interval the diode is non conducting

• capacitor is connected directly between input

and output signals

• resistor and the diode are connected in parallel

with the output signal.
Contd…

A clamper circuit
 Biased Clamper Circuits

• The input signal can be any type

of waveform such as sine,
square, and triangle waves.

• The DC source lets you adjust

the DC clamping level.
Contd…
• In fact, one approach to the analysis of
clamping networks with sinusoidal inputs is;

– to replace the sinusoidal signal by a square

wave of the same peak values.

• The resulting output will then form an envelope

for the sinusoidal response.
Summary of Clamper Circuits
 7, Power supplies

Figure 2.52 Block diagram of a D.C power supply

Figure 2.53 Block diagram of a D.C power supply

showing principal components
 Voltage Doublers

• During the positive voltage half cycle across the

transformer;
– secondary diode D1 conducts
– and diode D2 is cut off
• The capacitor C1 Charges up to the peak voltage (Vm
).
• Diode D1 is ideally a short during this half-cycle,
Contd…
• During the negative half-cycle of the secondary
voltage,
• diode D 1 is cut off and
• diode D 2 conducts charging capacitor C 2 .

• Since diode D2 acts as a short during the negative

half-cycle (and diode D 1 is open);

• we can sum the voltages around the outside loop

 Half-wave voltage
doubler

Double operation, showing each half-cycle of operation: (a)

positive half-cycle; (b) negative half-cycle.
Contd…

• On the next positive half-cycle, diode D 2 is non

conducting and capacitor C2 will discharge through
the load.
• the voltage across capacitor C2 drops during the
positive half-cycle (at the input) and
• the capacitor is recharged up to 2Vm during the
negative halfcycle.
 6, Zener Diode as a voltage regulator

The Zener is a diode operated

in reverse bias at the Zener
Voltage (Vz).

• When Vi  VZ
– The Zener is on
– Voltage across the Zener is VZ
– Zener current: IZ = IR – IRL
– The Zener Power: PZ = VZIZ

• When Vi < VZ
– The Zener is off
– The Zener acts as an open circuit

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 Zener Resistor Values
If R is too large, the Zener diode cannot conduct because the available amount of
current is less than the minimum current rating, IZK. The minimum current is
given by:
I Lmin  I R  I ZK

The maximum value of resistance is:

VZ
RLmax 
I Lmin

If R is too small, the Zener current exceeds the maximum current

rating, IZM . The maximum current for the circuit is given by:
VL V
I L max   Z
RL RL min
The minimum value of resistance is:
RVZ
RL min 
Vi  VZ

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