SEMICONDUCTOR DIODES

By
RAJARAO MANDA
Asst. Professor SS,
Department of electronics,
UPES
REFERENCE TEXT BOOKS:

1. Electronics Devces and Corcuits By Boylestad & Nashelsky 10th

ED : PEARSON
2. Basic Electronics By Santiram Kal, 2013: PHI
3. Electronic devices by Thomas L Floyd 9th edition.
INTRODUCTION

 The branch of physics that deals with conduction (motion of

charge carriers (electrons)) in semiconductors or vacuum or
gas is known as “electronics”.
 This deals with electronic devices and their utilization
 Electronic devices such as diodes, transistors, and integrated
circuits are made of a semi-conductive material.
 Electronic devices or components are connected together to
create an electronic circuit with a particular function.
E.g.: an amplifier, radio receiver, or oscillator.
Electronic equipments
 Electronic systems:

Radio Television Smart phones

Desktop laptop
Security access systems:
Printer system Automated assembly line system

Oil and gas industries

aircraft
 ATOMIC STRUCTURE

 According to the modern atomic

theory,
 All materials or elements are
composed of atoms.
 All atoms consists nucleus and
electrons revolving around the
nucleus in different orbits.
 The nucleus consists of positively
charged particles called protons
and uncharged particles called
neutrons.
 Electrons are positively charged
particles
 Each orbit from the nucleus
corresponds to a certain energy
level; these orbits are grouped
into energy levels known as
shells.
 The Maximum Number of
Electrons in Each Shell The
maximum number of electrons
(Ne) that can exist in each shell
of an atom is a fact of nature
and can be calculated by the
formula,
N e  2n 2

Where n is the number of the

shell.
 The energy of an electron increases
as its distance from nucleus
increases. Thus, an electron in the
second orbit possesses more energy
than the electron in the first orbit
and so on.
 It is clear that the electrons in orbits
(outer most orbits) farther from the
nucleus have higher energy and are
less tightly bound to the atom than
those closer to the nucleus.
 This outermost shell is known as the
valence shell and electrons in this
shell are called valence electrons.
 These valence electrons contribute
to chemical reactions and bonding
within the structure of a material
and determine its electrical
properties.
ENERGY BANDS
 When atoms combine to form a solid, crystal, they arrange
themselves in a symmetrical pattern, the energy levels no
longer remains “discrete”.
 They become energy “bands”. Each band really consists of
a very large number of discrete energy levels which are
very closely spaced. So these bands may be thought of as
continuous.
 Energy band: The large number of discrete and very
closely spaced energy levels is known as energy band.
 In a solid crystal, energy band that originated from the
shells occupied by valence electrons in an atom is known
as valence band.
 When an electron acquires
enough additional energy, it can
leave the valence band, become
a free electron, and exist in
what is known as the
conduction band.
 The difference in energy
between the valence band and
the conduction band is called
an energy gap or band gap (i.e.
no electron can have any
energy value within forbidden
bands).
 This is the amount of energy
that a valence electron must
have in order to jump from the
valence band to the conduction
band.
CLASSIFICATION OF MATERIALS BASED ON THEIR
ELECTRICAL PROPERTIES:

 Materials can be classified into three groups: conductors,

semiconductors, and insulators.
 Insulators:
 An insulator is a material that does not conduct electrical
current under normal conditions. Most good insulators have
very high resistivity.
 For insulators, the energy gap Eg >>> kT ( ~ 4 - 8 eV),
 Valence electrons are tightly bound to the atoms; therefore,
there are very few free electrons in an insulator. Thus,
insulators or dielectrics are extremely poor conductors of
electricity.
 Examples of insulators are rubber, plastics, glass, mica, and
quartz.
 Conductors:
 A conductor is a material that easily conducts electrical current.
Most metals are good conductors.
 For metals or conductors, the CB and the VB overlap each other (
Eg=0). So the large no. of valence band electrons (1022 per cm3) are
available for conduction.
 Examples: copper (Cu), silver (Ag), gold (Au), and aluminum (Al),
 Semiconductors:
 A semiconductor is a material that the conductivity (ability to
conduct electrical current) is between conductors and insulators.
 A semiconductor in its pure (intrinsic) state is neither a good
conductor nor a good insulator.
 For semiconductors Eg lies in the range 0.1 – 3.0 eV. Thus,
appreciable numbers of electron-hole pairs are created by thermal
process.
 Increasing temperature causes creation of more electron-hole pairs,
hence resistivity falls.
 Examples: Single-element semiconductors are antimony (Sb),
arsenic (As), astatine (At), boron (B), polonium (Po), tellurium
(Te), silicon (Si), and germanium (Ge). Compound semiconductors
such as gallium arsenide, indium phosphide, gallium nitride, and
silicon carbide
 The single-element semiconductors are characterized by atoms
with four valence electrons. Silicon is the most commonly used
semiconductor.
 Silicon and germanium are most commonly used semiconductors
in electronic devices.
 Semiconductors

Extrinsic or
Intrinsic or pure
impure
semiconductors
semiconductors
INTRINSIC SEMICONDUCTORS
 which is made of the semiconductor material in its extremely
pure form. Ex: Silicon and Germanium

Material Band gap or energy gap Carrier concentration at 300 K

(eV)
Silicon (Si) 1.21 (at 00K); ~ 1010 per cm3
1.1 (at 3000K)
Germanium 0.785 (at 00K); ~ 1013 per cm3
(Ge) 0.72 (at 3000K)
Gallium 1.21eV (at 00K); ~ 107 per cm3
Arsenic 1.4eV (at 3000K)
(GaAs)
ATOMIC STRUCTURES OF SILICON AND GERMANIUM

 Both silicon and germanium have four valence electrons.

 The valence electrons in germanium are in the fourth shell
while those in silicon are in the third shell, closer to the
nucleus.
 From the atomic structure of Si and Ge, the Ge valence
electrons are at higher energy levels than those in Si
 Therefore, require a smaller amount of additional energy
to escape from the atom.
 This property makes Ge is more unstable at high
temperatures and results in excessive reverse current.
 This is why silicon is a more widely used as semi-
conductive material.
Covalent bond in semiconductor
Covalent bonds in a silicon crystal.
HOLE FORMATION IN INTRINSIC SEMICONDUCTORS
 An intrinsic (pure) silicon crystal at temperature 0 K, the
valence band (VB) is completely filled up with electrons
and the conduction band (CB) is perfectly empty.
 At room temperature (300 K), the valence electrons
acquire sufficient heat (thermal) energy and jump into the
CB, becoming free electrons. Free electrons are also called
conduction electrons
 When an electron jumps to the CB, a vacancy is left in the
VB within the crystal. This vacancy is called a hole.
 For every electron raised to the CB by external energy,
there is one hole left in the VB, creating what is called an
electron-hole pair.
 Recombination occurs when a CB electron loses energy
and falls back into a hole in the VB.
 In intrinsic semiconductor, the number of holes is equal to the
number of free electrons.
 The number of electrons in CB or holes in VB per unit
volume in a pure semiconductor crystal is called intrinsic
carrier concentration.

ni  A0T 3 exp( EG0 / kT )

2

For intrinsic semiconductors, n = p = ni

Where n and p are electron and hole concentrations respectively
EXTRINSIC SEMICONDUCTORS

 Semi-conductive materials do not conduct current well

because of the limited number of free electrons in the
conduction band and holes in the valence band.
 Intrinsic silicon (or germanium) must be modified by
increasing the number of free electrons or holes to increase
its conductivity and make it useful in electronic devices.
This is done by adding impurities to the intrinsic material.
This process, called doping
 A semiconductor material that has been subjected to the
doping process is called an extrinsic material.
The usual doping impurities are :
 pentavalent atoms having five valence electrons (arsenic
(As), antimony(Sb), phosphorus (P)) or
 trivalent atoms having three valence electrons (gallium
(Ga), indium (In), aluminium (Al), boron (B)).
 Pentavalent doping atom is known as donor atom because it
donates or contributes one electron to the conduction band of
pure germanium.
 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 : n-type and p-type
 Both the n- and p-type materials are formed by adding a
predetermined number of impurity atoms into a germanium or
silicon base.
N-TYPE SEMICONDUCTORS
 The n-type is formed by addition of the impurity elements that have five
valence electrons (pentavalent or donor atoms),
 Examples: phosphorus (P), arsenic (As), antimony (Sb), and bismuth (Bi).
 In an n-type material the electron is called the majority carrier
and the hole is the minority carrier.
P-TYPE SEMICONDUCTORS
 The p-type material is formed by doping a pure germanium or silicon
crystal with impurity atoms having three valence electrons (trivalent
impurity atoms or acceptor atoms).
 These are atoms with three valence electrons such as boron (B), indium
(In), and gallium (Ga).
 In a p-type material the hole is the majority carrier and the electron is the
minority carrier
CURRENT IN SEMICONDUCTORS
 The current in a metal is due to the flow of negative
charge carries (electrons) whereas in semiconductor, the
current is due to the movement of both electrons and
holes
 Electron current in silicon semiconductor

 When a voltage is applied across a piece of intrinsic silicon, as

shown in Figure
 the thermally generated free electrons in the conduction band,
which are free to move randomly in the crystal structure, are
now easily attracted toward the positive end.
 This movement of free electrons is one type of current in a
semi-conductive material and is called electron current.
Hole current in silicon semiconductor
CONDUCTIVITY OF A METAL

 When no external field is applied to the metal, the free

electrons move randomly in all directions as shown in Fig.
(a). So the average current is zero.
 However, when an external electric field is applied to the
metal, the free electron motion becomes directed a shown in
Fig. (b)
 As a result of a constant electric field (E), the electrons would be
accelerated and directed opposite to that of the electric field with
some velocity. This velocity is known as drift velocity (v).
 The drift velocity of the electron is proportional to the electric
field (E)
v  E
Where 𝜇 (𝑚2 /V-sec) is called mobility of the
electron
Consider a conductor of length L and it contains N number of
electrons. The current through the conductor (total charge per unit
time) is
𝑁𝑞 𝑁𝑞𝑣
I= =
𝑇 𝐿
𝐼 𝑁𝑞𝑣
And current density = J = = = 𝑛𝑞𝑣 = 𝜌𝑣
𝐴 𝐿𝐴
𝑁
Where 𝑛 = 𝑛 = electron concentration (electrons per 𝑚3 )
𝐿𝐴
and 𝜌 = 𝑛𝑞 𝑖𝑠 𝑐𝑎𝑙𝑙𝑒𝑑 𝑎𝑠 𝑐ℎ𝑎𝑟𝑔𝑒 𝑑𝑒𝑛𝑠𝑖𝑡𝑦 (𝐶𝑜𝑙𝑜𝑢𝑚𝑠 𝑝𝑒𝑟 𝑚3 )
 𝐽 = 𝑛𝑞𝑣 = 𝑛𝑞𝜇𝐸 = 𝜎𝐸 (𝑂ℎ𝑚𝑠 𝑙𝑎𝑤)
Where 𝜎 = 𝑛𝑞𝜇
Ω
𝑖𝑠 𝑘𝑛𝑜𝑤𝑛 𝑎𝑠 𝑐𝑜𝑛𝑑𝑢𝑐𝑡𝑖𝑣𝑖𝑡𝑦 𝑜𝑓 𝑡ℎ𝑒 𝑐𝑜𝑛𝑑𝑢𝑐𝑡𝑜𝑟 .
𝑚
For semiconductors

The current density for semiconductors is given by

𝐽 = (𝑛𝜇𝑛 +p𝜇𝑝 )qE
The conductivity is σ = (𝑛𝜇𝑛 +p𝜇𝑝 )q
𝜇𝑛 = electron mobility and 𝜇𝑝 = hole mobility
MASS ACTION LAW
 Under thermal equilibrium, the product of the free
electron and hole concentrations is a constant
independent of the amount of donor and acceptor
impurity doping.
𝑛𝑝 = 𝑛𝑖 2
 Law of electrical neutrality:

Total number of +ve charge density = total –ve charge

density
𝑝 + 𝑁𝐷 = n + 𝑁𝐴
For n-type semiconductors:
𝑁𝐴 = 0 𝑎𝑛𝑑 𝑛 ≫ 𝑝
𝑁𝐷 + 𝑝 = 𝑛
𝑛𝑖 2
𝑛 = 𝑁𝐷 and p =
𝑁𝐷

For p-type semiconductors:

𝑁𝐷 = 0 𝑎𝑛𝑑 𝑝 ≫ 𝑛
𝑝 = 𝑛 + 𝑁𝐴
𝑛𝑖 2
𝑝 = 𝑁𝐴 and n =
𝑁𝐴
GRADED SEMICONDUCTOR
 If there is a non-uniform concentration of electric charge, the
charge will move from higher to lower concentration. This
phenomenon is known as diffusion.
The hole/electron current density Jp/Jn due to diffusion is
proportional to the concentration gradient
𝑑𝑝 𝑑𝑛
𝐽𝑝 = −𝑞𝐷𝑝 𝑎𝑛𝑑 𝐽𝑛 = 𝑞𝐷𝑛 → (1)
𝑑𝑥 𝑑𝑥
Where Dp and Dn are diffusion constants of holes and
electrons respectively.

According to the Einstein equation, diffusion constant and

mobility are related as
𝐷𝑛 𝐷𝑝 𝑘𝑇 𝑇
= = = 𝑉𝑇 ≈ → 2
𝜇𝑛 𝜇𝑝 𝑞 11,000
Where k = Boltzmann's constant = 1.38× 10−23 J/K
The current densities due the drift hole and electrons (in the
presents of some electric field (E) is given by

𝐽𝑝 = 𝑝𝜇𝑝 qE and 𝐽𝑛 = 𝑛𝜇𝑛 qE → (3)

The total current densities due to diffusion and drift can be

expressed as
𝑑𝑝
𝐽𝑝 = 𝑝𝜇𝑝 qE − 𝑞𝐷𝑝 → (4)
𝑑𝑥

𝑑𝑛
𝑎𝑛𝑑 𝐽𝑛 = 𝑛𝜇𝑛 qE + 𝑞𝐷𝑛 → (5)
𝑑𝑥
Consider a doped semiconductor with non-uniform hole
concentration (p) and there is no external voltage applied across
the diode.

The net current density is zero. i.e. Jp = 0

𝑑𝑝
𝑝𝜇𝑝 qE = 𝑞𝐷𝑝
𝑑𝑥
𝐷𝑝 𝑑𝑝
E =
𝑝𝜇𝑝 𝑑𝑥
𝑉𝑇 𝑑𝑝 𝐷𝑝 𝑘𝑇
E = 𝑓𝑟𝑜𝑚 𝑒𝑞𝑢. 2 = = 𝑉𝑇
𝑝 𝑑𝑥 𝜇𝑝 𝑞
The electric field is related to the potential voltage as

𝑑𝑉
𝐸=− 𝑤ℎ𝑒𝑟𝑒 𝑉 = 𝑝𝑜𝑡𝑒𝑛𝑡𝑖𝑎𝑙 𝑣𝑜𝑙𝑡𝑎𝑔𝑒
𝑑𝑥
𝑉𝑇
−𝑑𝑉 = dp
𝑝
𝑥2 𝑥2
𝑑𝑝
− න 𝑑𝑉 = න
𝑝
𝑥1 𝑥1
−(𝑉2 − 𝑉1 ) = 𝑉𝑇 (ln 𝑝2 − ln 𝑝1 )

Potential difference between two points is defined as

𝑝1
𝑉21 = 𝑉𝑇 ln
𝑝2

𝑝1 = 𝑝2 𝑒 𝑉21/𝑉𝑇

𝑠𝑖𝑚𝑖𝑙𝑟𝑙𝑦 𝑖𝑛 𝑡ℎ𝑒 𝑐𝑎𝑠𝑒 𝑜𝑓 𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛𝑠 𝑛2 = 𝑛1 𝑒 𝑉21/𝑉𝑇

P-N JUNCTION
 If a piece of intrinsic silicon is doped so that half of the part is n-type and
the other half part is p-type, a pn junction forms at the boundary between
the two regions and a diode is created, as indicated in Figure.
 The p region has many holes (majority carriers) from the impurity atoms
and only a few thermally generated free electrons (minority carriers).
 The n region has many free electrons (majority carriers) from the impurity
atoms and only a few thermally generated holes (minority carriers).
FORMATION OF THE DEPLETION REGION
 When the pn junction is formed, the n region loses free electrons as they
diffuse across the junction. This creates a layer of positive charges
(pentavalent ions) near the junction.
 As the electrons move across the junction, the p region loses holes as the
electrons and holes combine. This creates a layer of negative charges
(trivalent ions) near the junction.
 These two layers of positive and negative charges form the depletion
region, as shown in Figure
 As electrons continue to diffuse across the junction, more and
more positive and negative charges are created near the junction
as the depletion region is formed.
 the depletion region has expanded to a point where equilibrium
is established and there is no further diffusion of electrons
across the junction.
 The forces between the opposite charges form an electric field,
as illustrated in Figure by the blue arrows between the positive
charges and the negative charges.
 This electric field is a barrier to the free electrons in the n region
 To move an electron through the electric field, its required to
apply the external energy across the barrier.
 The potential difference of the electric field across the depletion
region is the amount of voltage required to move electrons
through the electric field. This potential difference is called the
barrier potential and is expressed in volts.
Barrier potential or cut-in voltage (V0):

𝑝𝑝 𝑁𝐴 𝑁𝐷
𝑉0 = 𝑉𝑇 ln = 𝑉𝑇 ln
𝑝𝑛 𝑛𝑖 2

 The barrier potential of a pn junction depends on the type

of semi-conductive material, the amount of doping, and the
temperature.
 The typical barrier potential is approximately 0.7 V for
silicon and 0.3 V for germanium at 250 C
SEMICONDUCTOR P-N JUNCTION DIODE
 A diode is made from a small piece of semiconductor material,
usually silicon, in which half is doped as a p region and half is doped
as an n region with a pn junction and depletion region in between.
 The p region is called the anode and is connected to a conductive
terminal. The n region is called the cathode and is connected to a
second conductive terminal.
 The basic diode structure and schematic symbol are shown in Figure
BASIC OPERATION OF THE DIODE
 The application of a voltage across its terminals gives three
possibilities:
 no bias (VD = 0 V)
 forward bias (VD > 0 V), and
 reverse bias (VD < 0 V).
 No bias:
 In the absence of an applied bias voltage, the net flow of charge in
any one direction for a semiconductor diode is zero.
Reverse bias (VD < 0 V):
 Reverse bias is the condition that prevents current through
the diode
 the negative terminal of the VBIAS source is connected to the p
region, and the positive terminal is connected to the n region
 If the external reverse-bias voltage is increased to a large
enough value, reverse breakdown occurs
 minority conduction-band electrons acquire enough energy from
the external source to accelerate toward the positive end of the
diode, colliding with atoms and knocking valence electrons into
the conduction band
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 as shown in Fig.
 The application of a forward-bias potential VD will “pressure”
electrons in the n-type material and holes in the p-type
material to recombine with the ions near the boundary and
reduce the width of the depletion region as shown in
 The resulting minority-carrier flow of electrons from the p-type material to
the n-type material (and of holes from the n-type material to the p-type
material) has not changed in magnitude (since the conduction level is
controlled primarily by the limited number of impurities in the material),
 but the reduction in the width of the depletion region has resulted in a heavy
majority flow across the junction.
 An electron of the n-type material now sees a reduced barrier at the junction
due to the reduced depletion region and a strong attraction for the positive
potential applied to the p-type material.
 As the applied bias increases in magnitude the depletion region will continue
to decrease in width until a flood of electrons can pass through the junction,
DIODES RECAP

Diode symbol

Diode equivalent circuit

 Diode resistance

𝐼𝐷 = 𝐼𝑠 (𝑒 𝑉𝐷 Τη𝑉𝑇 − 1)

𝑉𝐷
DC 𝑜𝑟 𝑠𝑡𝑎𝑡𝑖𝑐 𝑟𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑅𝑑𝑐 =
𝐼𝐷

𝑑𝑉𝐷 η𝑉𝑇
𝐴𝐶 𝑜𝑟 𝑑𝑦𝑛𝑎𝑚𝑖𝑐 𝑟𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑟𝑎𝑐 = 𝑟𝑑 = =
𝑑𝐼𝐷 𝐼𝐷
LOAD LINE ANALYSIS
 The applied load will normally have an important impact
on the point or region of operation of a device.
 If the analysis is performed in a graphical manner, a line
can be drawn on the characteristics of the device that
represents the applied load.
 The intersection of the load line with the characteristics
will determine the point of operation of the system.
 Such an analysis is called load-line analysis. The
intersecting point is known as operating or quiescent (Q)
point.
Diode configurations in the circuit analysis
Example 1: Determine ID and V0 for the given circuit shown in fig.

E = 12 V > (0.7 V 0.3 V) = 1 V

Therefore both Si and Ge diodes are in
forward bias
 Example 2: Determine ID, VD2, and Vo for the circuit shown in fig.

First determine the state of diode:

D1 is forward bias
D2 is reverse bias

E=
Example 3:

Since the applied voltage is greater

than 0.7 V, both the diodes are in the
ON state or FB
Example 4:
• when the supply is turned on
it will increase from 0 to 12
V over a period of time
(probably measurable in
milliseconds).
• At the instant during the rise
that 0.3 V is established
across the germanium diode
it will turn “on” and
maintain a level of 0.3 V.
• The silicon diode will never
have the opportunity to
capture its required 0.7 V
and therefore remains in its
open-circuit state as shown
in Fig.
 Example 5: Determine ID and Vo for the circuit shown in fig.

Step 1: Assume that the diode is in

forward bias (ON) state)
Step 2: Find the current passing
through the diode, if ID > 0 then our
assumption is correct otherwise, the
diode is in reverse bias.
Example 6:
Example 7:
 DIODE AS SWITCH
 When forward-biased, the diode ideally acts as a
closed (on) switch
 When reverse-biased, it acts as an open (off) switch
 DIODE AS RECTIFIER
 The electric power distribution networks provide alternating
voltage (i.e. 230V and 50 Hz frequency).
 Most electronic circuits require DC supply.
 Examples: consumer electronics (televisions, DVDs, etc.),
computers, industrial controllers, and most laboratory
instrumentation systems and equipment
 When an electric device is powered by the electric power
distribution network
 the voltage needs to be turned into DC , this is called rectification
and it needs to be converted to a lower value.
 This can be done is several ways:
 a transformer can be used to decrease the amplitude of the
alternating signal and a rectifier is used to produce a DC
signal as shown in fig.
AC to DC conversion

Role of different circuit components

Transformer:
• Step down AC voltage amplitude to the desired DC voltage
(by selecting an appropriate turn ratio N1/N2 for the
transformer)
Rectifier:
• converts an ac input to a unipolar output
Filter:
• convert the pulsating input to a nearly constant dc output
Regulator:
• Reduce the ripple of the dc voltage
 RECTIFIER

 A device, which is capable of converting a sinusoidal

input wave form with a non-zero average component is
called a rectifier.
 Two types of diode rectifiers
 Half wave rectifier
 Full wave rectifier
 Center tapped rectifier
 Bridge rectifier
HALF WAVE RECTIFIER
 A diode is connected to an ac source and to a load resistor,
RL, forming a half-wave rectifier
During the interval t = 0 → T/2
For the period T/2 → T
Output signal is defined as

The current signal in the circuit is

defined as
 The root mean square (RMS) or ac value of the current
signal is defined as

Similarly for input voltage signal

Peak inverse voltage (PIV) or peak reverse voltage (PRV) is

the maximum value of reverse voltage which occurs at the peak
of the input cycle when the diode is reverse biased
For half wave rectifier PIV = Vm
Full wave rectifier: center tapped
Full-wave bridge rectifier

.
For the period 0 → T/2 (+ ve half cycle)
During negative half cycle (T/2 → T )
PERFORMANCE PARAMETERS

 Mainly two parameters are used to determine the

performance of rectifier
 Efficiency of the rectifier
 Ripple factor
EFFICIENCY OF THE RECTIFIER

The ratio of dc power output to the applied input

a.c power is known as rectifier efficiency, denoted
by η.

𝐼𝑑𝑐 2 𝑅𝐿
η=
𝐼𝑟𝑚𝑠 2 (𝑅𝐹 +𝑅𝐿 )
𝐼𝑚 𝐼𝑚
For half wave rectifier: 𝐼𝑑𝑐 = and 𝐼𝑟𝑚𝑠 =
𝜋 2
0.406𝑅𝐿
η= ≈ 0.406
(𝑅𝐹 +𝑅𝐿 )
2𝐼𝑚 𝐼𝑚
For full wave rectifier: 𝐼𝑑𝑐 = and 𝐼𝑟𝑚𝑠 =
𝜋 2
0.812𝑅𝐿
η= ≈ 0.812
(𝑅𝐹 +𝑅𝐿 )
 RIPPLE FACTOR
Ripple factor is a measure of effectiveness of a rectifier
circuit and defined as a ratio of RMS value of ac
component to the dc component in the rectifier output.

𝐼𝑚 𝐼𝑚
For half wave rectifier: 𝐼𝑑𝑐 = and 𝐼𝑟𝑚𝑠 = ,
𝜋 2
ripple factor = 1.21
2𝐼𝑚 𝐼𝑚
For full wave rectifier: 𝐼𝑑𝑐 = and 𝐼𝑟𝑚𝑠 = ,
𝜋 2
ripple factor = 0.48
CLIPPER (VOLTAGE LIMITERS)
 Clippers are the circuit that employ diodes to remove a
portion of an input signal without distorting the remaining
part of the applied waveform.
 Depending on the orientation of the diode, the positive or
negative region of the input signal is “clipped” off.
 Clipper Circuit - 1:
• If vi < VR, diode is reversed biased and
does not conduct. Therefore, vo = vi
• if vi > VR, diode is forward biased and
thus, vo= VR.

By KVL,
Vi = IR + V0 and V0 = VD+VR
Vi = IR + VD + VR
VD = Vi – IR – VR

For ideal diode if VD < 0 D is

in RB and VD > 0, D is in FB
 Clipper Circuit - 2:
• If vi > VR, diode is reverse
biased. vo = vi
• If vi < VR, diode is
forward biased. vo = VR

By KVL,
Vi = IR + V0 and V0 = – VD+VR
Vi = IR – VD + VR
VD = – Vi + IR + VR

For ideal diode if VD < 0 D is

in RB, I = 0 and VD > 0, D is
in FB
 Clipper Circuit - 3:

Vi = IR+VD1 + VR
VD1 = Vi – IR – VR > 0 ; D1 -- FB
Vi >VR
Vi – IR – VR < 0 D1 --- RB
Vi < VR
Or Vi = IR – VD2 – VR
VD2 = – Vi + IR – VR > 0 D2 ---FB
Vi < – VR
Vi – IR – VR < 0 D2 ---- RB
Vi > – VR
CLAMPERS
 A clamper adds a dc level to an ac voltage
 The network must have a capacitor, a diode, and a resistive
element
For sinusoidal input
Voltage multiplier (double)
ZENER DIODES
 A major application for Zener diodes is as a type of
voltage regulator for providing stable reference voltages
for use in power supplies, voltmeters, and other
instruments.
 Zener diodes are designed to operate in reverse
breakdown.
 If a diode is sufficiently reverse biased the diode will
allow the conduction of a wide range of currents in
reverse direction and the diode voltage approximately
constant at some value. This is known as breakdown
region.
 Two types of reverse breakdown mechanisms in a Zener
diode: (1) avalanche and (2) Zener.
AVALANCHE BREAKDOWN
 Avalanche breakdown occurs when a high reverse bias voltage
is applied to a diode and large electric field (or greater junction
potential) is created across the depletion region.
 The effect is dependent on the doping levels in the region of the
depletion layer.
 Minority carriers in the depletion region associated with small
leakage currents acquires energy and accelerated by the field so
that they collide with crystal ion and imports sufficient energy
to disrupt a covalent bond.
 A new hole-electron pair is created in addition to the original
carrier. These carriers also may pick up sufficient energy from
the applied field, collide with crystal ion and create another
electron hole pair.
 Thus each new carrier may in turn produce additional carrier
through collision and the action of disrupting bonds. This
cumulative process is referred as avalanche multiplication. It
results in large reverse current and the diode is said to be in the
region of avalanche breakdown.
ZENER BREAKDOWN
 Breakdown occurs with heavily doped junction regions (i.e.
highly doped regions are better conductors).
 Because of the high doping levels, the depletion layer is very
thin and, as a consequence, a strong field (106 V/cm, or greater)
exists across it.
 Near the Zener breakdown voltage (VZ), the field is intense
enough to pull electrons from their covalent bonds and create
current. This is known as Zener break down.
 The Zener break down occurs at a field of approximately 2 ×
107 𝑉/𝑚
 Zener diodes with breakdown voltages of less than
approximately 6 V operate predominately in Zener breakdown.
Those with breakdown voltages greater than approximately 6 V
operate predominately in avalanche breakdown. Both types,
however, are called Zener diodes.
Zener diode symbol

Characteristics of Zener diode

 Zener diode as voltage regulator

Step:1 Determine the state of the Zener

diode by removing it from the network and
calculating the voltage across the resulting
open circuit.

Fig: Zener voltage regulator circuit

Step:2 If V ≥ VZ, the Zener diode is on,

and the appropriate equivalent model can
be substituted.
If V < VZ, the diode is off, and the open-
circuit equivalence is substituted.
Example 1: Determine whether the diode in the circuit shown in fig. below is
operating in breakdown region or not. When (i) Vi = 16 V and (ii) Vi = 24 V and
also find IZ, IL and PZ

(i) The voltage across the diode is

𝑅𝐿 16 1.2 𝑘
𝑉𝐿 = 𝑉𝑖 = = 8.73 𝑉
𝑅𝐿 + 𝑅 1𝑘 + 1.2𝑘
This value is less than the breakdown
voltage (i.e. VZ = 10 V), therefore the (ii) Vi = 24 V,
diode acts as open circuit, not operating 𝑅𝐿
𝑉𝐿 = 𝑉𝑖 𝑅 +𝑅
24 1.2 𝑘
= 1𝑘+1.2𝑘 = 13.1 𝑉
in breakdown region 𝐿

VL > VZ, Therefore the diode

operating in breakdown region
𝑉𝐿 = 𝑉𝑍 = 10 𝑉
𝑉𝑅 = 𝑉𝑖 − 𝑉𝑍 = 14 𝑉
𝑉𝑍 10
𝐼𝐿 = = 𝑚𝐴 = 8.33 𝑚𝐴
𝑅𝐿 1.2
𝑉𝑅
𝐼𝑅 = = 14 𝑚𝐴
𝑅
IZ = IR - IL = 5.67 mA