CHAPTER 1DISCRETE DEVICES

1. Introduction

We are living in an age of Information Technology. Electronics is at the very

foundation of the Information and Computer Age. The giant strides that we have made in the

areas of Communications and Computers are possible only because of the great successes

that we have achieved in the field of Electronics.

It is sometimes unbelievable, how many electronics gadgets that we carry these days in our

person –Digital Wrist-watch, Calculator, Cell-phone, Digital Diary or a PDA, Digital Camera

or a Video camera, etc.

The different type of Electronic equipments that has invaded our offices and homes

these days is also mind boggling. Many things we use at home and office are “remote

controlled”, for example, Television (TV), Air-Conditioners, Audio equipment, Telephone,

etc. It is almost close to “magic” how even a child, now-a-days, can switch channels, or

increase decrease the volume of sound in a TV at home by just clicking on a few buttons

sitting at the comfort of a sofa away from the Television apparently without any physical

wiring or connection!

Again, we are astonished, how we are able to talk to our near and dear living several

thousands of kilometres away, from wherever we are, at home, office, on the road in a car, or

in a classroom –by just clicking a few n numbers on our palm sized cellular phones!

Electronics has made deep impact in several vital areas such as health care, medical

diagnosis and treatment, Air and space travels, Automobiles, etc. In short, the technological

developments of several countries of the globe are directly related to their strengths in

electronics design, manufacture, products and services. It appears as though we have to add

inevitably an “E” to the three “R”s, namely, Reading, writing, and arithmetic, to declare a

Man or Woman to be “literate”! Needless to add that the “E” here means “Electronics”! Thus

Electronics has become surely a “Basic Science”. It is no more an “applied science”. Just as

we teach physics, chemistry, biology and mathematics in our schools, it is high time we start

teaching our children at school, Electronics as a separate subject by itself.

1.1 Semiconductors:

We know the importance of using the materials like copper, aluminum etc. in

electrical applications. This is because copper, aluminum etc are good conductors. Similarly,

some materials like glass, wood, paper etc. Also, find wide applications in electrical and

electronic applications. These are called insulators. There is another category of materials

whose ability to carry current, called conductivity, lies between that of conductor and

insulators. Such materials are known as semi conductors. Germanium and silicon are two

well-known semiconductors.

A silicon crystal is different from an insulator because at any temperature above

absolute zero temperature, there is a finite probability that an electron in the lattice will be

knocked loose from its position, leaving behind an electron deficiency called a "hole”. If a

voltage is applied, then both the electron and the hole can contribute to a small current flow.

The semiconductors in the pure form are known as intrinsic semiconductor.

The addition of a small percentage of foreign atoms in the regular crystal lattice of

silicon or germanium produces dramatic changes in their electrical properties, producing n-

type and p-type semiconductors.

In an n-type semiconductor, pentavalent impurities such as antimony, arsenic or

phosphorous are added to intrinsic semiconductor. These dopants contribute extra electrons,

dramatically increasing the conductivity. The addition of trivalent impurities such as boron,

aluminium or gallium to an intrinsic semiconductor makes it p-type semiconductor. The

dopant produces extra vacancies or holes, which likewise increase the conductivity. It is

however the behaviour of the p-n junction which is the key to the enormous variety of solid-

state electronic devices.

1.2 PN Junction Diode:

One of the crucial keys to solid-state electronics is the nature of the P-N junction.

When p-type and n-type materials are placed in contact with each other, the junction behaves

very differently than either type of material alone. Specifically, current will flow in one

direction (forward biased) but not in the other (reverse biased), creating the basic diode.

Figure 1.2.1: Diode

Figure 1.2.1 shows the circuit symbol of a diode and photograph of typical diode.

Since the diode is a two terminal device, the application of a voltage across its terminals

leaves three possibilities:

No bias

Forward bias

Reverse bias

No Bias

In the absence of an applied bias voltage, the net flow of charge in any one direction

for a semiconductor is zero. The current, which flows under the unbiased condition, is called

diffusion. Diffusion is a process in which the charge carriers move from the region of higher

concentration to the region of lower concentration. The concentration of holes in the p region

is more compared to n region and similarly the concentrations of electrons are more in n

region than p region. There will be diffusion of charge carriers and then they undergo

recombination with the opposite charge carriers. The recombined carriers are neutral in

charge and they oppose further movements of charge carriers. The region near the junction

occupied by the recombined charges is called as depletion region. The difference of potential

across the depletion region is called barrier potential. For silicon diodes barrier potential is in

the range of 0.6 to 0.7 V and for Germanium it ranges from 0.2V-0.3V.

Forward Bias

A forward bias or ON condition is established by applying positive potential to the

p-type material and the negative potential to the n-type material as shown in figure 1.2.2

Figure 1.2.2: Forward biasing of PN Junction Diode.

On forward biasing a diode initially, no current flows due to the barrier potential. The applied

forward potential repels the charge carriers and hence pushes it towards the junction. This

results in construction of the depletion region. As the applied potential increases, it exceeds

the barrier potentials at one value (above cut-off value), and the charge carriers gain

sufficient energy to cross the potential barrier and enter the other region. The holes, which are

majority carriers in the p-region, becomes minority carrier on entering the n-region, and the

electrons, which are majority carriers in n-region, become minority carriers on entering the

p-region. This injection of the majority carriers into the opposite region results in current

called diode forward current IF.

The application of a forward-bias potential 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 figure 1.2.2. There is no change the

flow of minority charge carriers, but there is heavy flow of majority charge carriers across the

junction. An electron of the n-type material will cross the reduced depletion region at the

junction and attracted by the positive potential applied to the p-type material. As the applied

bias increases in magnitude, the depletion region width continues to decrease and finally

flood of electronics will pass through the junction, resulting in an exponential rise in the

current as shown the VI characteristic curve in figure 1.2.4.

Reverse Bias

Under reverse bias condition, the positive terminal of the DC supply is connected to the n-

type and negative terminal to the p-type semiconductor as shown in the figure 1.2.3.

Variable DC Voltage

- +

Figure 1.2.3: Reverse biasing of PN- Junction diode

On reverse biasing the majority charge carriers are attracted towards the terminals of the

applied potential. This results in the widening of the depletion region. That is number of

uncovered positive ions in the depletion region of the n-type material will increase due to the

large number of electrons are flown towards the applied positive potential and similarly the

number of negative ions in the p-type also will increase due to applied negative potential. The

net effect is widening of the depletion region, which will introduce a great barrier for the

majority carriers to overcome resulting in zero current flow due to majority charge carriers.

The current due to minority charge carriers still do not change, and takes part in the diode

current. So the current that exist under the reverse bias conditions is called the reverse

saturation current and is represented by I0 or IS it is in the range of few micro amperes.

The Diode Current

The Forward diode current flowing during the forward bias is given by the following

equation.

(1)

ID= Diode Forward Current

I0 = Reverse saturation current.

VD= Applied bias voltage

(T in Kelvin), Volt equivalent of temperature.

η= Constant for Germanium η =1 and for Silicon η =2

When the diode is forward biased, the applied voltage is positive and is large

compared to VT and exp(VD/ηVT) >>1, there for 1 can be neglected from the equation and

final equation will be

(2)

The ID current will increase exponentially with an increase in the forward voltage VD after the

cut in voltage is reached. When the diode is reverse biased, the applied voltage is negative

and is small compared to VT and exponential term can be neglected. Then the diode equation

becomes ID≈I0.

V–I characteristics of PN Junction diode

As we can see from the V-I characteristics when the diode is forward biased initially,

the forward current is zero and when we increase the forward voltage, the forward current

will vary in small magnitude, as the barrier potential is not reached. Once the applied voltage

is exceeds the barrier potential or cut-in voltage or Vknee, then there will be exponential rise in

the forward current. The forward current is in the range of milli amperes.

When the diode is reverse biased and when we increase the reverse applied voltage, as

we know only reverse saturation current flows, which is due to the minority charge carriers.

The reverse current is in the range of few micro amperes. Finally, when the reverse voltage is

increased beyond certain limit, the diode breaks down and reverse current shoots up to a very

large value. The breakdown of diode can be either zener breakdown or avalanche

multiplication, which will be discussed next.

Vkne

e

m

A

(V)

μA

(V

)

Figure 1.2.4: VI characteristics of the PN Junction diode

The Diode Breakdown

The reverse break down in diodes can occur due to two mechanisms, each of them

require critical electric field at the depletion region of the diode. They are

Zener breakdown

Avalanche Multiplication

Zener breakdown

When the doping is very high (≥ 1025 atoms/m3), the depletion region is very narrow,

which results in tunnelling of electrons from p-type valance band to the n-side conduction

band constitutes a reverse current from n to p, this is called zener effect. The basic

requirement for the tunnelling current is a large number of electrons separated from a large

number of empty states by a narrow potential barrier.

The electric field resulting due to the depletion region causes field emission where by

the force on outer orbit electrons due to field is very high that they are pulled out from the

parent nucleus to become free carriers. This ionization by electro-static attraction is known as

“Zener breakdown” and causes an increase in the free carriers density and hence an increase

in the reverse current of the junction. Only for the lower level of reverse voltage the zener

effect is exhibited

Avalanche Multiplication

When the diode is reverse biased, carriers acquire sufficient energy from the thermal

energy and along with the applied reverse bias results in the high electric field in the

depletion region. An electron entering from the p-side may be accelerated to high kinetic

energy to cause ionizing collision. This ionizing collision results in the breakage of covalent

bonds of the bound charges, this result in the generation of new electron-hole pair. The

original electron and generated electron are both swept to the n-side of the junction and

generated hole is swept to the p-side. The generation of electron-hole pair results in the

generation of enormous energy by the process called fission. The liberated fission energy

along with the applied potential and thermal energy colloid with other non-ionized bonds.

This collision and generation of new electron-hole pairs are continuous and multiplicative,

which results in a large amount of charge carriers and thus an increase in the reverse current.

Effect of Temperature on the Reverse current

Since the reverse saturation current is temperature dependent parameter, the reverse

saturation current approximately doubles for every 10o C rise in temperature. Let I01 is the

reverse saturation current at temperature T1 and I02 is the reverse saturation current at

temperature T2, where T2 > T1. The rise in reverse saturation current is given by the relation.

The Diode resistance

The static resistance(R) of the diode is defined as the ratio of voltage to current at any

point on the characteristics. It is reciprocal of the slope of the line joining the operating point

to the origin. The study of the static resistance is very important when the diode characteristic

is linearised from the exponential from the modelling point of view. The value of the static

resistance remains constant for the region of operation.

The dynamic resistance (r) of a diode is defined as the ratio of change in voltage to

the change in current. The dynamic resistance is not as constant as static resistance; it

depends upon the operating voltage.

ID= Diode Forward Current

I0 = Reverse saturation current.

VD= Applied bias voltage

(T in 0Kelvin) Volt equivalent of temperature.

η= Constant for Germanium η =1 and for Silicon η =2

Peak Inverse Voltage (PIV)

This is defined as the voltage that the diode has to withstand under reverse biased condition.

Solved Problems

1. A Silicon diode has a saturation current of 1pA at 20oC. Find Diode bias voltage when

diode current is 3mA. Diode bias current when the temperature is 100OC assuming the

diode voltage to be constant.

Solution:

Given

The diode current ID=3mA,

Reverse saturation current IO=1x10-12 A,

Temperature T=20OC = 273+20 = 293OK

The diode is silicon η=2

The equation for the diode current ID is given by

and

i. The diode bias voltage

ii. The diode current when the temperature is 100OC

The temperature is raised to 100OC (So the reverse saturation current I0 changes) use

the relation.

2. Find the static and dynamic resistance of a p-n junction germanium diode if the

temperature is 27OC and IO=1μA for an applied forward bias of 0.2V.

Solution

Given

Applied forward voltage= 0.2 V

Reverse saturation current IO=1x10-6 A,

Temperature T=20OC = 273+27 = 300OK

The diode is Ge η=1

Exercise Problems:

1. A Silicon diode has a saturation current of 0.1pA at 20OC. Find its forward voltage

when the current is 0.3mA.

2. A Germanium diode has IO=10μA. Determine its forward voltage when it is carrying

50mA of current. Compute the dynamic resistance at this operating point.

3. A Silicon diode at room temperature conducts 5mA at 0.7V. If the voltage increases

to 0.8V. Find reverse saturation current.

4. Calculate the factor by which reverse saturation current IO of Germanium diode is

multiplied when the temperature increases from 25 to 100OC.

5. Determine the voltage for which the reverse current in a germanium diode reaches 70% of its reverse saturation value at room temperature.

1.4 BIPOLAR JUNCTION TRANSISTOR

Introduction

Demonstrated by a team of scientists at Bell laboratories in 1947.

Brought an end to the era of vacuum tube devices.

Advantages:

Smaller size, light weight

No heating elements required

Low power consumption

Low operating voltages

Used in applications such as signal amplifiers, electronic switches, oscillators, etc.

Transistor structure

Three terminal, Three-layered, two-junction device

Two types:

Thin layer of n-type material sandwiched between two p-type materials (called PNP

transistor)

Thin layer of p-type material sandwiched between two n-type materials (called NPN

transistor)

Fig 1.4.1: Transistor structure

Emitter is heavily doped – supplies charge carriers

Base is lightly doped – allows most of the charge carriers to pass through it

Collector is moderately doped – collects the charge carriers

Two junctions are:

Emitter-base junction (or E-B diode)

Collector-base junction (or C-B diode)

For normal operation, E-B diode should be forward biased and C-B diode should be reverse

biased.

Transistor operation

Working of NPN transistor is discussed here. Working of PNP transistor is similar

(roles of free electrons and holes are interchanged and current directions are reversed)

EB diode is forward biased. So, depletion region at EB junction is narrow

CB diode is reverse biased. So, depletion region at CB junction is wide

Free electrons from emitter region cross the junction and reach base region. (Repelled

by the negative potential at the emitter terminal)

Some of these free electrons combine with the holes in the base region. They move

towards the base terminal and form the base current.

There are very less number of holes available in base. Therefore, most electrons

(about 99%) coming from emitter do not combine with holes. They fall down the

potential gradient and enter collector region. (Attracted by the positive potential at the

collector terminal)

So, emitter emits electrons, collector collects these electrons.

Directions of three currents are shown in figure 1.4.2.

Fig. 1.4.2: Transistor operation

Current directions are opposite to electron-flow directions. IE is emitter current, IB is base

current, IC is collector current

Current relationship:

- (1.1)

When emitter circuit is opened, there is no supply of free electrons from emitter to

collector. Even then, there will be small collector current called reverse saturation collector

current . This is due to thermally generated electron-hole pairs.

Even during normal operation, is present. So, total collector current is:

- (1.2)

where, is fraction of emitter current, which flows to collector. From (1.2),

- (1.3)

Since ICBO is very small,

- (1.4a)

Also,

- (1.4b)

Transistor symbols

Fig. 1.4.3: Transistor symbols

Arrow head represents the direction of current through emitter.

Transistor configurations

Transistor is 3-terminal device. For amplifier circuit, four terminals are required –

two for input and two for output. So, one of three terminals of transistor is made common for

both input and output. Accordingly, there are 3 configurations:

Common base (CB) configuration

Common emitter (CE) configuration

Common collector (CC) configuration

Common base configuration

Fig: 1.4.4 Common Base configuration

Base is common, emitter is input terminal, and collector is output terminal. We get two

characteristics: input characteristics and output characteristics

Input characteristics

It is the plot of input current IE, versus input voltage VEB, for various values of output

voltage VCB. As VEB is increased, IE increases similar to diode characteristics. If VCB is

increased, then IE increases slightly. This is due to the increase in electric field aiding the

flow of electrons from emitter.

Fig 1.4.5: CB Input and Output characteristics

Output characteristics

Plot of output current IC versus output voltage VCB for various values of input current IE.

Three regions can be identified: Active, cutoff and saturation

Active region: Region to the right of y-axis, above IE=0 curve, where the curves are linear.

IE is positive nonzero (i.e., E-B diode is forward biased) and VCB is positive (i.e., C-B diode is

reverse biased),When VCB is increased, IC increases slightly. This is because, when VCB is

increased, depletion region width at C-B junction increases, so effective base width

decreases, so IB decreases. Hence IC increases (IC = IE – IB) This effect is known as Early

effect (also called base width modulation).If IE is increased, IC also increases. When IE=0,

IC=ICBO (reverse saturation Collector current in common Base with emitter Open). ICBO

doubles for every 10 degree rise in temperature

Cutoff region: Region below IE=0 curve

Here IE is less than zero (E-B diode is reverse biased) and VCB is positive (C-B diode

is reverse biased).Transistor is said to be in OFF state since IC is zero.

Saturation region: Region to the left of y-axis, above IE=0 curve.

Here IE is positive nonzero (E-B diode forward biased) and VCB is negative (C-B

diode is forward biased) IC decreases exponentially in this region.

Common emitter configuration

Emitter is common, base is input terminal, collector is output terminal

Again we get two characteristics: input characteristics and output characteristics

Fig. 1.4.6: Common-Emitter configuration

Input characteristics

It is the plot of input current IB versus input voltage VBE for various values of output

voltage VCE. As VBE is increased, IB increases similar to diode characteristics. If increased,

then IB decreases slightly. This is due to Early effect.

Output characteristics

Plot of output current IC versus output voltage VCE for various values of input current IB.

Three regions can be identified: Active, cutoff and saturation

Fig1.4.7: Input and output characteristics of CE mode transistor.

Active region: Region to the right of VCE Sat, above IB=0 curve, where the curves are linear.

Note that VCE = VCB + VBE - (1.5)

If VCE > VCE Sat, then VCB becomes positive (i.e., C-B diode is reverse biased)

VCE Sat is around 0.3V for silicon transistor. If IB > 0, then it means E-B diode is forward

biased. When VCE is increased, IC increases slightly due to Early effect. Note that slope of

curve is more than that of CB o/p characteristics. If IB is increased, IC also increases

When IB=0, IC=ICEO (Collector current in common Emitter with base Open) ICEO is much more

than ICBO of CB configuration.

Cutoff region: Region below IB=0 curve Here E-B diode and C-B diode are both reverse

biased Transistor is said to be in OFF state since IC is almost zero.

Saturation region: Region to the left of VCE Sat and right of y-axis Here E-B diode and C-B

diode are both forward biased

Note: Common collector characteristic is similar to that of common emitter, hence not

discussed here.

Relation between αdc and βdc

From equation (1.1) we have

Dividing throughout by IC we get:

From equations (1.4a) and (1.4b) we get:

Rearranging, we get: - (1.6)

Rearranging again, we get: - (1.7)

In the above two equations, we can replace αdc and βdc by αac and βac respectively without

causing any harm.

Relation between ICBO and ICEO

From equation (1.2) we have

Using eq. (1.1) we get:

Rearranging, we get:

Hence, we get:

We know that, at IB = 0, IC = ICEO.

Substituting IB = 0, we get: - (1.8)

Practical transistor circuits

In the circuit diagrams shown earlier, there were no resistors. Without resistors,

currents may be high enough to burn the transistor!

Figure shows practical transistor circuit used to determine input and output characteristics in

CE configuration

Fig. 1.4.8: Practical Common Emitter Transistor circuit

Rearranging, we get: - (1.9)

Applying KVL to the output loop: VCC – ICRC – VCE = 0

Rearranging, we get: - (1.10)

Equations (1.9) and (1.10) are two important design equations

VBE is often taken as +0.7 V for Silicon and +0.2 V for Germanium, for simplicity.

Note: for PNP transistor, VBE is negative.

Transistor maximum ratings

There are limits on voltage, current and power dissipation in transistor. If these limits

are exceeded, then transistor will not function properly, or may even burn.

For CE configuration, limits are set on VCE, IC and PC = VCEIC.

i.e., VCE should not cross VCEMAX, IC should not cross ICMAX, and PC should not cross PCMAX.

All three conditions should be satisfied at the same time.

For the transistor to operate in active region, within the maximum ratings, we require:

Problems

1. In pnp transistor circuit, the ammeter reads the base current as 16 µA. If the

emitter current is 1.618 mA, determine the collector current.

2. A BJT has α = 0.99, IB = 25 µA and ICBO = 200 nA. Find the collector current.

3. For problem 2, find the emitter current. Also find the emitter current by

neglecting ICBO and then find the percentage of error.

4. For a certain BJT, β = 50, ICEO = 3 µA and IC = 1.2 mA. Find IB and IE.

5. A Ge transistor with β = 100 has base-to-collector leakage current of 5 µA. If the

transistor is connected in common-emitter operation, find the collector current for

base current (a) 0 and (b) 40 µA.

6. A Ge Transistor has collector current of 51 mA when the base current is 0.4 mA.

If β = 125, then what is its collector cutoff current ICEO?

7. In a transistor circuit, when the base current is increased from 0.32 mA to 0.48

mA, the emitter current increases from 15 mA to 20 mA. Find αac and βac values.

8. A transistor with α = 0.98 and ICBO = 5 µA has IB = 100 µA. Find IC and IE.

1.5 Light Emitting Diode:

The increasing use of digital displays in calculators, watches and all forms of

instrumentation has contributed to an extensive inherent in structures that emit light when

properly biased. The two types of displays commonly used are light emitting diode (LED)

and liquid crystal display(LCD).

Light emitting diode is a diode that gives of visible or invisible (infrared) light when

energized. In any p-n junction there is a recombination of holes and electrons. During this

process energy possessed by the free electron is transferred to another state, some of this

energy is transferred into heat and some in the form of photons. In silicon and germanium

greater percentage is converted into heat and the emitted light is insignificant.

Diodes constructed of GaAs emit light in the infrared zone during the process of

recombination. Even though the light is not visible, they have numerous applications like,

security systems, industrial processing, optical coupling etc. where visible light is not a

desirable effect visible light can be generated.

By using elements like gallium, arsenic and phosphorous LEDs producing red,

green, yellow, blue, orange or infrared (visible). LED’s have replaced incandescent lamps in

many applications because of their low voltage, long life, and fast on-off switching.\

Fig1.5.1 LED symbol and circuit

Brightness of LED depends on current brightness is usually controlled by current source.

Seven Segment Display:

Fig 1.5.2: Seven segment display

Figure shows seven segment display. It contains seven LEDs. It can be used to display

any alphanumeric character. Fig is schematic diagram of seven segment display, where all

the anodes connected together.

External series resistance is used to limit the current. By grounding one or more

resistors we can display a character.

Application of LED:

In burglar alarm system

Picture phones

Multi meters and digital meters

Electronic panels

Optical communication system

1.6 Photo Diode:

When a p-n junction diode is reverse biased the current flow is only due to the

minority charge carriers. These carriers exists because of thermal energy, which dislocates

valance electrons from their orbits, producing electron hole-pairs.

When light energy bombards a p-n junction, it can dislodge valance electrons. The

more light striking the junction, reverse current increases. In photo diode light is made to fall

on p-n junction by providing a window to allow the light fall.

Fig1.6.1: Photo diode

Application of Photo diodes:

As light detectors

As demodulators

Encoders

Optical Communications

High speed counting

Switching circuits

1.7 Photo Transistor:

The photo transistor is like a normal transistor, but the base is kept open. The

incident light is made to fall on the base terminal so that base current is generated and the

output current is multiplied by the β of the transistor. The symbol and typical application

circuit is as shown in fig.1.7.1.

(a) (b)

Fig 1.7.1 : Photo Transistor a) Symbol and b) Typical application

Applications:

In high speed reading of computer punched cards and tapes

Light detector systems

Light operated switches

Production line counting objects

1.8 Opto Coupler: Opto coupler or opto isolator combines an LED and a photo diode in a

single package as shown below in Fig. no.1.8.1.

When input voltage is applied to LED emits light and this light is detected by photo

diode. The reverse current flowing in the photo diode circuit produces a voltage drop across

series resistor, which is proportional to reverse current, which in turn proportional to input

voltage. This device can couple an input signal to the output circuit.

Advantage of opto coupler is the isolation between input and output circuits.

(a) (b)

Fig 1.8.1:Opto coupler a) Symbol b) Typical aplication

1.9 Varactor Diode:

The depletion layer formed in a p-n junction is like a parallel plate capacitor. The

capacitance of this depends on the width of the depletion layer. Width of the depletion layer

is directly -proportional applied reverse voltage. Thus capacitance can be controlled by

reverse voltage. Diodes used for this purpose are called varactor or voltage variable capacitor

or varicaps.

Symbol and variation in capacitance are as shown:

Fig1.9.1: Varactor Diode

Because the capacitance is voltage controlled, varactors have replaced

mechanically tuned capacitors in many applications such as television receivers automobile

radios and other communication equipments.

When it is connected in parallel with inductor it forms a resonant circuit, having

resonant frequency which is function of applied voltage. This is the principle behind

electronic tuning of a radio station, or a TV channel.

Applications

FM radio and TV receivers

AFC circuits

Self adjusting bridge circuits

Adjustable band pass filters

Tuning LC resonant circuits

CHAPTER 2

DIODE CIRCUITS

2.1 Clipper: Clipping circuits are used to select that part of the input wave which lies above or below some reference level. A clipper is a device designed to prevent the output of a circuit from exceeding a predetermined voltage level without distorting the remaining part of the applied waveform.

A clipping circuit consists of linear elements like resistors and non-linear elements like diodes or transistors. Clipping circuits are used to select for purposes of transmission, that part of a signal wave form which lies above or below a certain reference voltage level.

Clipping circuits can be classified as positive clipper and negative clippers.

Positive clipper: Fig. shows positive clipper.

The action of the circuit is explained below. When the input signal voltage is negative, the diode D is reverse-biased and behaves as an open-switch, the entire negative half cycle appears across the load( output). When the input signal voltage is positive but does not exceed battery voltage VR, the diode D remains reverse-biased and most of the input voltage appears across the output. When during the positive half cycle of input signal, the signal voltage exceeds the battery voltage VR, the diode D is forward biased i.e conducts heavily. The output voltage is equal to VR and stays at VR as long as the input signal voltage is greater than battery voltage VR in magnitude. Thus a biased positive clipper removes input voltage when the input signal voltage exceeds the battery voltage. Clipping can be changed by reversing the battery and diode connections.

That is Vo = Vi if Vi<VR

Vo = VR if Vi>VR

Negative biased clipper: the clipping circuit which removes part of the negative input is as shown in Fig. below

When the input signal voltage is positive, the diode D is reverse-biased and behaves as an open-switch, the entire positive half cycle appears across the load. When the input signal voltage is negative but does not exceed battery voltage V, the diode D remains reverse-biased and most of the input voltage appears across the output. When during the negative half cycle of input signal, the signal voltage exceeds the battery voltage V, the diode D is forward biased i.e conducts heavily. The output voltage is equal to – V and stays at – V as long as the input signal voltage is greater than battery voltage V in magnitude. Thus a biased negative clipper removes input voltage when the input signal voltage exceeds the battery voltage

Consider another circuit shown below

In this circuit,

Vo = Vi if Vi>VR

Vo = VR if Vi<VR

It is a circuit which removes signal voltage above or below a reference level. It is useful in

signal shaping and protecting circuits. Circuit shown in fig 2.1.1 removes all positive half

cycles. During positive half cycle diode turns on. So ideally zero voltage across Rl

During negative half cycle diode is off. So input voltage appears across Rl But practically

diode voltage 0.7V will appear at output. If we reverse the polarity of diode we get negative

clipper and connecting battery serially with diode we get biased clipper.

Clipping at two independent levels

VR1 < VR2

2.2 Clamper: A clamper is an electronic circuit that prevents a signal from exceeding a certain defined magnitude by shifting its DC value. The clamper does not restrict the peak-to-peak excursion of the signal, but moves it up or down by a fixed value. A diode clamp (a simple, common type) relies on a diode , which conducts electric current in only one direction. Resistors and capacitors in the circuit are used to maintain an altered dc level at the clamper output.These circuits are also known as DC voltage restorers. Clampers can be constructed in both positive

and negative polarities. When unbiased, clamping circuits will fix the voltage lower limit (or upper

limit, in the case of negative clampers) to 0 Volts.

Positive unbiased

In the negative cycle of the input AC signal, the diode is forward biased and conducts, charging the capacitor to the peak positive value of VIN. During the positive cycle, the diode is reverse biased and thus does not conduct. The output voltage is therefore equal to the voltage stored in the capacitor plus the input voltage again, so VOUT = 2VIN

Negative unbiased

A negative unbiased clamp is the opposite of the equivalent positive clamp. In the positive cycle of the input AC signal, the diode is forward biased and conducts, charging the capacitor to the peak value of VIN. During the negative cycle, the diode is reverse biased and thus does not conduct. The output voltage is therefore equal to the voltage stored in the capacitor plus the input voltage again, so VOUT = -2VIN

2.3 Diode Rectifiers:

A rectifier is an electrical device, comprising one or more semiconductive devices

(such as diodes) for converting alternating current to direct current. When just one diode is

used to rectify AC (by blocking the negative or positive portion of the waveform) the

difference between the term diode and the term rectifier is merely one of usage, e.g. the term

rectifier describes a diode that is being used to convert AC to DC. Rectification is a process

whereby alternating current (AC) is converted into direct current (DC). Almost all rectifiers

comprise a number of diodes in a specific arrangement for more efficiently converting AC to

DC than is possible with just a single diode. Rectification is commonly performed by

semiconductor diodes.

The nature of the p-n junction is that it will conduct current in the forward direction

but not in the reverse direction. It is therefore a basic tool for rectification in the building of

DC power supplies.

There are two types of rectifirer

Half wave rectifier

Full wave rectifier

Half wave rectifier

The figure 2.3.3 shows the circuit diagram of half wave rectifier the voltage at point A

does the opposite of that at point B. When A is increasing in a positive direction, B is

increasing in a negative direction. It is rather like the two ends of a seesaw. During the first

half cycle of the waveform shown on the left, A is positive and B is negative. The diode is

forward biased and current flows around the circuit formed by the diode, the transformer

Fig 2.3.3: Half wave rectifier circuits and its corresponding waveforms

winding and the load. Since the current through the load and the voltage across the load are in

the same proportions, then the voltage across the load is as shown in the right hand diagram,

during the first half cycle. During the second half cycle, A and the anode is negative, B

and the cathode are positive. The diode is reverse biased and no current flows. This is

indicated by the horizontal line in the right hand diagram. The diode only conducts on every

other half cycle. The diode only conducts during half the cycle. Hence, HALF-WAVE

RECTIFICATION. The rectified voltage is DC (it is always positive in value). However, it is

not a steady DC but PULSATING DC. It needs to be smoothed before it becomes useful.

Peak Inverse Voltage

When the input voltage reaches its maximum value Vm during the negative half cycle

the voltage across the diode is also maximum. This maximum voltage is known as the peak

inverse voltage. Thus for a half wave rectifier

Let Vi be the voltage to the primary of the transformer. Vi is given by

where Vr is the cut-in voltage of the diode.

Ripple Factor

Ripple factor r is defined as the ratio of rms value of ac component to the dc

component in the output.

Vav the average or the dc content of the voltage across the load is given by

RMS voltage at the load resistance can be calculated as

Ripple Factor

Efficiency

Efficiency, η is the ratio of the dc output power to ac input power. Thus

Fig 2.3.4: Circuit diagram of practical full wave rectifier

Advantages Disadvantages

Low cost High Ripple factor

Simple Circuit Low efficiency

Low TUF

FULL Wave Rectifier:

A practical full-wave rectifier circuit is shown in figure 2.3.4 It uses two diodes (D1

and D2) and a center-tapped transformer (T1). When the center tap is grounded, the voltages

at the opposite ends of the secondary windings are 180 degrees out of phase with each other.

Thus, when the voltage at point A is positive with respect to ground, the voltage at point B is

negative with respect to ground. Let's examine the operation of the circuit during one

complete cycle.

During the first half cycle (indicated by the solid arrows), the anode of D1 is positive

with respect to ground and the anode of D2 is negative. The current flows from the ground up

through the load resistor (RL), through diode D1 to point A. In the transformer, current flows

from point A, through the upper winding, and back to ground (center tap). When D1

conducts, it acts like a closed switch so that the positive half cycle is felt across the load (RL).

During the second half cycle (indicated by the dotted lines), the polarity of the applied

voltage has reversed. Now the anode of D2 is positive with respect to ground and the anode

of D1 is negative. Now only D2 can conduct. Current now flows, as shown, from ground

(center tap), up through the load resistor (RL), through diode D2 to point B of T1. In the

transformer, current flows from point B up through the lower windings and back to ground

(center tap). Notice that the current flows across the load resistor (RL) in the same direction

for both halves of the input cycle.

Ripple Factor

The ripple factor for a Full Wave Rectifier is given by

The average voltage or the dc voltage available across the load resistance is

RMS value of the voltage at the load resistance is

Efficiency

Efficiency, h is the ratio of the dc output power to ac input power

The maximum efficiency of a Full Wave Rectifier is 81.2%.

Peak inverse voltage

Full Wave Rectifier is 2Vm because the entire secondary voltage appears across the

non-conducting diode.

Advantages Disadvantages

Low ripple factor Output voltage is only the half the secondary voltage

High efficiency High PIV rating is needed

High TUF Transformer is bulky, expensive and difficult to

adjust the center tap accurately.

Full-wave bridge rectifier:

The voltages at points A and B on the transformer are changing in opposite directions.

When A is increasing in a positive direction, B is increasing negatively. It is like the opposite

ends of a seesaw. During the first half cycle, A is positive and B is negative. D1 has positive

on its anode, D2 has negative on its cathode. Both are forward biased. Current flows around

the circuit formed by these diodes, the load and the transformer winding, as shown in the

second diagram.

Figure 2.3.5: The full wave bridge wave rectifier and its waveforms

The current flowing up through the load produces a pulse of voltage across the load as

shown in the right hand waveform. During the next half cycle, A is negative and B is

positive. D4 has positive on its anode, D3 has negative on its cathode. Both are forward

biased. Current flows around the circuit as shown in the bottom diagram, again flowing in the

same direction through the load and producing another pulse of voltage. Since the full cycle

is used, this circuit is called a FULL-WAVE rectifier. The following parameters are same as

the full wave rectifier they are Idc, Vdc, Irms, Vrms, Ripple factor, Efficiency Form factor, peak

factor. Its Peak Inverse Voltage (PIV) is Vm.

Advantages Disadvantages

Low ripple Uses four diodes, which reduces voltage by

two diode drops for every half cycle.

High efficiency

TUF is higher than centre tapped FWR

Less bulky and expensive

PIV is only Vm

As TUF is high, it can be used for high

power applications.

Rectifiers with Capacitor Filters:

Fig2.3.7 Capacitor filter

A capacitor filter connected directly across the load is shown above. The property of a

capacitor is that it allows ac component and blocks dc component. The operation of the

capacitor filter is to short the ripple to ground but leave the dc to appear at output when it is

connected across the pulsating dc voltage.

During the positive half cycle, the capacitor charges up to the peak vale of the

transformer secondary voltage, Vm and will try to maintain this value as the full wave input

drops to zero. Capacitor will discharge through RL slowly until the transformer secondary

voltage again increases to a value greater than the capacitor voltage. The diode conducts for a

Fig 2.3.6: Full wave rectifier circuits with capacitor filter

period, which depends on the capacitor voltage. The diode will conduct when the transformer

secondary voltage becomes more than the diode voltage. This is called the cut in voltage. The

diode stops conducting when the transformer voltage becomes less than the diode voltage.

This is called cut out voltage.

Referring to the figure below, with slight approximation the ripple voltage can be

assumed as triangular. From the cut-in point to the cut-out point, whatever charge the

capacitor acquires is equal to the charge the capacitor has lost during the period of non-

conduction, i.e., from cut-out point to the next cut-in point.

The charge it has acquired

The charge it has lost

Figure 2.3.8

If the value of the capacitor is fairly large, or the value of the load resistance is very large,

then it can be assumed that the time T2 is equal to half the periodic time of the waveform.

From the above assumptions, the ripple waveform will be triangular and its rms value is given by

The ripple may be decreased by increasing C or RL (both) with a resulting increase in

the dc output voltage.

2.4 Zener Diodes

A Zener diode is a type of diode that permits current to flow in the forward direction

like a normal diode, but also in the reverse direction if the voltage is larger than the rated

breakdown voltage or "Zener voltage".

Figure 2.4.1: Symbol of a Zener Diode

A conventional solid-state diode will not let current flow if reverse-biased below its

reverse breakdown voltage. By exceeding the breakdown voltage, a conventional diode is

destroyed in the breakdown due to excess current which brings about overheating. The

process is however reversible, if the device is operated within limitation. In case of forward-

bias (in the direction of the arrow), the diode exhibits a voltage drop of roughly 0.6 volt for a

typical silicon diode. The voltage drop depends on the type of the diode.

A Zener diode exhibits almost the same properties, except the device is especially

designed so as to have a greatly reduced breakdown voltage, the so-called Zener voltage. A

Zener diode contains a heavily doped p-n junction allowing electrons to tunnel from the

valence band of the p-type material to the conduction band of the n-type material. A reverse-

biased Zener diode will exhibit a controlled breakdown and let the current flow to keep the

voltage across the Zener diode at the Zener voltage. For example, a 3.2-volt Zener diode will

exhibit a voltage drop of 3.2 volts if reverse biased. However, the current is not unlimited, so

the Zener diode is typically used to generate a reference voltage for an amplifier stage, or as a

voltage stabilizer for low-current applications.

The breakdown voltage can be controlled quite accurately in the doping process.

Tolerances to within 0.05% are available though the most widely used tolerances are 5% and

10%.The effect was discovered by the American physicist Clarence Melvin Zener.

Another mechanism that produces a similar effect is the avalanche effect as in the

avalanche diode. The two types of diode are in fact constructed the same way and both

effects are present in diodes of this type. In silicon diodes up to about 5.6 volts, the zener

effect is the predominant effect and shows a marked negative temperature coefficient. Above

5.6 volts, the avalanche effect becomes predominant and exhibits a positive temperature

coefficient.

Figure 2.4.2 : VI Characteristics of a Zener diode

The VI characteristic of a zener diode is shown in figure 2.10. With the application of

sufficient reverse voltage, a p-n junction will experience a rapid avalanche breakdown and

conduct current in the reverse direction. Valence electrons, which break free under the

influence of the applied electric field, can be accelerated enough that they can knock loose

other electrons and the subsequent collisions quickly become an avalanche. When this

process is taking place, very small changes in voltage can cause very large changes in

current. The breakdown process depends upon the applied electric field, so by changing the

thickness of the layer to which the voltage is applied, zener diodes can be formed which

break down at voltages from about 4 volts to several hundred volts.

Zener Voltage Regulator:

Figure 2.4.3: Zener voltage regulator

Zener diodes are widely used to regulate the voltage across a circuit. When connected

in parallel with a variable voltage source so that it is reverse biased, a zener diode conducts

when the voltage reaches the diode's reverse breakdown voltage. From that point it keeps the

voltage at that value.

In the circuit shown, resistor R provides the voltage drop between input and output.

The value of R must satisfy two conditions:

R must be small enough that the current through D keeps D in reverse breakdown.

The value of this current is given in the data sheet for D. For example, the common

BZX79C5V6 device, a 5.6 volt 0.5 watt zener diode, has a recommended reverse

current of 5 mA. If insufficient current flows through D, then output will be

unregulated, and could rise as high as . When calculating R, allowance must be made

for any current flowing through the external load, not shown in this diagram,

connected across the output.

R must be large enough that the current through D does not destroy the device. If the

current through D is ID, its breakdown voltage VB and its maximum power dissipation

PMAX, then IDVB < PMAX.

A zener diode used in this way is known as a shunt voltage regulator (shunt meaning

connected in parallel), and voltage regulator being a class of circuit that produces a stable

voltage across any load.

Consier the following circuit for the voltage regulator

Figure 2.4.4: Zener voltage regulator

The circuit has to mainatin constant voltage across a load resisitor RL. The circuit

holds the voltage across the load RL almost equal to the voltage across zener VZ even after th

input Vin andload resistor RL undergo changes. If the unrgulated dc voltage Vin rises, the

current through R increases. This extra current is directed to the zener diode instesd of

flowing through the load. The zener diode voltage is virtually unaffected by the increase in

this current and load voltage which is same as the diode voltage Vz remains constant. If the

load requires more current when RL is decreased, the zener didoe can supply the extra current

without affecting the load voltage.

Let I be the current through the resister R , we can write

The power dessipated in the diode is Pz=IZ Vz

The selection of Rs is very important here. We have

After substituting the value if I we get,

For Line regulation RL is constant. And is also constant

And Vin varies between Vin(min) to Vin(max)

For Load Regulation, Vin is constant and RL varies between RLmin and RLmax and load current is

given by and

When Vin=Vin(min),and IL is constant then

,

Similarly when Vin=Vin(max) we have ,

The selected R must be small enough to permit minimum zener current to ensure that

the diode is in its breakdown region. That is R must be small enough to ensure that minimum

current IZ(min ) flows under worst condition. This is when Vin falls to its smallest possible value

Vinmin and IL is its largest possible value ILmax (Load Regulation). At the same time R must be

selected large enough to ensure that the current through the zener diode should not exceed the

maximum zener current Izmax so that power desipation in the diode will not will not exceed P z.

That is the condition when Vin rises to the value of V inmax and load current IL to its minimum

ILmin

SO we can write

and

Applications:

As Voltage regulators

As Voltage Limiters

Wave shaping

Protection diode

Fixed reference voltage

Solved Problems

In a zener voltage regulator if Vz=10V, Rs=1KΩ, RL-2KΩ. If the input voltage Vin

varies from 22 to 40 V, find the maximum and minimum values of zener current.

Solution:

and

Similarly and

Using above relation we can find

ans

2.5 IC voltage regulators

Although voltage regulators can be designed using OP AMPS and other discrete

components, it is easier and quicker to use IC voltage regulators. Furthermore IC voltage

regulators are versatile, relatively inexpensive and are available with features such as

programmable output, current / voltage boosting is possible.

IC voltage regulators are available as

1. Fixed voltage regulator

2. Adjustable voltage regulators

Fixed voltage regulators:

78XX series are three terminal positive voltage regulators. In 78XX, XX indicates the

output voltage. They are available as 7805, 7806, 7808, 7815, 7818, and 7819. 79Xx series

are negative fixed voltage regulators which are complements to the 78Xx series devices.

MC7805 is a 3-terminal 1A positive voltage regulator. It is designed for a wide range

of applications. These applications include on-card regulation for elimination of noise and

distribution problems associated with single-point regulation. In addition, it can be used with

power-pass elements to make high current voltage regulators. The internal limiting and

thermal shutdown features of this regulator make it essentially immune to overload. When

used as a replacement for a zener diode-resistor combination, an effective improvement in

output impedance can be obtained together with lower-bias current.

Output current up to 1A no external components required.

Figure 2.5.1: IC voltage regulators

The input capacitor is used to cancel the inductive effects due to long distributive leads and

the output capacitor to improve the transient response.

Adjustable Voltage Regulators:

IC regulator like LM117, LM317, LM338 are adjustable voltage regulators. The

LM117 series of adjustable 3-terminal positive voltage regulators is capable of supplying in

excess of 1.5A over a 1.2V to 37V output range. They are exceptionally easy to use and

require only two external resistors to set the output voltage. Further, both line and load

regulation are better than standard fixed regulators. Normally, no capacitors are needed

unless the device is situated more than 6 inches from the input filter capacitors in which case

an input bypass is needed. An optional output capacitor can be added to improve transient

response.

Figure 2.5.2: Adjustable IC voltage regulators

Lm 317 is a three terminal positive voltage regulator that can supply 1.5A of load current

over an adjustable output range of 1.25V to 37V. Output voltage is given by the equation

Vo = I ADJ *R2 + Vref

Typical value of I adj = 50 µA and Vref = 1.25V, Vref is the voltage between output terminal and

center terminal, I adj is the current in center terminal.

SMPS

A switched-mode power supply (switching-mode power supply/SMPS, or simply

switcher) is an electronic power supply unit (PSU) that incorporates a switching regulator in

order to provide the required output voltage. An SMPS is a power converter that transmits

power from a source (e.g., a battery or the electrical power grid) to a load (e.g., a personal

computer). The function of the converter is to provide a regulated output voltage usually at a

different level from the input voltage.

Unlike a linear power supply, the pass transistor of a switching mode supply switches

very quickly (typically between 50 kHz and 1 MHz) between full-on and full-off states,

which minimizes wasted energy. Voltage regulation is provided by varying the ratio of on to

off time. In contrast, a linear power supply must dissipate the excess voltage to regulate the

output. This higher efficiency is the chief advantage of a switch-mode power supply.

The main advantage of this method is greater efficiency because the switching

transistor dissipates little power when it is outside of its active region (i.e., when the transistor

acts like a switch and either has a negligible voltage drop across it or a negligible current

through it). Other advantages include smaller size and lighter weight (from the elimination of

low frequency transformers which have a high weight) and lower heat generation due to

higher efficiency. Disadvantages include greater complexity, the generation of high-

amplitude, high-frequency energy that the low-pass filter must block to avoid electromagnetic

interference (EMI), and a ripple voltage at the switching frequency and the harmonic

frequencies thereof.

Very low cost SMPS may couple electrical switching noise back onto the mains

power line, causing interference with A/V equipment connected to the same phase. Non-

power-factor-corrected SMPSs also cause harmonic distortion.

Switching regulators are used as replacements for the linear regulators when higher

efficiency, smaller size or lighter weight is required. They are, however, more complicated,

their switching currents can cause electrical noise problems if not carefully suppressed, and

simple designs may have a poor power factor

CHAPTER 3

TRANSISTOR BIASING

3.1 Introduction

One of the most common applications of transistor is in amplifiers. E-B junction

should be forward biased; C-B junction should be reverse biased (active region) For faithful

amplification we require that transistor be operated in active region throughout the duration

of input signal. To ensure this, proper dc voltages should be applied. This is called Biasing.

3.2Operating point

When no input signal is applied to transistor circuit, and only dc voltages are supplied,

currents IC, IB and voltage VCE will have certain values.

If these values are plotted over the transistor output characteristics, the point we get is called

‘Operating point’. It is also called ‘Quiescent point’ or just Q-point.

Fig. 3.2.1: Quiescent point

In above figure, currents IBQ, ICQ and voltage VCEQ are plotted as point Q. In practice, we have

to choose Q-point according to our requirement. If we want to operate in the middle of active

region,

we may choose Q as Q-point. For Class A amplifier (discussed later) we want Q-point to be

in the middle of active region. If we want to operate near saturation, we may choose Q’ as Q-

point. If we want to operate near cutoff, we may choose C as Q’’-point. Note that if no

Figure 3.2.2: Fixed bias circuit

biasing is used, Q-point will be in the origin of graph. So, biasing is used to fix the Q-point

according to our need.

Types of bias

Fixed bias

Voltage divider bias

Fixed Bias IC voltage regulators using

Base resistor RB is connected to Vcc (Instead of VBB). Negative terminal of Vcc is not

shown. It is assumed to be at ground.

Applying KVL to the input side, we get:

Rearranging, we get

(3.21)

Vcc is constant, VBE is almost constant (0.7V for silicon). So by selecting proper RB, we can

fix IB as required Applying KVL to output side we get:

or (3.22)

IC is related to IB by β

So, VCE can be fixed by selecting proper RC.

Load line

From eq (3.22) we have .

This is an equation of straight line with VCE and IC as two variables. This straight line is called

load line Now, output characteristic is also a function of same two variables.

Intersection of load line and output characteristic for particular IB gives the common solution.

This is nothing but Q-point. Figure 3.2.3 shows load line superimposed on output

characteristics, with Q-point marked. Now if we vary RB, Q-point moves along the load line.

If RB is held constant, and RC is varied, then slope of load line varies.

If RB and RC are held constant and VCC is varied, then load line shifts, maintaining same

slope. From these graphs we infer that, with everything else held constant, if RB is increased,

transistor goes towards cutoff, if RB is decreased, transistor goes towards saturation. With

everything else held constant, if RC is increased, transistor goes towards saturation, if RC is

decreased, transistor goes towards active region. With everything else held constant, if VCC is

increased, transistor goes towards active region, if VCC is decreased, transistor goes towards

saturation.

Figure: 3.2.3 Transistor characteristics with load line

Advantages of fixed bias

Simple to analyze and design

Uses very few circuit components

Disadvantages of fixed bias

Q-point is not stable. i.e., if temperature varies, βwill vary, hence IC will vary.

If transistor is replaced by another transistor having different βthen Q-point will

shift

Voltage divider bias or Self bias

Uses two resistors R1 and R2 instead of RB. RE is connected between emitter and

ground

Figure 3.2.3 self bias

Input side of the above circuit is redrawn below in fig 2.2.4(a)

Figure 3.2.4: Fig (a) should be replaced by Thevenin’s equivalent circuit shown in fig (b)

VTH is the open circuit voltage between points A & B in fig (a) given by:

Figure 3.2.5: Equivalent circuit

- (3.23)

RTH is the resistance seen between A & B with VCC replaced by short circuit. See fig 3.13(c).

- (3.24)

Self bias circuit with its input loop replaced by Thevenin’s equivalent circuit is shown in fig

3.14.

Applying KVL to the input loop we get:

Substituting and rearranging, we get

- (3.25)

Applying KVL to the output loop, we get

Rearranging, we get

- (3.26)

Also,

- (3.27)

Where, VC is voltage from collector to ground

And, - (3.28)

Where, VE is voltage from emitter to ground

Since β>> 1, we have (β+1) ≈ β. If βRE >> RTH, then equation (12) reduces to:

- (3.29)

Now, - (3.30)

Since equation for IC does not contain β, we say that IC is independent of temperature

variation and transistor replacement.

Advantages of voltage divider bias

Collector current, and hence Q-point is independent of . Hence Q-point is stable

against variation in temperature and replacement of transistor

Disadvantages of voltage divider bias

Analysis and design are complex

More circuit components required

Problems

1. For a fixed bias circuit using Si transistor, RB = 500 kΩ, RC = 2 kΩ, VCC = 15 V,

ICBO = 20 µA and β = 70. Find the Q-point collector current ICQ.

2. A Si transistor is biased for a constant base current. If β = 80, VCEQ = 8 V, RC = 3

kΩ and VCC = 15 V, find ICQ and the value of RB required.

3. Repeat problem 2 if the transistor is a germanium device.

4. For a fixed bias circuit, VCC = 12 V and RC = 4 kΩ. The Ge transistor used is

characterized by β = 50, ICEO = 0 and VCE sat = 0.2 V. Find the value of RB that just

results in saturation.

5. For a self bias circuit using silicon transistor, RE = 300 Ω, RC = 500 Ω, VCC = 15

V, β = 100 and . Find the values of R1 and R2 to get VCEQ = VCC / 2.

6. For a self bias circuit, the transistor is a Si device, RE = 200 Ω, R1 = 10R2 = 10 kΩ,

RC = 2 kΩ, β = 100 and VCC = 15 V. Determine the values of ICQ and VCEQ.

7. For a self bias circuit using Si transistor with β = 100, RC = 330 Ω, RE = 100 Ω

and VCC = 12 V. Determine the values of R1 and R2 required to provide a base

bias current of 0.3 mA, so as to locate the operating point at ICQ = 18 mA and VCEQ

= 4.25 V.

8. A fixed bias circuit has VCC = 20 V, RC = 5 kΩ, RE = 4 kΩ and RB = 300 kΩ. The

Si transistor has ICBO = 0 and β = 50. Find ICQ and VCEQ.

9. Suppose if the transistor used in problem 8 failed, and was replaced with a new

transistor with ICBO = 0 and β = 75. Is the new transistor still biased for active

region operation?

Connecting ac signal to a Transistor:

After a transistor has been biased with the Q point near the middle of the load line, we

can couple a small AC voltage in to the base. This produces AC collector voltage which is

proportional to AC input voltage. For applying this voltage a coupling capacitors are used.

Coupling Capacitor:

Consider the RC circuit shown below. Here R represents the input resistance or the load

resistance of the amplifier.

Here a capacitor is used to connect the AC signal source to load R. Since capacitive

reactance is inversely proportional to frequency for DC voltages. This capacitor acts as a

open and at very high frequency it acts as a short circuit. When capacitor is used in this way it

is called Coupling capacitor. For this to work properly its reactance must be very small even

at the lowest frequency of the source.

As a rule Xc < 0.1 R

Where R is the input resistance of amplifier. For example if the frequency variation is 20 Hz

to 20 KHz, thus at 20 Hz, also < 0.1 R

Ex: If R = 2 KΩ, and frequency range is 20 Hz to 20 KHz, the value of the capacitor needed

is

Xc < 0.1 R

< R C= 39.8 µF

Emitter Bypass Capacitor:

Emitter resistance RE is used to stabilize the operating point. Similar to coupling

capacitor bypass capacitor must be open for DC signals and short for AC signals.

Fig shows an AC voltage connected to RC circuit. For high frequency capacitive reactance is

too small and acts like a short circuit. In other words point E is effectively connected to

ground. Similarly by connecting a capacitor in parallel it passes all AC components and

effectively grounding emitter, without disturbing DC conditions.

For bypass capacitor to work effectively, even at the lowest frequency capacitive reactance

must be too small. As a rule Xc < 0.1 RE.

Ex: In the circuit shown of f = 1 KHz, then

Xc < 0.1 RTh , RTh = R1|| R2 = 375Ω

C = , C = 4.2 µF

Small Signal Operation:

When a sinusoidal voltage (ac) is applied it appears across the emitter diode and produces

the sinusoidal variations in VBE . When input voltage increases to positive peak Q point moves

to QA, and when the input voltage reaches negative peak point moves to QB. Thus Q point is

moving along the curve. The size of the AC voltage determines how far the instantaneous

point moves away from the Q point. Large AC voltage produces large variations and small ac

voltage produces smaller variations.

If the movement of the instantaneous Q point is large it will produce distortions because of

the curvature of the graph. To reduce the distortion smaller swing in input voltage is desired.

AC Beta : When AC signal is applied ib and ic also changes and we define AC current gain β

= this is different from β dc = =

h-parameter model:

Another model used for transistor earlier is h-parameter model. Manufacturer

specification sheets provide this parameters. The H-parameter model of transistor in general

and for common emitter are as shown below

hie = input impedance =

hfe = forward current gain =

hoe = output conductance =

hre = reverse transfer ratio =

These parameters can be determined from the transistor static characteristics.

Transistor Amplifier

Amplifier is a circuit which increases the magnitude of input quantity applied

Bipolar junction transistor basically amplifies current

If base current is considered as input current, then collector current which is output current is

beta times the input current. This is known as transistor action

By suitably designing transistor circuit, we can get voltage amplification and power

amplification to work as amplifier, transistor should be in active region throughout the input

waveform cycle. i.e., base-emitter junction forward biased, collector-base junction reverse

biased. This is achieved by proper use of biasing circuit Consider the working of the circuit

shown below:

Batteries VBB and VCC ensure that transistor is operating in the active region. It causes

direct currents IB, IC and IE to flow Vin is a weak signal to be amplified. This causes an

alternating current ib to flow through input circuit Total base current iB is sum of IB and ib,

which is alternating current During positive quarter cycle of input waveform, as input voltage

increases, ib and hence iB increases. Due to transistor action, iC also increases.

Fig. 3.2.6: Common emitter amplifier

We have , where β = βac is current amplification factor Since β is very large, even for

small increase in iB, there is a large increase in iC. Hence large alternating voltage Vout =iCRL

develops across load resistor RL. During second quarter cycle of input waveform, as input

voltage decreases, iB decreases, and also iC decreases.

During negative half cycle of input waveform, E-B junction still remains forward biased

because, VBB is so chosen that it is greater than peak value of V in. So, during negative half

cycle when iB decreases, iC also decreases, and hence Vout decreases Thus output voltage Vout

will be exact replica of input voltage Vin, but magnified many times However, since current

direction through RL is from bottom to top, the output voltage is 180o out of phase with input.

3.3 Single stage CE transistor amplifier

A practical common-emitter transistor amplifier using voltage divider bias is shown

fig. The use of bias eliminates the need for two separate batteries VBB and VCC.

Resistors R1, R2, RC and RE, and voltage source VCC fix operating point in active region. This

is voltage divider bias, which is already discussed. CC is called coupling capacitor. At input

side, it blocks dc component of input voltage (or output of previous stage) from reaching the

base of transistor. If dc is not blocked, then it will shift the operating point. At output side,

CC blocks dc component from entering into the load (or next stage).

Figure3.3.1: RC coupled amplifier

CE is called emitter by-pass capacitor. It offers low reactance path for ac component, thus

preventing ac component from passing through RE. If ac is allowed to pass through RE, then

it will decrease VBE, bringing down output voltage. RL is the equivalent resistance of the load

connected at output of amplifier.

As explained earlier, when input voltage varies, iB varies and hence iC varies. Thus output

voltage is proportional to input voltage, but amplified.

Note that output can also be taken across RC.

3.4 Classification of amplifiers

Classified based on different criteria.

Based on signal frequency

Audio amplifier (frequencies between 20Hz and 20KHz)

Video amplifier (frequencies above 20KHz up to a few MHz)

Radio amplifier (frequencies up to several MHz)

Based on quantity amplified

Voltage amplifier (input voltage level is amplified)

Current amplifier (input current level is amplified)

Power amplifier (input power level is amplified)

Based on mode of operation

Class A amplifier (collector current flows throughout the input signal cycle)

Class B amplifier (collector current flows only during positive or negative half cycle

of input signal cycle)

Class C amplifier (collector current flows for less than half cycle of input signal)

Class AB amplifier (collector current flows for more than half, but less than full cycle

of input signal)

3.5 Gain of amplifier

Voltage gain of amplifier is given by

- (3.32)

It has no units as it is ratio of voltages. However, gain is measured in terms of decibels

defined by:

- (3.33)

Note that unit less gain AV is negative since Vout is 180o out of phase with Vin. However,

while expressing in terms of dB, negative sign is obviously not taken.

Usually gain of around 100 (approximately) (i.e., 40 dB) can be easily obtained using one

stage amplifier. Sometimes, this may not be sufficient. Especially when input is in micro

volts, we may require gain more than 1000 or 10000.

In such cases, we have to cascade amplifier stages. i.e., connect amplifiers in series, with

output of one stage given to input of next stage.

3.6 Multistage amplifiers

If high gain is required, then amplifier stages are cascaded as shown in figure 3.18.

Overall gain AV is product of individual gains: - (3.34)

In decibels, overall gain is sum of individual gains:

- (3.35)

However, practically the gain will be less than calculated AV due to loading effects

Fig 3.6.1: Multistage amplifier

3.7 Frequency response of amplifier

Plot of amplifier gain versus frequency of input signal is called frequency response.

Frequency of input signal is increased in steps. At each frequency, voltage gain is

determined and then plotted. It is found that gain is very small at lower frequencies and at

higher frequencies. Gain remains constant at mid frequencies. For audio amplifier, it is

required that gain should be constant over the audio frequency range from 20 Hz to 20

kHz.Bandwidth of amplifier is defined as range of frequencies over which gain is either equal

or greater than 0.707 (or 1/2)times the maximum gain Since 20 log (0.707) = – 3,

bandwidth is also defined as range of frequencies over which gain is within 3 dB of

maximum gain (in dB) Fig shows frequency responses of RC coupled amplifier

Figure 3.7.1 : Frequency response of amplifier

Here, f1 is called lower cutoff frequency; f2 is called upper cutoff frequency. These are also

called 3 dB frequencies

Bandwidth is: BW = f2 – f1 - (3.36)

Analysis of frequency response curve of RC coupled amplifier

At low frequencies, reactance of coupling capacitors is high. So, part of input does

not reach the transistor. So gain reduces. Also at low frequencies reactance of emitter bypass

capacitors is high. So, ac component of emitter current is not fully bypassed. Hence there

will be ac voltage drop across RE, which reduces gain.

At high frequencies, reactance of shunt capacitances due to wiring and reactance of

junction capacitances will become low. This offers low reactance path for signal to ground,

thus reducing voltage gain.

At mid frequencies, reactance of coupling and emitter bypass capacitors is low;

reactance of shunt capacitances is high. So there is no loss of signal. Hence gain is constant.

Note that this is only a qualitative analysis; exact analysis of RC coupled amplifier is

not required at this stage.

Problems

1. An amplifier is known to have a power gain of 40 dB. If the output power is 4

watts, determine the input power.

2. What output power is obtained from an amplifier whose power gain is 55 dB,

when the input power is 1 mW?

3. In a three-stage amplifier, the gain of first stage is 40 dB, gain of second stage is

200 (not in dB) and that of third stage is 0 dB. Find the overall gain of the

amplifier.

CHAPTER 4

OPERATIONAL AMPLIFIERS

4.1 Introduction: “An opamp is a very high gain directly coupled amplifier which can

amplify signals having wide range of frequencies.”

The term operational amplifier refers to a class of high-gain DC coupled amplifiers

with two inputs and a single output. The modern integrated circuit version is typified by the

famous 741 op-amp .Op-amps are high gain amplifier, and are used almost invariably with

overall loop-feedback

Figure 4.1 Op-Amp

4.2 Amplifier Circuit model:

The circuit model of an amplifier is shown in Figure (centre dashed box, with an input

port and an output port). The input port plays a passive role, producing no voltage of its own,

and is modelled by a resistive element Ri called the input resistance. The output port is

modelled by a dependent voltage source AVi in series with the output resistance Ro, where

Vi is the potential difference between the input port terminals. Figure 1 shows a complete

amplifier circuit, which consists of an input voltage source Vs in series with the source

resistance Rs, and an output “load” resistance RL. From this figure, it can be seen that we

have voltage-divider circuits at both the input port and the output port of the amplifier. This

requires us to re-calculate Vi and Vo whenever a different source and/or load is used:

R S

V S

V i

R i A V i

R o

V o

R L

SO URCE AMPLIF IER LO AD

+

_

+

_

INP

UT

PO

RT

OU

TP

UT

PO

RT

Figure 4.2: Circuit model of an amplifier circuit.

4.3 The Operational Amplifier: Ideal Op-Amp Model

The amplifier model shown in Figure 1 is redrawn in Figure 2 showing the standard

op-amp notation. An op-amp is a “differential-to-single-ended” amplifier, i.e., it amplifies the

voltage difference Vp – Vn = Vi at the input port and produces a voltage Vo at the output

port that is referenced to the ground node of the circuit in which the op-amp is used.

Figure 4.3.1: Standard op-amp Figure 4.3.2: Ideal op-amp

The ideal op-amp model was derived to simplify circuit analysis and it is commonly

used by engineers for first-order approximate calculations. The ideal model makes three

simplifying assumptions:

Gain is infinite: A = ∞

Input resistance is infinite: Ri = ∞

Output resistance is zero: Ro= 0

Applying these assumptions to the standard op-amp model results in the ideal op-amp

model shown in Figure 3. Because Ri = ∞ and the voltage difference Vp – Vn = Vi at the input

port is finite, the input currents are zero for an ideal op-amp:

in = ip = 0

Hence there is no loading effect at the input port of an ideal op-amp:

(7)

In addition, because Ro = 0, there is no loading effect at the output port of an ideal op-amp:

Vo = A * Vi (8)

Finally, because A = ∞ and Vo must be finite, Vi = Vp – Vn = 0, or

V i R i

AV i

R o

V o

+ _

+

_ + _

V p

V n

i p

i n

+

_

V i

AV i V o

+ _

+

_ + _

V p

V n

+

_

Vp = Vn (9)

4.4 The Ideal Op-amp: An Ideal Op-Amp has the following characteristics .

An infinite voltage gain

An infinite bandwidth

An infinite input resistance: The resistance b/w V1 and V2 terminals is

infinite .

Zero output resistance: Vo remains constant no matter what resistance is

applied across output.

Perfect balance : When V1 is equal to V2 the Vo is 0

Zero input offset voltage (i.e., exactly zero out if zero in)

Infinite CMRR

Infinite slew rate

Zero input offset current

The characteristic of an op-amp do not change with temperature

4.5 The 741 Op-amp

The most common and most famous op-amp is the mA741C or just 741, which is

packaged in an 8-pin mini-DIP. Here is the pin-out for a typical 741 op-amp in a DIP (Dual

In-line Package).

Figure 4.5.1:Pin-out for a typical 741 op-amp

OPAMP Characteristics/ Parameters:

1. output offset voltage Voo: The actual value of the output voltage when the inputs of

an op-amp are zero is called the output offset voltage. Output offset voltage is

basically due to two distinct phenomenon. a)input offset voltage b) input bias current

2. Input bias current(Ib): It is the average of the current that flows in to the inverting

and non inverting input terminals of the opamp.

3. Input offset current(Iio): it is the algebraic difference between the currents flowing in

to non inverting and inverting terminals.

4. Input resistance (Ri): It is the equivalent resistance that can be measured at either the

inverting or non-inverting terminal with the other terminal connected to ground.

5. CMRR: This is a figure of merit for an opamp. It is defined as the ratio of the

differential gain to the common mode gain.

6. Slew Rate: It is defined as the maximum rate of change of output voltage per unit

time

7. SVRR: Supply Voltage Rejection Ratio: The change in opamp input offset voltage

caused by variations in supply voltage is called SVRR.

8. Output resistance (Ro): The equivalent resistance can be measured between the

output terminal of opamp and the ground.

Common Mode Gain:

Recall that the op-amp amplifies the difference between the two input signals V+ and

V-, i.e. Vo = Aol(V+ - V-). So by this equation, if both input signals are the same then the

output will be zero. However, this is not the case in real op-amps. Any signal common to

both inputs will also be amplified by a common mode gain.

The common mode gain, Acm, is the ratio of the output voltage, Vo, to the common

mode input signal, Vcm, i.e. Vo = AcmVcm. For two independent input signals, the common

mode signal is often taken to be the average of the two input signal voltages, i.e. Vo = Acm((V+

+ V-) / 2) So the final gain equation is: Vo = Aol(V+ - V-) + Acm((V+ + V-) / 2) To limit the

effects of common mode gain on the output signal, the open loop gain, Aol, needs to be much

larger than the common mode gain, Acm. The common mode rejection ratio (CMRR) is a

measure of the 'quality' of the op-amp to reject common mode signals (the higher the better)

and is defined as:

CMRR = Aol / Acm

CMRR is often expressed in dB:

CMRR = 20 log10(Aol / Acm) dB

The Effect of Common Mode Gain

Common mode gain affects the closed loop gain of the non-inverting amplifier as

follows:

Vo = ViÃol(1 + 1/CMRR)

where Ãcl is the 'ideal' closed loop gain, i.e. Ãcl = 1 + R2/R1

Use the tool below to see the effect of common mode gain on the non-inverting amplifier.

Practical considerations: common-mode gain

As stated before, an ideal differential amplifier only amplifies the voltage difference

between its two inputs. If the two inputs of a differential amplifier were to be shorted together

(thus ensuring zero potential difference between them), there should be no change in output

voltage for any amount of voltage applied between those two shorted inputs and ground:

Voltage that is common between either of the inputs and ground, as "Vcommon-

mode" is in this case, is called common-mode voltage. As we vary this common voltage, the

perfect differential amplifier's output voltage should hold absolutely steady (no change in

output for any arbitrary change in common-mode input). This translates to a common-mode

voltage gain of zero.

The operational amplifier, being a differential amplifier with high differential gain,

would ideally have zero common-mode gain as well. In real life, however, this is not easily

attained. Thus, common-mode voltages will invariably have some effect on the op-amp's

output voltage.

The performance of a real op-amp in this regard is most commonly measured in terms

of its differential voltage gain (how much it amplifies the difference between two input

voltages) versus its common-mode voltage gain (how much it amplifies a common-mode

voltage). The ratio of the former to the latter is called the common-mode rejection ratio,

abbreviated as CMRR:

An ideal op-amp, with zero common-mode gain would have an infinite CMRR. Real

op-amps have high CMRRs, the ubiquitous 741 having something around 70 dB, which

works out to a little over 3,000 in terms of a ratio. Because the common mode rejection ratio

in a typical op-amp is so high, common-mode gain is usually not a great concern in circuits

where the op-amp is being used with negative feedback. If the common-mode input voltage

of an amplifier circuit were to suddenly change, thus producing a corresponding change in

the output due to common-mode gain, that change in output would be quickly corrected as

negative feedback and differential gain (being much greater than common-mode gain)

worked to bring the system back to equilibrium. Sure enough, a change might be seen at the

output, but it would be a lot smaller than what you might expect.

A consideration to keep in mind, though, is common-mode gain in differential op-amp

circuits such as instrumentation amplifiers. Outside of the op-amp's sealed package and

extremely high differential gain, we may find common-mode gain introduced by an

imbalance of resistor values. To demonstrate this, we'll run a SPICE analysis on an

instrumentation amplifier with inputs shorted together (no differential voltage), imposing a

common-mode voltage to see what happens. First, we'll run the analysis showing the output

voltage of a perfectly balanced circuit. We should expect to see no change in output voltage

as the common-mode voltage changes:

Common-mode rejection ratio:

The common-mode rejection ratio (CMRR) of an amplifier (or other device) measures

the tendency of the device to reject input signals common to both input leads. A high CMRR

is important in applications where the signal of interest is represented by a small voltage

fluctuation superimposed on a (possibly large) voltage offset, or when relevant information is

contained in the voltage difference between two signals. (An example is audio transmission

over balanced lines.)

The CMRR, measured in positive decibels, is defined by the following equation:

where Ad is the differential gain and As is the common-mode gain. This is a very important

specification, as it indicates how much of the common-mode signal will appear in your

measurement. The value of the CMRR often depends on signal frequency as well, and must

be specified as a function thereof.

CMRR is often important in reducing noise on transmission lines. For example, when

measuring a thermocouple in a noisy environment, the noise from the environment appears as

an offset on both input leads, making it a common-mode voltage signal. The CMRR of the

measurement instrument determines the attenuation applied to the offset or noise.

Applications of OPAMP:

Operational amplifiers can be used to perform mathematical operations on voltage

signals such as inversion, addition, subtraction, integration, differentiation, and multiplication

by a constant

Inverting amplifier:

Inverts and amplifies a voltage (multiplies by a negative constant)

Zin = Rin (because V − is a virtual ground)

Expression for gain:

Assuming that the input difference is small, we can write KCL at the inverting node:

(Notice the little red dot at the inverting node in the circuit diagram.) (Note also, that we

have defined two voltages, V1 and Vout that are both measured with respect to the ground.)

Here's the KCL equation using the assumption that the voltage at the amplifier input - at

the input node - is zero.

I1 + I0 = 0

Technically, we can write KCL in terms of all the voltages involved (taking V+ and V- as

the voltages - with respect to ground - at the "+" and "-" terminals respectively). Doing

that we obtain:

( V1 - V- )/R1 + ( Vout - V- )/R0 = 0

However, since we assume that there is no voltage difference between V+ and V-, we

can replace V- with V+ and we have the inverting input terminal connected to ground, so

V- = 0. That means we get:

V1/R1 + Vout / R0 = 0

Note that the situation where V+ 0 happens so often that it has a common name. The non-

inverting terminal in a connection like this - where the inverting input terminal is connected

to ground - is called a virtual ground.

Vout = - V1 R0 / R1

There are two things to note about this expression for the output voltage.

The input voltage is multiplied by a constant that depends only upon the two resistors, R 0 and

R1. Properties of the amplifier that are used in the argument for this expression are:

Very large gain (approaching infinity) Very large input resistance between the two input

terminals

Non-inverting amplifier:

Amplifies a voltage (multiplies by a constant greater than 1)

(realistically, the input impedance of the op-amp itself, 1 MΩ to 10 TΩ)

Expression for gain and

From these calculations, we can see that the effective voltage gain of the noninverting

amplifier is still set by the resistance ratio Rf/Rin, but is one greater than this ratio. Thus, if

the two resistors are of equal value, the non-inverting gain will be 2, rather than 1. To get a

non-inverting gain of 1, we can simply eliminate both Rf and Rin, and connect the output

directly to the (-) input. We would eliminate Rs at the same time, or else use equal resistances

in series with the two inputs.

Voltage follower:

Used as a buffer amplifier to eliminate loading effects or to interface impedances

(connecting a device with a high source impedance to a device with a low input impedance)

(realistically, the differential input impedance of the op-amp itself, 1 MΩ to 1

TΩ)

Summing amplifier:

Sums several (weighted) voltages

When , and Rf independent

When

Output is inverted, Input impedance Zn = Rn, for each input (V − is a virtual ground)

Subtractor:

The subtractor provides an output which is equal to the difference of the two input

signals or proportional to their difference . For minimum offset error R1 || R2 = R3 || R4

Integrator:

Integrates the (inverted) signal over time

(where Vin and Vout are functions of time, V initial is the output voltage of the integrator at

time t = 0.) Note that this can also be viewed as a type of electronic filter

Differentiators:

Differentiate the (inverted) signal over time.

(where Vin and Vout are functions of time)

Comparator :

Compares two voltages and outputs one of two states depending on which is greater

Problems:

1. Determine the gain of the amplifier shown in fig below given R0=100Ώ R1=4.7k Ώ

2. For the circuit of non inverting amplifier with R1=10 k Ώ and R0=100k Ώ determine

i) Closed loop gain Af ii) output voltage Vo

3.In this circuit, you have it set up for a gain of -10. The input voltage is 0.24V. What is the

output voltage?

4.For the same conditions as in Problem 2, the input is changed to -0.35 volts. What is the

output voltage now?

Op-amp voltage comparator

A simple op-amp comparator

An operational amplifier (op-amp) has a well balanced difference input and a very

high gain. The parallels in the characteristics allows the op-amps to serve as comparators in

some functions.[1]

A standard op-amp operating in open loop configuration (without negative feedback)

can be used as a comparator. When the non-inverting input (V+) is at a higher voltage than

the inverting input (V-), the high gain of the op-amp causes it to output the most positive

voltage it can. When the non-inverting input (V+) drops below the inverting input (V-), the

op-amp outputs the most negative voltage it can. Since the output voltage is limited by the

supply voltage, for an op-amp that uses a balanced, split supply, (powered by ± VS) this

action can be written:

Vout = Ao(V1 − V2)

A comparator is designed to produce well limited output voltages that easily interface

with digital logic. Compatibility with digital logic must be verified while using an op-amp as

a comparator.

Schmitt trigger:

Schmitt trigger is a comparator circuit that incorporates positive feedback.In the non-

inverting configuration, when the input is higher than a certain chosen threshold, the output is

high; when the input is below a different (lower) chosen threshold, the output is low; when

the input is between the two, the output retains its value. The trigger is so named because the

output retains its value until the input changes sufficiently to trigger a change. This dual

threshold action is called hysteresis, and implies that the Schmitt trigger has some memory.

In fact, the Schmitt trigger is a bistable multivibrator.

The symbol for Schmitt triggers in circuit diagrams is a triangle with an inverting or non-

inverting hysteresis symbol. The symbol depicts the corresponding ideal hysteresis curve.

Standard Schmitt trigger Inverting Schmitt trigger

Schmitt triggers are commonly implemented using a comparator] connected to have positive

feedback (i.e., instead of the usual negative feedback used in operational amplifier circuits).

For this circuit, the switching occurs near ground, with the amount of hysteresis controlled by

the resistances of R1 and R2:

The comparator extracts the sign of the difference between its two inputs. When the non-

inverting (+) input is at a higher voltage than the inverting (−) input, the comparator output

switches to +VS, which is its high supply voltage. When the non-inverting (+) input is at a

lower voltage than the inverting (−) input, the comparator output switches to -VS, which is its

low supply voltage. In this case, the inverting (−) input is grounded, and so the comparator

implements the sign function – its 2-state output (i.e., either high or low) always has the same

sign as the continuous input at its non-inverting (+) terminal.

Because of the resistor network connecting the Schmitt trigger input, the non-inverting (+)

terminal of the comparator, and the comparator output, the Schmitt trigger acts like a

comparator that switches at a different point depending on whether the output of the

comparator is high or low. For very negative inputs, the output will be low, and for very

positive inputs, the output will be high, and so this is an implementation of a "non-inverting"

Schmitt trigger. However, for intermediate inputs, the state of the output depends on both the

input and the output. For instance, if the Schmitt trigger is currently in the high state, the

output will be at the positive power supply rail (+VS). V+ is then a voltage divider between

Vin and +VS. The comparator will switch when V+=0 (ground). Current conservation shows

that this requires

and so Vin must drop below to get the output to switch. Once the comparator output

has switched to −VS, the threshold becomes to switch back to high.

Typical hysteresis curve (which matches the curve

shown on a Schmitt trigger symbol)

So this circuit creates a switching band centered

around zero, with trigger levels . The input

voltage must rise above the top of the band, and then below the bottom of the band, for the

output to switch on and then back off. If R1 is zero or R2 is infinity (i.e., an open circuit), the

band collapses to zero width, and it behaves as a standard comparator. The output

characteristic is shown in the picture on the right. The value of the threshold T is given by

and the maximum value of the output M is the power supply rail.

A practical Schmitt trigger configuration is shown below.

The output characteristic has exactly the same shape of the previous basic configuration, and

the threshold values are the same as well. On the other hand, in the previous case, the output

voltage was depending on the power supply, while now it is defined by the Zener diodes. In

this configuration, the output levels can be modified by appropriate choice of Zener diode,

and these levels are resistant to power supply fluctuations (i.e., they increase the PSRR of the

comparator). The resistor R3 is there to limit the current through the diodes, and the resistor

R4 minimizes the input voltage offset caused by the comparator's input leakage currents.

Feedback concepts

Introduction:

Feedback plays an important role in electronic circuits and the basic parameters

such as input resistance, output resistance, current gain or voltage gain and bandwidth

may be considerably changed by the use of feedback for a given amplifier.

Feedback The process of combining a fraction of the output back to its input is called

feedback. The network coupling employed for the process of feedback is called feedback

network.

Basic feedback amplifier is as shown

Input Vi Output

Vs

βVo

Basic amplifier

AFeedback network

β

It consist of an amplifier with a gain A and a feedback network with feedback

fraction β and drives an error signal β Vo. Depending upon whether the feedback energy

aids or opposes the input signal, there are two basic types of feed backs in amplifiers. They

are positive feedback and negative feedback.

Positive feedback:

When the feedback is in phase to the input the input signal increases this type of

feedback is called positive feedback.

Here Vi=Vs+Vf or Ii= Is+If

V s, is source signals

Vi , I i input signals to amplifiers

Vf, if feedback signals

Positive feedback increases the gain of amplifier and also increases noise, distortion and

reduces stability of an amplifier. Because of these disadvantages, +ve feedback is seldom

used in amplifiers. But +ve feedback is used in oscillators.

Negative feedback:

When the feedback is in opposition to the input, the input signal reduces this type of

feedback is called Negative feedback or degenerative feedback.

Here Vi = Vs – Vf or Ii = Is - If

Negative feedback reduces gain of the amplifier. It also reduces noise, distortion and

instability and increases the bandwidth. Due to these advantages negative feedback is used in

amplifiers.

Gain of feedback amplifier

I/P Is O/P

The output quantity (current or voltage) is sampled by a suitable sampler which is of two

types current or voltage, and fed to the feedback network. The output of the feedback

network is combined with source signal through a mixer and fed to the basic amplifier. Mixer

also known as comparator is of two types, namely series mixer and shunt mixer.

A -------> gain of the basic amplifier = Io/Ii

(Open loop gain)

B ------->feedback ratio = If/Io

Af ------->gain of the feedback amplifier = Io/Is

Basic Amp

A Sampler

Feedback

N/W

Mixer

Is ------>AC signal in the input (current or voltage)

If ------->feedback signal (V or I)

For positive feedback:

Af = Io/Is = Io/Ii – If [ Ii = Is + If ]

= = = A/1 – Aβ

Aβ ------> called loop gain

| Af | > |A|

When |Aβ| =1 , Af = ∞

That is amp. given output without input amplifier acts as an oscillator.

For negative feedback:

Af = Io/Is = Io/Ii + If [ Ic = Is - If ]

= = = A/(1 + Aβ)

Difference between +ve and -ve feedback

Positive feedback Negative feedback

Gain increases Gain decreases

Noise increases Noise decreases

Distortion increases Distortion decreases

Bandwidth decreases Bandwidth increases

Stability decreases Stability increases

Input and output resistance changes Input and output resistance changes

Used in oscillators Used in amplifiers

OSCILLATORS

An oscillator is a circuit that produces an AC signal without any externally applied

input signal or an oscillator is a circuit which converts DC energy into AC energy a desired

frequency.

Oscillations whose amplitude keeps decreasing with time are called damped

oscillations and oscillators whose amplitude remains constant are called undamped or

sustained oscillations. Oscillators use positive feedback for producing sustained oscillations.

Essential components of an oscillator are

1) Tank / oscillatory circuit

2) Amplifier

3) Feedback circuit

Tank / oscillatory circuit consist of an inductor (or resistor) in parallel with a capacitor.

The frequency of oscillations in the circuit depends upon the values of L, C or R, C

[f=1/2π√LC or f = 1 / 2πRC].

Amplifier receives DC power from the battery and converts it into AC power for

supplying it to the tank circuit. Oscillations of that tank circuit are fed to the amplifiers which

are amplified due to the active devices amplifying action.

Feedback circuit supplies a part of the output energy to the tank circuit in correct phase

to meet the losses in order to produce undamped oscillations.

Types of oscillators:

The oscillators may be classified in the following ways:

1) According to the waveform generated:

a) Sinusoidal ―generates sine

b) Non sinusoidal / relaxation oscillators ―like square, triangular, sweep etc.

2) According to the fundamental mechanism involved :

a) Feedback oscillator ―utilize positive feedback

b) Negative resistance oscillator ―A negative resistance is produced by

suitably operating the active device to neutralize the positive resistance of

the oscillating circuit.

3) According to the type of circuitry :

a) LC oscillators / Tuned circuit oscillators

b) RC oscillators

c) Crystal oscillators

4) According to the frequency generated :

a) Audio frequency Oscillators [AFO] ; up to 20 KHz

b) Radio frequency oscillators [RFO] ; 20 KHz to 30 MHz

c) Very high frequency oscillators [VHF] ; 30 MHz to 300 MHz

d) Ultra high frequency oscillators [UHF] ; 300 MHz to 3 GHz

e) Micro wave frequency oscillators ; above 3 GHz

Barkhausen Criterion for oscillations

The conditions for a circuit to produce undamped (sustained) oscillations are

a) The feedback must be positive

b) The loop gain must be equal to one with zero phase shift

i.e. Avβ = 1

The second condition is called Barkhausen criterion for oscillations.

In general Av and Avβ are complex quantities

(Avβ) real = 1 ―decides the condition for oscillations

(Avβ) Img = 0 ―determines the frequency of oscillations.

555 Timer

The 8-pin 555 timer must be one of the most useful ICs ever made and it is used in many

projects. With just a few external components it can be used to build many circuits, not all of

them involve timing.

The 555 can be used with a supply voltage (Vs) in the range 4.5 to 15V (18V absolute

maximum).

Square wave generator:

Square wave outputs are generated when the op-amp is forced to operate in saturation region.

That is the output of the op-amp repeatedly swings between positive (+Vsat ≈ +VCC) and

negative saturation (-Vsat ≈ -VEE), resulting in a square wave output. This square wave

generator is also known as free-running or astable multivibrator. The output of the op-amp

will be either positive or negative depending on whether the differential voltage vid is

negative or positive respectively.

Fig : (a)Square Wave generator (b) waveform across output and capacitor

Triangular wave generator:

The output of a integrator is triangular wave for a square wave input. This means a triangular

wave generator can be formed by simply connecting an integrator to a square wave generator.

Fig: Triangular waveform generator

Filters:

An electric filter is often a frequency selective circuit that passes a particular band of

frequencies and blocks or attenuates the signals of frequencies outside this band.

Filters can be classified as

1. Analog or Digital: depending on if they are designed to process analog or digital sig-

nals.

2. Audio (AF) or Radio frequency (RF).

3. Passive or active: depending on the elements used in the filter circuit.

A passive filter uses only passive elements such as resistors, capacitors and inductors. Active

filters on the other hand use transistors and op-amps in addition to the passive elements. The

elements used dictate the operating frequency range of the filters. In audio frequencies,

inductors are not often used as they are large, costly and may dissipate more power. Also

inductors emit magnetic field.

An active filter has following advantages over passive filters

1. Gain and frequency adjustment flexibility: Since the op-amp is providing some gain

the input signal is not attenuated as in case of the passive filters. Aslo they are easier

to tune and adjust.

2. No loading problem: Because of high input resistance and low output resistance the

active filter does not cause loading of the input source and the output load.

3. Cost: Typically, they are cheaper due to availability of cheap op-amps and the ab-

sence of inductors in the circuit.

Although active filters are most extensively used in the field of communications and signal

processing, they are employed in one form or another in almost all sophisticated electronic

systems. Radio, television, telephone, radar, space satellites, and biomedical equipment are

but a few systems that employ active filters. The most commonly used filters are these:

Low-pass filter - allows low frequencies to pass and attenuates high frequencies

High pass filter - allows high frequencies to pass and attenuates low frequencies

Band pass filter - allows a range of frequencies to pass

Band stop filter - attenuates a range of frequencies and allows all frequencies not within the

range to pass

A low-pass filter has constant gain for low frequency signals but attenuates signals with

frequencies higher than the cutoff frequency fH. At fH the gain is down 3dB and decreases

further as frequency increases. The frequencies between 0 Hz and fH are known as passband

frequencies while the range of frequencies beyond fH are attenuated and are therefore called

the stop-band frequencies.

High Pass Filter:

A high-pass filter with a stopband 0 < f < fL and a passband f > fL is shown in figure.b. Here

fL is the lower cut-off frequency and f is the operating frequency.

Band Pass Filter:

A band-pass filter has a passband between two cut-off frequencies fH and fL where fH > fL

and two stopbands at 0 < f < fL and f > fH. The bandwidth of the band-pass filter is,

therefore, equal to fH – fL.

Band Stop Filter:

Band-stop filter is exactly opposite to the band-pass filter in performance i.e., it has a

bandstop between two cut-off frequencies fH and fL and two passbands, 0 < f < fL and f > fH..

All Pass Filter:

This filter passes all frequencies equally well (i.e. the output and input voltages are equal in

magnitude for all frequencies) but with the phase shift between the two; phase shift being a

function of the input frequency. The highest frequency up to which the magnitudes of the

input and output remain equal depends on the unity gain BW of the op-amp. At this

frequency, however, the phase shift between the input and output is maximum.

First-order low-pass Butterworth filter:

Fig shows first-order low-pass Butterworth filter that uses an RC network for filtering. Note

that the op-amp is used in non-inverting configuration and hence it does not load down the

RC network. Resistirs R1 and RF determine the gain of the filter.

Fig:First-order low-pass Butterworth filter

The output voltage vo is given by,

Where AF = the passband gain of the filter.

f = frequency of the input signal fH is the high (or upper) cutoff frequency of the filter.

fH =

The gain magnitude and phase angle equations for the filter can be obtained as

The operation of the low-pass filter can be verified from the gain magnitude equation:

1. At very low frequencies that is f < fH ,

2. At cut-off frequency, that is f = fH,

3. At higher frequencies that is f > fH

First Order High Pass Butterworth Filter

Fig shows a first-order high-pass filter that uses an RC network for filtering. The circuit is

formed by interchanging the positions of R and C from the low-pass filter circuit.

First-order High-pass Butterworth filter

The output voltage vo is given by,

Where AF = the pass band gain of the filter.

f = frequency of the input signal and fL is the lower cutoff frequency of the filter.

fL =

The gain magnitude for the filter can be obtained as

Band-pass filter:

A band pass filter has a passband frequency between two cutoff frequencies fH and fL such

that fH > fL. Any input frequency outside the passband frequencies is attenuated. Basically

there are two types of band-pass filters: 1. Narrow band-pass and 2.wide band-pass filters.

Unfortunately, there is no set dividing line between the two.

However, a band-pass filter is defined as a wide band-pass if its figure of merit or quality

factor Q is less than 10 while the band-pass filters with Q > 10 are called the narrow band-

pass filters. Thus Q is a measure of selectivity, meaning the higher the value of Q the more

selective is the filter, or the narrower is the bandwidth (BW). The relationship between Q, 3-

db bandwidth, and the centre frequency fC is given by

For a wide band-pass filter the centre frequency can be defined as.

In a narrow band-pass filter, the output voltage peaks at the centre frequency fc.

A wide band-pass filter can be formed by simply cascading high-pass and low-pass sections

and is generally the choice for simplicity of design and performance though such a circuit can

be realized by a number of possible circuits. To form a ± 20 db/ decade band-pass filter, a

first-order high-pass and a first-order low-pass sections are cascaded; for a ± 40 db/decade

band-pass filter, second-order high- pass filter and a second-order low-pass filter are

connected in series, and so on. It means that, the order of the band-pass filter is governed by

the order of the high-pass and low-pass filters

.

Narrow band-pass filter

A narrow band-pass filter employing multiple feedbacks is depicted in figure. This filter

employs only one op-amp, as shown in the figure. In comparison to all the filters discussed so

far, this filter has some unique features that are given below.

1. It has two feedback paths, and this is the reason that it is called a multiple-

feedback filter.

2. The op-amp is used in the inverting mode.

The frequency response of a narrow band-pass filter is shown in fig(b).

Generally, the narrow band-pass filter is designed for specific values of centre frequency fc

and Q or fc and BW. The circuit components are determined from the following relationships.

For simplification of design calculations each of C1 and C2 may be taken equal to C.

R1 = Q/2π fc CAf

R2 =Q/2π fc C(2Q2-Af)

and R3 = Q / π fc C

where Af, is the gain at centre frequency and is given as

Af = R3 / 2R1

The gain Af however must satisfy the condition Af < 2 Q2.

The centre frequency fc of the multiple feedback filter can be changed to a new frequency fc‘

without changing, the gain or bandwidth. This is achieved simply by changing R2 to R’2 so

that

R’2 = R2 [fc/f’c]2

Narrow Band-Stop Filter

This is also called a notch filter. It is commonly used for attenuation of a single frequency

such as 60 Hz power line frequency hum. The most widely used notch filter is the twin-T

network illustrated in fig. (a). This is a passive filter composed of two T-shaped networks.

One T-network is made up of two resistors and a capacitor, while the other is made of two

capacitors and a resistor.One drawback of above notch filter (passive twin-T network) is that

it has relatively low figure of merit Q. However, Q of the network can be increased

significantly if it is used with the voltage follower, as illustrated in fig. (a). Here the output of

the voltage follower is supplied back to the junction of R/2 and 2 C. The frequency response

of the active notch filter is shown in fig (b).

Notch filters are most commonly used in communications and biomedical instruments for

eliminating the undesired frequencies.

A mathematical analysis of this circuit shows that it acts as a lead-lag circuit with a phase

angle, shown in fig. (b). Again, there is a frequency fc at which the phase shift is equal to 0°.

In fig. (c), the voltage gain is equal to 1 at low and high frequencies. In between, there is a

frequency fc at which voltage gain drops to zero. Thus such a filter notches out, or blocks

frequencies near fc. The frequency at which maximum attenuation occurs is called the notch-

out frequency given by

fn = Fc = 2πRC

Notice that two upper capacitors are C while the capacitor in the centre of the network is 2 C.

Similarly, the two lower resistors are R but the resistor in the centre of the network is 1/2 R.

This relationship must always be maintained.

All-pass filter is that which passes all frequency components of the input signal without

attenuation but provides predictable phase shifts for different frequencies of the input signals.

The all-pass filters are also called delay equalizers or phase correctors. An all-pass filter with

the output lagging behind the input is illustrated in figure.

The output voltage Vout, of the filter circuit shown in fig, can be obtained by using the

superposition theorem

Vout = Vin [-1 +( 2/ j2πRfc)]

or Vout / Vin = 1- j2∏Rfc/1+ j2πRfc

where / is the frequency of the input signal in Hz.

From equations given above it is obvious that the amplitude of vout / vin is unity, that is |vout | = |

vin| throughout the useful frequency range and the phase shift between the input and output

voltages is a function of frequency.

By interchanging the positions of R and C in the circuit, the output can be made leading the

input. These filters are most commonly used in communications. For instance, when signals

are transmitted over transmission lines (such as telephone wires) from one point to another

point, they undergo change in phase. To compensate for such phase changes, all-pass filters

are employed.

Chapter 4

DIGITAL ELECTRONICS

In analog system, the output can be continuously controlled by the input & the output is

linearly proportional to the input. In digital system, the digital logic used only two values,

either HIGH or LOW. i.e. they have only two discrete values and are called BINARY. The

binary may be either logic 0 or logic ‘1’. A logic value of ‘0’ or ‘1’ is often called as

BINARY DIGIT or BIT.

Number System: Many number systems are used in digital technology. Most common are

binary, decimal, octal & hexadecimal system.

Binary Number system: A number system that uses only two digits ‘0’&’1’ is called binary

number system. The binary umber system is also called as Base 2 system or Radix 2 system.

Examples: (100010)2

(0.1011)2

Convert the given binary number into decimal equivalent number

1. (100010)2=0×20+1×21+0×22+0×23+0×24+1×25

=0+2+0+0+0+32

=(34)10

2. (0.1011)2=1×2-1+0×2-2+1×2-3+1×2-4

=0.5+0+0.125+0.0625

=(0.6875)10

3. (10101.011)2

Integer part: (10101)2=1×20+0×21+1×22+0×23+1×24

=1+0+4+0+16 = (21)10

Decimal part: (0.011)2 =0×2-1+1×2-2+1×2-3

= (0.375)10

= (21.375)10

Octal Number System: A number system that uses 8 digit (0-7) is called an octal number system. It has base 8. Example: (723)8, (676)8

Hexadecimal Number System: The hexadecimal number system has base 16. It has 16

distinct digit symbols. It uses the digits 0-9 & letters A,B,C,D,E,F as 16 digit symbols.

Hexadecimal number system Equivalent binary number

8 4 2 1 (weights)

0 0 0 0 0

1 0 0 0 1

2 0 0 1 0

3 0 0 1 1

4 0 1 0 0

5 0 1 0 1

6 0 1 1 0

7 0 1 1 1

8 1 0 0 0

9 1 0 0 1

10 1 0 1 0 = A

11 1 0 1 1 = B

12 1 1 0 0 = C

13 1 1 0 1 = D

14 1 1 1 0 = E

15 1 1 1 1 = F

Convert the following octal number into decimal number system

1. (2376)8 = (?)10

= 2×83+3×82+7×81+6×80

= 1024+192+56+6

= (1278)10

2.

(1234.567)8=1×83+ 2×82+3×81+4×80

+5×8-1+6×8-2+7×8- 3

Octal Numbers Binary Equivalent number

4 2 1 (weights)

0 0 0 0

1 0 0 1

2 0 1 0

3 0 1 1

4 1 0 0

5 1 0 1

6 1 1 0

7 1 1 1

=512+128+24+4+0.625+0.09375+0.01367

= (668.7324219)10

Convert the following hexadecimal number into decimal number system

1. (269)16=2×162+6×161+9×160

= 2×256+96+9

= (617)10

2. 2B8D.E2)16=2×163+11×162+8×161+13×160 +14×16-1+2×16-2

= 8192+2816+128+13+0.875+0.0078125

= (11149.88281)10

Conversion form Decimal number system to Binary number system:

The given decimal number is repeatedly divided by 2, which is the base number of

binary system till quotient becomes ‘0’ and collect the remainder from bottom to top.

To convert the fractional part into binary, multiply fraction by 2 repeatedly, record

any carry in integer place. The string of integer obtained from top to bottom gives the

equivalent fraction in binary number system.

1. (734)10=(X)2

Take the numbers from bottom to top,

(734)10 = ( 1011011110)2

2. (0.705)10

0.705×2=1.410 ---1

0.410×2=0.820 ---0

0.82×2= 1.64------1

0.64×2= 1.28------1

0.28×2= 0.56------0

0.56×2=1.12-------1

0.12×2=0.24-------0

0.24×2=0.48-------0

0.48×2=0.96-------0

0.96×2=1.92-------1

Take the number from top to bottom, (0.705)10 = (0.1011010001)2

3.(41.915)10

(41)10 = (101001)2

0.915×2=1.830---1

0.830×2=1.660---1

0.660×2=1.320---1

0.32×2=0.64------0

0.64×2= 1.28-----1

(0.915)10 = (11101)2

(41.915)10= (101001.11101)2

Conversion form Decimal number system to Octal number system:

To convert a decimal number (integer) into a octal equivalent, repeatedly divide by 8

and take the remainder string from bottom to top.

For traction part repeatedly multiplied by 8, record carry in integer place & take the

string of integer from top to bottom.

1.(2003)10=(X)8

Take the numbers from bottom to top, (2003)10= (3723)8

2.(0.12)10 = (X)8

0.12×8=0.96---0

0.96×8=7.68---7

0.68×8=5.44---5

0.44×8=3.52---3

0.52×8=4.16---4

(0.12)10=(0.07534)8

3. (632.97) 10=(?)8

(632) 10=(1170)8

0.97×8=7.76---7

0.76×8=6.08---6

0.08×8=0.64---0

0.64×8=5.12---5

0.12×8=0.96---0

(0.97)10 =(0.76050) 8

(632.97)10= (1170.76050)8

Decimal number system to Hexadecimal number system:

To convert a decimal number (integer) into a hexadecimal equivalent, repeatedly divide by 16

and take the remainder string from bottom to top.

For traction part repeatedly multiplied by 16, record carry in integer place & take the string of

integer from top to bottom.

1. (0.368)10

0.368×16=5.888---5

0.888×16=14.208-14-E

0.208×16=3.328---3

0.328×16=5.248---5

0.248×16=3.968---3

(0.368)10=(0.5E353)16

2. (22.64)10= (?)8

(22)10= (16)16

0.64×16=10.24---10-A

0.24×16=3.84-----3

0.84×16=13.44—13-D

0.44×16=7.04---7

0.04×16=0.64---0

(22.64)10=(16.A3D70)16

Conversion from Octal number system into Binary number system:

When an octal number is to be converted to its equivalent binary number, each of its digits is

replaced by equivalent group of three binary digits.

1. (632)8

6 3 2

110 011 010

So, (632)8=(110011010)2

2. (7423.245)8

7 4 2 3 . 2 4 5

111 100 010 011 . 010 100 101

(7423.245)8= (111100010011.010100101)2

Conversion from Binary number system to Octal number system:

To convert, Starting from the binary point, the binary digits are arranged in groups of

three on both sides. Each in group of binary digit is replaced by its octal equivalent.

Note: 0’s can be added on either side, if needed to complete a group of three.

1. (011101.110)2=(?)8

011 101 . 110

3 5 . 6

(011101.110)2= (35.6)8

2. (11101101110.11111)2

011 101 101 110 . 111 110

3 5 5 6 . 7 6

(11101101110.11111)2 =(3556.72)8

Conversion from Hexadecimal number system to Binary number system

When a hexadecimal number is to be converted its equivalent binary number, each of

its digits is replaced by equivalent group of 4 binary digits.

1.(347.28)16

3 4 7 . 2 8

0011 0100 0111 . 0010 1000

(347.28)16= (001101000111.00101000)2

2. (8BE6.7A)16

8 B E 6 . 7 A

1000 1011 1110 0110 . 0111 1010

(8BE6.7A) 16 = (1000101111100110.01111010)2

Conversion from Binary number system to Hexadecimal number system:

To convert, Starting from the binary point, the binary digits are arranged in groups of

four on both sides. Each in group of binary digit is replaced by its hexadecimal equivalent.

Note: 0’s can be added on either side, if needed to complete a group of four.

1.(1011011110111110.11100011)2= (?)16

1011 0111 1011 1110 . 1110 0011

B 7 B E . E 3

(1011011110111110.11100011)2= (B7BE.E3)16

2. (110111101.01)2=(?)16

0001 1011 1101 . 0100

1 B D . 4

(110111101.01)2=(1BD.4)16

Conversion from Octal number system to Hexadecimal number system:

Write down the three bit binary equivalent of octal digit and then rearranging into

group of four bits with ‘0’s added on either side of decimal point, if needed to complete the

group of four.

1.(46) 8 = (?)16

Octal equivalent 4 6

100 110

Hexadecimal equivalent 0010 0110

2 6

(46) 8 = (26)16

2. (764.352) 8 = (?)16

Octal equivalent 7 6 4 . 3 5 2

111 110 100.011 101 010

Hexadecimal

equivalent

0001 1111 0100.0111 0101 0000

1 F 4 . 7 5 0

(764.352) 8 = (1F4.750)16

Conversion from Hexadecimal number system to Octal number system:

First write down the 4 bit binary equivalent of hexadecimal digit and then rearranging

into group of three bit each.

1.(2AB.9) 16 = (?)8

Hexadecimal

equivalent

2 A B . 9

0010 1010 1011 . 1001

Octal equivalent 001 010 101 011 . 100 100

1 2 5 3 . 4 4

(2AB.9) 16 = (1253.44)8

2. (3FC.82) 16 = (?)8

Hexadecimal

equivalent

3 F C . 8 2

0011 1111 1100 . 1000 0010

Octal equivalent 001 111 111 100 . 100 000 100

1 7 7 4 . 4 0 4

(3FC.82) 16 = (1774.404)8

BCD Numbers:

The Binary Coded Decimal (BCD) is a combination of four binary digits that

represent decimal numbers. It is also called 8421 code. It has four bits and represents the

decimal digits 0 to 9. Below table gives the BCD codes for the decimal number 0 to 15.

Decimal number BCD number

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

0000

0001

0010

0011

0100

0101

0110

0111

1000

1001

0001 0000

0001 0001

0001 0010

0001 0011

0001 0100

0001 0101

Represent the (743.3)10 in BCD

7 4 3 . 6

0111 0100 0011 . 0110

(743.3)10=(0111010000110110) BCD

Convert the following BCD into Decimal:

11011100001001

0011 0111 0000 1001

3 7 0 9

(11011100001001) BCD=(3709)10

Binary Addition: The rules adopted for binary additions are

0 0 1 1

+0 +1 +0 +1

C=0 S=0 C=0 S=1 C=0 S=1 C=1 S=0

The sum of two 1’s gives binary ‘10’ i.e.2, there is a carry. The carry is taken to the next

higher column.

1.(1010)2+(0111)2

1010 =10

+0111 =7

10001 =17

(1010)2+(0111)2=(10001)2

2. (101)2+(011)2

101=5

+011=3

1000=8

(101)2+(011)2=(1000)2

Addition in Octal number System: Add the digit in each column in decimal and convert

this sum into octal. Write the sum in that column and carry the carry term to the next higher

significant column.

Add ( 334.65)8 to (671.14) 8

3 3 4 . 6 5

6 7 1 . 1 4

10 10 6 . 8 9

C=1 S=2 C=1 S=2 C=0 S=6 . C=1 S=0 C=1 S=1

( 334.65)8 to (671.14) 8 =(1226.01)8

Addition in Hexadecimal number System:

Add the digit in each column in decimal and convert this sum into hexadecimal

number. Write the sum in that column and carry term to the next higher significant column.

Add ( 7AB.67)16 to (15C.71) 16

7 A B . 6 7

1 5 C . 7 1

9 16 23 . 13 8

C=0 S=9 C=1 S=0 C=1 S=7 . C=0 S=D C=0 S=8

( 7AB.67)16 + (15C.71) 16 =(0907.D8) 16

Problems:

1. Convert from binary to decimal number system

(11001.011) 2

(110011) 2

(11.111) 2

2. Convert from decimal to binary number system

(0.75) 10

(65.45) 10

(106) 10

3. Convert from octal to decimal number system

(337) 8

(4673) 8

(34.125) 8

(103.45) 8

4. Convert from decimal to octal number system

(654) 10

(890) 10

(453.023) 10

5. Convert from binary to octal number system

(10001111011.110010) 2

(111110001) 2

(01110.1100) 2

6. Convert from octal to binary number system

(567) 8

(34) 8

(482) 8

(17333.66) 8

7. Convert from hexadecimal to decimal number system

(ABC.DE) 16

(B6A) 16

(3A1.4) 16

(ABC) 16

8. Convert from binary to hexadecimal number system

(10001100)2

(00110111) 2

(11001110) 2

(11010.01101) 2

9. Convert from hexadecimal to binary number system

(E.C) 16

(B4D) 16

(7AF4) 16

(156.8F) 16

(1C00)16

10. Add the following octal numbers

(173) 8+(265) 8

(222) 8+(333) 8

(25.36) 8+(37.11) 8

(12) 8+(20) 8

11. Add the following hexadecimal numbers

(ABC) 16+(BCD) 16

(9349) 16+(AACE) 16

(AA.BB) 16+(BB.CC) 16

(A0FC) 16+(B75F) 16

Complements:

The subtraction operation and logical manipulations become easy in digital computers

by using the concept of complements.

For a given number ‘N’ in base-‘r’, we can define two types of complements

r’s complement

(r-1)’s complement

2’s & 1’s complement for binary numbers

8’s & 7’s complement for octal numbers

10’s & 9’s complement for decimal numbers

16’s & 15’s complement for hexadecimal numbers

1’s complement:

1’s form of any binary number can be obtained by replacing 0’s by 1’s and 1’s by 0’s.

Example:

Binary number 1’s complement

10101 01010

11100 00011

1111 0000

1’s complement subtraction:

Step1: Add minuend to the 1’s complement of the subtrahend.

Step2: Inspect the result obtained in step1 for an end carry. (a) If an end carry occurs, add 1

to the least significant bit. (end round carry) (b) If an end carry doesn’t occur, take 1’s

complement of the number obtained in step1 and place a negative sign in front of it.

1. ( 1000)2 from (1101)2

1101—minuend

1000— subtrahend

1’s complement of subtrahend = 0111

Add minuend and 1’s complement of subtrahend,

1 1 0 1

+ 0 1 1 1

1 0 1 0 0

End carry Add to LSB +1

0 1 0 1

(1101)2 - ( 1000)2= (0101)2

2. ( 0101)2 from (1111)2

1111—minuend

0101— subtrahend

1’s complement of subtrahend = 1010

Add minuend and 1’s complement of subtrahend,

1 1 1 1

+ 1 0 1 0

1 1 0 0 1

End carry Add to LSB +1

1 0 1 0

(1111)2 - ( 0101)2= (1010)2

3. (6)10-(14)10

6=0110—minuend

14=1110— subtrahend

1’s complement of subtrahend = 0001

Add minuend and 1’s complement of subtrahend,

0 1 1 0

+ 0 0 0 1

No End

carry0 1 1 1

Take 1’s complement of the 0111 & place negative sign in front of it =-1000

(0110)2 - ( 1110)2= -(1000)2

2’s complement:

To find the 2’s form of any binary number, obtain the 1’s complement of the given

number and then add ‘1’ to the LSB.

(100100)2

Take 1’s complement of the number = 011011

Add ‘1’ to LSB to get 2’s complement = 011011

+1

011100

2’s complement = (011100)2

2’s complement subtraction:

Step1: find 2’s complement of subtrahend

Step2: Add minuend and 2’s complement subtrahend

Step3: (a) If an end carry occurs, discard it. (b) If an end carry doesn’t occur, take 2’s

complement of the number obtained in step2 and place a negative sign in front of it.

1.(1111)2-(1100)2

1111—minuend

1100— subtrahend

2’s complement of subtrahend = 0100

Add minuend and 2’s complement of subtrahend,

1 1 1 1

+ 0 1 0 0

1

Neglect

end carry

0 0 1 1

(1111)2-(1100)2=(0011)2

2.(15)10-(31)10

(1111)2-(11111)2

1111—minuend

11111— subtrahend

2’s complement of subtrahend = 00001

Add minuend and 2’s complement of subtrahend,

0 1 1 1 1

+ 0 0 0 0 1

No end 1 0 0 0 0

carry

So, take the 2’s complement of the answer and place negative sign in front of it,

i.e.= -(10000)2

(1111)2-(11111)2= -(10000)2

9’s complement:

The 9’s complement of a decimal number is formed by subtracting each digit form 9.

Find the 9’s complement of the number (8147)10

9 9 9 9

8 1 4 7

1 8 5 2

9’s complement of (8147)10 is (1852)10

9’s complement subtraction:

Step1: Add minuend to the 9’s complement of the subtrahend.

Step2: Inspect the result obtained in step1 for an end carry. (a) If an end carry occurs, add 1

to the least significant bit. (end round carry) (b) If an end carry doesn’t occur, take 1’s

complement of the number obtained in step1 and place a negative sign in front of it.

1. ( 487)10 - (354)10

487—minuend

354— subtrahend

9’s complement of subtrahend = 645

Add minuend and 9’s complement of subtrahend,

4 8 7

+ 6 4 5

1 1 3 2

End carry Add to LSB +1

1 3 3

( 487)10 - (354)10 = (133)10

2.( 213)10 - (546)10

213—minuend

546— subtrahend

9’s complement of subtrahend = 453

Add minuend and 9’s complement of subtrahend,

2 1 3

+ 4 5 3

No 6 6 6

End carry

Take the 9’s complement of the answer (666)10 and place the negative sign in front of it.

i.e.= -(333)10

( 213)10 - (546)10= -(333)10

10’s complements:

The 10’s complement of the decimal number is equal to 9’s complement of number plus 1.

Find 10’s complement of ( 731)10

999

-731

268 9’s complement

+1

269 10’s complement

10’s complement of ( 731)10is( 269)10

10’s complement subtraction:

Step1: find 10’s complement of subtrahend

Step2: Add minuend and 10’s complement subtrahend

Step3: (a) If an end carry occurs, discard it. (b) If an end carry doesn’t occur, take 10’s

complement of the number obtained in step2 and place a negative sign in front of it.

1. (347)10-(265)10

347—minuend

265— subtrahend

10’s complement of subtrahend = 735

Add minuend and 10’s complement of subtrahend,

3 4 7

+ 7 3 5

1

Neglect end carry0 8 2

(347)10-(265)10=(082)10

2. (23)10-(64)10

23—minuend

64— subtrahend

10’s complement of subtrahend = 36

Add minuend and 10’s complement of subtrahend,

2 3

+ 3 6

No end carry 5 9

So, take the10’s complement of the answer and place negative sign in front of it, i.e.= -(41)10

Problems:

1. Subtract using 1’s complement

a. (1101) 2-(11001) 2

b. (1111) 2-(1011) 2

c. (110011) 2-(100101) 2

d. (10001) 2from(10011) 2

2. Subtract using 2’s complement

a. (1101) 2-(11001) 2

b. 125 and -68

c. -83 and +16

d. (1111) 2-(1101) 2

e. (10111) 2-(10011) 2

f. (1101) 2-(1001) 2

3. Subtract using 7’s and 8’s complement method

a. (4317.64) 8from(42.345) 8

b. (2447.15) 8 from (6573.16) 8

4. Subtract using 9’s and 10’s complement method

a. (8437) 10 –( 27) 10

b. (308) 10-(1333) 10

c. (320.3 44) 10-(1048.05) 10

5. Subtract using 15’s and 16’s complement method

a. (A47) 16-(843) 16

b. (1B76) 16-(4A) 16

c. (231.AC) 16-(22.AB) 16

BOOLEAN ALGEBRA

George Boole in 1854 invented a new kind of algebra known as Boolean algebra. It is

sometimes called switching algebra. Boolean algebra is the mathematical frame work on

which logic design based. It is used in synthesis & analysis of binary logical function.

Basic Laws of Boolean algebra:

1. Laws of complementation: The term complement means invert. i.e. to change 0’s to

1’s and 1’ to 0’s. The following are the laws of complement. =1; = 0; =A.

2. “ OR” laws

0+0=0; 0+1=1; 1+0=1;1+1=1

1+A=1; A+ =1; A+A=A; 1+ =1

3. “ AND’ laws

0.0=0; 0.1=0;1.0=0; 1.1=1; A. =0; A.A=A

Commutative Law:

Property 1: This states that the ord3r in which the variables OR’ed makes no difference in

output. i.e. A+B=B+A

A B A+B B A B+A

0 0 0 0 0 0

0 1 1 = 1 0 1

1 0 1 0 1 1

1 1 1 1 1 1

Property 2: This property of multiplication states that the order in which the variables are

AND’ed makes no difference in the output. i.e. A.B=B.A

A B A.B B A B.A

0 0 0 0 0 0

0 1 0 = 1 0 0

1 0 0 0 1 0

1 1 1 1 1 1

Associative property:

Property1: This property states that in the OR’ing of the several variables, the result is same

regardless of grouping of variables. For three variables i.e.(A OR’ed with B)or’ed with C is

same as A OR’ed with (B OR’ed with C)

i.e. (A+B)+C = A+(B+C)

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

0 0 0 0 0 0 0

0 0 1 0 1 1 1

0 1 0 1 1 1 1

0 1 1 1 1 1 = 1

1 0 0 1 0 1 1

1 0 1 1 1 1 1

1 1 0 1 1 1 1

1 1 1 1 1 1 1

Property2: The associative property of multiplication states that, it makes no difference in

what order the variables are grouped when AND’ing several variables. For three variables(A

AND’ed B)AND’ed C is same as A AND’ed (B AND’ed C)

i.e. (A.B)C = A(B.C)

AB C A.B B.C (A.B)C A(B.C)

0 0 0 0 0 0 0

0 0 1 0 0 0 0

0 1 0 0 0 0 0

0 1 1 0 1 0 = 0

1 0 0 0 0 0 0

1 0 1 0 0 0 0

1 1 0 1 0 0 0

1 1 1 1 1 1 1

Distributive property:

Property 1: A(B+C) = A.B + A.C

1 2 3 4 5 6 7 8

A B C B+C A(B+C) A.B A.C A.B+A.C

0 0 0 0 0 0 0 0

0 0 1 1 0 0 0 0

0 1 0 1 0 0 0 0

0 1 1 1 0 0 0 0

1 0 0 0 0 0 0 0

1 0 1 1 1 0 1 1

1 1 0 1 1 1 0 1

1 1 1 1 1 1 1 1

Column number 5= Column number 8, hence the proof.

Property 2: A+ B = A+B

A B B A+ B A+B

0 0 1 0 0 0

0 1 1 1 1 = 1

1 0 0 0 1 1

1 1 0 0 1 1

Duality:

The important property to Boolean algebra is called Duality principle. The Dual of

any expression can be obtained easily by the following rules.

1. Change all 0’s to 1’s

2. Change all 1’s to 0’s

3. .’s (dot’s) are replaced by +’s (plus)

4. +’s (plus) are replaced by .’s (dot’s)

Examples:

=1≡ =0

X +0=X ≡ X .1=X

X+Y=Y+X ≡ X.Y=Y.X

X+1=0 ≡ X.0=1

De Morgon’s Theorems:

It is one of the important properties of Boolean algebra. It is extensively useful in

simplifying complex Boolean expression.

De Morgon’s First Theorem:

It states that “ the complements of product of two variables equal to sum of the

complements of individual variable”.

i.e. = +

A B A.B +

0 0 1 1 0 1 1

0 1 1 0 0 1 ≡ 1

1 0 0 1 0 1 1

1 1 0 0 1 0 0

De Morgon’s Second Theorem:

It states that complement of sum of two variables is equal to product of complement

of two individual variables.

i.e. = .

A B A+B .

0 0 1 1 0 1 1

0 1 1 0 1 0 ≡ 0

1 0 0 1 1 0 0

1 1 0 0 1 0 0

Simplify the Boolean expression

1. Z+ YZ

= Z[ +Y]

= Z[1]= Z

2. f=X( +Y)

=X +XY = 0+XY= XY

3. f = B(A+C)+C

=BA+BC+C

=BA+C(1+B)

=BA+C

4.XY+XYZ+XY + YZ

=XY(Z+ )+XYZ+XY + YZ

XYZ+XY +XY + YZ+XYZ

XYZ(1+1)+XY (1+1)+ YZ

XYZ+XY + YZ

XY(Z+ )+ YZ

XY+ YZ

Y(X+ Z)

Y(X+Z)

5.XYZ+ Y + XY

=Y( + X )+ XY

= Y( + )+ XY

= Y +Y + XY

=Y +Y(Z+ X )

=Y +Y(Z+ X)

=Y(Z+ +X)

=Y(Z+1)

=Y

6. Y(W +WZ)+XY

=YW +YWZ+XY

=YW( +Z)+XY

=YW+XY

=Y(W+X)

7. ABC+ BC+A C+AB =AB+BC+CA

LHS: ABC+ BC+A C+AB

BC[A+ ]+A C+AB

=BC+A C+AB

=C[B+ A]+AB

=C[B+A]+AB

BC+AC=AB

=BC+A[C+ B]

=BC+A[C+B]

= AB+BC+CA = RHS

8. (A+B)(A+C)=A+BC

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

=A+AC+A.B+B.C

=A(1+C)+BA+BC

= A.1+BA+BC

=A(1+B)+BC

= A+BC

Logic Gates:

It is an electronic circuit, which makes logic decisions. A logic gate is a digital circuit

with one or more input signal and only one output signal. All input or output signals either

low voltage or high voltage. A digital circuit is referred to as logic gate for simple reason i.e.

it can be analyzed based on Boolean algebra.

To make logical decisions, three gates are used. They are OR, AND and NOT gate.

These logic gates are building blocks, which are available in the form of IC.

The input and output of the binary variables for each gate can be represented in a

tabular column or truth table.

OR Gate:

The OR gate performs logical additions commonly known as OR function. The OR

gate has two or more inputs and only one output. The operation of OR gate is such that a

HIGH(1) on the output is produced when any of the input is HIGH. The output is LOW(0)

only when all the inputs are LOW.

If A & B are the input variables of an OR gate and c is its output, then A+B. similarly

for more than two variables, the OR function can be expressed as Y=A+B+C.

Logical Symbol: Two Input OR gate

Truth table for two input OR gate:

Input Output

A B Y= A+B

0 0 0

0 1 1

1 0 1

1 1 1

Realization of OR gate using diodes:

Two input OR gate using "diode-resistor" logic is shown in figure below. Where X, Y

are the inputs and F is the output.

If X = 0 and Y = 0, the both the diodes D1 and D2 are reverse biased and thus both

the diodes are in cut-off and thus F is low.

If X = 0 and Y = 1, D1 is reverse biased, thus does not conduct. But D2 is forward

biased, thus conducts and thus pulling F to HIGH

If X = 1 and Y = 0, D2 is reverse biased, thus does not conduct. But D1 is forward

biased, thus conducts and thus pulling F to HIGH.

If X = 1 and Y = 1, the both the diodes D1 and D2 are forward biased and thus both

the diodes conduct and thus F is HIGH

AND Gate:

The AND gate performs logical multiplication, commonly known as AND function.

The AND gate has two or more inputs and a single output. The output of an AND gate is

HIGH only when all the inputs are HIGH. Even if any one of the input is LOW, the output

will be LOW. If a & b are input variables of an AND gate and c is its output, then Y=A.B

Logical Symbol: Two input AND gate

Truth table for two input AND gate:

Input Output

A B Y=A.B

0 0 0

0 1 0

1 0 0

1 1 1

Realization of AND gate using diodes:

Two input AND gate using "diode-resistor" logic is shown in figure below. Where X,

Y are inputs and F is the output.

If X = 0 and Y = 0, the both the diodes D1 and D2 are forward biased and thus both

the diodes conduct and pulling F to LOW.

If X = 0 and Y = 1, D1 is reverse biased, thus does not conduct. But D2 is forward

biased, thus conducts and thus pulling F to LOW.

If X = 1 and Y = 0, D2 is reverse biased, thus does not conduct. But D1 is forward

biased, thus conducts and thus pulling F to LOW.

If X = 1 and Y = 1, the both the diodes D1 and D2 are reverse biased and thus both

the diodes are in cut-off and thus there is no drop in voltage at F. Thus F is HIGH.

Not Gate (Inverter):

The NOT gate performs the basic logical function called inversion or

complementation. The purpose of his gate is to convert one logic level into the opposite logic

level. It has one input and one output. When a HIGH level is applied to an inverter, a LOW

level appears at the output and vice-versa.

Logical Symbol:

Truth Table:

Input output

A Y=

0 1

1 0

Realization of NOT gate using Transistors:

A NOT gate using a transistor is shown in below figure. ‘A’ represents the input and

‘F’ represents the output. When the input is HIGH, the transistor is in the ON state and the

output is LOW. If the input is LOW, the transistor is in the OFF state and the output F is

HIGH.

If A = 0, then the transistor is OFF thus pulling F to HIGH.

If A = 1, then the transistor is ON thus driving F to HIGH.

NAND Gate:

The output of a NAND gate is LOW only when all inputs are HIGH and output of the

NAND is HIGH if one or more inputs are LOW.

Logical Symbol: Two input AND gate

Truth Table:

Input Output

A B Y =

0 0 1

0 1 1

1 0 1

1 1 0

NOR Gate:

The output of the NOR gate is HIGH only when all the inputs are LOW.

Logical Symbol: Two input NOR Gate

Truth Table:

Input Output

A B Y =

0 0 1

0 1 0

1 0 0

1 1 0

XOR Gate or Exclusive OR gate:

In this gate output is HIGH only when any one of the input is HIGH. The circuit is

also called as inequality comparator, because it produces output when two inputs are

different.

Logical Symbol: Two input XOR Gate

Truth Table:

Input Output

A B Y =

0 0 0

0 1 1

1 0 1

1 1 0

Y= =A + B

XNOR Gate or Exclusive NOR Gate:

An XNOR gate is a gate with two or more inputs and one output. XNOR operation is

complementary of XOR operation. i.e. The output of XNOR gate is High, when all the inputs

are identical; otherwise it is low.

Logical Symbol: Two input XNOR Gate:

Truth Table:

Input Output

A B Y = +AB

0 0 1

0 1 0

1 0 0

1 1 1

Universal Logic Gate:

NAND and NOR gates are called Universal gates or Universal building blocks,

because both can be used to implement any gate like AND,OR an NOT gates or any

combination of these basic gates.

NAND gate as Universal gate

1. NOT operation:

2. AND operation:

3. OR operation:

4. NOR operation:

NOR gate as Universal gate:

1. NOT operation:

2. AND operation:

3. OR operation:

4. NAND operation:

Examples:

Draw the logic circuit for the Boolean expression.Y= BC+A C+ABC.

Types of Digital Circuits:

Basically digital circuits can be classified into two types.

Sequential Digital Circuits

Combinational Digital Circuits

Sequential Digital Circuits:

The logic circuits whose output at any instant of time depend not only on the present

input but also on the past outputs are called Sequential Circuits.

In sequential circuits, the output signals are feedback to the input side. Thus, an

output signal is a function of present input signals and a sequences of the past input signal.

i.e. the output signals.

Combinational Digital Circuits:

The logic circuits whose output at any instant of time are entirely dependent upon the

input signals present at that time are known as combinational digital circuits. In particular, the

output of the combinational circuit doesn’t depend upon any past input or output So that the

circuit doesn’t possess any memory. The output signals of combinational circuits are not

feedback to any other part of the circuit. Combinational circuit are faster, since the operation

don’t have to be performed in sequences.

Combinational circuits can be constructed using sum of products (SOP) or product of sums

(POS). Sum is logically OR operation of different literals or signals. Product is logically

AND operation of different literals or signals.

SOP: It is sum of many products. That is literals are ORed first then those outputs are

ANDed.

Eg: F1 = YZ +Z +XY

F2 = XYZ + W

POS: It is the product of many sums. That is literals are ANDed first then those outputs are

ORed.

Eg: F1 = (Y+ Z)( + Z)(X+Y)

F2 = (X+Y+Z)W

Half Adder:

An electronic combinational circuit which performs the arithmetic addition of two

binary digits is called Half Adder. In the half adder circuit, there are two inputs, one is

addend and augend and two outputs are Sum and Carry.

Logical Symbol

InputOutput

A B Sum Carry

0 0 0 0

0 1 1 0

1 0 1 0

1 1 0 1

Truth Table for Half Adder

Sum= B+A =A

Carry= A.B

The circuit for Half Adder using Basic Gates is as follows:

The circuit for Half Adder using XOR gate:

Full Adder:

The full adder is a combinational circuit that performs the arithmetic sum of three

input bits.It consists of three inputs and two outputs. Two of the inputs are variables, denoted

by A and B, represent the two significant bit to be added The third input Cin represents carry

form the previous lower significant position.

Logical Symbol:

Truth Table for Full Adder

Input Output

A B Cin Sum Carry

0 0 0 0 0

0 0 1 1 0

0 1 0 1 0

0 1 1 0 1

1 0 0 1 0

1 0 1 0 1

1 1 0 0 1

1 1 1 1 1

Sum= Cin+ B +A +ABCin

= [ Cin+ B ]+A[ +BCin]

= [B Cin]+A[ ]

= A B Cin

Carry = BCin+A Cin+AB +ABCin

= BCin+A Cin+AB( +Cin)

= BCin+A Cin+AB

= BCin+A( Cin+B)

= BCin+AB+ACin

= B( Cin+A)+ACin

=B(A+Cin)+ACin

= AB+BCin+ACin

Implementation of Full Adder:

Problems

1. Realize NOR and NAND gate using discrete components

2. Realize NOR and NAND gate using Basic gates

3. Implement Full Adder using Basic gates

4. Simplify and realize using only NAND gates

XYZ+XYZ+YZ+

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

5. Simplify and realize using only NOR gates

Y=A + + +A

K Map:-

Karnaugh maps generally become more cluttered and hard to interpret when adding

more variables. A general rule is that Karnaugh maps work well for up to four variables, and

shouldn't be used at all for more than six variables. For expressions with larger numbers of

variables, the Quine–McCluskey algorithm can be used. Nowadays in general the

minimization process is carried out by computer, for which the Espresso heuristic logic

minimizer has become the standard minimization program.

Procedures

The K-Map method may theoretically be applied for the simplification of any boolean

expression regardless of its number of variables, but is most often used when there are fewer

than six variables because K-Maps of expressions with more than six variables are complex

and tedious to simplify. Each variable contributes two possibilities: the initial value, and its

inverse; it therefore organizes all possibilities of the system. The variables are arranged in

Gray code in which only one variable changes between two adjacent grid boxes.

Once the variables have been defined, the output possibilities are transcribed

according to the grid location provided by the variables. Thus for every possibility of a

boolean input or variable the output possibility is defined.

When the Karnaugh map has been completed, to derive a minimized function the "1s"

or desired outputs are grouped into the largest possible rectangular groups in which the

number of grid boxes (output possibilities) in the groups must be equal to a power of 2. For

example, the groups may be 4 boxes in a line, 2 boxes high by 4 boxes long, 2 boxes by 2

boxes, and so on. "Don't care(s)" possibilities (generally represented by a "X") are grouped

only if the group created is larger than the group with "Don't care" is excluded. The boxes can

be used more than once only if it generates the least number of groups. Each "1" or desired

output possibilities must be contained within at least one grouping.

The groups generated are then converted to a boolean expression by: locating and

transcribing the variable possibility attributed to the box, and by the axiom laws of boolean

algebra—in which if the (initial) variable possibility and its inverse are contained within the

same group the variable term is removed. Each group provides a "product" to create a "sum-

of-products" in the boolean expression.To determine the inverse of the Karnaugh map, the

"0s" are grouped instead of the "1s". The two expressions are non-complementary

Size of map

The size of the Karnaugh map with n Boolean variables is determined by 2n. The size

of the group within a Karnaugh map with n Boolean variables and k number of terms in the

resulting Boolean expression is determined by 2nk. Common sized maps are of 2 variables

which is a 2×2 map, 3 variables which is a 2×4 map, and 4 variables which is a 4×4 map.

K-map of the given truth table will be as follows:

Follwing are the examples for K-map optimization:

Basic Flip-Flop Circuit

A flip-flop circuit can be constructed from two NAND gates or two NOR gates. These flip-

flops are shown in Figure 2 and Figure 3. Each flip-flop has two outputs, Q and Q', and two

inputs, set and reset. This type of flip-flop is referred to as an SR flip-flop or SR latch. The

flip-flop in Figure 2 has two useful states. When Q=1 and Q'=0, it is in the set state (or 1-

state). When Q=0 and Q'=1, it is in the clear state (or 0-state). The outputs Q and Q' are

complements of each other and are referred to as the normal and complement outputs,

respectively. The binary state of the flip-flop is taken to be the value of the normal output.

When a 1 is applied to both the set and reset inputs of the flip-flop in Figure 2, both Q and Q'

outputs go to 0. This condition violates the fact that both outputs are complements of each

other. In normal operation this condition must be avoided by making sure that 1's are not

applied to both inputs simultaneously.

(a) Logic diagram

(b) Truth table

Figure 2. Basic flip-flop circuit with NOR gates

(a) Logic diagram

(b) Truth table

Figure 3. Basic flip-flop circuit with NAND gates

The NAND basic flip-flop circuit in Figure 3(a) operates with inputs normally at 1 unless the

state of the flip-flop has to be changed. A 0 applied momentarily to the set input causes Q to

go to 1 and Q' to go to 0, putting the flip-flop in the set state. When both inputs go to 0, both

outputs go to 1. This condition should be avoided in normal operation.

Clocked SR Flip-Flop: The clocked SR flip-flop shown in Figure 4 consists of a basic NOR

flip-flop and two AND gates. The outputs of the two AND gates remain at 0 as long as the

clock pulse (or CP) is 0, regardless of the S and R input values. When the clock pulse goes to

1, information from the S and R inputs passes through to the basic flip-flop. With both S=1

and R=1, the occurrence of a clock pulse causes both outputs to momentarily go to 0. When

the pulse is removed, the state of the flip-flop is indeterminate, ie., either state may result,

depending on whether the set or reset input of the flip-flop remains a 1 longer than the

transition to 0 at the end of the pulse.

(a) Logic diagram

(b) Truth table

Figure 4. Clocked SR flip-flop

D Flip-Flop

The D flip-flop shown in Figure 5 is a modification of the clocked SR flip-flop. The D input

goes directly into the S input and the complement of the D input goes to the R input. The D

input is sampled during the occurrence of a clock pulse. If it is 1, the flip-flop is switched to

the set state (unless it was already set). If it is 0, the flip-flop switches to the clear state.

(a) Logic diagram with NAND gates

(b) Graphical symbol

(c) Transition table

Figure 5. Clocked D flip-flop

JK Flip-Flop

A JK flip-flop is a refinement of the SR flip-flop in that the indeterminate state of the SR type

is defined in the JK type. Inputs J and K behave like inputs S and R to set and clear the flip-

flop (note that in a JK flip-flop, the letter J is for set and the letter K is for clear). When logic

1 inputs are applied to both J and K simultaneously, the flip-flop switches to its complement

state, ie., if Q=1, it switches to Q=0 and vice versa.

A clocked JK flip-flop is shown in Figure 6. Output Q is ANDed with K and CP inputs so

that the flip-flop is cleared during a clock pulse only if Q was previously 1. Similarly, ouput

Q' is ANDed with J and CP inputs so that the flip-flop is set with a clock pulse only if Q' was

previously 1.

Note that because of the feedback connection in the JK flip-flop, a CP signal which remains a

1 (while J=K=1) after the outputs have been complemented once will cause repeated and

continuous transitions of the outputs. To avoid this, the clock pulses must have a time

duration less than the propagation delay through the flip-flop. The restriction on the pulse

width can be eliminated with a master-slave or edge-triggered construction. The same

reasoning also applies to the T flip-flop presented next.

(a) Logic diagram

(b) Graphical symbol

(c) Transition table

Figure 6. Clocked JK flip-flop

COUNTERS:

In Figure 2, four Negative-Edge-Triggered J-K Flip-flops are connected in a cascade mode

(the output Q of one Flip-flop is connected to the input CLOCK of the next Flip-flop) to form

a Binary Counter. Inputs J and K of each Flip-flop are always 1, according to the Truth-

Table, the Flip-flop changes its state upon each H to L transition of its CLOCK.

Figure 1: Timing Diagram of the J-K Flip-flop Counter

In this Binary Counter, outputs A to D represent a 4-bit Binary Number, in which A is the

LSB and D is the MSB.The 4-bit Binary Number is increased by one on each CLOCK cycle.

The count goes from (0)10 to (15)10 and then cycles back to (0)10, Table 3.

Table 3: Truth-Table of a 4-bit Binary

Counter

Decimal

Binary

D C B A

0 0 0 0 0

1 0 0 0 1

2 0 0 1 0

3 0 0 1 1

4 0 1 0 0

5 0 1 0 1

6 0 1 1 0

7 0 1 1 1

8 1 0 0 0

9 1 0 0 1

10 1 0 1 0

11 1 0 1 1

12 1 1 0 0

13 1 1 0 1

14 1 1 1 0

15 1 1 1 1

Ripple counter

Fig. Output waveforms

The basic idea behind this is when J and K inputs are high in a JK filpflops the output

value gets toggled.

Assume that A, B, C, and D are lamps and that all the FFs are reset. The lamps will all

be out, and the count indicated will be 00002. The negative-going pulse of clock pulse 1

causes FF1 to set. This lights lamp A, and we have a count of 00012. The negative-going

pulse of clock pulse 2 toggles FF1, causing it to reset. This negative-going input to FF2

causes it to set and causes B to light. The count after two clock pulses is 0010 2, or 210. Clock

pulse 3 causes FF1 to set and lights lamp A. The setting of FF1 does not affect FF2, and lamp

B stays lit. After three clock pulses, the indicated count is 00112. Clock pulse 4 causes FF1 to

reset, which causes FF2 to reset, which causes FF3 to set, giving us a count of 01002. This

step shows the ripple effect. This setting and resetting of the FFs will continue until all the

FFs are set and all the lamps are lit. At that time the count will be 11112 or 1510. Clock pulse

16 will cause FF1 to reset and lamp A to go out. This will cause FF2 through FF4 to reset, in

order, and will extinguish lamps B, C, and D. The counter would then start at 00012 on clock

pulse 17. To display a count of 1610 or 100002, we would need to add another FF. The ripple

counter is also called an ASYNCHRONOUS counter. Asynchronous means that the events

(setting and resetting of FFs) occur one after the other rather than all at once. Because the

ripple count is asynchronous, it can produce erroneous indications when the clock speed is

high. A high-speed clock can cause the lower stage FFs to change state before the upper

stages have reacted to the previous clock pulse. The errors are produced by the FFs’ inability

to keep up with the clock.

Ripple Up/down counter

Here And-Or logic is used to implement Up down counter. When Up/down signal is

high all upper and gates enabled. So all Q values are considered and it upcounts. When When

Up/down signal is low all lower And gates enabled. So all Q bar values are considered and it

downcounts.

SHIFT REGISTER

The term register can be used in a variety of specific applications, but in all cases it

refers to a group of flip-flops operating as a coherent unit to hold data. This is different

from a counter, which is a group of flip-flops operating to generate new data by

tabulating it.

In this context, a counter can be viewed as a specialized kind of register, which counts

events and thereby generates data, rather than just holding the data or changing the way

it is handled. More commonly, however, counters are treated separately from registers.

The two are then handled as separate concepts which work together in many

applications, and which have some features in common.

The demonstration circuit below is known as a shift register because data is shifted

through it, from flip-flop to flip-flop. If you apply one byte (8 bits) of data to the initial

data input one bit at a time, and apply one clock pulse to the circuit after setting each bit

of data, you will find the entire byte present at the flip-flop outputs in parallel format.

Therefore, this circuit is known as a serial-in, parallel-out shift register. It is also known

sometimes as a shift-in register, or as a serial-to-parallel shift register.

By standardized convention, the least significant bit (LSB) of the byte is shifted

in first.

IC555 and timers

Figure 555 timer

The 555 timer consists of two voltage comparators, a bistable flip-flop, a discharge

transistor, and a resistor divider network. To understand the basic concept of the timer let’s

first examine the timer in block form as in Figure. The resistive divider network is used to set

the comparator levels. Since all three resistors are of equal value, the threshold comparator is

referenced internally at 2/3 of supply voltage level and the trigger comparator is referenced at

1/3 of supply voltage. The outputs of the comparators are tied to the bistable flip-flop. When

the trigger voltage is moved below 1/3 of the supply, the comparator changes state and sets

the flip-flop driving the output to a high state. The threshold pin normally monitors the

capacitor voltage of the RC timing network. When the capacitor voltage exceeds 2/3 of the

supply, the threshold comparator resets the flip flop which in turn drives the output to a low

state. When the output is in a low state, the discharge transistor is “on”, thereby discharging

the external timing capacitor. Once the capacitor is discharged, the timer will await another

trigger pulse, the timing cycle having been completed.

Astable multivibrator

Fig. Astable multivibrator

Fig. Waveforms at the output and capacitor.

With the output high (+Vs) the capacitor C1 is charged by current flowing through R1

and R2. The threshold and trigger inputs monitor the capacitor voltage and when it reaches 2/3Vs (threshold voltage) the output becomes low and the discharge pin is connected to 0V.

The capacitor now discharges with current flowing through R2 into the discharge pin.

When the voltage falls to 1/3Vs (trigger voltage) the output becomes high again and the

discharge pin is disconnected, allowing the capacitor to start charging again.

This cycle repeats continuously unless the reset input is connected to 0V which forces

the output low while reset is 0V.

An astable can be used to provide the clock signal for circuits such as counters.

A low frequency astable (< 10Hz) can be used to flash an LED on and off, higher

frequency flashes are too fast to be seen clearly. Driving a loudspeaker or piezo transducer

with a low frequency of less than 20Hz will produce a series of 'clicks' (one for each low/high

transition) and this can be used to make a simple metronome.

An audio frequency astable (20Hz to 20kHz) can be used to produce a sound from a

loudspeaker or piezo transducer. The sound is suitable for buzzes and beeps. The natural

(resonant) frequency of most piezo transducers is about 3kHz and this will make them

produce a particularly loud sound.

Monostable Multivibrator

Fig. Monostable Multivibrator with waveform

ADC and DAC

In electronics, a digital-to-analog converter (DAC or D-to-A) is a device that converts a

digital (usually binary) code to an analog signal (current, voltage, or electric charge). An

analog-to-digital converter (ADC) performs the reverse operation.

A DAC converts an abstract finite-precision number (usually a fixed-point binary number)

into a concrete physical quantity (e.g., a voltage or a pressure). In particular, DACs are often

used to convert finite-precision time series data to a continually varying physical signal.

A typical DAC converts the abstract numbers into a concrete sequence of impulses that are

then processed by a reconstruction filter using some form of interpolation to fill in data

between the impulses. Other DAC methods (e.g., methods based on Delta-sigma modulation)

produce a pulse-density modulated signal that can then be filtered in a similar way to produce

a smoothly varying signal.

Introduction To ADC and DAC

In electronics, a digital-to-analog converter (DAC or D-to-A) is a device that converts a

digital (usually binary) code to an analog signal (current, voltage, or electric charge). An

analog-to-digital converter (ADC) performs the reverse operation.

An ADC inputs an analog electrical signal such as voltage or current and outputs a binary

number. In block diagram form, it can be represented as such:

A DAC, on the other hand, inputs a binary number and outputs an analog voltage or current

signal. In block diagram form, it looks like this:

Together, they are often used in digital systems to provide complete interface with analog

sensors and output devices for control systems such as those used in automotive engine

controls:

It is much easier to convert a digital signal into an analog signal than it is to do the reverse.

Therefore, we will begin with DAC circuitry and then move to ADC circuitry.

The R/2nR DAC

This DAC circuit, otherwise known as the binary-weighted-input DAC, is a variation on the

inverting summer op-amp circuit. If you recall, the classic inverting summer circuit is an

operational amplifier using negative feedback for controlled gain, with several voltage inputs

and one voltage output. The output voltage is the inverted (opposite polarity) sum of all input

voltages:

For a simple inverting summer circuit, all resistors must be of equal value. If any of the input

resistors were different, the input voltages would have different degrees of effect on the

output, and the output voltage would not be a true sum. Let's consider, however, intentionally

setting the input resistors at different values. Suppose we were to set the input resistor values

at multiple powers of two: R, 2R, and 4R, instead of all the same value R:

Starting from V1 and going through V3, this would give each input voltage exactly half the

effect on the output as the voltage before it. In other words, input voltage V1 has a 1:1 effect

on the output voltage (gain of 1), while input voltage V2 has half that much effect on the

output (a gain of 1/2), and V3 half of that (a gain of 1/4). These ratios are were not arbitrarily

chosen: they are the same ratios corresponding to place weights in the binary numeration

system. If we drive the inputs of this circuit with digital gates so that each input is either 0

volts or full supply voltage, the output voltage will be an analog representation of the binary

value of these three bits.

If we chart the output voltages for all eight combinations of binary bits (000 through 111)

input to this circuit, we will get the following progression of voltages:

Binary Output voltage

000 -1.25V

001 -2.50V

010 -3.75V

011 -5.00V

100 -6.25V

101 -7.50V

110 -8.75V

111 -10.00V

Note that with each step in the binary count sequence, there results a 1.25 volt change in the

output.

The R/2R DAC

An alternative to the binary-weighted-input DAC is the so-called R/2R DAC, which uses

fewer unique resistor values. A disadvantage of the former DAC design was its requirement

of several different precise input resistor values: one unique value per binary input bit.

Manufacture may be simplified if there are fewer different resistor values to purchase, stock,

and sort prior to assembly.

Of course, we could take our last DAC circuit and modify it to use a single input resistance

value, by connecting multiple resistors together in series:

Unfortunately, this approach merely substitutes one type of complexity for another: volume

of components over diversity of component values. There is, however, a more efficient

design methodology.

By constructing a different kind of resistor network on the input of our summing circuit, we

can achieve the same kind of binary weighting with only two kinds of resistor values, and

with only a modest increase in resistor count. This "ladder" network looks like this:

Mathematically analyzing this ladder network is a bit more complex than for the previous

circuit, where each input resistor provided an easily-calculated gain for that bit. For those

who are interested in pursuing the intricacies of this circuit further, you may opt to use

Thevenin's theorem for each binary input. you should obtain the following table of figures:

Binary Output voltage

000 0.00V

001 -1.25V

010 -2.50V

011 -3.75V

100 -5.00V

101 -6.25V

110 -7.50V

111 -8.75V

As was the case with the binary-weighted DAC design, we can modify the value of the

feedback resistor to obtain any "span" desired. For example, if we're using +5 volts for a

"high" voltage level and 0 volts for a "low" voltage level, we can obtain an analog output

directly corresponding to the binary input (011 = -3 volts, 101 = -5 volts, 111 = -7 volts, etc.)

by using a feedback resistance with a value of 1.6R instead of 2R.

Flash ADC

Also called the parallel A/D converter, this circuit is the simplest to understand. It is

formed of a series of comparators, each one comparing the input signal to a unique reference

voltage. The comparator outputs connect to the inputs of a priority encoder circuit, which

then produces a binary output. The following illustration shows a 3-bit flash ADC circuit:

Vref is a stable reference voltage provided by a precision voltage regulator as part of the

converter circuit, not shown in the schematic. As the analog input voltage exceeds the

reference voltage at each comparator, the comparator outputs will sequentially saturate to a

high state. The priority encoder generates a binary number based on the highest-order active

input, ignoring all other active inputs.

When operated, the flash ADC produces an output that looks something like this:

For this particular application, a regular priority encoder with all its inherent complexity isn't

necessary. Due to the nature of the sequential comparator output states (each comparator

saturating "high" in sequence from lowest to highest), the same "highest-order-input

selection" effect may be realized through a set of Exclusive-OR gates, allowing the use of a

simpler, non-priority encoder:

And, of course, the encoder circuit itself can be made from a matrix of diodes, demonstrating

just how simply this converter design may be constructed:

Not only is the flash converter the simplest in terms of operational theory, but it is the most

efficient of the ADC technologies in terms of speed, being limited only in comparator and

gate propagation delays. Unfortunately, it is the most component-intensive for any given

number of output bits. This three-bit flash ADC requires seven comparators. A four-bit

version would require 15 comparators. With each additional output bit, the number of

required comparators doubles. Considering that eight bits is generally considered the

minimum necessary for any practical ADC (255 comparators needed!), the flash

methodology quickly shows its weakness. An additional advantage of the flash converter,

often overlooked, is the ability for it to produce a non-linear output. With equal-value

resistors in the reference voltage divider network, each successive binary count represents the

same amount of analog signal increase, providing a proportional response. For special

applications, however, the resistor values in the divider network may be made non-equal.

This gives the ADC a custom, nonlinear response to the analog input signal. No other ADC

design is able to grant this signal-conditioning behavior with just a few component value

changes.

Chapter 8

COMMUNICATION SYSTEMS

8.1 Introduction:

In a broad sense the term communication refers to the sending, receiving and

processing of information by electronic means. It can also be defined as a process of

transmitting information or signal from one point known as source to another point known as

destination. Information can be continuous such as speech music, picture etc. or discrete

signals like data from computer etc.

The frequency range of voice is 300Hzs to 3000Hzs and that of music is 20 to

20KHzs. The frequency range of video signal is 1 to 6MHzs.

As shown in the figure 8.1, the first block at the source is an input transducer which is

used to convert physical quantity (non electrical) to electrical quantity. For example voice is

converted to electrical quantity using microphone. Similarly at the destination output

transducer is used to convert electrical back to physical quantity. For example a loudspeaker

is used to convert voice signal in the form of electrical back to physical quantity. Likewise

picture signal can be converted to electrical signal by using image sensor. The image sensors

used mostly in digital Camera. If the signal to be transmitted is picture input transducer can

Transmitter

Noise

Transmission

channel

Receiver Output transducer

Input

Transducer

Input Message

Input Signal

Transmitted signal

Received signal

Output signal

Output Message

Fig. 8.1 Block Diagram of Communication System

be the digital camera. The output transducer can be any picture display unit such as CRT or

LCD.

There are basically three essential blocks in a communication system.

Transmitter

Transmission Channel

Receiver

8.1.1 Transmitter:

The output signal of the transducer is a complex signal. It is restricted to desired range of

frequencies. On this signal modulation is performed. Modulation is a process of altering the

characteristics of carrier signal in accordance with the information. There are basically three

types of modulation technique

Amplitude modulation.

Frequency modulation.

Phase modulation.

The modulated signal is then transmitted over a transmission channel.

8.1.2 Transmission channel:

It is a medium over which the electronic signal is transmitted from one point to

another. This medium can be either wired or wireless.

An example for wired communication is telephony where a pair of physical wires is

running parallel between transmitter and receiver. Now a days optical fibers are used in

between transmitter and receiver in which light carries the information. Similarly an example

for wireless communication is radio communication where two antennas are employed, one

at the transmitter and other at the receiver. The transmitter antenna transmits the modulated

information into free space and the receiver antenna picks up the modulated information

which is later demodulated to get the information back.

8.1.3 Noise:

It is a random, undesirable electrical energy that interferes with the transmitted signal. It

can be either natural noise such as noise caused by lightning during rainy season or man

made noise produced by ignition system of cars etc. Noise is a serious problem which cannot

be eliminated but one can reduce the effect caused by it on the signal.

8.1.4 Receiver:

It is a collection of electronic circuits designed to convert the modulated signal back

to modulating signal. This process is known as demodulation. Finally an output transducer is

employed to convert back the information in electrical form to physical form.

8.2 Frequency Bands:

The radio-frequency spectrum is divided arbitrarily into a number of bands from very low

frequencies. Sections of the spectrum have been allocated to the various users, such as

telegraph, telephonic speech, telemetry, and radio and television broadcasting.

Each frequency range has a band designator and each range of frequencies behaves

differently and performs different functions. The frequency spectrum is shared by civil,

government, and military users of all nations according to International Telecommunications

Union (ITU) radio regulations. For communications purposes, the usable frequency spectrum

now extends from about 30Hz to about 300GHz. Frequency band standard is described in

International Telecommunications Union radio regulations. And it looks as follows.

Table.8.1 Frequency band standard.

Designation Frequency Wavelength Sample Uses

ELFextremely low frequency

30Hz to 300Hz 10000km to 1000kmPower Transmission

VF Voice frequency 300Hz to 3000Hz 1000km to 100km Audio

VLFvery low frequency

3kHz to 30kHz 100km to 10kmSubmarine communication

LF low frequency 30kHz to 300kHz 10km to 1km Navigation

MF medium frequency300kHz to 3000kHz

1km to 100mAM Broadcast

HF high frequency 3MHz to 30MHz 100m to 10mShort wave broadcast commercial

VHFvery high frequency

30MHz to 300MHz

10m to 1mTV BroadcastFM Broadcast

UHFultra high frequency

300MHz to 3000MHz

1m to 10cm

Communication satellites, Microwave Ovens, Cellular Telephones etc.

SHFSuper high frequency

3GHz to 30GHz 10cm to 1cmRadar

EHFextremely high frequency

30GHz to 300GHz

1cm to 1mmRadio Astronomy and remote sensing

8.3 Types of Noise in Communication Systems:

Noise can be divided into two types: Internal Noise, which originates within the

communication equipment, and External Noise, which is a property of the channel.

8.3.1 Internal Noise:

Noise is generated in all electronic equipment. Several types of internal noise are as follows:

Thermal Noise: Produced by the random motion of electrons in a conductor due to heat.

Shot Noise: produced by random variations in current flow in active devices such as tubes,

transistors, and semiconductor diodes.

Partition Noise: It occurs only in devices where a single current separates into two or more

paths.

Excess Noise: or Flicker noise caused by variations in carrier density.

Transit-Time Noise: Occurs when the time taken by the charge carriers to cross a junction is

comparable to the period of the signal.

8.3.2 External Noise:

If the channel is a radio link, there are following possible sources of noise:

Equipment Noise: Noise is generated by equipment that produces sparks. Examples include

automobile engines and electric motors with brushes.

Atmospheric Noise: Often called static because lightning, which is a static-electricity

discharge.

Space Noise: occurs due to radiation from Sun and other stars.

8.4 Transmission Media:

Describes the type of physical system used to carry a communication signal from one system

to another. The transmission medium can be wired or wireless.

8.4.1 Wire media:

Examples of wire media include Twisted-pair, Co-axial cable and Optical fiber.

Twisted-pair:

A basic twisted-pair cable consists of two strands of copper wire twisted together as shown

in the figure 8.2.

Fig. 8.2 Twisted-pair wire

This twisting reduces the sensitivity of the cable to electromagnetic interference and also

reduces the tendency of the cable to radiate radio frequency noise that interferes with nearby

cables and electronic components. This is because the radiated signals from the twisted wires

tend to cancel each other out.

These are divided into two major categories: Unshielded Twisted Pair (UTP), and Shielded

Twisted Pair (STP).

Applications:

Most common transmission media for both digital and analog signals

Less expensive compared to coaxial cable or optical fiber

Limited in terms of data rate and distance

Telephone network

Individual units (residence lines) to local exchange (end office)

Subscriber loops

Supports voice traffic using analog signaling

May handle digital data at modest rates using modems

Communications within buildings

Connection to digital data switch or digital pbx within a building

Allows data rate of 64 kbps.

Coaxial Cable:

Consists of two conductors with construction that allows it to operate over a wider

range of frequencies compared to twisted pair

Hollow outer cylindrical conductor surrounding a single inner wire conductor

Inner conductor held in place by regularly spaced insulating rings or solid dielectric

material

Outer conductor covered with a jacket or shield

Diameter from 1 to 2.5 cm

Shielded concentric construction reduces interference and crosstalk

Can be used over longer distances and support more stations on a shared line than

twisted pair.

The Coaxial cable is as shown in the figure 8.3.

Fig. 8.3 Coaxial cable

Applications:

Most common use is in cable tv

Traditionally part of long distance telephone network

Can carry more than 10,000 voice channels simultaneously using frequency-division

multiplexing

Short range connections between devices

Optical Fiber:

Thin, flexible material to guide optical rays

Cylindrical cross-section with three concentric links

1. Core

Innermost section of the fiber

One or more very thin (dia. 8-100 µm) strands or fibers

2. Cladding

Surrounds each strand

Plastic or glass coating with optical properties different from core

Interface between core and cladding prevents light from escaping the core

3. Jacket

Outermost layer, surrounding one or more claddings

Made of plastic and other materials

Protects from environmental elements like moisture, abrasions, and crushing

Fig. 8.4 Optical Fiber Cable

Comparison with twisted pair and coaxial cable

Capacity

Much higher bandwidth

Can carry hundreds of Gbps over tens of kms

Smaller size and light weight

Very thin for similar data capacity

Much lighter and easy to support in terms of weight (structural properties)

Significantly lower attenuation

Electromagnetic isolation

Not affected by external em fields.

Not vulnerable to interference, impulse noise, or crosstalk

No energy radiation; little interference with other devices; security from

eavesdropping

Greater repeater spacing

Lower cost and fewer error sources

Applications

_ Long haul trunks

_ Increasingly common in telephone networks

_ About 1500km in length with high capacity (20000 to 60000 voice channels)

_ Metropolitan trunks

_ Average length of about 12 km with a capacity of 100,000 voice channels

_ Mostly repeaterless to join phone exchanges in metro areas

_ Rural exchange trunks

_ Circuit lengths from 40 to 160 km

_ Fewer than 5000 voice channels

_ Connect exchanges of different phone companies

_ Subscriber loops

_ Central exchange to subscriber

_ May be able to handle image and video in addition to voice and data

_ Local area networks

_ 100Mbps to 1Gbps capacity

_ Can support hundreds of stations on a campus

8.4.2 Wireless Communications:

Transmission and reception are achieved using an antenna

Transmitter sends out the electromagnetic (em) signal into the medium

Receiver picks up the signal from the surrounding medium

Directional transmission

Transmitter sends out a focused em beam

Transmitter and receiver antennae must be carefully aligned

More suitable for higher frequency signals

Omnidirectional transmission

Transmitted signal spreads out in all directions

May be received by many antennae

Frequency ranges for wireless transmission

1. 2 GHz to 40 GHz

Microwave frequencies

Highly directional beams for point-to-point communications

Also used for satellite communication

2. 30 MHz to 1 GHz

Broadcast radio range

Suitable for omnidirectional purposes

3. 3 x 1011 Hz to 2 x 1014 Hz

Infrared portion of the spectrum

Useful for local point-to-point and multipoint applications

within confined areas

TV remote, Bluetooth

Chapter 9

Analog Modulation:

9.1 Introduction:

The communication system can be of an analog or digital type. The design of analog

communication system is relatively simple. The transmitter consists of a modulator and the

receiver consists of a demodulator. The different modulation and demodulation techniques

used are Amplitude, Frequency and Phase modulation.

In contrast, a digital communication system is considerably more complex. If the message

signal is analog form, the transmitter performs the A/D conversion to convert it into digital

form. The transmitter may involve the additional operations of data compression and channel

encoding before digital modulation. At the receiver, the operations are reversed by using

respective demodulation, decoding and then D/A conversion to produce original message

signal.

9.2 Need for modulation:

1. The height of the antenna required to transmit and receive radio waves is a

function of wavelength of the frequency used. i.e.λ = c/f. At low frequency, λ is

high and hence the height of the antenna should be more to transmit the signal

(since ‘λ’ is proportional to ‘h’). Therefore high frequencies are used to transmit

the information which requires antenna of lesser height.

2. At low frequency radiation is poor and signal gets highly attenuated. Therefore

signal cannot be transmitted over longer distance. Modulation effectively

increases the frequency of the signal to be radiated and thus increases the distance

over which signal can be transmitted faithfully.

3. The modulation permits multiplexing to be used. Multiplexing is method of

transmitting two or more information simultaneously over a single channel. In this

method each message signal is modulated using different carrier signal

frequencies and then transmitted over a single channel. At the receiver the

message signals are extracted individually by tuning to their respective carrier

frequencies.

9.3 Amplitude Modulation:

It is defined as a process of varying the amplitude of the carrier wave proportional to the

instantaneous amplitude of modulating signal. Figure 9.1 shows the diagram for AM

generation.

Fig. 9.1 Diagram for Amplitude Modulation.

9.3.1 Time domain analysis:

Let the equation of carrier signal be c(t) = Accos(2пfct) where Ac is the peak amplitude

of carrier signal and fc is the frequency of the carrier signal.

Let the equation of modulating signal be m(t) = Amcos(2пfmt) where Am is the peak

amplitude of modulating signal and fm is the frequency of the modulating signal.

Then by the definition of AM:

VAM(t) = [ + cos(2пfmt)]cos(2пfct) (9.1)

= cos(2пfct) + cos(2пfmt) cos(2пfct)

= cos(2пfct) + cos[2п(fc + fm)t] + cos[2п(fc - fm)t]

Where ‘m’ is the modulation index of AM signal which is defined as ratio of amplitude of

modulating signal to that of carrier signal i.e. . The significance of modulation index is, it

decides the depth of modulation. If it is less than one, then AM signal is known as under

modulated signal. If it is more than one, then AM signal is known as over modulated signal.

If it is equal to one, then AM signal is known as perfect modulated signal. To obtain the

original information, modulation index should always be less than or equal to one.

VAM(t) = cos(2пfct) + cos[2п(fc + fm)t] + cos[2п(fc - fm)t] (9.2)

9.3.2 Spectrum of AM signal:

Fig. 9.2 Frequency Spectrum of AM signal

As shown in the figure 9.2, the spectrum consisted of three frequency components,

one at fc and other two at fc + fm , fc- fm. The frequencies fc + fm and fc- fm are known as

sideband frequencies i.e.fc + fm is known as upper sideband frequency and fc- fm is known as

lower sideband frequency . The separation between these two frequencies is defined as

bandwidth of AM signal. Therefore the bandwidth of AM signal is 2fm.

Total power required to transmit AM signal:

The total power required to transmit AM signal ( PT ) is sum of power required to

transmit carrier signal ( PC ) and power required to transmit side band signals ( PTSB ).

Therefore PT = PC + PTSB (9.3)

= PC + PLSB + PUSB

= + + (9.4)

= 1 + (9.5)

PT = PC 1 + (9.6)

mAc/2 mAc/2

Ac

fc - fm fc + fm f Hzs fc

lVAM( f ) l

The above equation gives the total power required to transmit AM signal in terms of

carrier power and modulation index.

For 100% modulation : m = 1, Therefore PT = PC 1 +

= PC

Or PC = PT = 0.6666 PT

Or PC = 66.66%PT

i.e. 66.66% of total power is wasted in transmitting carrier signal.

Current calculation:

PT = PC 1 +

= 1 +

where is the current with modulation , is the current without modulation and R is the

resistance of the antenna.

Modulation by several sine waves:

In modulation by several sine waves, modulating signal consists of several sine waves

i.e. m(t) = cos(2п t) + cos(2п t) + . . . . . . . (9.8)

For modulation by several sine waves overall modulation index will be

= 1 + (9.7)

m t = (9.9)

m t = (9.10)

Therefore Total power will be

Similarly current with modulation will be

Problems:

1. An audio signal 10sin (2п1000t) amplitude modulates a carrier of 40sin (2п2000t).

Find

i. Modulation index

ii. Sideband frequencies.

iii. Bandwidth.

iv. Total power delivered if RL = 1KΩ.

v. Amplitude of each side band components.

Solution:

i) Modulation index: m = = = 0.25.

ii) Sideband frequencies :

Upper side band = fC + fm = 300Hz.

Lower side band = fC - fm = 1000Hz.

iii) Bandwidth = 2fm = 2KHz.

PT = PC 1 + (9.11)

IT = IC (9.12)

iv) Total power delivered:

PT = ( 1 + )

= ( 1 + )

=

v) Amplitude of each sideband = m =0.25 * = 5V.

2. The antenna current of an AM transmitter is 8A when only carrier is transmitted, but

increases to 8.93A when carrier is modulated by a single sine wave. Find the

percentage modulation. Determine the antenna current when the depth of modulation

changes to 0.8A.

Solution:

i) Given : IT = 8.93A.

IC = 8A.

IT = IC

m = = 0.701 =70.1%.

ii) IT = ? when m = 0.8

IT = IC = 9.19A.

3. A certain transmitter radiates 9KW with carrier unmodulated and 10.125KW when

carrier is sinusoidally modulated. Calculate modulation index. If another sine wave

corresponding to 40% modulation is transmitted simultaneously, determine the total

power radiated.

Solution:

i) Given: P T = 9KW.

PC = 10.125KW.

PT = PC 1 +

m = = 0.5.

ii) m1 = 0.5 , m2 = 0.4 , PC = 9KW.

m t = = 0.64.

PT = PC 1 + = 10.84KW.

Problems:

1. Show that modulation index = , where VMAX and VMIN are maximum and

minimum voltages of AM signal.

2. A 360W carrier is simultaneously modulated by two audio waves with

percentage modulation of 55 and 65 respectively. Find the modulation index and total

power radiated and power in each sideband. Assume RL=1Ώ.

[mt = .85, PT =490W, Pusb = Plsb = 65W]

9.4 AM Demodulation:

Amplitude modulation, AM, is one of the most straightforward ways of modulating a radio

signal or carrier. The process of demodulation, where the audio signal is removed from the

radio carrier in the receiver is very simple. The easiest method of achieving amplitude

demodulation is to use a simple diode detector. This consists of just a handful of

components:- a diode, resistor and a capacitor. The circuit diagram of AM demodulator or

detector is as shown below.

Fig9.3 AM detector

In this circuit, the diode rectifies the signal, allowing only half of the alternating waveform

through. The capacitor is used to store the charge and provide a smoothed output from the

detector, and also to remove any unwanted radio frequency components. The resistor is used

to enable the capacitor to discharge.

9.5 Single Sideband (SSB) Technique:

It is any AM scheme in which only one of the two sidebands is transmitted.

The two sidebands of an AM signal are mirror images of each other. Thus one sideband is

redundant, and it is not necessary to transmit both sidebands. Removing one sideband reduces

the bandwidth by at least a factor of two. Thus resulting signal will require less transmitted

power, and perfectly acceptable communication will be possible.

Applications:

SSB modulation offers a far more effective solution for two way radio communication for the

transmission of voice because it provides a significant improvement in efficiency.

9.6 Double Sideband (DSB) Technique:

It is an Amplitude modulation in which the modulated wave is composed of a carrier, an

upper sideband whose frequency is the sum of the carrier and modulation frequencies, and a

lower sideband whose frequency is the difference between the carrier and modulation

frequencies.

9.7 Vestigial Sideband (VSB) Technique:

It is a form of amplitude modulation where one sideband is completely present, and the other

sideband that has been only partly cut off or suppressed. It is widely used for analogue

television transmissions. It is useful because the baseband video signal is wide (typically 6

MHz). To transmit this using AM would require a bandwidth of 12 MHz.

9.8 Frequency Modulation:

It is defined as a process of altering the frequency of the carrier signal w.r.t.

instantaneous amplitude of modulating signal.

Fig.9.4 Diagram for Frequency Modulation

9.8.1 Time domain analysis:

From the definition: f FM = fC + Kf m(t) ; (9.13)

Where Kf is known as frequency sensitivity. (2Πfmt)

= fC + Kf Amcos(2Πfmt)

= fC + Δf cos(2Πfmt) (9.14)

where Δf is known as frequency deviation. Its signifies, by how much amount carrier

frequency gets deviated.

Multiplying by 2Π on both sides :

2ΠfFM = 2ΠfC + 2ΠΔf cos(2Πfmt)

ΔWFM = ΔWC + ΔWcos(2Πfmt) (9.15)

Since WFM = , integrating both the sides : WFMt =

WFMt = WCt + (9.16)

= WCt + sin(2Πfmt) (9.17)

Therefore equation of FM Signal: VFM(t) = AC cos[ ]

= AC cos[ WCt + sin(2Πfmt) ]

= AC cos[ WCt + sin(2Πfmt) ]

= AC cos[ WCt + sin(2Πfmt) ]

= AC cos[ WCt + βsin (2Πfmt) ] (9.18)

where β = is defined as modulation index of FM. Unlike AM modulation index is not

restricted to one. It can be more than unity.

9.8.2 Frequency spectrum:

The frequency spectrum of FM signal consisted of infinite number of sideband

components ( using Fourier Transform ). Hence theoretically the bandwidth of FM signal is

infinity. But practically the bandwidth of FM signal is restricted using Carson’s rule.

According to Carson’s rule the bandwidth of FM signal is given by 2(Δf + fm).

Problems:

1. Given a FM equation VFM(t) = 10 cos [ 2 Π 108t + 5 sin(2 Π 15000t) ] , Calculate

i. Carrier frequency.

ii. Modulating frequency.

iii. Frequency deviation.

iv. Bandwidth using Carson’s rule.

Soilution:

Carrier frequency: fc = 108Hz.

Modulating frequency : fm = 15KHz.

Frequency deviation : Δf = β fm = 5 * 15 = 75KHz.

Bandwidth = 2(Δf + fm ) = 2( 75 + 15 ) = 180KHz.

2. In an FM system when the audio frequency is 50Hz , modulating voltage is 2.5V ,

the deviation produced is 5KHz. If the modulating voltage is now increased to 7.5V ,

calculate the new value of frequency deviation. If the AF voltage is raised to 10V

while the modulating frequency is dropped to 250Hz , what is the frequency deviation

produced. Also calculate modulation index in each case.

Solution:

Given : fm = 50Hz , Am = 2.5V , Δf = 5 103Hz.

Modulation index: β = = = 100

ii) If Am = 7.5V , Δf = ?

Kf = = = 2KHz/V.

Δf = Kf Am = 2 7.5 = 15KHz.

Modulation index: β = = = 300.

iii) Δf = Kf Am = 2 10 = 20KHz.

Modulation index: β = = = 800.

Problems:

1. A carrier of amplitude 5V and frequency 90MHz is frequency modulated by

asinusoidal voltage of amplitude 5V and frequency 15KHz. The frequency sensitivity

is 1Hz/V. Calculate the frequency deviation and modulation index.

2. Compare and contrast AM and FM.

9.9 The Super-heterodyne Receiver:

To heterodyne means to mix two frequencies together so as to produce a beat frequency,

namely the difference between the two. The term superheterodyne refers to creating a beat

frequency that is lower than the original signal.

9.9.1 AM- Superhetrodyne Receiver:

There are a great variety of receivers in communication systems based on the requirements

such as the modulation scheme, the operating frequency and its range and the type of display

required. One of them AM-super-heterodyne type, whose block diagram is as shown in

fig.9.5.

Fig.9.5AM Superhetrodyne Receiver and waveforms at each stage.

When heterodyning the incoming signal and the local oscillator signal in the mixer stage, four

frequencies are produced. They are the two basic input frequencies and the sum and the

difference of those two frequencies. The amplifier that follows (IF amplifier) will be tuned to

the difference frequency. This difference frequency is known as the intermediate frequency

(IF). A typical value of IF for an AM communications receiver is 455 kilohertz. The

difference frequency is a lower frequency than either the rf input or oscillator frequencies.

This lower frequency gives slightly better gain but does increase the chances of image

frequency interference.

Once the IF stages have amplified the intermediate frequency to a sufficient level, it is fed to

the detector. The detector extracts the modulating audio signal. The detector stage consists of

a rectifying device and filter, which respond only to the amplitude variations of the IF signal.

This develops an output voltage varying at an audio-frequency rate. The output from the

detector is further amplified in the audio amplifier and is used to drive a speaker or

earphones.

9.9.2 FM Superhetrodyne Receiver:

The FM superheterodyne receiver block diagram has many similarities to that of the AM

superheterodyne receiver studied earlier.

Fig. 9.6 FM Superhetrodyne Receiver

As the figure 9.6 shows, the FM receiver is quite similar to AM receiver, and the only

apparent differences are the use of limiter-discriminator circuit in place of detector section

and the addition of a de-emphasis network. The other sections perform almost identical

functions as in AM receiver.

The universally standard IF frequency for FM is 10.7MHz , as compared to 455kHz for AM.

The additional components inside the FM superheterodyne receiver and their functions are:

Limiter: Its function is to remove any unwanted amplitude modulation and the amplitude

variations due to noise, where they would carry an undesirable effect if carried through to

the speaker.

Discriminator: Its function is to extract the information that has been modulated onto the

carrier via frequency variations.

Pre- and de-emphasis network: Its function is to improve the signal-to-noise ratio where at

the transmitter there will be the pre-emphasis circuit. The pre-emphasis will amplify the high

frequency component. And the de-emphasis will provide a normal frequency response. The

combined effect of pre-emphasis and de-emphasis is to increase the high-frequency

components during the transmission so that they will be stronger and not masked by noise.

Chapter 10

Digital Modulation

10.1 Introduction:

As we know for any analog information to be transmitted using digital communication

system, the signal has to be converted to digital form. The A/D conversion is nothing but

sampling, quantizing and coding the analog signal. We then modulate the digitized signal

using digital modulation techniques. First let us know the sampling.

10.2 Sampling Theorem:

Harry Nyquist proved the sampling theorem which states that it is possible to reconstruct a

band-limited analog signal from periodic samples, as long as the sampling rate is at least

twice the highest frequency component of the signal.

Or in mathematical terms: fs ≥ 2 fc (10.1)

fs is the sampling frequency and fc is highest frequency contained in the signal.

The theorem is commonly called the Nyquist sampling theorem.

Consider for example a signal composed of a single sine wave at a frequency of 1 Hz:

Fig.10.1 Sinusoidal signal of frequency 1 Hz

If we sample this waveform at 2 Hz (as dictated by the Nyquist theorem), that is sufficient to

capture each peak and trough of the signal:

Fig.10.2 Sinusoidal signal of 1 Hz sampled at 2Hzs

If we sample at a frequency higher than this, for example 3 Hz, then there are more than

enough samples to capture the variations in the signal:

Fig.10.2 Sinusoidal signal of 1 Hz sampled at 3Hzs

If however we sample at a frequency lower than 2 Hz, for example at 1.5 Hz, then there are

now not enough samples to capture all the peaks and troughs in the signal:

Fig.10.4 Sinusoidal signal of 1 Hz sampled at 1.5Hzs

Note here that we are not only losing information, but we are getting the wrong information

about the signal. The person receiving these samples, without any previous knowledge of the

original signal, may well be mislead into thinking that the signal has quite a different form:

Fig.10.5 wrongly reconstructed signal

From this example, we can see the reason for the term aliasing. That is, the signal now takes

on a different \persona," or a false presentation, due to being sampled at an insufficiently high

frequency.

Now we are ready to think about the sampling of a complex signal composed of many

frequency components. By Fourier's theorem, we know that any continuous signal may be

decomposed in terms of a sum of sines and cosines at different frequencies. For example, the

following waveform is composed by adding together sine waves at frequencies 1 Hz, 2 Hz,

and 3 Hz:

Fig.10.6 Signal formed by adding the three sine waves of frequencies 1, 2 and 3 Hzs.

According to the Nyquist sampling theorem, the signal must be sampled at twice the highest

frequency contained in the signal. In this case, we have fc=3 Hz, and so the Nyquist theorem

tells us that the sampling frequency, fs, must be at least 6 Hz. And sure enough, this appears

to be sufficient:

Fig.10.7 Signal sampled at 6 Hzs

Thus, when a signal contains not just one but many different frequencies added together, the

minimal sampling rate needed to avoid aliasing is just twice whatever the highest frequency

is, irrespective of how many other frequency components there are.

10.3 Modulation Techniques:

There are three basic types of digital modulation techniques. These are:

Amplitude Shift Keying (ASK)

Frequency Shift Keying (ASK)

Phase Shift Keying (ASK)

All these technique vary a parameter to represent the information which we wish to send. A

sinusoidal carrier has three different parameters that can be varied. These are its amplitude,

phase and frequency. Here the digitized information get mapped into some aspect of sine

wave and then transmits this sine wave. The sine wave on the other side (receiver) is

remapped back to the information.

10.3.1 Amplitude Shift Keying (ASK)

Here the amplitude of the carrier is changed in response to information and all else is kept

fixed. Bit 1 is transmitted by a carrier of one particular amplitude. Bit 0 is transmitted by

changing the amplitude. The ASK also called On-Off keying (OOK) is as shown below.

10.3.2 Frequency Shift Keying (FSK):

Here we change the frequency of the carrier in accordance with the binary information, one

particular frequency for a 1 and another frequency for a 0. FSK signal is as shown below for

the same bit sequence as above.

Fig.10.8 Binary FSK signal

10.3.3 Phase Shift Keying (PSK):

Here we change the phase of the sinusoidal carrier to indicate information. Phase in this

context is the starting angle at which the sinusoid starts. To transmit 0, we shift the phase of

the sinusoid by 180o. Phase shift represents the change in the state of the information. The

figure below shows the PSK representation.

Fig.10.9 Binary Signal (Note 1800 phase shifts at bit edges).

10.4 Time Division Multiplexing:

It is a technique of transmitting multiple digitized data, voice, and video signals

simultaneously over one communication media by interleaving pulses representing bits from

different channels or time slots.

The Public-Switched Telephony Network (PSTN) is based on the TDM technologies and

often called a TDM access network.

Telephony switches support TDM in a few formats: DS0, T1/E1 TDM and BRI TDM.

E1 TDM provides a 2.048Mbps communications link divided into 32 time slots of 64kbps

each.

T1 TDM provides a 1.544Mbps communication link divided into 24 time slots of 64kbps

each and an 8kbps channel for synchronisation and maintenance.

E1 and T1 TDM were first used by telephone companies for the transport of digitised voice.

TDM are now also used for wide area network links.

BRI TDM support is provided by a switch Basic Rate Interface which can be used for Basic

Rate ISDN.

Fig.10.10 Time division Multiplexing.

10.5 Frequency Division Multiplexing (FDM):

Frequency Division Multiplexing (FDM) is a technique, the carrier bandwidth is divided into

sub-channels of different frequency widths, each signal is modulated to a different carrier

frequency. Carrier frequencies separated so that signals do not overlap (guard bands).

E.g. broadcast radio.

Fig.10.11 Frequency Division Multiplexing.

FDM is used in analog transmission such as twisted pair telephone line, cable access, cellular,

radio and TV communications.

10.6 Introduction to Mobile Communication:

A cellular radio system provides a wireless connection to the public telephone network for

any user location within the radio range of the system. The term mobile has traditionally been

used to classify a radio terminal that can be moved during communication. Cellular systems

accommodate a large number of mobile units over a large area within a limited frequency

spectrum. There are several types of radio transmission systems. We consider only full duplex

systems. These are communication systems that allow simultaneous two-way communication.

Transmission and reception for a full duplex system are typically on two different channels,

so the user may constantly transmit while receiving signals from another user. Figure 10.12

shows a basic cellular system that consists of mobiles, base stations, and a switching center.

Fig.10.12 An illustration of a cellular system

10.6.1 Mobile to Mobile Communication:

Mobile phone networks are divided into thousands of overlapping, individual geographic

areas or cells each with a Base station. Each mobile communicates via radio with one or

more base stations. An illustration of Mobile to mobile communication is as shown in the

figure 10.13.

Fig10.13 Illustrtion of Mobile to Mobile Communication

Each mobile contains a transceiver (transmitter and receiver), an antenna, and control

circuitry. The base stations consist of several transmitters and receivers, which

simultaneously handle full duplex communications and generally have towers that support

several transmitting and receiving antennas. The base station connects the simultaneous

mobile calls via telephone lines, microwave links, or fiber-optic cables to the switching

center. The switching center coordinates the activity of all of the base stations and connects

the entire cellular system to the public telephone network.

The channels used for transmission from the base station to the mobiles are called forward or

downlink channels, and the channels used for transmission from the mobiles to the base

station are called reverse or uplink channels. The two channels responsible for call initiation

and service request are the forward control channel and reverse control channel.

Once a call is in progress, the switching center adjusts the transmitted power of the mobile

(this process is called power control) and changes the channel of the mobile and base station

(handoff) to maintain call quality as the mobile moves in and out of range of a given base

station. A call from a user can be transferred from one base station to another during the call.

The process of transferring is called handoff.