ppt of analog communication

Unit-1Signal Analysis

04/11/2023prepared by Arun Kumar & Shivendra

Tiwari 1

Prepared by: MR . Arun Kumar (Asst.Prof. SISTec-E EC dept.)

MR . Shivendra Tiwari (Asst.Prof. SISTec-E EC dept.)

Content• Periodic Function• Fourier Series• Complex Form of the Fourier Series• Impulse Train• Analysis of Periodic Waveforms• Half-Range Expansion


Tiwari 2

Periodic Function

• Any function that satisfies

( ) ( )f t f t T

where T is a constant and is called the period of the function.


Tiwari 3

Example:

Find its period.4

cos3

cos)(tt

tf

)()( Ttftf )(4

1cos)(

3

1cos

4cos

3cos TtTt

tt

Fact: )2cos(cos m

mT

23

nT

24

mT 6

nT 8

24T smallest T


Tiwari 4

Example:

Find its period.tttf 21 coscos)(

) ( ) (T t f t f )(cos)(coscoscos 2121 TtTttt

mT 21

nT 22n

m

2

1

2

1

must be a rational

number


Tiwari 5

Example:

Is this function a periodic one?

tttf )10cos(10cos)(

10

10

2

1 not a rational number


Tiwari 6

Fourier Series


Tiwari 7

Introduction

• Decompose a periodic input signal into primitive periodic components.

A periodic sequenceA periodic sequence

T 2T 3T

t

f(t)


Tiwari 8

Synthesis

T

ntb

T

nta

atf

nn

nn

2sin

2cos

2)(

11

0

DC PartEven Part Odd Part

T is a period of all the above signals

)sin()cos(2

)( 01

01

0 tnbtnaa

tfn

nn

n

Let 0=2/T.


Tiwari 9

Orthogonal Functions

• Call a set of functions {k} orthogonal on an interval a < t < b if it satisfies

nmr

nmdttt

n

b

a nm

0)()(


Tiwari 10

Orthogonal set of Sinusoidal Functions

Define 0=2/T.0 ,0)cos(

2/

2/ 0 mdttmT

T0 ,0)sin(

2/

2/ 0 mdttmT

T

nmT

nmdttntm

T

T 2/

0)cos()cos(

2/

2/ 00

nmT

nmdttntm

T

T 2/

0)sin()sin(

2/

2/ 00

nmdttntmT

T and allfor ,0)cos()sin(

2/

2/ 00

We now prove this one


Tiwari 11

Proof

dttntmT

T 2/

2/ 00 )cos()cos(

0

)]cos()[cos(2

1coscos

dttnmdttnmT

T

T

T

2/

2/ 0

2/

2/ 0 ])cos[(2

1])cos[(

2

1

2/

2/00

2/

2/00

])sin[()(

1

2

1])sin[(

)(

1

2

1 T

T

T

Ttnm

nmtnm

nm

m n

])sin[(2)(

1

2

1])sin[(2

)(

1

2

1

00

nmnm

nmnm

00


Tiwari 12

Proof

dttntmT

T 2/

2/ 00 )cos()cos(

0

)]cos()[cos(2

1coscos

dttmT

T 2/

2/ 02 )(cos

2/

2/

00

2/

2/

]2sin4

1

2

1T

T

T

T

tmm

t

m = n

2

T

]2cos1[2

1cos2

dttmT

T 2/

2/ 0 ]2cos1[2

1

nmT

nmdttntm

T

T 2/

0)cos()cos(

2/

2/ 00


Tiwari 13

Proof

dttntmT

T 2/

2/ 00 )cos()cos(

0

)]cos()[cos(2

1coscos

dttmT

T 2/

2/ 02 )(cos

2/

2/

00

2/

2/

]2sin4

1

2

1T

T

T

T

tmm

t

m = n

2

T

]2cos1[2

1cos2

dttmT

T 2/

2/ 0 ]2cos1[2

1

nmT

nmdttntm

T

T 2/

0)cos()cos(

2/

2/ 00


Tiwari 14

Orthogonal set of Sinusoidal Functions

Define 0=2/T.

0 ,0)cos(2/

2/ 0 mdttmT

T0 ,0)sin(

2/

2/ 0 mdttmT

T

nmT

nmdttntm

T

T 2/

0)cos()cos(

2/

2/ 00

nmT

nmdttntm

T

T 2/

0)sin()sin(

2/

2/ 00

nmdttntmT


2/

2/ 00 04/11/2023

prepared by Arun Kumar & Shivendra Tiwari

15

Decomposition

dttfT

aTt

t

0

0

)(2

0

,2,1 cos)(2

0

0

0

ntdtntfT

aTt

tn

,2,1 sin)(2

0

0

0

ntdtntfT

bTt

tn

)sin()cos(2

)( 01

01

0 tnbtnaa

tfn

nn

n


Tiwari 16

ProofUse the following facts:

0 ,0)cos(2/

2/ 0 mdttmT

T0 ,0)sin(

2/

2/ 0 mdttmT

T

nmT

nmdttntm

T

T 2/

0)cos()cos(

2/

2/ 00

nmT

nmdttntm

T

T 2/

0)sin()sin(

2/

2/ 00

nmdttntmT


2/

2/ 00


Tiwari 17

Example (Square Wave)

112

200

dta

,2,1 0sin1

cos2

200

nntn

ntdtan

,6,4,20

,5,3,1/2)1cos(

1 cos

1sin

2

200

n

nnn

nnt

nntdtbn

2 3 4 5--2-3-4-5-6

f(t)1

ttttf 5sin

5

13sin

3

1sin

2

2

1)(


Tiwari 18

Harmonics

T

ntb

T

nta

atf

nn

nn

2sin

2cos

2)(

11

0

DC PartEven Part Odd Part

T is a period of all the above signals

)sin()cos(2

)( 01

01

0 tnbtnaa

tfn

nn

n


Tiwari 19

Harmonics

tnbtnaa

tfn

nn

n 01

01

0 sincos2

)(

Tf

22 00Define , called the fundamental angular frequency.

0 nnDefine , called the n-th harmonic of the periodic function.

tbtaa

tf nn

nnn

n

sincos2

)(11

0


Tiwari 20

Harmonics

tbtaa

tf nn

nnn

n

sincos2

)(11

0

)sincos(2 1

0 tbtaa

nnnn

n

12222

220 sincos2 n

n

nn

nn

nn

nnn t

ba

bt

ba

aba

a

1

220 sinsincoscos2 n

nnnnnn ttbaa

)cos(1

0 nn

nn tCC


Tiwari 21

Amplitudes and Phase Angles

)cos()(1

0 nn

nn tCCtf

20

0

aC

22nnn baC

n

nn a

b1tan

harmonic amplitude phase angle


Tiwari 22

Fourier SeriesComplex form of the Fourier Series


Tiwari 23

Complex Exponentials

tnjtne tjn00 sincos0

tjntjn eetn 00

2

1cos 0

tnjtne tjn00 sincos0

tjntjntjntjn eej

eej

tn 0000

22

1sin 0


Tiwari 24

Complex Form of the Fourier Series

tnbtnaa

tfn

nn

n 01

01

0 sincos2

)(

tjntjn

nn

tjntjn

nn eeb

jeea

a0000

11

0

22

1

2

1

0 00 )(2

1)(

2

1

2 n

tjnnn

tjnnn ejbaejba

a

1

000

n

tjnn

tjnn ececc

)(2

1

)(2

12

00

nnn

nnn

jbac

jbac

ac


Tiwari 25


1

000)(

n

tjnn

tjnn ececctf

1

10

00

n

tjnn

n

tjnn ececc

n

tjnnec 0

)(2

1

)(2

12

00

nnn

nnn

jbac

jbac

ac


Tiwari 26


2/

2/

00 )(

1

2

T

Tdttf

T

ac

)(2

1nnn jbac

2/

2/ 0

2/

2/ 0 sin)(cos)(1 T

T

T

Ttdtntfjtdtntf

T

2/

2/ 00 )sin)(cos(1 T

Tdttnjtntf

T

2/

2/

0)(1 T

T

tjn dtetfT

2/

2/

0)(1

)(2

1 T

T

tjnnnn dtetf

Tjbac )(

2

1

)(2

12

00

nnn

nnn

jbac

jbac

ac


Tiwari 27


n

tjnnectf 0)(

dtetfT

cT

T

tjnn

2/

2/

0)(1 )(

2

1

)(2

12

00

nnn

nnn

jbac

jbac

ac

If f(t) is real, *

nn cc

nn jnnn

jnn ecccecc

|| ,|| *

22

2

1|||| nnnn bacc

n

nn a

b1tan

,3,2,1 n

00 2

1ac


Tiwari 28

Complex Frequency Spectra

nn jnnn

jnn ecccecc

|| ,|| *

22

2

1|||| nnnn bacc

n

nn a

b1tan ,3,2,1 n

00 2

1ac |cn|

amplitudespectrum

n

phasespectrum


Tiwari 29

Example

2

T

2

T TT

2

d

t

f(t)A

2

d

dteT

Ac

d

d

tjnn

2/

2/

0

2/

2/0

01

d

d

tjnejnT

A

2/

0

2/

0

0011 djndjn ejn

ejnT

A

)2/sin2(1

00

dnjjnT

A

2/sin1

002

1dn

nT

A

TdnT

dn

T

Adsin


Tiwari 30

TdnT

dn

T

Adcn

sin

82

5

1

T ,

4

1 ,

20

1

0

T

dTd

Example

40 80 120-40 0-120 -80

A/5

50 100 150-50-100-150


Tiwari 31

TdnT

dn

T

Adcn

sin

42

5

1

T ,

2

1 ,

20

1

0

T

dTd

Example

40 80 120-40 0-120 -80

A/10

100 200 300-100-200-300


Tiwari 32

Example

dteT

Ac

d tjnn

0

0

d

tjnejnT

A

00

01

00

110

jne

jnT

A djn

)1(1

0

0

djnejnT

A

2/0

sindjne

TdnT

dn

T

Ad

TT d

t

f(t)

A

0

)(1 2/2/2/

0

000 djndjndjn eeejnT

A


Tiwari 33

Fourier SeriesImpulse Train


Tiwari 34

Dirac Delta Function

0

00)(

t

tt and 1)(

dtt

0 t Also called unit impulse function.


Tiwari 35

Property

)0()()(

dttt

)0()()0()0()()()(

dttdttdttt

(t): Test Function


Tiwari 36

Impulse Train

0 tT 2T 3TT2T3T

n

T nTtt )()(


Tiwari 37

Fourier Series of the Impulse Train

n

T nTtt )()(T

dttT

aT

T T

2)(

2 2/

2/0

Tdttnt

Ta

T

T Tn

2)cos()(

2 2/

2/ 0 0)sin()(

2 2/

2/ 0 dttntT

bT

T Tn

n

T tnTT

t 0cos21

)(


Tiwari 38

Complex FormFourier Series of the Impulse Train

Tdtt

T

ac

T

T T

1)(

1

2

2/

2/

00

Tdtet

Tc

T

T

tjnTn

1)(

1 2/

2/

0

n

tjnT e

Tt 0

1)(

n

T nTtt )()(


Tiwari 39

Fourier SeriesAnalysis of

Periodic Waveforms


Tiwari 40

Waveform Symmetry

• Even Functions

• Odd Functions

)()( tftf

)()( tftf 04/11/2023


41

Decomposition

• Any function f(t) can be expressed as the sum of an even function fe(t) and an odd function fo(t).

)()()( tftftf oe

)]()([)( 21 tftftfe

)]()([)( 21 tftftfo

Even Part

Odd Part


Tiwari 42

Example

00

0)(

t

tetf

t

Even Part

Odd Part

0

0)(

21

21

te

tetf

t

t

e

0

0)(

21

21

te

tetf

t

t

o


Tiwari 43

Half-Wave Symmetry

)()( Ttftf and 2/)( Ttftf

TT/2T/2


Tiwari 44

Quarter-Wave Symmetry

Even Quarter-Wave Symmetry

TT/2T/2

Odd Quarter-Wave Symmetry

T

T/2T/2


Tiwari 45

Hidden Symmetry

• The following is a asymmetry periodic function:

Adding a constant to get symmetry property.

A

TT

A/2

A/2

TT


Tiwari 46

Fourier Coefficients of Symmetrical Waveforms

• The use of symmetry properties simplifies the calculation of Fourier coefficients.– Even Functions– Odd Functions– Half-Wave– Even Quarter-Wave– Odd Quarter-Wave


Tiwari 47

Fourier Coefficients of Even Functions

)()( tftf

tnaa

tfn

n 01

0 cos2

)(

2/

0 0 )cos()(4 T

n dttntfT

a


Tiwari 48

Fourier Coefficients of Even Functions

)()( tftf

tnbtfn

n 01

sin)(

2/

0 0 )sin()(4 T

n dttntfT

b


Tiwari 49

Fourier Coefficients for Half-Wave Symmetry

)()( Ttftf and 2/)( Ttftf

TT/2T/2

The Fourier series contains only odd harmonics.The Fourier series contains only odd harmonics.


Tiwari 50

Fourier Coefficients for Half-Wave Symmetry

)()( Ttftf and 2/)( Ttftf )sincos()(

100

n

nn tnbtnatf

odd for )cos()(4

even for 02/

0 0 ndttntfT

na T

n

odd for )sin()(4

even for 02/

0 0 ndttntfT

nb T

n


Tiwari 51

Fourier Coefficients forEven Quarter-Wave Symmetry

TT/2T/2

])12cos[()( 01

12 tnatfn

n

4/

0 012 ])12cos[()(8 T

n dttntfT

a04/11/2023


52

Fourier Transform and ApplicationsBy Njegos Nincic

Fourier04/11/2023


53

Overview• Transforms

– Mathematical Introduction• Fourier Transform

– Time-Space Domain and Frequency Domain– Discret Fourier Transform


Tiwari 54

Transforms

• Transform:– In mathematics, a function that results when a

given function is multiplied by a so-called kernel function, and the product is integrated between suitable limits. (Britannica)

• Can be thought of as a substitution


Tiwari 55

Transforms

• Example of a substitution:• Original equation: x + 4x² – 8 = 0• Familiar form: ax² + bx + c = 0• Let: y = x²• Solve for y• x = ±√y

4


Tiwari 56

Fourier Transform

• Property of transforms:– They convert a function from one domain to

another with no loss of information• Fourier Transform:

converts a function from the time (or spatial) domain to the frequency domain


Tiwari 57

Time Domain and Frequency Domain

• Time Domain:– Tells us how properties (air pressure in a sound function,

for example) change over time:

• Amplitude = 100• Frequency = number of cycles in one second = 200 Hz


Tiwari 58


• Frequency domain:– Tells us how properties (amplitudes) change over

frequencies:


Tiwari 59

Time Domain and Frequency Domain• Example:

– Human ears do not hear wave-like oscilations, but constant tone

• Often it is easier to work in the frequency domain


Tiwari 60


• In 1807, Jean Baptiste Joseph Fourier showed that any periodic signal could be represented

by a series of sinusoidal functions

In picture: the composition of the first two functions gives the bottom one04/11/2023prepared by Arun Kumar & Shivendra

Tiwari 61



Tiwari 62

Fourier Transform

• Because of the property:

• Fourier Transform takes us to the frequency domain:


Tiwari 63

Fourier Series

Half-Range Expansions


Tiwari 64

Non-Periodic Function Representation

• A non-periodic function f(t) defined over (0, ) can be expanded into a Fourier series which is defined only in the interval (0, ).


Tiwari 65

Without Considering Symmetry


T


Tiwari 66

Expansion Into Even Symmetry


T=2


Tiwari 67

Expansion Into Odd Symmetry


T=2


Tiwari 68

Expansion Into Half-Wave Symmetry


T=2


Tiwari 69

Expansion Into Even Quarter-Wave Symmetry


T/2=2

T=4


Tiwari 70

Expansion Into Odd Quarter-Wave Symmetry


T/2=2 T=4


Tiwari 71

What is a System?

• (DEF) System : A system is formally defined as an entity that manipulates one or more signals to accomplish a function, thereby yielding new signals.

system output signal

input signal


Tiwari 72

Some Interesting Systems

• Communication system• Control systems• Remote sensing system• Biomedical system(biomedical signal

processing)• Auditory system


Tiwari 73


• Communication system


Tiwari 74

http://www.handphone.com/dsub.htm?hit=9&name=SPH-V4400&code=6


• Control systems


Tiwari 75


Papero04/11/2023


76


• Remote sensing system

Perspectival view of Mount Shasta (California), derived from a pair of stereo radar images acquired from orbit with the shuttle Imaging Radar

(SIR-B). (Courtesy of Jet Propulsion Laboratory.)04/11/2023


77


• Biomedical system(biomedical signal processing)


Tiwari 78


• Auditory system


Tiwari 79

Classification of Signals

• Continuous and discrete-time signals• Continuous and discrete-valued signals• Even and odd signals• Periodic signals, non-periodic signals• Deterministic signals, random signals• Causal and anticausal signals• Right-handed and left-handed signals• Finite and infinite length


Tiwari 80

Continuous and discrete-time signals

• Continuous signal - It is defined for all time t : x(t)• Discrete-time signal - It is defined only at discrete instants of time :

x[n]=x(nT)


Tiwari 81

Continuous and Discrete valued singals

• CV corresponds to a continuous y-axis• DV corresponds to a discrete y-axis

Digital signal


Tiwari 82

Even and odd signals

• Even signals : x(-t)=x(t)• Odd signals : x(-t)=-x(t)• Even and odd signal decomposition

xe(t)= 1/2·(x(t)+x(-t)) xo(t)= 1/2·(x(t)-x(-t))


Tiwari 83


Tiwari 84

Periodic signals, non-periodic signals

• Periodic signals - A function that satisfies the condition x(t)=x(t+T) for all t - Fundamental frequency : f=1/T - Angular frequency : = 2/T

• Non-periodic signals


Tiwari 85

Deterministic signals, random signals

Deterministic signals -There is no uncertainty with respect to its value at any

time. (ex) sin(3t)

Random signals - There is uncertainty before its actual occurrence.


Tiwari 86

Causal and anticausal Signals

• Causal signals : zero for all negative time• Anticausal signals : zero for all positive time• Noncausal : nozero values in both positive

and negative time

causal signal

anticausal signal

noncausal signal


Tiwari 87

Right-handed and left-handed Signals

• Right-handed and left handed-signal : zero between a given variable and positive or negative infinity


Tiwari 88

Finite and infinite length

• Finite-length signal : nonzero over a finite interval tmin< t< tmax

• Infinite-length singal : nonzero over all real numbers


Tiwari 89

Unit-2Modulation Techniques


Tiwari 90

Amplitude Modulation

prepared by Arun Kumar & Shivendra Tiwari 04/11/2023 91


Content

• What is Modulation• Amplitude Modulation (AM)• Demodulation of AM signals

04/11/2023 92


What is Modulation

• Modulation– In the modulation process, some characteristic of a high-

frequency carrier signal (bandpass), is changed according to the instantaneous amplitude of the information (baseband) signal.

• Why Modulation– Suitable for signal transmission (distance…etc)– Multiple signals transmitted on the same channel– Capacitive or inductive devices require high frequency AC

input (carrier) to operate.– Stability and noise rejection

04/11/2023 93


About Modulation

• Application Examples– broadcasting of both audio and

video signals. – Mobile radio communications, such

as cell phone.

• Basic Modulation Types– Amplitude Modulation: changes the amplitude.– Frequency Modulation: changes the frequency.– Phase Modulation: changes the phase.

04/11/2023 94

04/11/2023 prepared by Arun Kumar & Shivendra Tiwari

95

AM Modulation/Demodulation

Modulator Demodulator

Baseband Signalwith frequency

fm(Modulating Signal)

Bandpass Signalwith frequency

fc(Modulated Signal)

Channel

Original Signalwith frequency

fm

Source Sink

fc >> fm Voice: 300-3400Hz GSM Cell phone: 900/1800MHz


96


• The amplitude of high-carrier signal is varied according to the instantaneous amplitude of the modulating message signal m(t).

Carrier Signal: or

Modulating Message Signal: or

The AM Signal:

cos(2 ) cos( )

( ) : cos(2 ) cos( )

( ) [ ( )]cos(2 )

c c

m m

AM c c

f t t

m t f t t

s t A m t f t


* AM Signal Math Expression*• Mathematical expression for AM: time domain

• expanding this produces:

• In the frequency domain this gives:

( ) (1 cos )cosAM m cS t k t t

( ) cos cos cosc cAM mS t t k t t

)cos()cos(coscos :using 21 BABABA

2 2( ) cos cos( ) cos( )c c ck k

AM m mS t t t t

frequency

k/2k/2Carrier, A=1.

upper sideband

lower sideband

Amplitude

fcfc-fm fc+fm

04/11/2023 97


AM Power Frequency Spectrum

• AM Power frequency spectrum obtained by squaring the amplitude:

• Total power for AM:

.

2 22

2

4 4

12

k kA

k

freq

k2/4k2/4

Carrier, A2=12 = 1Power

fcfc-fm fc+fm

04/11/2023 98



• The AM signal is generated using a multiplier.• All info is carried in the amplitude of the

carrier, AM carrier signal has time-varying envelope.

• In frequency domain the AM waveform are the lower-side frequency/band (fc - fm), the carrier frequency fc, the upper-side frequency/band (fc + fm).

04/11/2023 99


AM Modulation – Example

• The information signal is usually not a single frequency but a range of frequencies (band). For example, frequencies from 20Hz to 15KHz. If we use a carrier of 1.4MHz, what will be the AM spectrum?

• In frequency domain the AM waveform are the lower-side frequency/band (fc - fm), the carrier frequency fc, the upper-side frequency/band (fc + fm). Bandwidth: 2x(25K-20)Hz.

frequency

1.4 MHz

1,385,000Hz to 1,399,980Hz

1,400,020Hz to 1,415,000Hz

fc

04/11/2023 100


101

Modulation Index of AM Signal

m

c

Ak

A

)2cos()( tfAtm mm Carrier Signal: cos(2 ) DC: c Cf t A

Modulated Signal:

( ) [ cos(2 )]cos(2 )

[1 cos(2 )]cos(2 )AM c m m c

c m c

S t A A f t f t

A k f t f t

For a sinusoidal message signal

Modulation Index is defined as:

Modulation index k is a measure of the extent to which a carrier voltage is varied by the modulating signal. When k=0 no modulation, when k=1 100% modulation, when k>1 over modulation.



04/11/2023 102



04/11/2023 103



04/11/2023 104


High Percentage Modulation• It is important to use as high percentage of modulation as

possible (k=1) while ensuring that over modulation (k>1) does not occur.

• The sidebands contain the information and have maximum power at 100% modulation.

• Useful equation

Pt = Pc(1 + k2/2)

Pt =Total transmitted power (sidebands and carrier)Pc = Carrier power

04/11/2023 105


Demodulation of AM Signals

Demodulation extracting the baseband message from the carrier.

• There are 2 main methods of AM Demodulation:

• Envelope or non-coherent detection or demodulation.• Synchronised or coherent demodulation.

04/11/2023 106


107

Envelope/Diode AM Detector

If the modulation depth is > 1, the distortion below occurs

K>1


Synchronous or Coherent Demodulation

This is relatively more complex and more expensive. The Local Oscillator (LO) must be synchronised or coherent, i.e. at the same frequency and in phase with the carrier in the AM input signal.

04/11/2023 108



If the AM input contains carrier frequency, the LO or synchronous carrier may be derived from the AM input.

04/11/2023 109



If we assume zero path delay between the modulator and demodulator, then the ideal LO signal is cos(ct).

04/11/2023 110

Unit-3Angle Modulation


Tiwari 111

Angle Modulation

• Introduction

• Types of Angle Modulation – FM & PM

• Definition – FM & PM

• Signal Representation of FM & PM

• Generation of PM using FM

• Generation of FM using PM


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Angle Modulation

Consider again the general carrier cccc φ+tωV=tv cos

cc φ+tω represents the angle of the carrier.

There are two ways of varying the angle of the carrier.

a) By varying the frequency, c – Frequency Modulation.

b) By varying the phase, c – Phase Modulation


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Phase Modulation• One of the properties of a sinusoidal wave is its phase, the

offset from a reference time at which the sine wave begins.

• We use the term phase shift to characterize such changes.

• If phase changes after cycle k, the next sinusoidal wave will start slightly later than the time at which cycle k completes.


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Introduction to Angle Modulation

• High degree of noise immunity by bandwidth expansion.

• They are widely used in high-fidelity music broadcasting.

• They are of constant envelope, which is beneficial when amplified by nonlinear amplifiers.04/11/2023


115

Introduction to Angle Modulation


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FM and PM


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Types of FM

• Basically 2 types of FM:

– NBFM (Narrow Band Frequency Modulation)

– WBFM (Wide Band Frequency Modulation)


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Generation of FM• Mainly there are 2 methods to generate FM Signal.

They are:

1. Direct Method1. Hartley Oscillator2. Basic Reactance Modulator

2. Indirect Method1. Amstrong Modulator (Using NB Phase Modulator)2. Frequency Multiplier


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Generation of FM• Basically two methods:

1. Direct method• Build a voltage controlled oscillator (VCO) where the

frequency is varied in response to an applied modulating voltage by using a voltage-variable capacitor

• The main difficulty is that it is very difficult to maintain the stability of the carrier frequency of the VCO when used to generate wide-band FM.

2. Indirect method• Use a narrow-band FM modulator followed by frequency

multiplier and mixer for up conversion.• Allows to decouple the problem of carrier frequency stability

from the FM modulation.04/11/2023


120

Edwin Howard Armstrong (1890 - †1954)

Edwin Howard Armstrong received his engineering degree in 1913 at the Columbia University.

He was the inventor of the following basic electronic circuits underlying all modern radio, radar, and television:

Regenerative Circuit (1912) Superheterodyne Circuit (1918) Superregenerative Circuit (1922) FM System (1933).


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Indirect Method – Amstrong Modulator


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Indirect Method


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Narrow Band Phase Modulator (NBPM)


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Detection of FM

• Types of FM Detectors:

1. RL Discriminator2. Tuned FM Discriminator3. Balanced Slope Detector4. Centre Tuned Discriminator / Phase Discriminator /

Foster – Seeley Discriminator5. Phase Locked Loop (PLL) Demodulator6. Ratio Detector


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Unit-4Radio Transmitters and Receiver


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Transmitters and Receivers• Generalized Transmitters

• AM PM Generation

• Inphase and Quadrature Generation

• Superheterodyne Receiver

• Frequency Division Multiplexing


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Generalized Transmitters

Re cos

cos sin

Where

cj tc

c c

j t

v t g t e R t t t

v t x t t y t t

g t R t e x t jy t

Any type of modulated signal can be represented by

The complex envelope g(t) is a function of the modulating signal m(t)

TransmitterModulating

signalModulated

signal

Example:

( )

Type of Modulation g(m)

AM : [1 ( )]

PM : p

c

jD m t

c

A m t

A e


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R(t) and θ(t) are functions of the modulating signal m(t) as given in TABLE 4.1

• Two canonical forms for the generalized transmitter:

cos cv t R t t t

1. AM- PM Generation Technique: Envelope and phase functions are generated to modulate the carrier as

Generalized transmitter using the AM–PM generation technique.


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x(t) and y(t) are functions of the modulating signal m(t) as given in TABLE 4.1

ttyttxtv cc sincos

2. Quadrature Generation Technique: Inphase and quadrature signals are generated to modulate the carrier as

Fig. 4–28 Generalized transmitter using the quadrature generation technique.


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IQ (In-phase and Quadrature-phase) Detector


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Generalized Receivers

Receivers

Tuned Radio Frequency (TRF) Receiver:Composed of RF amplifiers and detectors. No frequency conversionIt is not often used.Difficult to design tunable RF stages.Difficult to obtain high gain RF amplifiers

Superheterodyne Receiver:Downconvert RF signal to lower IF frequencyMain amplifixcation takes place at IF

Two types of receivers:


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Tuned Radio Frequency (TRF) Receivers

ActiveTuningCircuit

DetectorCircuit

LocalOscillator

BandpassFilter

BasebandAudio Amp

Composed of RF amplifiers and detectors. No frequency conversion. It is not often used. Difficult to design tunable RF stages. Difficult to obtain high gain RF amplifiers


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Heterodyning(Upconversion/Downconversion)

SubsequentProcessing(common)

AllIncomingFrequencies

FixedIntermediateFrequency

Heterodyning


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Superheterodyne Receivers

Superheterodyne Receiver Diagram04/11/2023prepared by Arun Kumar & Shivendra

Tiwari

135

Superheterodyne Receiver


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Superheterodyne Receivers The RF and IF frequency responses H1(f) and H2(f) are important in providing

the required reception characteristics.


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fI

F

fIF

RF Response

IF Response


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Superheterodyne Receiver Frequencies


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Superheterodyne Receiver Frequencies


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Frequency Conversion Process


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Image frequency not a problem.

Image Frequencies

Image frequency is also received


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AM Radio Receiver


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Superheterodyne Receiver Typical Signal Levels


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Double-conversion block diagram.


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Unit-5Noise


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Noise is the Undesirable portion of an electrical signal that interferes with the intelligence

04/11/2023 148


Why is it important to study the effects of Noise?

a) Today’s telecom networks handle enormous volume of datab) The switching equipment needs to handle high traffic volumes as wellc) our ability to recover the required data without error is inversely

proportional to the magnitude of noise

What steps are taken to minimize the effects of noise?

d) Special encoding and decoding techniques used to optimize the recovery of the signal

b) Transmission medium is chosen based on the bandwidth, end to end reliability requirements, anticipated surrounding noise levels and the distance to destination

c) Elaborate error detection and correction mechanisms utilized in the communications systems

04/11/2023 149


The decibel (abbreviated dB) is the unit used to measure the intensity of a sound.! The smallest audible sound (near total silence) is 0 dB. A sound 10 times more powerful is 10 dB. A sound 1,000 times more powerful than near total silence is 30 dB.

Here are some common sounds and their decibel ratings:

Normal conversation - 60 dB A rock concert - 120 dB

It takes approximate 4 hours of exposure to a 120-dB sound to cause damage to your ears, however 140-dB sound can result in an immediate damage

04/11/2023 150


Signal to Noise ratio It is a ratio of signal power to Noise power at some point in a Telecom system expressed in decibels (dB)

It is typically measured at the receiving end of the communications system BEFORE the detection of signal.

SNR = 10 Log (Signal power/ Noise power) dB

SNR = 10 Log (Vs/VN)2 = 20 Log (Vs/VN)

04/11/2023 151


1) The noise power at the output of receiver’s IF stage is measured at 45 µW. With receiver tuned to test signal, output power increases to 3.58 mW. Compute the SNR

SNR = 10 Log (Signal power/ Noise power) dB = 10 Log (3.58 mW/ 45 µW) = 19 dB

2) A 1 kHZ test tone measured with an oscilloscope at the input of receiver’s FM detector stage. Its peak to peak voltage is 3V. With test tone at transmitter turned off, the noise at same test point is measure with an rms voltmeter. Its value is 640 mV. Compute SNR in dB.

SNR = 20 Log (Vs/Vn) = 20 Log ((.707 x Vp-p/2)/Vn)= 20 Log (1.06V/640 mV)= 4.39 dB

04/11/2023 152


Noise Factor (F) It is a measure of How Noisy A Device Is

Noise figure (NF) = Noise factor expressed in dB

F = (Si/Ni) / (So/No)

NF = 10 Log F

04/11/2023 153


Noise Types

• Atmospheric and Extraterrestrial noise

• Gaussian Noise• Crosstalk• Impulse Noise

04/11/2023 154


Atmospheric and Extraterrestrial Noise

• Lightning: The static discharge generates a wide range of frequencies

• Solar Noise: Ionised gases of SUN produce a wide range of frequencies as well.

• Cosmic Noise: Distant stars radiate intense level of noise at frequencies that penetrate the earth’s atmosphere.

04/11/2023 155


Gaussian Noise: The cumulative effect of all random noise generated over a period of time (it includes all frequencies).

Thermal Noise: generated by random motion of free electrons and molecular vibrations in resistive components. The power associated with thermal noise is proportional to both temperature and bandwidth

Pn = K x T x BW

K = Boltzmann’s constant 1.38x10 -23

T = Absolute temperature of deviceBW = Circuit bandwidth

04/11/2023 156


Shot Noise Results from the random arrival rate of discrete current carriers at the output electrodes of semiconductor and vaccum tube devices.

Noise current associated with shot noise can be computed as

In = √ 2qIf

In = Shot noise current in rmsq = charge of an electronI = DC current flowing through the devicef = system bandwidth (Hz)

04/11/2023 157


Crosstalk: electrical noise or interference caused by inductive and capacitive coupling of signals from adjacent channels

In LANs, the crosstalk noise has greater effect on system Performance than any other types of noise

Problem remedied by using UTP or STP. By twisting the cable pairs together, the EMF surrounding the wires cancel out eachother.

04/11/2023 158


Near end crosstalk: Occurs at transmitting station when strong signals radiating from transmitting pair of wires are coupled in to adjacent weak signals traveling in opposite direction

Far end crosstalk: Occurs at the far end receiver as a result of adjacent signals traveling in the same direction

04/11/2023 159


Minimizing crosstalk in telecom systems

1) Using twisted pair of wires2) Use of shielding to prevent signals from radiating in to other conductors3) Transmitted and received signals over long distance are physically separated and shielded4) Differential amplifiers and receivers are used to reject common-mode signals5) Balanced transformers are used with twisted pair media to cancel crosstalk

signals coupled equally in both lines6) Maximum channels used within a cable are limited to a certain value

04/11/2023 160


Impulse Noise: Noise consisting of sudden bursts of irregularly shape pulses and lasting for a few Microseconds to several

hundred milliseconds.

What causes Impulse noise?

a) Electromechanical switching relays at the C.O. b) Electrical motors and appliances, ignition systemsc) Lightning

04/11/2023 161

Noise factor

• IEEE Standards: “The noise factor, at a specified input frequency, is defined as the ratio of (1) the total noise power per unit bandwidth available at the output port when noise temperature of the input termination is standard (290 K) to (2) that portion of (1) engendered at the input frequency by the input termination.”

sourcetoduenoiseoutputavailable

powernoiseoutputavailableF


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Noise factor (cont.)

• It is a measure of the degradation of SNR due to the noise added -

• Implies that SNR gets worse as we process the signal

• Spot noise factor• The answer is the bandwidth7/1/2013163

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i

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oi

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NfG

N

S

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N

S

SN

SNfGNF

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i

SNR

SNRF

kT

NF

a1


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Noise factor (cont.)

• Quantitative measure of receiver performance wrt noise for a given bandwidth

• Noise figure– Typically 8-10 db for modern receivers

• Multistage (cascaded) system

)log(10 FNF

12121

3

1

21

1...

11

n

n

GGG

F

GG

F

G

FFF

04/11/2023


164

Thank you


Tiwari 165

ppt of analog communication

Engineering