Analog Communication

1

Analog Communication

Biyani's Think Tank Concept based notes

Analog Communication (B.Tech Vth Sem, EC)

Mukul Sharma Asst. Professor (EC) Deptt. of Engineering Biyani International Institute of Engineering and Technology

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Published by :

Think Tanks Biyani Group of Colleges

Concept & Copyright :

Biyani Shikshan Samiti Sector-3, Vidhyadhar Nagar, Jaipur-302 023 (Rajasthan) Ph : 0141-2338371, 2338591-95 Fax : 0141-2338007 E-mail : [email protected] Website :www.gurukpo.com; www.biyanicolleges.org

Edition : 2011

While every effort is taken to avoid errors or omissions in this Publication, any mistake or omission that may have crept in is not intentional. It may be taken note of that neither the publisher nor the author will be responsible for any damage or loss of any kind arising to anyone in any manner on account of such errors and omissions.

Leaser Type Setted by: Biyani College Printing Department


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Preface

I

am glad to present this book, especially designed to serve the needs of the students. The

book has been written keeping in mind the general weakness in understanding the fundamental concepts of the topics. The book is self-explanatory and adopts the “Teach Yourself” style. It is based on question-answer pattern. The language of book is quite easy and understandable based on scientific approach. Any further improvement in the contents of the book by making corrections, omission and inclusion is keen to be achieved based on suggestions from the readers for which the author shall be obliged. I acknowledge special thanks to Mr. Rajeev Biyani, Chairman & Dr. Sanjay Biyani, Director (Acad.) Biyani Group of Colleges, who are the backbones and main concept provider and also have been constant source of motivation throughout this Endeavour. They played an active role in coordinating the various stages of this Endeavour and spearheaded the publishing work. I look forward to receiving valuable suggestions from professors of various educational institutions, other faculty members and students for improvement of the quality of the book. The reader may feel free to send in their comments and suggestions to the under mentioned address. Mukul Sharma



Content Name of Topic

S.No 1

Amplitude Modulation

2

Frequency Modulation

3

Noise

4

Noise in AM, FM


4

5


Amplitude Modulation Q.1 Definite of Communication:Ans. It is the Basic process of exchange information the communication process essentially consists of three basic building blocks. Transmitter

Channel

Receiver

Transmitter:- A transmitter is physical system that transmit information. Receiver:- It is physical system that receiver the information. Channel:- I is the medium through which information takes place depending upon the type of channel used for information exchange, there are two types of communication. a>

Line or Wire Communication:- In this type of communication a physical channel is created between transmitter and receiver through copper wires, coaxial cables, optical fiber cable etc. before the information exchange can take place. Ex.:- basic telephone system, telegraphy etc. b> Radio or Wireless Communication:- In this type of communication, there is no physical connection between transmitter & receiver, the space is used as a channel for information exchange. Ex.:- Mobile Communication Satellite Communication Wireless phone Broad Casting



6

Modulation:Modulation is process of super imposing the information contents of a baseband modulating signed on a high freq carried signed by altering its chartn. Ex.:amplitude, phase, freq. C (t) =

AC

Amplitude 

Q.2

Phase = WCt

W Ct

Freq

Modulation process translates a low freq. Baseband signal into a high freq. Band pass signed.

Explain Need of modulation:-

Ans. (1) Avoid mixing of signal

-3

0

0

3 KHz

f

3 kHZ

997

1003 1004 Grass Band


1110

7


0

3kHZ

The modulation process translates different baseband signals at different carries frequency so that spectrum overlap does not take place & mixing of signal can be avoided. Allow multiplexing of signal:Multiplexing means transmission of two or more signal simultaneously over same channel once the different baseband signal are translate at different frequency now they can be simultaneously transmitted over the same channel without any loss of information. Reduce height of Antenna:(i)

= c/ Practice antenna height = λ/4 1

(ii)

= 15 KHz =

= 20,000 m

=

= 5 km

ƒ = 15 MHz λ=

= 20 m

=5m the high of antenna required for transmission & reception of Radio wave in Radio transmission is a fusi of frequency used the min. height of antenna is given a λ/4 from the above two examples it is clear that the signal should be



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transmitted at highest frequency to achieve practical height of antenna Increase Range of Communication:At low frequency, the radiation is poor & signal gets highly attenuated directly and distance modulation effectively increase the frequency of signal to be radiated and thus increase the distance over which signal can be transmitted faithfully Improves Quality of Reception:The signal communication using modulation techniques such as FM & PCM reduces the effect of noise to great extent. Reduction in noise improves quality of Reception. Q. 3

Specify three Basic Properties:-

Ans. Three basic operation are performed on a signal x (t) 1

1

(i)

a>

0 X (E) – 1 0 Time Shifting:Y (t) =

: :

3 E - 1 << t << 3 otherwise

x (t + )

Time delay:If < 0 y (t) = x (t -3)



9

1

2

b>

6

t

Time advance:if > 0 y (t) = x ( t + 4) 1

-5

-1

0

(ii) Time Reversal:y (t) = x (t) y (t)

-3

1

(iii) Time Sealing:-

a>

y (t) = x ( t) Time compression:-

>1

y (t) = x (2 t)



-½

3/2

t

b> Time expansion:0< <1 y (t) = x (t/2)

-1

3

-2

6

Unit impulse Signal:- [S (t)] S (t) = 1 ; 0 :

t= 0 t

0

1

t =0

t


10

11


Q.4 Explain three Properties of impulse:Ans. 1> S( = S (t) 2>

Sealing Property:-

Product Property:x (t) – (t) = x (o). (t) x (t). (t-to) = x (to). (t-to) x (t) x (o)

0

to

t=0 3>

t=t

Shifting Property:= x (t₀)

cos ot Cos ₀t =

[ (

+

]

+



12

j ₀t e 2

( - ₀) ( - ₀)

2 (

Q. 5 Explain Amplitude Modulation and derive equation for A.M Ans. In A.M. the amplit6ude of high frequency carries signal is varied in accordance with instananes value of Base band modulating signal keeping frequency & phase carst. Edn. for A.M.:m (t) = any modulating signal with max. Frequency n C (t) = Ac os ₀t XAM (t) = A os ₀t A = (Ac + M (E)) (E) XAM = [Ac + M (E)] os ₀t modulated signal (E) XAM = Ac os ₀t + m(t) os ₀t Let m (t) = Am os ₀t C (t) = Ac os ₀t A = Ac + Am os nt (t) XAM = [Ac + Am os ₀t =

Ac os

c

[1+

os nt]

= m = modulation index

XAM(t) = Ac os ct + MAc os ct os nt [ 2 os A os B = os (A+B) + os (A-B)]


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XAM (t) = Ac os ct + Carries

Q.6

os ( c+ n) + USB

os (

c

n)

LSB

Explain time domain and frequency domain representation of A.M

Ans. Time domain Representation for AM:-

Am

m (t)

t

- Am

Ac C (t) -Ac



Frequency Domain Representation:AC os ₀t + m (t)

XAM (E) = XAM (

)

=

Ac [ ( - c) +

+ [M ( – [ os ₀t =

)+

[ ( - ₀) +

os ₀t

( + )]

( +

c)]

( + ₀)]

Convolution in time domain equal multiplication in frequency domain x (t) – y (t)

x( )Y( )

x (t) y (t)

[X, ( ) * Y( )]

(t)

Unit impulse signal:-

1

(t) = 1 : t = 0 0 : otherwise t =0 Properties of impulse funn.:1>

Scaling Property:-


14


15

(∝t) =

ii>

Product Property:x (t) ,

(t)

=

x (0) .

(t)

x (t) . (t-t₀) =

x (t₀)

(t t₀)

x (t)

x (t₀) x (0)

x (0)

iii)

Shifting Property:x (t). (t)

dt

x (t). (t-t₀) dt

=

=

x (t

x (t M( )



-

om

- ( c+ n) - c

16

m

-( c- n)

the transmitted AM signal contains three components that is correct, USB, LSB. the intimation simultaneously by upper and lower side band, the caries does not contain any information. the transmission between of Am signal is m in red/see

Q. 7 Derive equation for Power Relation and current in Am Ans. Pt

=

+

=

+

Pc

=

PSB

=

Pt

= Pt

+

=

-

= PC

PC + =

PC

Current Relation in AM:-


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Pt =

P Pn I t²

= = ;

I t² =

IC² (

I²R I² PC = It²

It = IC

Transmission Efficiency (modulation efficiency):It gives the % of useful power in the total transmitted power & given by ratio of total S.B. power to the total TA power. =

x 100%

η =

η=

z 100%

Concept of modulation index:-

It gives the depth to which modulation has occurred.

-

For m=0 of represent no modulation. For m=1 maximum modulation has occurred. For m>1 overlapping of envelop take place which results in envelop distortion this condition is known as “over modulation” & should always be avoided. m=1 ;

Am = A c



Amin

;

Am – Ac = 0 m =1

t


18

19


M>1

t

(i) Pt = Pc For m = 1 Pt = 1.5 Pc

(ii) η =

x 100% =

= 33.33%

Simultaneous modulation by several line work:-

M (t) C (t) A

M1 (t) = Am1 s m1t M2 (t) = Am2 m2t m (t) = m1 (t) + m2(t) = Am1 s m1t + Am2 s m1t = Ac s m1t = Ac + Am1 s m1t + Am2 m2t

XAM(t) = [Ac + Am1 s m1t + Am2 s m1t] s

ct

XAM (t) = Ac M1 = XAM (t) = Ac s

,

m2 =

ct + M1 Ac s ct. s

mt + m2 Ac s ct +


s mt


XAM (t) = Ac s ct +

s( c+

causes s( c-

+

20

m1)t

USB m1)t

s( c+

LSB

m₂)t

USB₂

s ( c - m₂)t LSB₂ Generalized ResultWhen a high frequency signal is simultaneously modulated by several line waves of maximum frequency m1, m₂, m3 ……………… then a> for each addition of modulating signal a pair of sideband getting added in the resultant A.M. signal that is why amplitude modulation in also known as linear modulation. b> The transmission between for resu….. A.M signed given by B.W. = 2 max [ m1, m₂, m3 …..] Power Relation:Pt

=

Pt

=

Pc

=

+ +

+

+

+

+


21


Ps.B1

=

= Pc.

Ps.B2

=

= Pc.

Pt

= Pc

Pt

Mr =

= Pc

+…

DSB-SC (Double side band suppress carries) Transmission of full A.M signal is not advisable because a> Since carries { } also transmitted that does not contain any information. b> For m=1, 2/3 power appears in the carries which is complete wastage So instead of transmitting full A.M signal the carries is suppressed before transmission such type of modulation known as DSB-SC modulation.

m (t)

y (t)

c (t) y (t) = m (t). C (t) = m (t). Ac os ct y( )=

[M ( -

c)

+ M ( + c)]



1

-

- ( c+

m)

- c

m

- ( c- m)

22

M( )

0

m

c- m

Ring Modulated:Diagram:-


c

c+ m

23


(i)

Positive half cycle

During positive half cycle of carries signed D1 & D2 are on and D3 D4 are ON and D1 & D2 are off but in any case the Net O/P is zero because currents are in opp direction

(ii)

Negative half cycle



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During positive half cycle of carries signed D3& D4are on and D3 D4 are ON and D1 & D2 are off but in any case the Net O/P is zero because currents are in opp direction

m (t) + ve

c (t) +Ve

O/P +Ve

D1 & D2 ON

+ ve

-Ve

- Ve

D3 & D4 ON

- ve

+Ve

-Ve

D1 & D2 ON

- ve

-Ve

+Ve

D3 & D4 ON


25




26

Power saving in DSB-SC modulation :=> Total power saved = Pc %age power saving = =

x 100%

X 100% = 66.67% X 100% = 88.88% SSB-SC (Single Side Band Suppress Carries):In case of DSB-SC modulation, both the side bands are transmitted which contains same information so DSB-SC transmission is further redundant. Instead of transmitting both the SB we can suppress one SB as well to achieve maximum efficiency. Such type of modulation in which are Q.8

Describe DSB-SC (Double Side Band Suppress Carries) and method to modulate and demodulate it

Ans. In case of DSB-SC modulation both the sidebands are transmitted which contains same information so DSB-SC transmission is further redundant. Instead of transmitting both the SB we can suppress one SB as well to achieve maximum efficiency. Such type of modulation in which either upper or lower sideband is transmitted is known as SSB-SC modulation. There are two methods for generation of SSB-SC signal


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(i)

Frequency Discrimination method:It is also known as fitted method m (t) DSB-SC SSB-SC BPF

Signal

Signal

a(t) = Ac os ct

- ( c+ m

- c

- ( c- m)

c- m

c

c+

n

Disadvantage of frequency discrimination methods: In case of frequency discrimination method the band pass filled should be as ideal as possible but ideal filters are not practically possible because they are unstable system so this method can only be used when upper & lower S.B do not meet at caries frequency such as voice signal. (ii) Phase Discrimination method:m (t) y1 (t)

s ct M (t)

O/P

M (t) Hilbert Transformations



28

M (t)

Sin ct

XSSB (t)

=

m (t)

s ct

m (t) = (t) = sin XSSB (t)

= = =

(t) sin

ct

mt mt

os ct mt os ( c- m)t os ( c- m)t

sin

ct.

mt

Disadvantage of phase Discrimination method:- The phase discrimination method is based upon 90° phase shift of the modulating signal but for higher modulation frequency. It is very difficult to generate a phase shift of exact 90° this method can be used only for low modulation frequency up to flow kHz. Power Saving in SSB-SC:Pt = Pt = Total power served = % power saving = =

X 100% X 100%

For m =1 = 5/3 x 100% = 83.33% Demodulation of A.M. Signal-


29


The recovery of the baseband signal, a process which is referred to as demodulation or detection there are two method for detection i. Synchronous detection:In this method a local carries is generated at the receiving and where phase is exactly synchronize with the transmitted carries phase the received signal is multiplied by locally generated carries signal & the product is passes through a low pass filter to detect Original baseband y1 (t)

y (t) LPF

os ct i.

Detection of A.M. signal:XAM (t) = [AC + m (t) ] os ct y1 (t)

=

[AC + m (t)] os²

y1 (t)

=

[AC + m (t)]

y1 (t)

=

y (t)

=

+

m

+

(AC + m (t))

1

-

+

ct

M( )

m


os ct


(2 c+ n)

-2 c

-(2 c- m) - m

m

HLPF(

2 c- m

2 c

30

2 c+ c

)

1

- m

m

When the phases of transmitted locally generated carries are not synchronies we always obtain a distorted signal at O/P of detector & it = 90 y (t) = 0 this condition is known as “Quardature null effect”. (ii)

A synchronous detection:It is also known as “envelop detector or diode detector.”

RD D A.M

C

R


V0(t) => To LPF

31


AC

Let‟s initially assume that the O/P of fixed amplitude. The capacitor charges to the peak positive voltage of carries. -

Detection of DSB-SC SignalXDSB(t) = Ac m(t) os ct y1(t)

=

Ac m(t) os ct

= y1(t)

=

y (t)

=

+

Detection of SSB-SC signal:XSSB(t)

=

m (t)

os ct

(t) sin ct

Y1 (t)

=

m (t)

s²

(t) sin

y1(t)

=

y (t)

=

[1 +

s2

y (t)

ct]

s ct

(t) sin2

y (t) LPF c= m


ct


32

os ( ct+ ) XDSB(t)

= Ac m (t) s ct

y1(t)

= Ac m (t) s

ct + s( ct + )

y1(t)

=

[ s

ct + ) +

y (t)

=

os

if -

os ]

= /2 y(t) = 0 It is necessary to include the resistor R so that the capacitor may discharge If RC is very-very high

SSB-SC (Single Side Band Suppress Carries):In case of DSB-SC modulation both the side bands are transmitted which contains same information so DSB-SC transmission is further redundant Instead of transmitting both the SB we can suppress one SB as well to achieve maximum efficiency such type of modulation in which either upper or lower sideband is transmitted is known as SSB-SC signal. i.

Frequency Discrimination Method:It is also known as fitted method. m (t) DSB-SC BPF


SSB-SC

33


Signal c (t) = Ac

- ( c+ m

- c

Signal

s ct

- ( c- m)

c- m HBPF (

- ( c+ m)

- c

- c

- ( c+ m)

c

c+ m

)

c

c+ m

c- m

c

XSSB(

- ( c+ m)

- c

c


c+ m


34

XSSB(

- ( c+ m) -

c- m

c- m

c

c+ m

USB

Q.9

Explain VSB (Vestigial Side Band) Modulation and its advantage over SSB

Ans. SSB modulation is well suited for transmission of voice because of frequency gap that exist in the spectrum of voice signals between „O‟ & few hundred Hz when the baseband signal contains significant components at extremely low frequency as in case of T.V. picture signal, the upper & lower side band meet at carries frequency this means that use of SSB modulation is in appropriate for


35


transmission of such base band signals. Due to difficulty of isolating one sideband

In VSB modulation one sideband is passed almost completely whereas just a trace or vestige of unwanted sideband is retained specifically the vestige part of unwanted sideband components for the part removed from the desired side band. DSB-SC M (t) Signal C (t) =

DSB Bitta

s (t)

LPF = n

y (t)

s ct Y (t)

S (t)

s ct XDSB(t) S (t)

= =

m (t) s ct [m(t) s ct ] * h (t)

S( )

=

Y1 (t)

=

Y1 ( )

=

[S ( - c) + ( + c)]

Y1 ( )

=

[M ( - c –

[S ( - c) + ( + c)] h ( ) S (t)

s ct c) + M ( - c +


c) H ( - c)


+ [M ( + c – Y( )

=

c) + M ( + c +

36

c) H ( + c)

[M ( ) [H ( - c) + H ( - c)] H ( - c) + H ( + c) = const.

In T.V. transmission the picture signal is VSB modulated & the sound signal is frequency modulated & the total transmission B.W. 7 MHz *+(5.75 MHz for picture signal and 0.25 MHz for sound signal)

A.M. Receiver Q.10

Explain different Function of Receiver To collect the electromagnetic waves transmitted by the transmitters. To select desired signal & reject all other, this is known as “selectivity of the Receiver”. To amplify the selected modulated signal this is known as sensitivity of the receiver. To defect baseband modulating signal from the modulated R.F. signal. To amplify the modulated signal as to operate the loud speaker. AM Band – 540-1650 KHz fm : 5 KHz B.W. : 10 KHz I.F. : 455 KHz ANGLE MODULATION In angle modulation the phase angle of high frequency carries signal is varied in accordance with instantaneous value of modulating signal keeping amplitude const. C (t) c (t)

= =

Ac s ct

ct

= =


37




38

UNIT 2 Q.11 Explain Frequency Modulation and phase modulation and derive equation for it. Ans. In F.M. the frequency of high frequency carries signal is varied in accordance with instantaneous value of modulating signal keeping amplitude const. phase is varied indirectly. Phase Modulation :=> In P.M. the phase is varied directly in accordance with instateous value of modulating signal keeping amplitude const. frequency is varied indirectly. F.M. P.M. n (t) = any arbitrary modulating signal m (t) = any arbitrary modulating with maximum frequency m signal c (t) = A ct c s c (t) = Ac s ct c (t) = ct c (t)= ct C (t) = Ac s c (t) c (t) = Ac s c (t0 XPM (t) = Ac s i (t) XFM (t) = Ac s i (t) i (t) = c (t) – KP m (t) XPM(t) = Ac s [ ct) + KP m (t) i = c + Kf m (t) XPM(t) = Ac s [ ct + KP m (t)] i (t) = i (t) = i (t) =

ct + Kf

AFM(t) = Ac s ( ct + Kf


39


Q.12 Derive Relation between FM & PM signal:Ans. XFM(t) = Ac s [ ct + Kf XPM(t) = Ac s [ ct + KP m (t)] m (t) m (t) FM

PM

Ac Ac s ( ct + Kf Ac s [ ct + KP m (t)] m (t)

PM

FM

Ac s ( ct + Kf Sinusoidal FM m (t) = Am s nt c (t) = Ac s ct c (t) = ct XFM(t) = Ac s i (t) i (t) = c + s mt

Sinusoidal PM m (t) = Am s nt c (t) = Ac s ct c (t) = ct XPM(t) = Ac s i (t) XPM (t) = Ac s ( ct + PM sin

i (t) = i (t) = i (t) =

s mt]dt ct +

Modulation Index =

i (t) = ct + FM sin XFM (t)= Ac s ( ct +

= mt FM sin

mt


mt


Q.13

Different between FM and PM FM =

i (t) =

ct +

=

ct +

i (t) =

sin mt

=

c + K f AM s

mt

/FM = Kf Am

PM

=

i (t)PM = i (t)

=

=

ct + KP AM s mt c – K P AM

m sin

mt

/PM = KP AM m m PM

=

= K P AM

Types of Frequency Modulation:Depending upon value of , there are two types of frequency modulation. i.

Narrowband F.M.:When is very small os

=1 0

Sin

= 0


40

41


XFM (t) = =

Ac os ( ct +

sin

Ac [ os ct ( sin os ( sin

mt) mt) – sin

ct sin ( sin

mt)

mt) = 1

0 Sin ( sin

mt) =

sin mt

0 XNBFM (t) =

Ac [ os ct - sin

ct

sin mt]

=

Ac os ct -

[ os ( c- m)t –

=

Ac os ct -

os ( c- m)t +

os ( c- m)t] os ( c- m)t

Ac

c- m c

c+

m

Q.14 Explain Wide Band FM derive equation for wide band FM



When the value of modulation index

42

is large than a large number of

FM

sidebands are produced hence the B.W of FM is large. XFM (t)

=

A

s ( ct +

FM sin

mt)

This equation may be considered as Real part of exponential phases. FM (T)

=

A.e j (

ct +

=

A.e j (

ct

FM sin

ej

mt)

FM sin

mt

The coefficient Xn is given by Xn

=

FM

SinX-nx)dx

nth order Bessel function Xn = Jn (mf) Since the changing in frequency causes the time required to complete one half of a cycle to differ from time required to complete next half cycle, so the actual wave is a disturbed sinusoidal oscillation. The higher mathematical analysis using Bessel function shows that the putting the value of Xn in equation (1) ej

t sin

XFM (t)

=

mt =

Jn

=

Ae j

A

Jn

( t)e jn

ct

( t)e j (

Jn

mt

( t)e jn

mt

mt )t

Real part provide FM signal


43


XFM (t) =

A

Jn

( t) os (

mt

)

Bessel functions amp. Properties i.

Jn

( t) = Jn ( t) for even n

Jn

( t) = - Jn ( t) for odd n

Making use of property XFM (t)

= A J0 (

f

(t) os ct + AJ1 ( f) [ os ( c +

m)t

-

os ( c - m)t] + AJ2 ( f) [ os ( c +

m)t

+

os ( c -

m)t] + AJ3 ( f) [ os ( c +

m)t

-

os ( c -

m)t] + AJ3 ( f) [ os ( c +

m)t

Since the spectrum of wideband F.M The higher sideband are neglected, it does not affect the quality of transmission so the practical transmission B.W for wideband FM & wideband PM signals is given by Carson‟s Rule. (B.W)FM =

2(

+ m)

Rad/sec

=

2(

+ m)

Hz

=

2 (2 ( + 1) ƒm

Observations:-

In F.M. the total transmitted power is the carries power & is always remain const.



-

C (t) =

Ac os ct

XFM (t) =

Ac os

ct +

44

sin mt)

The modulation index determine how many sideband component hence signification amplitude. The co-efficient occasionally have negative value signaling a 180° phase for that pair of side band

-

Q.15 Explain different Generation method of F.M. wave Ans. There are two methods for generation of F.M. waves. i.

Direct method:- The basic concept of F.M. is

c

in accordance with

modulating signal m () the carries is generated by an LC Oscr. In an LC Oscr. The frequency of Oscr is CV

=

Voltage Variable capacities (Varicap)

Co

=

Fixed capacities

Semiconductor diodes when operated in R.B. have chat suitable to permit their use as voltage variable capacitor the modulating signal. Voltage across CV the capacitance of CV changes and causes corresponding change in frequency. Any oscr. Whose frequency is controlled by the modulating signal voltage is called a voltage controlled oscr or VCO FET and PIN can also used in place of VCO. Disadvantage of Direct Method:Most LC oscr are not stable enough to provide a carries signal the carries frequency usually vary due to temp. Variation, humidity, ageing of component etc. so instead of using LC oscr, a crystal oscr must be used but since they provide highly stable carries frequency so only a


45


very small frequency. Deviation is possible that is why indirect method of FM generation is used.

Indirect method (Armstrong method):NBFM m (t)

Integrator

NBFM

Frequency Multiplies

NBFM

Crystal Oscr

A Balance modulator is employed to generate the DSB-SC signal using sin ct as the carries as the carries of the modulator this carries is than shifted in phase by 90° and when added to the balance modulator output thereby forms an NBFM signal Ac s ct 90° Phase shift

NBFM Crystal Oscr

Ac sin

Addu.

ct

Balance Modular



Ac

sin

ct sin

46

mt

y (t) = xn (t) y (t) = xn (t) x (t) = Ac os ( ct + y (t) = Ac² os² ( ct + =

[1+

os

sin mt) sin mt) ct +

c n

sin

mt)] n c n m n

Detection of F.M. Wave:FM demodulator is basically a frequency to amplitude convertor. It is expected to convert the frequency variations in FM wave at its input into amplitude variations at its output to recover the original modulating signal. Q.16

Explain different FM Demodulation technique

Ans.

The process of expecting signal from FM modulator wave is called FM Demodulation -

In FM change in carries frequency shows change in amplitude of message signal. Frequency Discriminator senses rising amplitude of message signal by sensing the changes of carries frequency. O/P of frequency Discriminator is fed to AM detector that expects the message signal from AM. Frequency


47


ƒc + ƒ

c-

ƒ Voltage An

ƒi =

FM In

c

-Am

+ Kƒ m (t)

frequency variation

Frequency Selective N/W

Amp modulation

m (t)

Envelop detector

Disadvantage of Slope detector:i. The ckt is non-liner so harmonies are generated ii. The discriminator also respond for amplitude variation of i/p signal Balanced Slope Detector:Slope Ckt 1

Envelop detector

+ FM in

Σ

- Slope Ckt 2

Envelop detector


m (t)


48

Voltage

c

-

ƒ c

+ ƒ

ƒ

Useful range

Working:This ckt is also known as triple tuned ckt as three tuned ckt are used. The i/p tuned ckt is tuned at carries frequency ƒc T1 is tuned at ƒc + ƒ & T2 is tuned at ƒc - ƒ When fin = ƒc than gain provided by T1 & T2 will be same hence the O/P due to T1 is same as due to T2 but in phase opposition so net O/P voltage is zero.


49


Phase Locked Loop:The Phase Lock Loop (PLL) is a f/b system which may be used to extract a baseband signal from a frequency modulated carries. The basic component building blocks of a Phase Locked Loop arei. Phase detector ii. Low pass filter iii. Voltage Control Oscr (VCO) Phase detector

Vs fc

fo

Ve

LPF

Vo

Ve

VCO

if an input signal Vs of frequency fc is applied to the PLL the phase detector compares the phase & frequency of incoming signal to that of the O/P of VCO. If the two signal differ in frequency and/or phase, an error voltage V e is generated the phase detector is basically a multiplies & produces as control voltage Vc to VCO. Vs (t) = (t) = Vo (t) = Ve (t) =

A os [ ct + (t)] 0 B os ( 0t + ) AB os ( ct. os (

Ve (t) =

os ( c +

Vc

os

=

0t

o) t +

+ ) os [(


5

- o) t – 0]


=

50

/2

Vc = 0 The signal Vc shifts the signal frequency in a direction to reduce the frequency difference between fs & f0. One this action start we say that the signal is in capture range the VCO continue to change frequency till its o/p frequency is exactly the same as the i/p signal frequency the ckt is then said to be locked exact locking is achieved when the two signals are having same frequency & phase difference of /2 between them. - Let the input signal makes on abrupt change the abrupt frequency change causes the phase (t) to begin to increase linearly with time. - The phase different at the comparator i/p will generate a positive O/P V 0 which increase the frequency of the VCO. - Thus the O/P voltage is proportional to the frequency change as required in an FM demodulates. Pre-emphasis & De-emphasis:=> FM Band ; 88 – 108 MHz ƒm ; 15 KHz ƒnex ; 75 KHz B.W. ; 200 KHz Guard Band ; 20 KHz I.F. ; 10.7 MHz Sn (f) Y2


51


F

SX (f)

F At higher modulating frequency the effect of noise is more pronounced as compared to low frequency the power contents becomes very small as a result it is desirable to increase the amplitude at higher modulating frequency before modulation. This boosting of higher modulating frequency in accordance with a pre arranged curve is known as preemphasis. At the receiving and after demodulation, the same level of higher modulating signal frequency is maintained by using do emphasis.



52

UNIT-3 NOISE Q.17 What is noise and how noise can be classified Noise may be defined as any unwanted form of energy tending to interfere with propel & easy reception & reproduction of wanted signal. - Depending upon whether noise is internal or external to the system there are two types of noise. i. External noise:- The noise which to the system is known as extender noise Ex.: atmosphere noise extraterrestrial noise ii. Internal noise:- The noise which is generated within system is known as internal noise. There are five types of internal noise Thermal noise:- This type of noise arises due to constitutes and electric current flow in the register, the direction current flow is random & it has zero mean value. - Noise power available from a register is directly proportional to its absolute temp. In addition this power is also directly proportional to the B.W. over which noise is measured. P T P

B

P

TB

Pn = KTB

K = Boltzmann const. = 1.30 x 10- 23 J/K T = Absolute temp in K


53


B = Bandwidth in Hz

Thermal noise is also known as “Jhonson‟s noise”

Thermal noise is a zero mean Gaussian random variable -

It is also known as ‘white noise’ As white light contain equal amount of all frequency within the visible band of electromagnetic radiation. Similarly thermal noise has a uniform power spectral density over useful range of common. Sn (f) /2

|η=KT|

0

f

η/2

x 2B = ηB

=Two sided PSD -B

0

B


F


The auto ccerelation function of thermal noise is an impulse at T = 0 Rn ( )

=0 Eqt ckt of Resistor as noise generator:-

RL = R

= Pn = KTB

Vη


54

55


High frequency or transit time noise:In semiconductor devices, the is the transitive is the time taken by the carriers to cross a junction, when the signal frequency is high periodic time of signal becomes very small & hence may be comparable to transitive of carriers in such situations some of the carriers may diffuse back to the source the noise produce due to this condition is known as high frequency or transit time noise. Signal to noise ratio:It is defined as the ratio of signal power to the noise power & is given by -

Noise Figure (F): PSi

System

Pηi

Psi Pη0

For better system performance the noise figure should be as low as possible. PSC Pni = KTB

Ampulation C PM

PSO = GPsi PSO = GPni

PNi = Pni + Pna



56

Pno = FKTBG = PNi = FKTB Pni + Pna =FKTB KTB + Pna = FKTB Pni = FKTB –KTB Q.18

Derive Equivalent Noise Temp. for any amplifier

Ans. It is defined as temp. of the Ampr (system) at which the noise contribution by Ampr becomes thermal noise power Pna = (F-1) KTB (F-1) KTB = KTeB Te = T (T1) Cascading of Ampr.:Ampler

Ampler

Ampler

+ ………………….


57


UNIT-4 Narrow Band Noise:η/2

Sn ( f )

HBPF ( f )

fm

0

fm

(g+ (t)) Pre envelop:- the pre envelop of a band pass signal g (t) is given by g+ (t) = g (t) + j (t) g+ (t) = g (t) + j (t) G+ ( ) = G ( ) + j (-jsgn ( ) G ( ) G+ ( ) = G ( ) + sgn ( ) G ( ) (t) = g+ (t) e –jafct G+ (f – fc)



58

(f)

fm

+fm

x (t) = os (2 fct + (-)) calculate its pre envelop & complex envelop Xf (t) = os (2 fct + (+ )) +j sin (2 fct + ) Xf (t) = ej (2

fct +

)

(t) = ej (2

fct +

) – j2

(t) = ej

fct

(t)

S (t) = e –at os [( c +

) t] u (t)

The Hilbert transform of a low part signal multiplies with

s ct is equal

to same low pass signal multiplied by Hilbert transform of signal S+ (t) = e-at u (t) [ os ( S+ = e-at u (t) ej (

c

+

c

+

)t + j sin (

c

+

)

)t


59


(t) = e-at u (t) ej ( = e-at u (t) e- j

c

+

)t e- j

ct

ct

X( ) 1/2

-(

ct

– m)

- c

- ( c- m)

c- m - c


c∓ m


60

j

-j

c- m -(

ct

– m)

-

c

- ( c- m)


c

c∓ m

61


RX ( ) os 2 r fc [Sx (f-fc) + SX (f + fc)]

Given the power spectral density of noise wave form N (t), the power spectral density n (t) os 2 fCt is carries at as followsDivide Sn (t) by 4 shifts the divided plot to the L.H.S. as well as to the R.H.S. by fc & add the shifted plots. Noise performance of continuous wave modulation :-> Si (t)

Sd (t) LPF fc=fm

BPF

n (t)

N0 (t)

os 2 fCt i.

Noise performance of SSB-SC system Sd (t) = m (t).

S0 (t)

os² ct sin2

ct

m (t)



62

PSO = S0 (f )

η/2

- (fC + f m)

- fC

fC

Sn0 (f) /8

- fm

0

fm

PSi =

=


fC + m

f

63


Noise performance of DSB-SC system:Si (t) = Ac – m (t)

Sd (t) = AC m(t) os²

s ct

ct s

ct ]

Noise performance of full A.M. system:XAM (t) = [Ac + m (t)] s

ct

] s

ct

= Ac [ 1 + x (t) ] s ct

Sd (t) = AC [ 1 + x (t)] s

ct ]



=

+

- fm

0

fm

η2

- fm

0

fm

f OM for SSB-SC = 1 f OM for DSB-SC = 1 FOM for full AM < 1 XAM (t) = [Ac + m (t)] s ct


64

65


= Ac [1 + x (t)] s ct Let m (t) = AM s mt XAM (t) = Ac [1 + m s mt] s

ct

x (t) = m s ct

For 100% modulation (FOM)AM Figure of merit in F.M.: * (FOM)FM =

²

Pre-emphasis & De-emphasis FM Band fm fmex B.W Guard Band i.f.

: : : : : :

88-108 MHz 15 KHz 75 KHz 200 KHz 20 KHz 10.7 MHz



66

Sn (f) η/2

0

f

SX (f )

0

f

At higher modulating frequency the effect of noise Pre-emphasis: At the receiving and after demodulation, the same level of higher modulating signal frequency is maintained by using de-emphasis.

m (t)

Preemphasis

FM

Detector

Deemphasis

m (t)


67


Vi (S)

R1

R2

V0 (S)

R1 C = 75 H sec = 2.122 KHz Gain (dB) 20 dB/dec

If an input signal is subjected system whose frequency response H ( ) a phase spectrum which is a non-linear fun of

than the differ frequency components

present in the signal will be shifted in a mann that results in a change in their relative phases when all these frequency component are aided we objective a signal that may look considerable different from the I/p signal.



H( )

= e –j

68

to

|H ( )|= | < H ( ) = - t0

-

t0

So for a system with frequency response H ( ) = |H( )| < ( ) Phase delay:- (Te) the delay provide Group delay (tg):- the delay prove at group of frequency is known as group delay & given by tg.

“if ( ) varies linearly with frequency than group delay & phase delay not only const. but are also equal.


69


-

X =4 ; y = 0

4} = erfc (0) =

½

½

4 The noise is added to the system with a power spectral density Sn (f)

the

sum of signal & noise forms the i/p of a filter with frequency response H (f) calculate a)

SNR at the i/p of the signal P =2

f dt

=2 300



b) The filter response is as shown below H (f) 1

-2

0

2

f


70

Analog Communication

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