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UNIT – I

Review of Semiconductor Physics

Energy band in solids : 

1. 

INTRODUCTION TO COMMUNICATION SYSTEM:

Communication is the process of establishing connection or link between two points

for information exchange (or) communication is the process of conveying message at

a distance (or) communication is a basic process of exchanging information.

The electronic equipments which are used for communication purpose are called

communication equipments. Different communication equipments when assembledtogether form an electronic communication system.

The block diagram of a basic electronic communication system is as shown in thefigure:

In the block diagram the information source produces the required message which has

to be transmitted. The transducer converts the information into electrical in nature.

The transmitter modifies the information (or message) signal for efficient

transmission. This process is called as modulation. The channel is the media which is

used for transmitting the information from source to destination. The process oftransmitting the information from source to destination is called as transmission.

During the process of transmission the signal gets distorted due to noise introduced by the system. At the destination a receiver is used to reproduce the message signal in

electrical form from the distorted received signal. The process of recovering messagefrom received modulated signal is called as demodulation. Output transducer is used

to convert an electrical message signal into its original form.

According to type of media used as channel, electronic communication may bedivided into:

Line communication:  In this method the transmitter and receiver are connected

through a wire or line. Ex: land – line telephone systems, optical communication etc.

Wireless or radio communication: In wireless communications, a message is

transmitted through open space by electromagnetic waves called as radio waves. Ex:

radio, TV, satellite communication etc.

Syllabus

Introduction: Introduction to communication system, need for modulation,

classification of modulations. Amplitude Modulation: Time domain and frequency domain description; Single tone

and multi tone AM modulation; Power and current relations in AM wave; Generation ofAM Waves – Square Law Modulator, Switching Modulator. Detection of AM wave:

Square Law Detector, Envelope Detector.

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Depending upon the message signal, communication may also be classified as:

Analog communication:  Analog communication is a type of communication in

which the message or information signal to be transmitted is in analog nature (or)continuous nature with respect to time.

Digital communication: In digital communication, the signal to be transmitted is in

digital nature (or) discrete nature with respect to time.

2.  MODULATION:

Modulation is a process in which characteristic of a carrier is varied in accordance

with a modulating wave. Modulating signal means message signal/baseband

signal/information/intelligence signal.

Modulations are two types:

Analog modulation:  A continuous signal (Pulse or Sinusoidal signal) is used as

carrier.Digital Modulation: A discrete (or digital) signal is used as carrier.

3. 

NEED FOR MODULATION:

Frequency Translation:

It means translation of the signal in the frequency domain, from one region to anotherregion. For example, the band limited signal in the range from f 1  to f 2  can be

translated to the range f 1’ to f 2’. The new signal in the range f 1’ to f 2’ bears the same

information as that in the signal from f 1 to f 2.

Frequency multiplexing:Suppose several different signals are required to transmit along a single

communication channel. All these signals need to be separately recoverable and

distinguishable from each other at the receiving end. The single channel may be a

single pair of wires or the free space that separates one radio antenna from another.Such multiple transmissions, i.e., multiplexing may be achieved by translating each

one of the original signals to a different frequency range.

Practicability of antennas:

When free space is the communication channel, antennas radiate and receive thesignals. In such case antennas operate effectively only when their dimensions are of

the order of magnitude of the wavelength of the signal being transmitted.

For example a signal of frequency 1 KHz (an audio tone) corresponds to awavelength of 300,000m, by relation     f c  . Since an antenna of 300,000m is

impractical, it can be reduced by translating the audio tone to a higher frequency.

Narrow banding:

Suppose the audio range extends from, say 50Hz to 10 KHz. In such case the ratio of

the highest audio frequency to the lowest is 200. Therefore, an antenna suitable for

use at one end of the range would be entirely too short or too long for the other end.

Suppose if it is translated so that it occupies the range from (106+50) Hz to (10

6+ 10

4)

Hz. In this case the ratio of highest to lowest frequency would be only 1.01. Thus

with the process of frequency translation, wideband signal can be changed tonarrowband signal which is more conveniently processed.

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Common Processing:

When number of different signals occupying different spectral ranges is there fortransmission, it is necessary to adjust the frequency range of processing apparatus. So

the processing apparatus is made elaborate to operate in same fixed frequency rangeinstead to translate the frequency range of each signal.

Reduction of Noise and Interference:

The effect of noise and interference cannot be completely eliminated in

communication system. However it is possible to minimize their effects by using

certain types of modulation schemes. These schemes generally require a transmission

 bandwidth much larger than the bandwidth of the message signal. Here bandwidth is

traded for noise reduction. 

4. 

CLASSIFICATION OF SINUSOIDAL MODULATIONS:

If a sinusoidal signal is used as carrier in analog modulation, then that type of

modulation is called as sinusoidal modulation.

Usually in sinusoidal modulation, the modulating frequency is considerably lower

than the carrier frequency but in exceptional cases the carrier frequency may be lower

than modulating frequency.

Let the sinusoidal carrier voltage represented as: cccc

  t CosV t v         

Therefore three types of modulations are possible sinusoidal carrier modulation:

i)  Amplitude modulation (AM) (Change in c A with respect to modulating signal)

ii)  Frequency modulation (FM) (Change in c  with respect to modulating signal)

iii) 

Phase modulation (PM) (Change inc  with respect to modulating signal)

In the above FM and PM are commonly known as “angle modulation”.

5. 

SINGLE TONE AMPLITUDE MODULATION:

In case of amplitude modulation, a modulating signal may be translated to a new

spectral range by multiplying the signal with a carrier sinusoidal signal, as shown in

the figure.

Consider a sinusoidal signal (modulating signal) given by:

  t  f  jt  f  jmmmmmm

mm eeV 

t  f CosV t CosV t v      

22

22

   

Where mV   is the amplitude and m f   is the frequency of modulating signal.

The two sided spectral pattern is shown in fig. below, which consists of two lines

each with amplitude2

mV  , each located at m f  f   and m f  f    .

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Consider carry signal as:

  t  f  jt  f  jcccccc cc eeV t  f CosV t CosV t v        2222    

Where cV   is the amplitude and c f   is the frequency of modulating signal.

Time domain representation: 

Since in AM, the amplitude of carrier varies with time in accordance with instaneousvalue of modulating signal, which is given by expression:

t CosV k V t vmmac    )(  

Instaneous value of modulated carrier wave is given by:

 

t CosV m

t CosV m

t CosV 

t Cost CosmV t Cost CosV 

V k V 

t Cost CosV k V t Cost vv

mcca

mcca

cc

cmaccm

c

mac

cmmacc AM 

     

    

   

22

11

Where am is called as modulation index of AM signal.

The corresponding time domain representation (envelop) of AM is as shown in thefigure:

The above equation reveals that the amplitude modulated carrier voltage consists ofthree sinusoidal voltages of frequencies:

Original carrier signal of frequency c  of amplitude cV  .

 Lower sideband signal (LSB) of frequency mc       of amplitude

2

caV m .

Upper sideband signal (USB) of frequency mc       of amplitude2

caV m

.

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Frequency domain representation: 

The new spectral pattern of AM is as shown below:

It is very clear that original spectral lines of message signal have been translated, both

in the positive frequency direction by amount c f   and also in the negative frequency

direction by the same amount.

With this, four spectral components are resulted in two sinusoidal waveforms, one at

mc  f  f   and the other at mc   f  f   , with spectral component of each of amplitude

4

cmV V  .

The bandwidth of AM signal is:

  mmcmc AM    f  f  f  f  f  BW  2  

6. 

MULTI TONE AMPLITUDE MODULATION:

Consider the number of sinusoidal components defined at sharply frequencies which

are non-periodic, finite energy signal is represented in the frequency domain in terms

of its Fourier transforms.

The spectral density of such non-periodic, finite energy signal is represented in the

frequency domain in terms of its Fourier transforms.

If the modulating signal )(t m   be band limited to the frequency range 0 to  H  f  , its

Fourier transform is   M  .

After multiplication with t Cos c  , the spectral density is given by:

            ccc   M  M t Cost m 21)(

The operation of multiplying a signal with a carrier signal is called mixing or

heterodyning.

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In the translated signal, the part of the signal which consists of spectral components

above the carrier signal in the range c f   to mc   f  f   is called upper sideband signal.

The other part in the rangemc

  f  f   toc

 f   is called the lower sideband signal.

7. 

MODULATION INDEX IN SINGLE TONE AM: 

The ratio between amplitude of modulating signal and the amplitude of carrier signal

is called as modulation index or modulation factor or depth of modulation of AM.

c

maV 

V m    

In practical cases modulation index is proportional to the ratio between amplitude of

modulating signal and the amplitude of carrier signal.

c

maa

c

ma

V 

V k m

V 

V m    

If the envelop of the AM given as:

From the above figure:

minmax

minmax

minmax

minmax

minmax

minmax

2

2

2

2

V V 

V 

V 

V V 

V V 

V V m

V V V 

V V V 

m

c

a

c

m

 

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If the value ofa

m is less than ‘1’, then the AM is called as under modulated AM and

if it is greater than ‘1’, then that AM is called as over modulated AM.

8. 

MODULATION INDEX IN MULTI TONE AM: 

Let V1, V2, V3 … be the simultaneous modulating voltages (rms). Then total effective

(rms) modulating voltage is given by:

232

2

2

1   V V V V t   

2

3

2

2

2

1

2

2

3

2

2

2

2

2

1

2

3

2

2

2

1

mmm

V 

V 

V 

V 

V 

V 

V 

V V V 

V 

V m

ccccc

t a

 

9. 

POWER/CURRENT RELATIONS AM: 

The total power in the AM modulated wave may be expressed as:

Pt = Pc + PLSB + PUSB R

V 

 R

V 

 R

V USB LSBCarrier 

222

 

Where all the three voltages are r.m.s. values and R is the resistance in which the

 power is dissipated (load resistance).

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21

21

21

21

242

8

22

2

2

2

2

2

2

22

222222

222

22

act 

c

t 

c

t a

c

t 

ac

accact 

cacaUSB LSB

ccc

m I  I 

 I  I 

 R I  R I m

PP

mP

m

 R

V 

 R

V m

 R

V P

 R

V m

 R

V mPP

 R

V 

 R

V P

 

10. 

AM MODULATORS:

The process of modulation translates the frequency spectrum. Hence the response of

modulator contains frequencies that are different from those present in the input

signal. It is therefore impossible to produce modulation by using linear time –

invariant systems, because the response of such systems cannot contain frequencies

other than those present in the input signal. So the modulation can be achieved by twomethods only:

  Linear modulator (Linear time variant system)   Non linear modulator

11. 

NON LINEAR MODULATOR TO GENERATE AM WAVES (SQUARE LAW

DIODE MODULATOR):

Square law diode modulator circuits make use of non – linear V – I characteristics of

diode. This method is useful at low voltage levels because of the fact that V – I

characteristics of a diode is highly non – linear in the low voltage region.

When carrier and modulating voltage are applied simultaneously at the input of diode

as shown in the figure, then the diode current has different frequency components. Ifthis current is passed through a tuned circuit which is tuned to carrier frequency and

has a narrow band width just to pass two sidebands along with the carrier, then thevoltage drop across tuned circuit is similar to an AM signal.

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Mathematical Analysis: Let:

t CosV v

t CosV v

mmm

ccc

 

 

 

The total a.c. voltage across diode is given by:

t CosV t CosV v mmcc D         

Due to non – linear relationship in diode characteristics, the diode current is given by:

t Cost CosV cV 

t CoscV 

t CoscV 

t CosbV t CosbV cV cV 

a

t CosV t CosV ct CosV t CosV ba

vcvbai

mcmcmc

mm

cc

mmccmc

mmccmmcc

 D D D

    

    

    

22

2222

2222

2

2

 

If we use a narrow band tuned circuit, which is centered aboutc  , then the current

 passes through tuned circuit will be:

  t Cost CosmbV t Cost Cosb

cV bV 

t Cost CosV cV t CosbV t Cost CosV cV t CosbV i

cmaccmm

c

mcmccc

mcmcmccc D

    

        

12

1

2

The equation for  Di is similar to an AM signal.

12. 

LINEAR MODULATOR METHOD TO GENERATE AM WAVES

(SWITCHING MODULATOR):

A linear modulator, in general, may be described as a system whose gain (or transfer

function) is varied with time by applying a time – varying signal at a certain point as

shown in the figure.

The linear time variant modulator is also called as switching modulator or chopping

modulator. This method is useful at high voltage levels because of the fact cV t m   )( .

The schematic diagram of switching modulator is as shown in the figure.

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Mathematical Analysis:

We know that:

)(1   t mt CosV t v cc        Where cV t m   )(  

The output voltage )(2   t v can be represented as:

0)(0

0)()()(

1

2t c

t ct vt v  

That is, the load voltage )(2   t v varies periodically between the values )(1  t v and zero at

a rate equal to the carrier frequencyc

 f  .

We can express the equation for  )(2   t v , mathematically as:

  )()(2   t gt mt CosV t v  pcc        

Where )(t g p is a periodic pulse grain of duty cycle equal to one half and

 period  00 1   f T   . Representing the )(t g p  by its Fourier series, we have:

  termsunwanted t Cost mV 

V t v

componentsharmonicodd t Cost nCosn

t g

c

c

c

c

n

c

n

 p

 

  

  

  

)(4

12

2

2

112

12

12

2

1)(

2

1

1

The first term in the above equation is the desired AM and the unwanted terms are

removed from )(2   t v  by using band pass filter.

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13. 

DEMODULATION OF AM WAVES:

The process of detection or demodulation contains in recovering the original

modulating voltage from the modulated carrier voltage. Thus detection is a reverse process of the modulation.

To demodulate AM waves two methods are normally used.

  Square law diode detector  Linear diode detector (or envelop detector)

14. 

DEMODULATION OF AM WAVES (SQUARE LAW DIODE DETECTOR): 

Square law diode detector utilizes non – linear (square law) portion of the dynamic

V _ I characteristics of a diode. It differs from the linear diode detector is that in this

case the applied input carrier voltage is of small magnitude.

The figure gives the basic circuit of a square law detector. The diode is biased positively to shift the zero – signal point to the small current non – linear region of

the diode. The capacitor and resistor combination is acting as a load.

By super imposing the AM signal on non – linear region of V – I characteristics ofthe diode, the o/p current waveform has its lower half compressed and this results theaverage current as shown in the figure.

We know that AM wave is expressed as:

t Cost CosmV vcmac AM       1  

Due to non – linear characteristics of the diode, the diode current is given by:

    211   t Cost CosmV bt Cost CosmV ai cmaccmacd          This diode current contains a DC component and AC components at the frequencies

  etcmcmccmcm              2,,2,2,, . The shunt capacitor ‘C’ bypassesall the higher radio frequency components and leaving only the m    component to

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flow through the load resistor ‘R’ providing the desired detected output.

15. 

DEMODULATION OF AM WAVES (LINEAR DIODE DETECTOR): 

Linear diode detectors are extremely popularly used in commercial radio receivers.

However, a linear diode detector for satisfactory operation requires modulated carrier

amplitude of 5V or more. So for this voltage the operation may be considered to be

taking place over the linear portion of diode V – I characteristics of curve.

In this method detector diode utilizes rectification characteristics. In the circuit the

modulated carrier voltage is applied to the series combination of diode and the load

impedance consisting of ‘R’ in shunt with capacitor ‘C’. Since applied voltage of

large magnitude, the diode conducts during the positive half cycle of the carrier and it

does not conduct during negative half cycle. The presence of capacitor modifies the

output. During positive half cycle, diode conducts, thereby charging the capacitor ‘C’

to positive peak value of the carrier voltage. During the negative half cycle, the diodedoes not conduct and hence the capacitor discharges. This output voltage curve is of

spiky nature but it traces almost envelope of the carrier voltage and hence it isnothing but the original modulation voltage. The deviation of output voltage curve

from original modulation voltage may be reduced by proper choice of ‘R’ and ‘C’,

depending uponma

  f and m .

16. 

CHOICE OF TIME CONSTANT FOR RC IN LINEAR DIODE DETECTOR: 

The time constant ‘RC’ cannot be chosen either too high or too low. If the time

constant ‘RC’ is quite low, the discharging curve is almost vertical which results in

large fluctuations in output voltage. Whereas, if the time constant RC is very large,the discharging curve is almost horizontal and it then misses several peaks of the

rectified output voltage as shown in the figure. Therefore, with high time constant‘RC’ the circuit is not able to handle larger depths of modulation and the signal

 becomes clipped at the negative peaks.

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Hence, it may conclude that the time constant used must be as large possible subject

to clipping does not taking place. The maximum allowable value of time constant is

such that the rate of discharge of capacitor ‘C’ is the same as the rate of decrease of

the modulation envelope.

The equation for amplitude (or envelop) of AM modulated voltage is given by:

t SinmV dt 

dv

t CosmV v

mamc

mac

  

 

1

 

The relation for capacitor voltage while it is discharging is:

 RC t t oc

 RC t t 

oc

e RC 

v

dt 

dvevv

0

0

 

Where the time 0t t   is time when the capacitor ‘C’ just starts discharging through

the resistor ‘R’. Then at that time:

0

0

1

0

0

t Cosm RC 

V 

 RC 

v

dt 

dv

t SinmV dt 

dv

maco

t t 

c

mamc

t t 

 

  

 

  

 

 

  

 

 

If clipping is to be avoided clipping at time 0t t   , the slope of capacitor voltage

cv should be less than or equal to the slope of the envelope voltage.

0

0

00

1

1

1

t Cosm

t Sinm

 RC 

t SinmV t Cosm RC 

V 

dt 

dv

dt 

dv

ma

mam

mamcmac

t t t t 

c

oo

 

  

   

 

  

  

  

 

 

The maximum possible value of 0

0

1   t Cosmt Sinmma

ma

  

is given by:

210

1  amam

ma

ma mt Sinand mt Cost Cosm

t Sinm

dt 

d 

    

 

  

Therefore at 0t t   , the time constant ‘RC’ is given by:

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2

2

1

1

1

11

a

am

aa

aam

m

m

 RC 

mm

mm

 RC 

 

 

 

17. PROBLEMS:

1) 

A 400W carrier is modulated to a depth of 75%. Calculate the total power inthe modulated wave.

W m

PP   act  5.5122

75.01400

21

22

 

2)  A certain transmitter radiates 9kW with the carrier modulated and

10.125kW when the carrier is sinusoidally modulated. Calculate the

modulation index. If another sine wave corresponding to 40% modulation istransmitted simultaneously, determine the total radiated power.

5.025.0122

1 22

  a

c

t a

act    m

P

Pm

mPP  

64.04.05.0 22222

1     mmma  

kW m

PP   act  84.102

12

 

3) 

The antenna current of an AM transmitter is 8A, when only the carrier is

sent, but it increases to 8.93A when the carrier is modulated by a sine wave.

Find the percentage of modulation.

701.0122

1

22

 

  

 

c

t a

act 

 I 

 I m

m I  I   (or) 70.1%

4) 

A 1000KHz carrier is simultaneously amplitude modulated with 300Hz,800Hz, and 2kHz audio sine waves. What will be the frequencies present in

the modulated signal and bandwidth?(i)

 

1000kHz

(ii) 

1000kHz ± 300Hz = 1000.3kHz and 999.7kHz

(iii) 

1000kHz ± 800Hz = 1000.8kHz and 999.2kHz(iv)

 

1000kHz ± 2kHz = 1002kHz and 998kHz

(v)  Bandwidth   max2 m f  4kHz

5) 

A transistor class C amplifier has maximum permissible collector dissipation

of 20W and collector efficiency of 75%. It is collector modulated to a depth of

90%. Calculate (i) the maximum unmodulated carrier power, (ii) the

sideband power, (iii) if the maximum depth of modulation is now restricted

to 70%, calculate the maximum sideband power.

(i)  Since permissible collector dissipation is 20W and it is corresponding to25%.

Therefore the total power = 20 X 4 = 80W

W m

PP

mPP

a

t c

act  9.56

21

21

2

2

 

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(ii) 

Sideband power = (Total power – Carrier power)/2 = 11.53W

(iii) 

W m

PP

a

t c

26.64

21

2 

 

Sideband power = 7.87W

6)  The tuned circuit of the oscillator in AM transmitter uses 50µH coil and a

1nF capacitor. Now if the oscillator output is modulated by 8kHz signal, find

the frequency range occupied by the sidebands.

kHz LC 

 f c

7122

1

  

LSB = 704 kHz and USB = 720 kHz.

7)  A diode detector with a load resistance R = 250 kΩ in parallel with a

capacitor C = 100 pF is used to detect an amplitude modulated carrier with

60% modulation. Find the highest carrier frequency that can be detected

without excessive distortion. 

kHz f 

 RC m

m

m

m

 RC 

m

a

a

m

a

am

10

333,631

1

1

2

2

 

 

 

Prepared by: Dr. A. S. Srinivasa Rao

Prof. (ECE) & Dean (FS)