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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)