Transcript Wireless Communications and Networks

Principles of analogue
modulation
Lecture 3
Analogue Modulation
Techniques
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Theory of amplitude modulation
Representation of AM
Power relations in the AM wave
Single-sideband techniques
Amplitude Modulation
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This is the simplest and oldest form of
modulation. In this type, the
information signal (intelligence) causes
the amplitude of the carrier to vary in
time, in proportion to the instantaneous
magnitude of their sum
Amplitude Modulation
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Apart from transforming the signal into
a form suitable for transmission,
modulation allows many signals
originally at the same frequency to be
transferred to other parts of the
electromagnetic spectrum.
Mathematical description
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To describe amplitude modulation
mathematically, consider the carrier
wave given as a sinusoidal wave v c ,
with a frequency of f c and amplitude V
.c
This can be written as
vc  Vc sin 2f ct
Amplitude Modulation
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Without modulation this sine wave will convey no
information.
Reason: We can calculate its value at anytime from
previously known values.
What modulation does is to modify the constant
value with the signal, which carries the
information. This results in the amplitude of the
modulated carrier varying in proportion to the
amplitude of the information signal.
Derivation of the AM equation
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Let the information signal be given by
vs  Vs sin 2f st
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Let
and
s  2f s
then vc  Vc sin ct
and v  V sin  t
s
s
s
c  2f c
Derivation of the AM equation
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The amplitude of the resulting
modulation is the sum of the amplitude
of the carrier and the signal.
A  Vc  vs
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Substituting for
vs
A  Vc  Vs sin  st
A  Vc 1 m sin  st 
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where
Vs
m
Vc
this is index of modulation
The resulting AM wave will thus be
v  A sin  ct
 Vc 1  m sin  st sin  ct
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Expanding the brackets
v  Vc sin ct  mVc sin  st sin ct
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(sin a)(sin b) 
but
such that
1
cosa  b  cosa  b
2
m
v  Vc sin  ct  Vc cos c   s t
2
m
 Vc cos c   s t
2
If we rewrite this in terms of frequencies
m
v  Vc sin 2f ct  Vc cos 2  f c  f s t
2
m
 Vc cos 2  f c  f s t
2
Examples
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In an AM radio broadcast the tone has a frequency of
1000Hz and the carrier frequency is 1500kHz. What are
the resulting sidebands.
What will be the frequency of the sidebands if the carrier
is at 1250kHz?
If the tone has a spectrum of 300 to 3000Hz and the
carrier is at 100kHz then one of the sidebands will range
from 100.3 to 103 and the other will be from 97 to
99.7kHz.
Modulating with different carriers
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Modulation can be used to translate signals originally at the same
frequency to different parts of the frequency spectrum.
Assume that AM radio stations have a voice and music spectrum from 0
to 5kHz.
Assume that they are spaced 10kHz apart in the broadcast band.
If the broadcast from each station is then modulated with a different
carrier frequency, then the broadcast will not overlap. Reason: the signal
is less than half the difference between adjacent carriers.
Example: Stations broadcast at 1000, 1010 and 1020kHz. Draw the
frequency spectrum of the stations if the signal bandwidth is 5kHz
What happens if the modulating signal bandwidth is now 8kHz?
Modulation Index and Signal Power
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It is a measure of how fully the carrier has been modulated.
modulated peak volta ge - unmodulate d carrier vo ltage
m
unmodulate d carrier vo ltage
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Examples: The modulated peak value of a signal is 10 V and the
unmodulated carrier is 8 V. Find the modulation index.
A modulated signal seen on an oscilloscope has a maximum span
of 5 V and a minimum of 1 V. What is the modulation index?
Signal Power
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The power in a system can be defined through voltage as
V2
P
R
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and through current as
P  I 2R
Assume that R = 1 ohm
2
The carrier power is then
Pc  Vc
Power in each side band is the given as
2
2
mV
m


Ps   c   Vc2
4
 2 
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The power in both side-bands
2
m2 2 m2 2
 mVc 
P2 s  2 x 
 2 x Vc  Vc

4
2
 2 
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The total transmitted power is
m2 2
m2 
2
PT  Vc  Vc  Vc 1 

2
2 

2
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since
Pc  Vc2
 m 
PT  Pc 1  
2 

2
Comment
The maximum power in the sidebands is 50% of the carrier power at
m = 1.
The carrier and one sideband may be suppressed without destroying
the information
Examples
A carrier of 1000W is modulated with an index of 0.8. What is the
total power?
For a carrier of 250W and 90% modulation, what is the total power?
What is the carrier power if the total power is 1000W and the
modulation index is 0.95.
Single-sideband techniques
Conventional AM systems have two main disadvantages:
Two thirds or more of the total transmitted power is in
the carrier
The bandwidth required is twice that which will be
needed in SSB
Such systems are therefore both power and bandwidth
inefficient.
The mathematical foundation for single sideband systems was
laid in 1914.
There are many variations of the single sideband systems
AM SSB Full carrier (SSBFC)
Carrier is transmitted at full power with only one of the sidebands.
In this only half as much bandwidth will be required
The power relations will be as follows:
Power in carrier =
Vc
2
Power in lower sideband = 0
2
2
m
m
Power in upper sideband =
Vc2 
Pc
4
4
Total power
2
m2 2
m2 
 m 
2
PT  Vc  Vc  Vc 1    Pc 1  
4
4 
4 


2
What is the ratio of sideband power to carrier power at 100%
modulation?
AM Single sideband suppressed carrier (SSBSC)
In this the carrier is totally removed together with one of the
sidebands. Only half the bandwith is required.
Power Relations
The sideband power will constitute 100% of the total transmitted
power.
Power in carrier, Pc  0
Power in lower sideband = 0
Power in upper sideband =
m2
PT 
Pc
4
AM SSB Reduced carrier (SSBRC)
In this one sideband is removed and the carrier reduced to about
10% of the unmodulated amplitude.
The carrier will have to be reinserted at reduced amplitude for the
purpose of demodulation
Power relations
Power in carrier,
Pc
 0.1V 
2
 0.01V 2
Power in lower sideband = 0
Power in upper sideband = m 2
Pc
4 2
m
Total power =
PT  0.01Pc 
Pc
4
Comparison of SSB to Double sideband AM
Advantages of SSB
Bandwidth conservation: Only half the bandwidth is required
Power conservation: Only one sideband with carrier removed or
suppressed. Hence total transmitted power will be less. This allows
smaller transmitters to be used.
Selective fading: In double sideband, the two sidebands may experience
different impairments as the propagate along different paths in the
medium. This could result in carrier phase shift. This cannot happen if
only one sideband is transmitted.
Noise Reduction: Thermal noise is reduced to half, because the bandwidth
is also half.
Disadvantages
Complex receivers
Tuning Difficulties: More difficult to tune than conventional AM
receivers. More expensive tuning circuits can be used.
Examples: A double sideband AM radio transmitter gives a power
output of 5 kW when the carrier is modulated to a depth of 95%. A
speech signal is then used to modulate the carrier with a depth of
20% and the carrier and one sideband are suppressed. Find the
output power in the other sideband.