Transcript S-72.245

S-72.1140 Transmission Methods in
Telecommunication Systems (5 cr)
Linear Carrier Wave Modulation
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Linear carrier wave (CW) modulation
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Bandpass systems and signals
Lowpass (LP) equivalents
Amplitude modulation (AM)
Double-sideband modulation (DSB)
Modulator techniques
Suppressed-sideband amplitude
modulation (LSB, USB)
Detection techniques of linear modulation
– Coherent detection
– Non-coherent detection
AM
DSB
LSB
USB
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Baseband and CW communications
carrier
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Baseband communications is used in
– PSTN local loop
– PCM communications for instance baseband
CW
between exchanges
– Ethernet
– Fiber-optic communication
Using carriers to shape and shift the frequency spectrum (eg
CW techniques) enable modulation by which several
advantages are obtained
– different radio bands can be used for communications
– wireless communications
– multiplexing techniques as FDM
– modulation can exchange transmission bandwidth to
received SNR (in frequency/phase modulation)
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Defining bandpass
signals

The bandpass signal is band limited
V b p ( f )  0, f  f c  W  f  f c  W
V b p ( f )  0, o th e rw ise
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We assume also that (why?)
W  f C
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In telecommunications bandpass signals are used to convey
messages over medium
In practice, transmitted messages are never
strictly band limited due to
– their nature in frequency domain (Fourier series coefficients
may extend over very large span of frequencies)
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– non-ideal filtering
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Example of a bandpass system

Consider a simple bandpass system: a resonant (tank) circuit
j L / j C
z 
z  R  z V ( ) H ( )  V ( )
j L  1 / j C
p
i
p
in
out
H ( )  V out ( ) / V in ( )  z p / z i  H ( )  1 /[1  jQ ( f / f 0  f 0 / f )]
 Q  R C / L

1
f

(2

L
C
)
 0
zp
Tank circuit
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Bandwidth and Q-factor
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Bandwidth is inversely proportional to Q-factor:
B3 dB  f 0 / Q
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( fo r th e ta n k circu it : Q  R C / L )
System design is easier if the Q-factor is kept in the range:
10  Q  100
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For broadband circuits Q is small that requires the overall resistance to
be made small. For very narrow band circuits resistor is very large and
the resonance circuit is a high-impedance device whose interface can
be sensitive to interference. Also, components might turn out difficult
to realize if Q is outside of this range.
Some practical examples (Q = 50):
Band
L o n g w a ve ra d io
S h o rtw a ve ra d io
UHF
M ic ro w a ve
C a rrie r
100 kH z
5 MHz
100 M H z
5 GHz
BW
2 kHz
100 kH z
2 MHz
100 M H z
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I-Q (in-phase-quadrature) description for
bandpass signals

In I-Q presentation bandpass signal carrier and modulation parts
are separated into different terms
v bp ( t )  A ( t ) cos[ C t   ( t )]
v bp ( t )  v i ( t ) cos( C t )  v q ( t ) sin( C t )
v i ( t )  A ( t ) cos  ( t ), v q ( t )  A ( t ) sin  ( t )
Bandpass signal
in frequency
domain
Bandpass signal
in time
domain
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cos(    )  cos(  ) cos(  )
dashed line
denotes envelope
 sin(  ) sin(  )
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The phasor description of bandpass signal
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Bandpass signal is conveniently represented by a phasor
rotating at the angular carrier rate  t   ( t ) :
C
v bp ( t )  v i ( t ) cos( C t )  v q ( t ) sin( C t )
v i ( t )  A ( t ) cos  ( t ), v q ( t )  A ( t ) sin  ( t )
A(t ) 
vi (t )  vq (t )
2
2
 v i ( t )  0, arctan( v q ( t ) / v i ( t ))
 (t )  
 v i ( t )  0,   arctan( v q ( t ) / v i ( t ))
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Assignment
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Lowpass (LP) signal

Lowpass signal is defined by
yielding in time domain
1
 v bp ( t )  v i ( t ) cos(  c t )  v q ( t ) sin(  c t )

 v i ( t )  A ( t ) cos  ( t )
 v ( t )  A ( t ) sin  ( t )
 q
V lp ( f )
V lp ( f )  
Taking rectangular-polar
conversion yields then
v lp ( t )  F
1
2
1
2
V i ( f )  jV q ( f ) 
 v i ( t )  jv q ( t ) 
v lp ( t )  A ( t )  cos  ( t )  j sin  ( t )  / 2
v lp ( t )  A ( t ) / 2, arg v lp ( t )   ( t )
v lp ( t ) 
1
2
A ( t ) exp j ( t )
compare: v bp ( t )  A ( t ) cos[ C t   ( t )]
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Transforming lowpass signals
and bandpass signals
v bp ( t )  A ( t ) cos[ c t   ( t )]
v bp  R e  A ( t ) exp[ j c t   ( t )]
v bp


 A (t )

 2 Re 
exp[ j ( t )] exp[ j c t ] 
 2

v
(
t
)
lp


v bp  2 R e  v lp ( t ) exp[ j c t ]

This means that the lowpass signal is modulated to the carrier
frequency  when it is transformed to bandpass signal.
Bandpass signal can also be transformed into lowpass signal by
V lp ( f )  V bp ( f  f C ) u ( f  f C )
Give a physical interpretation of this BP to LP transformation!
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Assignment
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Amplitude modulation (AM)
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We discuss three linear mod. methods: (1) AM (amplitude
modulation), (2) DSB (double sideband modulation), (3) SSB
(single sideband modulation)
AM signal:
0    1
x C ( t )  Ac [1   x m ( t )] cos( c t   ( t ))
 Ac cos( c t   ( t ))  Ac  x m ( t ) cos( c t   ( t ))
C arrier


 xm (t )  1
Inform ation carrying part
(t) is an arbitrary constant. Hence we note that no information
is transmitted via the phase. Assume for instance that (t)=0,
then the LP components are
v i ( t )  A ( t ) cos( ( t ))  A ( t )  Ac [1   x m ( t )]
v q ( t )  A ( t ) sin( ( t ))  0

The carrier component contains no information
-> Waste of power to transmit the unmodulated carrier, but can
still be useful (why?)
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AM: waveforms and bandwidth
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AM in frequency domain:
x c ( t )  Ac [1   x m ( t )] cos( c t )
 Ac cos( c t )   x m ( t ) cos( c t )
C a rrie r
In fo rm a tio n ca rryin g p a rt
X c ( f )  Ac  ( f  f c ) / 2   Ac X m ( f  f c ) / 2 f  0 ( for brief notations )
C a rrie r

In fo rm a tio n ca rryin g p a rt
AM bandwidth is twice the message bandwidth W:
v ( t ) cos( c t   ) 
1
2
V ( f
 f c ) exp j  V ( f  f c ) exp  j 
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AM waveforms
(a): modulation
(b): modulated carrier
with <1
(c): modulated carrier
with >1
Envelope distortion!
( A M signal: x c ( t )  Ac [1   x m ( t )] cos( c t ))
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AM power efficiency

AM wave total power consists of the idle carrier part and the
2
2
2
useful signal part:
 x c ( t )    Ac cos ( c t ) 
C arrier
   Ac x m ( t ) cos ( c t ) 
2
( A M sig n a l: x c ( t ) 
Ac [1   x m ( t )] cos( c t ))
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C arrier pow er

2
 Ac / 2   Ac S X / 2
2
2
2
2 PSB
Assume AC=1, SX=1, then for =1 (the max value) the total
power is
PT m ax  1 / 2 

2
P ow er: S X
PC

2
3
1/2
M odulation pow er
Therefore at least half of the total power is wasted on carrier
Detection of AM is simple by enveloped detector that is a reason
why AM is still used. Also, sometimes AM makes
system design easier, as in fiber optic
communications
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Assignment
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DSB signals and spectra
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In DSB the wasteful carrier is suppressed:
x c ( t )  Ac x m ( t ) cos( c t )
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The spectra is otherwise identical to AM and the transmission
BW equals again double the message BW
X c ( f )  Ac X m ( f  f c ) / 2, f  0
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In time domain each modulation signal zero crossing produces
phase reversals of the carrier. For DSB, the total power ST and
the power/sideband PSB have the relationship
S T  Ac S X / 2  2 PSB  PSB  Ac2 S X / 4 ( D SB )
2

Therefore AM transmitter requires twice the power of DSB
transmitter to produce the same coverage assuming SX=1.
However, in practice SX is usually smaller than 1/2, under which
condition at least four times the DSB power is required for the
AM transmitter for the same coverage
AM : x c ( t )  Ac [1   x m ( t )] cos( c t )
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Linear modulation - PART II
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DSB and AM spectra
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AM in frequency domain with x ( t )  A cos(  t )
m
m
m
X c ( f )  Ac  ( f  f c ) / 2   Ac X m ( f  f c ) / 2, f  0 (general expression)
C arrier
Inform ation carrying part
X c ( f )  Ac  ( f  f c ) / 2   Ac Am  ( f c  f m ) / 2 (tone m odulation)

In summary, difference of AM and DSB at frequency domain is
the missing carrier component. Other differences relate to power
efficiency and detection techniques.
(a) DSB spectra, (b) AM spectra
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Linear modulators
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Note that AM and DSB systems generate new frequency
components that were not present at the carrier or at the
message.
Hence modulator must be a nonlinear system
Both AM and DSB can be generated by
– analog or digital multipliers
– special nonlinear circuits
• based on semiconductor junctions (as diodes, FETs etc.)
• based on analog or digital nonlinear amplifiers as
– log-antilog amplifiers:
p  log v 1  log v 2
p
10  v 1 v 2
v1
v2
Log
Log
10
p
v1 v 2
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
(a) Product modulator
(b) respective schematic
diagram
=multiplier+adder
( A M signal: x c ( t )  Ac [1   x m ( t )] cos( c t ))
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Square-law modulator (for AM)

Square-law modulators are based on nonlinear elements:
(a) functional block diagram, (b) circuit realization
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Balanced modulator (for DSB)

By using balanced configuration non-idealities on square-law
characteristics can be compensated resulting a high degree of
carrier suppression:

Note that if the modulating signal has a DC-component, it is not
cancelled out and will appear at the carrier frequency of the
modulator output
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Assignment
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Synchronous detection
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All linear modulations can be detected by synchronous
detector
Regenerated, in-phase carrier replica required for signal
regeneration that is used to multiple the received signal
Consider an universal*, linearly modulated signal:
x c ( t )  [ K c  K  x ( t )] cos( c t )  K  x q ( t ) sin( c t )

The multiplied signal y(t) is:
x c ( t ) A L O cos( c t ) 
AL O

AL O
2
2
[ K
c
 K  x ( t )][1  cos(2  c t ) ]  K  x q ( t ) sin(2  c t )
[ K c  K  x ( t )]
Synchronous
detector
*What are the parameters
for example for AM or DSB?
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
The envelope detector

Important motivation for using AM is the possibility to use the
envelope detector that
– has a simple structure (also cheap)
– needs no synchronization
(e.g. no auxiliary, unmodulated
carrier input in receiver)
– no threshold effect (
SNR can be very small and
receiver still works)
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Envelope detector analyzed

Assume diode half-wave rectifier is used to rectify AM-signal.
Therefore, after the diode, AM modulation is in effect multiplied
with the half-wave rectified sinusoidal signal w(t)
1 2
v R   A  m ( t )  cos  C t

2 

vR 



1

1


cos

t

cos
3

t

...


C
C
3


w (t )
 A  m ( t )  + other higher order terms
The diode detector is then followed by a lowpass circuit to
remove the higher order terms
The resulting DC-term may also be blocked by a capacitor
Note the close resembles of this principle to the synchronousdetector (why?)
co s ( x ) 
2
1
2
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1  co s( 2 x ) 
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AM phasor analysis,tone modulation

AM and DSB can be inspected also by trigonometric expansion
yielding for instance for AM
x ( t )  A A  cos(  t ) cos(  t )  A cos(  t )
C

C
AC Am 
2
m
m
cos(  C   m ) t 
C
C
AC Am 
2
C
cos(  C   m ) t
 A C cos(  C t )

This has a nice phasor interpretation;
take for instance =2/3, Am=1:
2


A ( t )  Ac  1  cos  m t 
3


Am  
2
3
A M sig n a l: x c ( t )  Ac [1   x m ( t )] cos( c t )
A (t )
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Assignment
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Solutions
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