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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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Helsinki University of Technology, Communications Laboratory, Timo O. Korhonen
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)
Helsinki University of Technology, Communications Laboratory, Timo O. Korhonen
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Defining bandpass
signals
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The bandpass signal is band limited
Vbp ( f )  0, f  f c  W  f  f c  W
Vbp ( f )  0, otherwise

We assume also that (why?)
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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

W  f C
Helsinki University of Technology, Communications Laboratory, Timo O. Korhonen
Example of a bandpass system

Consider a simple bandpass system: a resonant (tank) circuit
jL / jC
zp 
zi  R  z p Vin ( ) H ( )  Vout ( )
jL  1 / jC
H ( )  Vout ( ) / Vin ( )  z p / zi  H ( )  1/[1  jQ( f / f 0  f 0 / f )]
Q  R C / L

1
 f 0  (2 LC )
zp
Tank circuit
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Bandwidth and Q-factor
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Bandwidth is inversely proportional to Q-factor:
B3 dB  f0 / Q
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(for the tank circuit: 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
Longwave radio
Shortwave radio
UHF
Microwave
Carrier
100 kHz
5 MHz
100 MHz
5 GHz
BW
2 kHz
100 kHz
2 MHz
100 MHz
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Helsinki University of Technology, Communications Laboratory, Timo O. Korhonen
I-Q (in-phase-quadrature) description for
bandpass signals

In I-Q presentation bandpass signal carrier and modulation parts
are separated into different terms
vbp (t )  A(t )cos[C t   (t )]
vbp (t )  vi (t ) cos(C t )  vq (t ) sin(C t )
vi (t )  A(t )cos  (t ), vq (t )  A(t )sin  (t )
Bandpass signal
in frequency
domain
Bandpass signal
in time
domain
Helsinki University of Technology, Communications Laboratory, Timo O. Korhonen
cos(   )  cos( ) cos(  )
 sin( ) sin(  )
dashed line
denotes envelope
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The phasor description of bandpass signal

Bandpass signal is conveniently represented by a phasor
rotating at the angular carrier rate  C t   (t ) :
vbp (t )  vi (t )cos(C t )  vq (t )sin(C t )
vi (t )  A(t )cos  (t ), vq (t )  A(t )sin  (t )
vi (t )  0,arctan(vq (t ) / vi (t ))
2
2
A(t )  vi (t )  vq (t )  (t )  
vi (t )  0,  arctan(vq (t ) / vi (t ))
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Assignment
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Lowpass (LP) signal
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Lowpass signal is defined by
yielding in time domain
vbp (t )  vi (t ) cos(ct )  vq (t )sin(ct )

vi (t )  A(t ) cos  (t )
v (t )  A(t )sin  (t )
 q
Vlp ( f )
1
2
Vi ( f )  jVq ( f ) 
vlp (t )  F 1 Vlp ( f )   12 vi (t )  jvq (t ) 
Taking rectangular-polar
conversion yields then
vlp (t )  A(t )  cos  (t )  j sin  (t )  / 2
vlp (t )  A(t ) / 2, arg vlp (t )   (t )
vlp (t )  12 A(t )exp j (t )
compare:
vbp (t )  A(t )cos[C t   (t )]
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Helsinki University of Technology, Communications Laboratory, Timo O. Korhonen
Transforming lowpass signals
and bandpass signals
vbp (t )  A(t )cos[ct   (t )]
vbp  Re A(t )exp[ jct   (t )]


 A(t )

vbp  2 Re 
exp[ j (t )]exp[ j ct ]
 2

v
(
t
)
lp


vbp  2 Re vlp (t ) exp[ j ct ]

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
Vlp ( f )  Vbp ( f  fC )u( f  fC )
Give a physical interpretation of this BP to LP transformation!
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Helsinki University of Technology, Communications Laboratory, Timo O. Korhonen
Assignment
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Helsinki University of Technology, Communications Laboratory, Timo O. Korhonen
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:
xC (t )  Ac [1   xm (t )]cos( ct   (t ))
 Ac cos( ct   (t ))  Ac  xm (t )cos( ct   (t ))
Carrier
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0    1

 xm (t )  1
Information 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
vi (t )  A(t )cos( (t ))  A(t )  Ac [1   xm (t )]
vq (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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Helsinki University of Technology, Communications Laboratory, Timo O. Korhonen
AM: waveforms and bandwidth
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AM in frequency domain:
xc (t )  Ac [1   xm (t )]cos( ct )
 Ac cos( ct )   xm (t ) cos( ct )
Carrier
Information carrying part
X c ( f )  Ac ( f  f c ) / 2   Ac X m ( f  f c ) / 2 f  0(for brief notations)
Carrier
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Information carrying part
AM bandwidth is twice the message bandwidth W:
v(t )cos( ct   ) 
1
2
V ( f  f c )exp j  V ( f  f c )exp j 
Helsinki University of Technology, Communications Laboratory, Timo O. Korhonen
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AM waveforms
(a): modulation
(b): modulated carrier
with <1
(c): modulated carrier
with >1
Envelope distortion!
(AM signal: xc (t )  Ac [1   xm (t )]cos(ct ))
Helsinki University of Technology, Communications Laboratory, Timo O. Korhonen
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AM power efficiency
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AM wave total power consists of the idle carrier part and the
useful signal part:
 xc2 (t )   Ac2 cos 2 ( ct ) 
Carrier
   2 Ac2 xm2 (t ) cos 2 ( ct ) 
(AM signal: xc (t ) 
Ac [1   xm (t )]cos( ct ))
Power: SX
 Ac2 / 2   2 Ac2 S X / 2
PC

2 PSB
Assume AC=1, SX=1, then for =1 (the max value) the total
power is
3
3
PT max  1 / 2  1 / 2
Carrier power
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Modulation power
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
Helsinki University of Technology, Communications Laboratory, Timo O. Korhonen
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Assignment
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Helsinki University of Technology, Communications Laboratory, Timo O. Korhonen
DSB signals and spectra

In DSB the wasteful carrier is suppressed:

The spectra is otherwise identical to AM and the transmission
BW equals again double the message BW
xc (t )  Ac xm (t )cos(ct )
X c ( f )  Ac X m ( f  f c ) / 2, f  0

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
ST  Ac2 S X / 2  2 PSB  PSB  Ac2 S X / 4( DSB)
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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: xc (t )  Ac [1   xm (t )]cos(ct )
Helsinki University of Technology, Communications Laboratory, Timo O. Korhonen
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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 xm (t )  Am cos( mt )
X c ( f )  Ac ( f  f c ) / 2   Ac X m ( f  f c ) / 2, f  0 (general expression)
Carrier
Information carrying part
X c ( f )  Ac ( f  f c ) / 2   Ac Am ( f c  f m ) / 2 (tone modulation)

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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Helsinki University of Technology, Communications Laboratory, Timo O. Korhonen
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:
v1
Log
p  log v1  log v2
p v1v2
p
10
10  v1v2
v2
Log
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
(a) Product modulator
(b) respective schematic
diagram
=multiplier+adder
(AM signal: xc (t )  Ac [1   xm (t )]cos(ct ))
Helsinki University of Technology, Communications Laboratory, Timo O. Korhonen
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Square-law modulator (for AM)

Square-law modulators are based on nonlinear elements:
(a) functional block diagram, (b) circuit realization
Helsinki University of Technology, Communications Laboratory, Timo O. Korhonen
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Balanced modulator (for DSB)
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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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Helsinki University of Technology, Communications Laboratory, Timo O. Korhonen
Synchronous detection
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
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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:
xc (t )  [ Kc  K  x(t )]cos(ct )  K  xq (t )sin(ct )

The multiplied signal y(t) is:

ALO
[ K c  K  x(t )][1  cos(2 ct ) ]  K  xq (t )sin(2 ct )
2
ALO

[ K c  K  x(t )]
2
xc (t ) ALO cos( ct ) 
Synchronous
detector
*What are the parameters
for example for AM or DSB?
Helsinki University of Technology, Communications Laboratory, Timo O. Korhonen
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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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Helsinki University of Technology, Communications Laboratory, Timo O. Korhonen
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
1 2 

vR   A  m(t )  cos  C t    cos  C t  cos3 C t  ...  
3

2  
vR 



1

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?)
cos 2 ( x) 
Helsinki University of Technology, Communications Laboratory, Timo O. Korhonen
1
1  cos(2 x)
2
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AM phasor analysis,tone modulation

AM and DSB can be inspected also by trigonometric expansion
yielding for instance for AM
xC (t )  AC Am  cos( m t )cos( C t )  AC cos( C t )


AC Am 
AA
cos( C   m )t  C m cos( C   m )t
2
2
 AC cos( C t )
This has a nice phasor interpretation;
take for instance =2/3, Am=1:
 2

A(t )  Ac 1  cos mt 
 3

Am  
2
3
AM signal: xc (t )  Ac [1   xm (t )]cos( ct )
A( t )
Helsinki University of Technology, Communications Laboratory, Timo O. Korhonen
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Assignment
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Solutions
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Helsinki University of Technology, Communications Laboratory, Timo O. Korhonen