03 linear mod
TRANSCRIPT
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S-72.245 Transmission Methods in Telecommunication Systems (4 cr)
Linear Carrier Wave Modulation
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Helsinki University of Technology, Communications Laboratory, Timo O. Korhonen
Linear carrier wave (CW) modulation
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– Noncoherent detection
AM
DSB
LSB
USB
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Helsinki University of Technology, Communications Laboratory, Timo O. Korhonen
Baseband and CW communications
Baseband communications is used in– PSTN local loop– PCM communications for instance between exchanges– (fiber-) optical communication
Using carrier 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 become applicable– exchanging transmission bandwidth to received SNR
CWbaseband
carrier
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Helsinki University of Technology, Communications Laboratory, Timo O. Korhonen
Defining bandpass signals
The bandpass signal is band limited
We assume also that (why?)
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)– non-ideal filtering
( ) 0,
( ) 0,otherwise
bp c c
bp
V f f f W f f W
V f
W fC
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Helsinki University of Technology, Communications Laboratory, Timo O. Korhonen
Example of a bandpass system Consider a simple bandpass system: a resonant (tank) circuit
zj L j C
j L j Cp
/
/1z R z
i p V H V
in out( ) ( ) ( )
( ) ( ) / ( ) /out in p iH V V z z 0 0( ) 1/[1 ( / / )]H jQ f f f f
10
/
(2 )
Q R C L
f LC
pzTank circuit
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Helsinki University of Technology, Communications Laboratory, Timo O. Korhonen
The bandwidth is inversely proportional to Q-factor:
System design is easier (next slide) if the fractional bandwidth 1/Q=B/f0 is kept relatively small:
Some practical examples:
Bandwidth and Q-factor
B f QdB3 0 /
0 01 0 10
. / . B f
( : / )Q R C Lfor the tank circuit
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Helsinki University of Technology, Communications Laboratory, Timo O. Korhonen
Why system design is easier for smaller fractional bandwidths (FB)?
Antenna and bandpass amplifier design is difficult for large FB:s:– one will have “difficult to realize” components or
parameters in circuits as • too high Q• too small or large values for capacitors and inductors
These structures have a bandpass nature because one of their important elements is the resonant circuit. Making them broadband means decreasing resistive losses that can be difficult
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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
( ) ( )cos[ ( )]bp Cv t A t t t ( ) ( ) ( )cos( ) sin( )Cbp i q Cv t v tt tt v
( ) ( )cos ( ), ( ) ( )sin ( )i qv t A t t v t A t t
cos( ) cos( )cos( )
sin( ) sin( )
Bandpass signal
in frequencydomain
Bandpass signal
in timedomain dashed line
denotes envelope
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Helsinki University of Technology, Communications Laboratory, Timo O. Korhonen
The phasor description of bandpass signal Bandpass signal is conveniently represented by a phasor
rotating at the angular carrier rate :
A t v t v ti q
( ) ( ) ( ) 2 2
( ) ( )cos( ) ( )sin( )bp i C q Cv t v t t v t t ( ) ( )cos ( ), ( ) ( )sin ( )i qv t A t t v t A t t
( ) 0,arctan( ( ) / ( ))( )
( ) 0, arctan( ( ) / ( ))i q i
i q i
v t v t v tt
v t v t v t
Ct t ( )
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Helsinki University of Technology, Communications Laboratory, Timo O. Korhonen
Lowpass (LP) signal
Lowpass signal is defined byyielding in time domain
Taking rectangular-polar conversion yields then
12( ) ( ) ( )lp i qV f V f jV f
( ) ( )cos( ) ( )sin( )
( ) ( )cos ( )
( ) ( )sin ( )
bp i c q c
i
q
v t v t t v t t
v t A t t
v t A t t
1 12( ) ( ) ( ) ( )lp lp i qv t V f v t jv t F
( ) ( ) cos ( ) sin ( ) / 2
( ) ( ) / 2, arg ( ) ( )
lp
lp lp
v t A t t j t
v t A t v t t
12( ) ( )exp ( )lpv t A t j t
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Helsinki University of Technology, Communications Laboratory, Timo O. Korhonen
Transforming lowpass signals and bandpass signals
Physically this means that the lowpass signal is modulated to the carrier frequency when it is transformed to bandpass signal. Bandpass signal can be transformed into lowpass signal by (tutorials). What is the physical meaning of this?
Re ( )exp[ ( )]bp cv A t j t t
( ) ( )cos[ ( )]bp cv t A t t t
( )
( )2Re exp[ ( )]exp[ ]
2lp
bp c
v t
A tv j t j t
2Re ( )exp[ ]bp lp cv v t j t
( ) ( ) ( )lp bp C C
V f V f uf f f
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Helsinki University of Technology, Communications Laboratory, Timo O. Korhonen
Amplitude modulation (AM) We discuss three linear mod. methods: (1) AM (amplitude
modulation), (2) DSB (double sideband modulation), (3) SSB (single sideband modulation)
AM signal:
(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
Also, the carrier component contains no information-> Waste of power to transmit the unmodulated carrier, but can still be useful (how?)
Carrier Information carrying part
( ) [1 ( )]cos( ( ))
cos( ( )) ( )cos( ( ))C c m c
c c c m c
x t A x t t t
A t t A x t t t
( ) ( )cos( ( )) ( ) [1 ( )]
( ) ( )sin( ( )) 0i c m
q
v t A t t A t A x t
v t A t t
0 1
( ) 1mx t
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Helsinki University of Technology, Communications Laboratory, Timo O. Korhonen
AM: waveforms and bandwidth
AM in frequency domain:
AM bandwidth is twice the message bandwidth W:
( ) [1 ( )]cos( )
cos( ) ( )cos( )c c m c
c c m c
x t A x t t
A t x t t
Carrier Information carrying part
( ) ( ) / 2 ( ) / 2c c c c m cX f A f f A X f f Carrier Information carrying part
f 0( )for brief notations
12( )cos( ) ( )exp ( )expc c cv t t V f f j V f f j
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Helsinki University of Technology, Communications Laboratory, Timo O. Korhonen
AM waveforms
(a): modulation(b): modulated carrierwith <1(c): modulated carrierwith >1
Envelope distortion!( : ( ) [1 ( )]cos( ))c c m cx t A x t t AM signal
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Helsinki University of Technology, Communications Laboratory, Timo O. Korhonen
AM power efficiency AM wave total power consists of the idle carrier part and the useful
signal part:
Assume AC=1, SX=1, then for =1 (the max value) the total power is
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 makessystem design easier, as in fiber opticcommunications
X
2 2 2
Carrier
2 2 2 2
Power: S
2 2 2
2
( ) cos ( )
( ) cos ( )
/ 2 / 2C SB
c c c
c m c
c c X
P P
x t A t
A x t t
A A S
PT max
/ / 1 2 1 2Carrier power Modulation power3 3
( : ( )
[1 ( )]cos( ))c
c m c
x t
A x t t
AM signal
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Helsinki University of Technology, Communications Laboratory, Timo O. Korhonen
In DSB the wasteful carrier is suppressed:
The spectra is otherwise identical to AM and the transmission BW equals again double the message BW
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
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
DSB signals and spectra
( ) ( )cos( )c c m cx t A x t t
( ) ( ) / 2, 0c c m cX f A X f f f
2 / 2 2T c X SB
S A S P 2 / 4( )SB c XP A S DSB
AM: ( ) [1 ( )]cos( )c c m c
x t A x t t
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Helsinki University of Technology, Communications Laboratory, Timo O. Korhonen
DSB and AM spectra AM in frequency domain with
In summary, difference of AM and DSB at frequency domain is the missing carrier component. Other differences relate to power efficiency and detection techniques.
x t A tm m m( ) cos( )
Carrier Information carrying part
( ) ( ) / 2 ( ) / 2, 0 (general expression)c c c c m cX f A f f A X f f f
( ) ( ) / 2 ( ) / 2 (tone modulation)c c c c m c mX f A f f A A f f
(a) DSB spectra, (b) AM spectra
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Helsinki University of Technology, Communications Laboratory, Timo O. Korhonen
AM phasor analysis,tone modulation
AM and DSB can be inspected also by trigonometric expansion yielding for instance for AM
This has a nice phasor interpretation; take for instance =2/3, Am=1:
x t A A t t A t
A At
A At
A t
C C m m C C C
C m
C m
C m
C m
C C
( ) cos( )cos( ) cos( )
cos( ) cos( )
cos( )
2 2
( )
: ( ) [1 ( )]cos( )c c m c
A t
x t A x t t AM signal
2
3mA
2( ) 1 cos
3c cA t A t
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Helsinki University of Technology, Communications Laboratory, Timo O. Korhonen
Linear modulators
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 v v
v vp
log log
1 2
1 210
Log
Log10 p
1v
2v1 2v v
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Helsinki University of Technology, Communications Laboratory, Timo O. Korhonen
(a) Product modulator(b) respective schematic diagram =multiplier+adder
( : ( ) [1 ( )]cos( ))c c m cx t A x t t AM signal
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Helsinki University of Technology, Communications Laboratory, Timo O. Korhonen
Square-law modulator (for AM) Square-law modulators are based on nonlinear elements:
(a) functional block diagram, (b) circuit realization
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Helsinki University of Technology, Communications Laboratory, Timo O. Korhonen
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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Helsinki University of Technology, Communications Laboratory, Timo O. Korhonen
Synchronous detection 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:
The multiplied signal y(t) is:
( ) [ ( )]cos( ) ( )sin( )c c c q cx t K K x t t K x t t
( ) cos( ) [ ( )][1 cos(2 )2LO
c LO c c c
Ax t A t K K x t t ] ( )sin(2 )q cK x t t
[ ( )]2LO
c
AK K x t
Synchronousdetector
*What are the parametersfor example for AM or DSB?
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Helsinki University of Technology, Communications Laboratory, Timo O. Korhonen
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 used to rectify AM-signal. Therefore after the diode AM modulation is in effect multiplied with the half-wave rectified sinusoidal signal w(t)
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 synchronous-
detector (why?)
( )
1 2 1( ) cos cos cos3 ...
2 3R C C C
w t
v A m t t t t
1( )
Rv A m t
+ other higher order terms
2 1cos ( ) 1 cos(2 )
2x x