1 s-72.1140 transmission methods in telecommunication systems (5 cr) linear carrier wave modulation

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S-72.1140 Transmission Methods in Telecommunication Systems (5 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– Non-coherent detection

AM

DSB

LSB

USB

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Baseband and CW communications

Baseband communications is used in

– PSTN local loop

– PCM communications for instance 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)

CWbaseband

carrier

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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,bp c c

bp

V f f f W f f W

V f

otherwise

W fC

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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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Bandwidth is inversely proportional to Q-factor:

System design is easier if the Q-factor is kept in the range:

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):

Bandwidth and Q-factor

B f QdB3 0 /

10 100Q

( : / )Q R C Lfor the tank circuit

Band Carrier BWLongwave radio 100 kHz 2 kHzShortwave radio 5 MHz 100 kHzUHF 100 MHz 2 MHzMicrowave 5 GHz 100 MHz

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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

( ) ( )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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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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Assignment

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Lowpass (LP) signal

Lowpass signal is defined byyielding in time domain

Taking rectangular-polar conversion yields then

compare:

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

( ) ( )cos[ ( )]bp Cv t A t t t

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Transforming lowpass signals and bandpass signals

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

Give a physical interpretation of this BP to LP transformation!

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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Assignment

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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

The carrier component contains no information-> Waste of power to transmit the unmodulated carrier, but can still be useful (why?)

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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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


( ) ( ) / 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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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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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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Assignment

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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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Linear modulation - PART II

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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( )


( ) ( ) / 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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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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(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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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 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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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)

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

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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 mA t A t

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Assignment

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Solutions

1 s-72.1140 transmission methods in telecommunication systems (5 cr) linear carrier wave modulation

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