1 S-72.245 Transmission Methods in Telecommunication Systems (4 cr) Linear Carrier Wave Modulation.

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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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 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

1 S-72.245 Transmission Methods in Telecommunication Systems (4 cr) Linear Carrier Wave Modulation.

Documents

bandpass system n

bandpass signals n

easier n

limited n

inductors n

medium n

n antenna

communications laboratory