Pi i lPrinciples off CiiCommunications - GitHub Pages · 2020. 10. 27. · Generation of SSB Waves: Frequency discrimination method Reqqgg()uirements on message signal m(t) Little

P i i l f C i iPrinciples of Communications

Chapter 3: Analog ModulationPart I: Amplitude Modulation

Textbook: Ch3

1

M d l tiModulation3 t i l t i i b d h l3-step signal transmission over a band-pass channel

A pure carrier (usually sinusoidal) is generated at the transmittertransmitterThe carrier is modulated with the information to be transmitted. Any reliably detectable change in signal characteristics can carry informationcharacteristics can carry informationAt the receiver the signal modifications or changes are detected and demodulated

Modify a signal

“Modulate”Detect the Modifications“Demodulate”

2009/2010 Meixia Tao @ SJTU 2

M d l tiModulationModulation objectives

Frequency translation from lowpass to passbandF di i i lti l iFrequency-division multiplexingIncreasing noise and interference immunity

Modulation typesModulation types

Carrier Message ModulationCarrier Message ModulationDigitalSinusoidal Digital modulation

Analog modulationAnalogPulse

Analog modulation

Pulse modulation


A l M d l tiAnalog ModulationCharacteristics that be modified in sin carrier

Amplitude → Amplitude modulationFrequencyPhase

→ Angle modulation

In the following we Consider the transmission and reception of analog signals by amplitude modulationC th i b d idth i t dCompare their bandwidth requirement and implementation complexityDiscuss the performance in the presence of noise


Discuss the performance in the presence of noise

A l M d l tiAnalog Modulation

3.1.Amplitude modulation

3.2. Effect of noise on AM systems

3.3.Angle modulation

3.4.Effect of noise on angle modulation


Double-Sideband Suppressed-Carrier AM(DSB-SC)

Carrier wave：Baseband signal (modulating wavel)

0( ) cos( )c cc t A ω θ= +

( )m tg ( g )Modulated wave

( )( ) ( ) ( ) ( ) coss t c t m t A m t tω θ= = +( )0( ) ( ) ( ) ( ) cosc cs t c t m t A m t tω θ= = +

Modulating wave Modulated wave


S t f DSB SC Si lSpectrum of DSB-SC Signals[ ]1 [ ])()(

21)( ccc ffMffMAfS ++−=

M(f)S f M(f)M(0)

Spectrum of message signal

W-W 0 f

Spectrum of DSBSC i l S(f) (1/2)AcM(0)DSBSC signal

USBUSB LSBLSB

0 ffc+Wfcfc-W-fc+W-fc-W -fc


B d idth d P f DSB SCBandwidth and Power of DSB-SCS(f)S(f) (1/2)AcM(0)

Channel bandwidth required to transmit the modulated

0 ffc+Wfcfc-W-fc+W-fc-W -fc

Channel bandwidth required to transmit the modulated signal is , 2 times of the message bandwidthPower content

2cB W=

o e co e/2 /22 2 2 2

0/2 /2

1 1lim ( ) lim ( )cos ( )T T

s c cT TT TP s t dt A m t t dt

T Tω θ

− −→∞ →∞= = +∫ ∫

[ ]2 2/2 2

0/2

1lim ( ) 1 cos(2 2 )2 2

Tc cc mTT

A Am t t dt PT

ω θ−→∞

= + + =∫


D d l ti f DSB SC Si lDemodulation of DSB-SC SignalsThe local oscillator is Product Low-passs(t) v(t) vo(t)The local oscillator is assumed to be exactly coherent or synchronized to

)2( fA

Productmodulator

Low passfilter

o

original c(t) => coherent detection or synchronous detection

)2cos( tfA cc π

Localoscillatordetection

If there is a phase error φ, then

)()4cos(1)()cos(1)()2cos()2cos()()2cos()(

tmtfAtmA

tmtftfAtstftv

ccc

cccc

φπφ

φππφπ

++=

+=+=

)()(2

)()(2

fccc φφ

Scaled version of Unwanted terms


message signal

Ph E φPhase Error φcos(φ) = Attenuation factor

)()cos( tmAc φ

cos(φ) Attenuation factorIf φ = 0 ⇒ amplitude of demodulated signal is maximizedmaximizedIf φ = ±π/2 ⇒ amplitude is zero, called quadrature null effecteffectIn practice, φ varies randomly with time, resulting in undesired effectundesired effectNeed additional circuitry to ensure synchronizationThe increased receiver complexity is the price that must be paid for suppressing the carrier wave to save t it


transmit power

S S SCExample: Single-tone DSBSC ModulationConsider a single tone modulating wave ( )tfAtm π2cos)( =Consider a single tone modulating waveThe DSBSC modulated wave is

( )tfAtm mm π2cos)(

( )tftfAAts mcmc 2cos)2cos()( = ππ ( )

[ ] [ ]tffAAtffAA

tftfAAts

mcmcmcmc

mcmc

)(2cos21)(2cos

21

2cos)2cos()(

−++= ππ

ππ

With perfect synchronization, the output of product modulator is

[ ]tffAAtfAA

tstftv c

)2(2cos1)2cos(1)()2cos()(

−+=

=

ππ

π

[ ]

[ ]tffAA

tffAAtfAA

mcmc

mcmcmmc

)2(2cos41

)2(2cos4

)2cos(2

++

−+=

π

ππ

Removed by LPF


[ ]ff mcmc )(4 Removed by LPF

Conventional Amplitude Modulationp

Modulated signal：

[ ] ( )( ) 1 ( ) cos 2s t A am t f tπ= + 1≤[ ] ( )

( )

( ) 1 ( ) cos 2

( )cos 2

c cs t A am t f t

A am t f t

π

π

+

=

1a ≤

( )( )

( ) cos 2

cos 2c c

c c

A am t f t

A f t

π

π+

1a >

( )m t :normalized message1a >

a :modulation index

overmodulated2009/2010 Meixia Tao @ SJTU 12

overmodulated

S t f C ti l AMSpectrum of Conventional AM

( ) ( ) ( ) ( )( )2 2

c cc c c c

A A aS f f f f f M f f M f fδ δ= − + + + − + +⎡ ⎤ ⎡ ⎤⎣ ⎦ ⎣ ⎦

(A /2)δ(f+f )S(f) (1/2)aAcM(0)

(Ac/2)δ(f-fc)(Ac/2)δ(f+fc)

0 ffc+Wfc

fc-W-fc+W-fc-W -fc


P f th C ti l AMPower for the Conventional AMPower [ ]{ }22 2 2

2 2 2 2 2 22

( ) 1 ( ) cosc cS E s t E A am t t

A a A A a A

ω⎡ ⎤= = +⎣ ⎦

⎡ ⎤2 ( )2 2 2 2c c c c

mA a A A a AE m t P⎡ ⎤= + = +⎣ ⎦

P i id b d

Modulation efficiency

Power in sidebandsPower in the carrier component2

22

2 2 22=

1

c mm

a A P a PEA P

= =power in sideband

l 2 2 22 1

2 2c m

c mA a a PA P ++total power


E lExampleThe signal is used to modulate the carrier . The modulation index is a=0 85 Determine the power in the carrier

( ) 3cos(200 ) sin(600 )m t t tπ π= +5( ) cos(2 10 )c t t−= ×

index is a=0.85. Determine the power in the carrier component and in the sideband components of the modulated signalg


Demodulation of AM signalsE l D t tiEnvelop Detection

On +ve half cycle, diode is forward-biased, ycapacitor is charged to peak valueOn –ve half cycle, diode is reverse-biased and capacitor discharges slowly throughand capacitor discharges slowly through load resistor Rl. Assume AM wave was supplied by voltage source with internal impedance Rs. Also assume short charging time, i.e.

RsC << 1/fc,RsC 1/fc, and long discharging time, i.e.

1/fc << RlC << 1/W. Ripple can be removed by low-pass filter

Envelop Detector is Simple and efficient


when percentage modulation < 100%

Si l Sid b d (SSB) AMSingle Sideband (SSB) AM

Common problem in AM and DSBSC: bandwidth wastage because the transmission bandwidth

equals to twice the message bandwidthequals to twice the message bandwidth

⇒ SSB is very bandwidth efficient

H(ω)

ω


Generation of SSB Waves: Frequency discrimination method

Requirements on message signal m(t)q g g ( )Little or no low-frequency components, i.e. “holes” at 0Hz. E.g: audio signal (speech or music). In telephony, the useful frequency content of a speech signal is restricted to 0.3~3.4 kHza speech signal is restricted to 0.3 3.4 kHzThe highest frequency component W << carrier frequency fc

Block diagram

Productmodulator

m(t) band-pass filter

SSBmodulated wave

Two conditions for bandpass filterPassband occupies the same frequency range as desired SSB wave

)2cos( tfA cc π

Passband occupies the same frequency range as desired SSB waveGuardband, separating the passband from the stopband where the unwanted sideband of the filter input lies, should be less than twice the lowest frequency f in m(t) i e must be between f f to f +f


lowest frequency, fl, in m(t), i.e. must be between fc-fl to fc+fl

E i f SSB i lExpression of SSB signalsTh b b d i l b i h f fi iThe baseband signal can be written as the sum of finite sinusoid signal

( ) cos(2 )n

m t x f t f fπ θ+ ≤∑Then its USB component is

1( ) cos(2 ) ,i i i i c

im t x f t f fπ θ

=

= + ≤∑

Aft i t ti

[ ]1

( ) cos 2 ( ) )2

nc

c i c i ii

Am t x f f tπ θ=

= + +∑After maniputation

1 1( ) cos(2 ) cos 2 sin(2 ) sin 2

2

n nc

c i i i c i i i ci i

Am t x f t f t x f t f tπ θ π π θ π= =

⎧ ⎫⎡ ⎤ ⎡ ⎤= + − +⎨ ⎬⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦⎩ ⎭

∑ ∑1 12

( ) cos 2 ( )sin 22 2

i i

c cc c

A Am t f t m t f tπ π

= =⎣ ⎦ ⎣ ⎦⎩ ⎭

= − )

Hilbert transform of m(t)


Hilbert transform of m(t)

)()]()([1)( ωωωωωω HMMS ++ )()]()([2

)( ωωωωωω HMMS ccSSB ++−=

)]()([21)( cc SgnSgnH ωωωωω −−+=

1 )]()([41)( ccSSB MMS ωωωωω −++=

))(1( tt

)]()()()([1 SgnMSgnM ωωωωωωωω −−−+++

)cos)(2

( ttm cω⇔

)]()()()([4 cccc SgnMSgnM ωωωωωωωω +++

)sin)(ˆ1( ttm ω⇔


))(2

( c

Ab t Hilb t T fAbout Hilbert Transform$ 1 ( ) 1x τ∞

∫$ $ 1 ( ) 1( ) ( )xx t d x tt tτ τ

π τ π∞

−∞= = ∗

−∫( ) ( )x t x t⇔

( ) ( )X w X w⇔ [ ]( ) sgn( ) ( )X w j w X w= −j( ) ( ) [ ]( ) g ( ) ( )j

, 0( ) 0

j fH f j f

− >⎧⎪⎨( ) , 0

0, 0H f j f

f

⎪= <⎨⎪ =⎩

1)(ωH 睔穗

90°

ω ω

90°2009/2010 Meixia Tao @ SJTU 21

-90°

H(ω), 0

( )j f

f f− >⎧⎪⎨

H(ω)j

ω

( ) , 00, 0

H f j ff

⎪= <⎨⎪ =⎩

0

j

ω

-j

)(ωH 睔穗

1)(ωH

ω

睔穗

90°

ω ω

-90°


V ti i l Sid b d VSBVestigial Sideband: VSBSSB is not suitable when signals have significant lowSSB is not suitable when signals have significant low frequency componentsVSB is a compromise between SSB and DSBSCpVSB frequency domain description

M(f) VSB signal bandwidth is

WW 0 f

VSB signal bandwidth is B = W+fvfv: width of the vestigial sideband

W-W 0 f

S(f)

VSB is used in TV broadcasting and similar signals where good phase h t i ti i d

0 ffc-fc

characteristics are required and low frequency components are significant

2009/2010 Meixia Tao @ SJTU

23fv WfvW

C i f AM T h iComparison of AM TechniquesConventional AM demodulation uses simple envelopConventional AM demodulation uses simple envelop detector or square-law detector. Avoids complexity of coherent detection. E.g. AM radio broadcast systemsS d i t ffi i tSuppressed-carrier systems are more power efficient, making transmitters less expensive. Suitable for point-to-point transmissionsSSB d l ti i i i t ittSSB modulation requires minimum transmitter power and bandwidth. Suitable for point-to-point and over long distancesVSB b d idth i t b t SSB dVSB bandwidth requirements are between SSB and DSBSC. Suitable for TV transmissionIn SSB and VSB, the role of the quadrature qcomponent is to interfere with the in-phase component so as to eliminate power in one of the sideband achieve bandwidth saving


g

24

F Di i i M lti l iFrequency-Division MultiplexingMultiplexing is a technique where a number of independent signals are combined and transmitted in a common channela common channelThese signal are de-multiplexed at the receiverTwo common methods for signal multiplexingTwo common methods for signal multiplexing

TDM (time-division multiplexing): usually used to transmit digital informationtransmit digital informationFDM (frequency-division multiplexing: may be used for either analog or digital signal transmission


Bl k Di f FDMBlock Diagram of FDM

LPF: ensure signal bandwidth limited to Wbandwidth limited to W

MOD (modulator): shift message frequency g q yrange to mutually exclusive high frequency bands

BPF: restrict the band of each modulated wave to its prescribed range


FDM li ti i T l hFDM application in Telephone comm.SSB豟劒

LPF1( )x t BPFf × LPF

豟劒

SSB豟劒

LPF2( )x t ∑ 这派豟劒

( )cx t这派訿豟

fc1

BPFfc2

× LPF

1cffc1

SSB豟劒

LPF3( )x t BPFfc3 × LPF

2cffc2

Voice signal: 300～3400HzMessage is SSB modulated.

3cffc3

gIn 1st-level multiplexing, 12 signal are stacked in frequency, with a freq. separation of 4 kHz between adjacent carriersA it 48 kH h l ll d h l t itA composite 48 kHz channel, called a group channel, transmits 12 voice-band signals Higher-order FDM is obtained by combining several group


g y g g pchannels => FDM hierarchy in telephone comm. systems

27

Q d t C i M lti l iQuadrature-Carrier MultiplexingQ d i l i l i iQuadrature-carrier multiplexing: transmit two messages on the same carrier as

( ) ( )( ) ( ) 2 ( ) i 2t A t f t A t f t

cos() and sin() are two quadrature carriers

( ) ( )1 2( ) ( ) cos 2 ( )sin 2c c c cs t A m t f t A m t f tπ π= +

Each message signal is modulated by DSB-SCDemodulation of m1(t):

( ) ( ) ( ) ( )

( ) ( )

21 2( ) cos 2 ( )cos 2 ( )sin 2 cos 2

( ) ( ) cos 4 ( )sin 4

c c c c c c

c c c

s t f t A m t f t A m t f t f tA A Am t m t f t m t f t

π π π π

π π

= +

+ +( ) ( )1 1 2( ) ( ) cos 4 ( )sin 42 2 2

c c cc cm t m t f t m t f tπ π= + +


LPF

A li ti AM R di B d tiApplication: AM Radio BroadcastingCommercial AM radio uses conventional AMCommercial AM radio uses conventional AMThe radio receiver is of the superheterodyne type, i.e. involves the freq conversion or heterodyning from the q y gvariable carrier freq of the incoming RF (radio freq) signal to the fixed IF (intermediate freq signal)

Typical freq parameters– RF carrier range = 0.535 ~ 1.605 MHz– fIF = 455kHz– IF bandwidth = 10kHz


– IF bandwidth = 10kHz

Pi i lPrinciples off CiiCommunications - GitHub Pages · 2020. 10. 27. · Generation of SSB Waves: Frequency discrimination method Reqqgg()uirements on message signal m(t) Little

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