elec 350 communications theory and systems: i analog

ELEC 350Communications Theory and

Systems: I

Analog Signal Transmission

and Reception

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Analog Modulation

• A large number of signals are analog

– speech

– music

– video

• These signals can be used to modulate a carrier for transmission

– AM and FM radio

– Television

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Objectives of Modulation

• Convert a lowpass signal to bandpass

• Accommodate the simultaneous transmission of signals from several sources

• Expand the signal bandwidth to increase noise immunity

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Amplitude Modulation

• Double-sideband suppressed carrier (DSB-SC)

• Conventional AM

• Single-sideband (SSB) AM

• Vestigal-sideband (VSB) AM

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Phase-Locked Loop

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Conventional AM

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Envelope Detector

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Assignment 2 Due Oct. 10, 2007

• P&S 3.2

• P&S 3.4

• P&S 3.7, problems 1 and 2 only

• P&S 3.14

• P&S 3.16

• P&S 3.18

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Nonlinear Device

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• Suppose that the nonlinear device is approximated by a second order polynomial

)()(2

1

tvatv n

i

n

no

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• Input to the nonlinear device

• Output of the nonlinear device

• A band pass filter with bandwidth 2W centered at yields

where by design

)2cos()()( tfAtmtv cci

)2cos()(2

1)2(cos)()(

)2cos()()2cos()()(

1

21

22

2

2

21

2

21

tftma

aaAtfAatmatma

tfAtmatfAtmatv

cccc

cccco

cff

)2cos()(2

1)(1

21 tftm

a

aaAtu cc

1/)(2 12 atma

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• Assume that

• Let

• The diode will turn on if and will turn off if

• The output across the load resistor is

• Since s(t) is a periodic rectangular function, the Fourier series is

)(tmAc

0)( tc 0)( tc

)2cos()( tfAtc cc

)()]2cos()([

)()(

0)(0

0)()()(0

tstfAtm

tstv

tc

tctvtv

cc

i

i

1

1

)12(2cos12

)1(2

2

1)(

n

c

n

ntfn

ts

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• Hence

• Passing through a bandpass filter, we have

sother term)2cos()(4

12

)()]2cos()([)(0

tftmA

A

tstfAtmtv

c

c

c

cc

)2cos()(4

12

)( tftmA

Atu c

c

c

)(0 tv

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Balanced Modulator

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• Ring modulator for DSB-SC AM

• If c(t) > 0, 1, 4 on, and 2, 3 off,

• If c(t) < 0, 1,4 off, and 2,3 on,

)()( tmtvo

2

3

4

1

)()( tmtvo

C(t)

)(tvo)(tm

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• Therefore, we have

• Since c(t) is a periodic function, the Fourier series can be expressed as

• The desired DSB-SC AM signal is obtained by passing through a bandpass filter with center frequency and bandwidth 2W.

)()()( tctmtvo

1

1

)12(2cos12

)1(4)(

n

c

n

tnfn

tc

)(0 tv

cf

tftmtu c

2cos)(4

)(

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AM Radio Broadcasting

• Commercial AM-radio broadcasting utilizes the frequency band 535-1605 kHz for the transmission of voice and music. Carrier spacing is 10 kHz.

• The baseband message signal m(t) is limited to 5 kHz.

• Conventional AM is used from an economic standpoint. The major objective is to reduce the cost of implementing the receiver.

• A Superheterodyne receiver is used in most AM radios.– Intermediate frequency

– Image frequency

kHz 455IFf

IFc ff 2

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• Rejection of the radio signal at the image frequency

• Assume there are two received signals

The mixer output consists of the two signals

• The RF amplifier bandwidth is designed to be sufficiently narrow so that the image frequency signal is rejected

• The IF amplifier has bandwidth of 10kHz to reject signal from adjacent channels.

IFLOc fff '

)2cos()](1[)(

)2cos()](1[)(

'

22

11

tftmAtr

tftmAtr

cc

cc

)2cos()](1[)(

)2cos()](1[)(

22

11

tftmAty

tftmAty

IFc

IFc

Desired signalDesired signal

Interference from image channel

Interference from image channel

IFRF fB 2

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AM Modulation Summary

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ModulationPower

EfficiencySpectral

Efficiency (xW)

Modulation Complexity Demodulation

Conventional AM

low 2 low simple

DSB-SC high 2 low complex

SSB high 1 high complex

VSB high 1-2 medium complex

38

Angle Modulation

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Angle Modulation

• Angle modulation

– Frequency modulation (FM): Frequency is changed by the message m(t).

– Phase modulation (PM): Phase is changed by the message m(t).

• Angle modulated signals have a high degree of noise immunity, but require larger bandwidth than AM signals.

• They are widely used in high-fidelity music broadcasting.

• They have a constant envelope, which is beneficial when using nonlinear amplifiers.

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• An angle-modulated signal

: the phase of the signal

• Instantaneous frequency is given by

• Since u(t) is a bandpass signal, it can be represented as

FM and PM Signals

))(cos()( tAtu c

)(t

)(tfi

)(2

1)( t

dt

dtfi

))(2cos()( ttfAtu cc

)(2

1)( t

dt

dftf ci

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• If m(t) is the message signal, then in a PM system we have

• In an FM system

• From the above relationships we have

• On the other hand

)()( tmkt p

)(2

1)()( t

dt

dtmkftf fci

FMdmk

PMtmkt t

f

p

)(2

)()(

FMtmk

PMtmdt

dk

tdt

d

f

p

)(2

)()(

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• Maximum phase deviation in a PM system

• Maximum frequency deviation in an FM system

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)(maxmax tmkp

)(maxmax tmkf f

46

• The message signal is used with either FM or PM for the carrier . Find the modulated signal in each case.

Solution:

we have

• Modulation index for a general m(t)

)2cos()( tfatm m

)2cos( tfA cc

)2cos()()( tfaktmkt mpp )2sin()(2)( tff

akdmkt m

m

ft

f

PMPM FMFM

FMtftfA

PMtftfAtu

mfcc

mpcc

))2sin(2cos(

))2cos(2cos()(

mff

pp

fak

ak

/

Modulation indexModulation index

WfWtmk

tmk

ff

pp

//)(max

)(max

max

max

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• Narrowband Angle Modulation: If for all t, we have

then we can use the approximation

• The modulation is very similar to conventional AM

1)( t

( ) cos(2 ( ))

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

cos(2 ) ( )sin(2 )

c c

c c c c

c c c c

u t A f t t

A f t t A f t t

A f t A t f t

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( ) 1 ( ) cos(2 )

cos(2 ) cos(2 )cos(2 )

cos(2 ) cos(2 ( ) ) cos(2 ( ) )2

c c

c c c m

cc c c m c m

u t A m t f t

A f t a f t f t

AA f t a f f t f f t

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( ) cos(2 )

( ) cos(2 2 cos(2 ) )

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

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

cos(2 ) cos(2 ( ) ) cos(2 (2

m

t

c c f m

c c f m c c f m

cc c f m c

cc c f c m c

m t a f t

u t A f t k a f d

A f t f t A f t f t

AA f t f t f t

AA f t f f t f f

) )m t

Conventional AM vs Narrowband FM

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• Assume that the message is a sinusoidal signal

• The signal is periodic with period The same is true for the complex exponential signal

• Fourier series representation with coefficients

Spectral Characteristics of Angle-Modulated Signals

)2sin(2Re

))2sin(2cos()(

tfjtfj

c

mcc

mc eeA

tftfAtu

)2sin( tfm mm fT /1

)2sin( tfj me

due

dteefc

nuujtfu

f tfjntfj

mn

m

m mm

2

0

)sin(2

1

0

2)2sin(

2

1 Bessel function of the first kind of order

Bessel function of the first kind of order n

)(nJ

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• Therefore, we have

• Finally we obtain

• The actual bandwidth of the modulated signal is infinite. However, the amplitude of the sinusoidal components of frequencies for large n is very small.

• Property:

n

tnfj

n

tfj mm eJe 2)2sin(

)(

n

mcnc

tfj

n

tnfj

nc

tnffJA

eeJAtu cm

))(2cos()(

)(Re)(22

mc nff

odd )(

even )()(

nJ

nJJ

n

n

n

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Varactor Diode Angle Modulator

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• A nonlinear device followed by a bandpass filter tuned to the desired center frequency can be used as a frequency multiplier.

• For example, assume a nonlinear device of the form

• The output signal will be

• The frequency is multiplied by a factor of 2.

2( ) ( )ny t u t

2 2

22

( ) cos (2 ( ))

1cos(2 (2 ) 2 ( ))

2 2

c c

cc c

y t A f t t

AA f t t

Armstrong Modulator• The Armstrong modulator cannot produce much deviation, so a

combination of multipliers and mixers is used to raise the carrier frequency and the deviation. The multipliers are used to multiply the carrier and the deviation. The mixers are used to decrease the carrier, while keeping the deviation constant so that additional multiplier stages can be used to obtain more deviation.

• Example: An FM station is authorized to operate at 90.9 MHz, with maximum deviation of 75 KHz. The FM signal is generated with an Armstrong modulator whose output is 500 KHz with a deviation of 15.432 Hz. The modulator output is applied to 4 triplers and a doubler to obtain a frequency of 81 MHz and a deviation of 2.5 KHz. The 81 MHz signal is mixed with a 77.97 MHz signal to produce a 3.03 MHz signal whose deviation is still 2.5 KHz. This signal is fed through a doubler, tripler and quintupler to multiply the carrier to 90.9 MHz and the deviation to 75 KHz.

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Broadcast FM Generation

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• Generate an AM signal from u(t)

• Use an AM demodulator to recover m(t)

• Pass the FM signal through a filter with response

• If the input to the system is

the output is

• This is an AM signal!

2for )()( 0

ccc

BffffkVfH

t

fcc dmktfAtu )(22cos)(

FM Demodulation

t

fcfc dmktftmkkVAtv )(22cos))(()( 00

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Phase-Locked Loop FM Demodulator

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Costas Loop Detector

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Assignment 3 Due Oct. 26, 2007

• P&S 3.24

• P&S 3.26

• P&S 3.27

• P&S 3.28

• P&S 3.30

• P&S 3.31

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Edwin Howard Armstrong

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– Transmission of voice and music signals (bandwidth of m(t) is 15 kHz)

– 87.8 - 108 MHz

– 200 kHz carrier spacing

– Maximum frequency deviation 75 kHz

– Superheterodyne receiver with intermediate frequency

FM Radio Broadcasting

MHz 7.10IFf

FM Stereo Broadcasting

• Most FM stations transmit music in stereo using the outputs of two microphones.

• A pilot tone at a frequency of 19 kHz is added to the signal for the purpose of demodulating the DSB-SC AM signal.

• A monophonic FM receiver can recover the sum signal L+R by using a conventional FM demodulator. Hence, FM stereo broadcasting is compatible with conventional FM.

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FM Stereo

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Sample RBDS Signal

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• Commercial TV broadcasting began as black-and-white picture transmission by BBC in 1936.

• The two dimensional image is converted to a one-dimensional electrical signal by sequentially scanning the image.

• The scanning of the electron beam in the CRT is controlled by two voltage applied across the horizontal and vertical deflection plates.

• In commercial TV broadcasting, the bandwidth of the video signal is limited to W = 4.2 MHz.

• VSB modulation is employed, the video transmission bandwidth is about 5.5 MHz.

Television Broadcasting

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Television Audio Signal

• The audio portion of the TV signal is limited to W= 10 kHz.

• The maximum frequency deviation in the FM signal is 25 kHz.

• The FM signal bandwidth is 70 kHz.

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