Generation & Detection of Amplitude Modulationeee.guc.edu.eg/Courses/Communications/COMM601... ·...

Dr. Ahmed El-Mahdy COMM 601: Modulation I

COMM 601: Modulation I

Lecture 3

Generation & Detection ofAmplitude Modulation


tfj cetCts2

Re

tCta

Instantaneous Amplitude

Instantaneous Phase

tCt

Instantaneous Frequency

tdt

dtf

2

1

Instantaneous Amplitude, Phase, and Frequency

Angle of C(t)

Magnitude of C(t)


tftmkAts cac 2cos)(1

tfj cetCts2

Re

tfj

accetmkAts

2)(1Re

)(1 tmkAtC ac INSTANTANEOUS

AMPLITUDE

INSTANTANEOUS

PHASE

)(1 tmkAt ac

INSTANTANEOUS

FREQUENCY

tdt

dtf

2

1

|)(1| tmkAta ac

Instantaneous Amplitude, Phase, and Frequency of Conventional AM


tftfakAts cmmac 2cos2cos1

tfjcetCts

2Re

tfj

mmaccetfakAts

22cos1Re

tfakAtC mmac 2cos1INSTANTANEOUS

AMPLITUDE

INSTANTANEOUS

PHASE

0)( tCt

INSTANTANEOUS

FREQUENCY

02

1 t

dt

dtf

tfakAta mmac 2cos1

tfakA mmac 2cos1

Instantaneous Amplitude, Phase, and Frequency of Conventional AM (Single Tone Modulating Signal)


0 0.05 0.1 0.15 0.2 0.25 0.3

0

5

10

15

Time [Sec.]

Insta

nta

neous A

mplit

ude

0 0.05 0.1 0.15 0.2 0.25 0.3

-100

0

100

Time [Sec.]

Insta

nta

neous P

hase

INSTANTANEOUS

AMPLITUDE

INSTANTANEOUS

PHASE


Generation of Conventional AM Signal

(1) Using Product Modulator

)(ts

tftmA

aA

tfAtftmats

c

c

c

ccc

2cos)](1[

2cos2cos)()(

1

1

1a

ak



• Let be the input signal. The output of the nonlinear device can be expressed as

)()(1

tvatv n

i

n

no

)(tvi

(2) Square Law Modulator

constants


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

)()(2

1

tvatv ni

n

no


• Input to the nonlinear device

)2cos()()( tfAtmtv cci

)()( 2

21 tvatva ii

(2) Square Law Modulator (Cont.)


• Output of the nonlinear device

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

where by design

cff

)2cos()(2

1)(1

21 tftm

a

aaAts cc

(2) Square Law Modulator (Cont.)

1)(2

1

2 tma

aak

)2cos()(2

1)]4cos(1[2

1)()(

)2cos()(2

1)2(cos)()(

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

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

1

21

2

2

2

21

1

21

22

2

2

21

2

22

2

2

211

2

21

tftma

aaAtfAatmatma

tftma

aaAtfAatmatma

tftmAatfAatmatfAatma

tfAtmatfAtmatv

cccc

cccc

cccccc

cccco


(3) Switching Modulator:


)(tg

We assume that the diode acts as an

ideal switch:

-- The diode will turn on When the carrier

voltage c(t)>0

- The diode will turn off When the carrier

voltage c(t)<=0

Assume that )(tmAc

i.e the carrier dominates the behavior


• Let

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

• The output across the load resistor is

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

0)( tc 0)( tc

)2cos()( tfAtc cc

)()]2cos()([

)()(

0)(0

0)()()(0

tgtfAtm

tgtv

tc

tctvtv

cc

i

i

1

1

)12(2cos12

)1(2

2

1)(

n

c

n

ntfn

tg

From Signals


• Hence

• Passing through a bandpass filter centered around fc

and has BW=2W, we have

)2cos()(4

12

)( tftmA

Ats c

c

c

)(0 tv

ak

termsfrequencyhighother ..)]4cos([11

2

)()2cos()(

41

2

termsfrequencyhighother...)2(cos2

)2cos()(2

)2cos(22

)(

)12(2cos12

)1(2

2

1)]2cos()([

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

2

1

1

0

tfAtm

tftmA

A

tfAtftmtfAtm

ntfn

tfAtm

tgtfAtmtv

ccc

c

c

ccccc

n

c

n

cc

cc

BPF centeredAround Carrier frequency with

BW=2W

)(0 tv )(ts


Demodulation of Amplitude Modulated signals


Envelope Demodulation:

• The block diagram of the conventional AM receiver is shown in fig. The LPF is used to make smoothing of the waveform after the envelope detector.

LPF

tdBPF

ts )(tY )(tVEnvelope Detector


Demodulation of Conventional AMEnvelope Detector

Envelope

detector is a

circuit that

produces a

waveform

proportional

to the

envelope of

the input

signal.


Demodulation of Conventional AMEnvelope Detector

Remember:

-Short Time constant Fast charging or discharging

-Long Time constant Slow charging or discharging


Demodulation of Conventional AM Envelope Detector


Demodulation of Conventional AM-Envelope Detector



If the time constant is long






AM Broadcasting Station Standard

Defined by FCC (Federal Communication commission) United States


Applications of AM: Superhetrodyne Receiver

535 to 1700 kHz

540 to 1695 kHz



The output of the mixer is the intermediate frequency which is given by:

We consider only and the other frequencyis considered as image frequency. This image frequency is rejected using band

pass filter as shown in the above block diagram

Common

Tuning

TunerBPF

Antenna

http://en.wikipedia.org/wiki/File:Superhet2.png



-It is difficult to design a filter when fc is tunable (It takes different values for different broadcasting stations)


Superhetrodyne Receiver: Hetrodyne Function

9


Superhetrodyne Receiver: IF Section


Advantages of Superhetrodyne Receiver

• It reduces the signal from very high frequency sources where ordinary components

wouldn't work (processing in low frequency is easier).

• It allows many components to operate at a fixed frequency (IF section) and

therefore they can be optimized or made more inexpensively.

• It can be used to improve signal isolation (interference rejection).


AM Properties Summary

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