Dr. Ahmed El-Mahdy COMM 601: Modulation I
COMM 601: Modulation I
Lecture 3
Generation & Detection ofAmplitude Modulation
Dr. Ahmed El-Mahdy COMM 601: Modulation I
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)
Dr. Ahmed El-Mahdy COMM 601: Modulation I
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
Dr. Ahmed El-Mahdy COMM 601: Modulation I
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)
Dr. Ahmed El-Mahdy COMM 601: Modulation I
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
Dr. Ahmed El-Mahdy COMM 601: Modulation I
Generation of Conventional AM Signal
(1) Using Product Modulator
)(ts
tftmA
aA
tfAtftmats
c
c
c
ccc
2cos)](1[
2cos2cos)()(
1
1
1a
ak
Dr. Ahmed El-Mahdy COMM 601: Modulation I
Generation of Conventional AM Signal
• 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
Dr. Ahmed El-Mahdy COMM 601: Modulation I
• Suppose that the nonlinear device is approximated by a second order polynomial.
)()(2
1
tvatv ni
n
no
Generation of Conventional AM Signal
• Input to the nonlinear device
)2cos()()( tfAtmtv cci
)()( 2
21 tvatva ii
(2) Square Law Modulator (Cont.)
Dr. Ahmed El-Mahdy COMM 601: Modulation I
• 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
Dr. Ahmed El-Mahdy COMM 601: Modulation I
(3) Switching Modulator:
Generation of Conventional AM Signal
)(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
Dr. Ahmed El-Mahdy COMM 601: Modulation I
• 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
Dr. Ahmed El-Mahdy COMM 601: Modulation I
• 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
Dr. Ahmed El-Mahdy COMM 601: Modulation I
Demodulation of Amplitude Modulated signals
Dr. Ahmed El-Mahdy COMM 601: Modulation I
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
Dr. Ahmed El-Mahdy COMM 601: Modulation I
Demodulation of Conventional AMEnvelope Detector
Envelope
detector is a
circuit that
produces a
waveform
proportional
to the
envelope of
the input
signal.
Dr. Ahmed El-Mahdy COMM 601: Modulation I
Demodulation of Conventional AMEnvelope Detector
Remember:
-Short Time constant Fast charging or discharging
-Long Time constant Slow charging or discharging
Dr. Ahmed El-Mahdy COMM 601: Modulation I
Demodulation of Conventional AM Envelope Detector
Dr. Ahmed El-Mahdy COMM 601: Modulation I
Demodulation of Conventional AM-Envelope Detector
Dr. Ahmed El-Mahdy COMM 601: Modulation I
Demodulation of Conventional AM-Envelope Detector
If the time constant is long
Dr. Ahmed El-Mahdy COMM 601: Modulation I
Demodulation of Conventional AM-Envelope Detector
Dr. Ahmed El-Mahdy COMM 601: Modulation I
Demodulation of Conventional AM-Envelope Detector
Dr. Ahmed El-Mahdy COMM 601: Modulation I
AM Broadcasting Station Standard
Defined by FCC (Federal Communication commission) United States
Dr. Ahmed El-Mahdy COMM 601: Modulation I
Applications of AM: Superhetrodyne Receiver
535 to 1700 kHz
540 to 1695 kHz
Dr. Ahmed El-Mahdy COMM 601: Modulation I
Applications of AM: Superhetrodyne Receiver
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
Dr. Ahmed El-Mahdy COMM 601: Modulation I
Applications of AM: Superhetrodyne Receiver
-It is difficult to design a filter when fc is tunable (It takes different values for different broadcasting stations)
Dr. Ahmed El-Mahdy COMM 601: Modulation I
Superhetrodyne Receiver: Hetrodyne Function
9
Dr. Ahmed El-Mahdy COMM 601: Modulation I
Superhetrodyne Receiver: IF Section
Dr. Ahmed El-Mahdy COMM 601: Modulation I
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).
Dr. Ahmed El-Mahdy COMM 601: Modulation I
AM Properties Summary
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