SEE 3533
COMMUNICATION PRINCIPLES
Chapter II – Amplitude Modulation
2.0 Amplitude Modulation (AM)
Objective:
• To learn AM modulation and demodulation technique.
• To learn AM generation and detection.
AM modulation technique will be studied:
• Double Side Band Full Carrier (DSBFC)
• Double Side band Suppressed Carrier (DSBSC)
• Single Side Band (SSB)
• Single Side Band Suppressed Carrier (SSBSC)
3
2.1 Introduction
Baseband: is a range of frequency signal to be transmitted. eg: Audio (0 - 4 kHz), Video (0 - 6 MHz).
Baseband Communication
Transmission without frequency shifting.
Transmission through twisted pair cable, coaxial cable and fiber optic cable.
Significant power for whole range of frequencies.
Not suitable for radio/microwave and satellite communication.
Carrier Communication
Use technique of modulation to shift the frequency.
Change the carrier signal characteristics (amplitude, frequency and phase) following the modulating signal amplitude.
2.2 DSB-FC – Full AM
• AM modulation is a fundamental modulation process in communication system.
• Carrier frequency signal >> than modulating frequency signal.
=> fc >> fm.
• Modulator is used to generate AM signal, amDSB-FC(t). It is shown in block diagram below.
E
v
t
t
t
v
AM(
)
c
m(
)
cos
cv
m(
t
)
v
c(
t
)
AM Modulator
Modulating signal
Carrier signal
5 • Let :
Therefore, amDSBFC signal can be expressed:
Given the modulation index :
amDSBFC can be deduced to:
From trigonometry identities:
Therefore: c m
E
E
m
m
t
t
E
t
v
AM(
)
c1
cos
mcos
c
A
B
A
B
B
A
cos
2
1
cos
2
1
)
cos(
)
cos(
t
mE
t
mE
t
E
t
t
mE
t
E
t
v
m c c m c c c c m c c c c AM
cos
2
cos
2
cos
cos
cos
cos
)
(
E
E
t
t
t
v
t
t
v
E
t
v
c m m c AM c m c AM
cos
cos
)
(
cos
)
(
t
E
t
v
c(
)
ccos
ct
E
t
• Signal frequency spectrum ; amDSBFC
t
t
mE
t
E
t
v
AM
c
c
ccos
c
m
cos
c
m2
cos
)
(
Carrier signal Sidebands signal
) (V Amplitud
) (rads1
c
c m mc
0
c
E
2
c
mE
2
c
mE
m
2 2
m
c E
mE
m
E
where
Jalur Sisi Bawah LSB
Jalur Sisi Atas USB Carrier band
7
0
m
1
c m
E
E
m
)
(
,
1
E
mE
cm
)
(
,
1
E
mE
cm
)
(
,
1
E
mE
cm
The modulation index is given by :
• The phase change for carrier signal when over-modulation
occurs and must be avoided.
•
Modulation depth
greater than 100% must be
avoided,
(
m
> 1 > 100%)
9
2.2.2 Modulation Index,
m
min max min max min max min max V V V V V V V V m p p p p p p p p V V V V m min max min max where m c E E
V max V min Ec Em
m m c m c m c m c E E E E E E E E E E m or dan Therefore m E m E m E m E
m t
E
Sampul c 1 cosm
m t
E
Sampul c 1 cosm
2.2.3 Power, AM
In the modulation process signal has been converted to electrical signal in terms of current or voltage.
The expression of AM signal components can be represented as follows:
) (V Amplitud
) (rads1
c
c m mc
0
c
E
2
c
mE
2
c
mE
2 2
m
c E
mE Di mana
t
mE
t
mE
t
E
t
v
AM
c
c
c
c
m
ccos
c
m2
cos
2
cos
)
(
11
R
E
m
R
E
m
R
E
R
mE
R
mE
R
E
R
V
R
V
R
V
P
P
P
P
c c c c c c USB LSB c USB LSB c T rms rms rms8
8
2
2
2
2
2
2
2 2 2 2 2 2 2 2 2 2 2
R
E
P
c c2
2
4
2 c USB LSBP
m
P
P
where Therefore
2
4
4
2 2 2 c c c USB LSB SBP
m
P
m
P
m
P
P
P
2
1
2
2 2m
P
P
m
P
P
P
P
c c c SB c T andTherefore the relationship between the total power transmitted, PT and the carrier signal power, Pc is as
2
1
2
m
P
P
P
T AM c%
100
T SB
P
P
Watt
Transmission efficiency, η for AM:
2 2 2
2 2
2
2
2
1
2
2
1
2
m
m
m
m
m
P
P
m
c
c
where PSB is the total sidebands signal power that contains information
If m = 1 (100% modulation), the average power, PSB = 50% Pc= Pc/2
13
2 2
2
m
m
From:The transmission efficiency with m = 1 is only 33.33% .
Therefore we can conclude that the transmitted power signal is mostly carrier power signal contributing of 66.67% from the total AM signal.
Whereas signal contains information in the LSB and USB transmitted is 33.33% from the total AM signal.
In practice, information signal is complex or non periodic signal,
eg: music, voice, image and etc. Its consists of many frequencies and harmonics components.
Its can be represented:
...
2
;
2
...
cos
cos
)
(
2 2
1 1
2 2
1 1
m m
m m
m m
m m
m
f
f
where
t
E
t
E
t
v
15
Each sideband is equal in bandwidth to that of the modulating signal and is a mirror image of the other.
Amplitude modulation is inefficient in terms of power usage and much of it is wasted. (66.67%)
At least two-thirds of the power is concentrated in the carrier signal, which
carries no useful information
The remaining power is split between two identical sidebands, though only one of these is needed since they contain identical information.
) (rads1
c
c m mc
0
c
E
2
c
mE
2
c
mE
2 2
m
c E
mE where
Amplitude(V)
2.3 DSBSC
•
To increase transmitter efficiency, the carrier can be
removed (suppressed) from the AM signal.
•
This produces a
reduced-carrier transmission
or
double-sideband suppressed carrier
(DSBSC) signal.
•
A suppressed carrier amplitude modulation scheme
is
three times more power efficient
than traditional
DSBFC.
DSBSC Modulator
v
DSBSC(
t
)
v
m(
t
)
cos
ct
vm(t)17
A B
A B
B
A cos
2 1 cos
2 1 ) cos( )
cos(
t
E
t
E
t
t
E
t
v
m c
m m
c m
m c
m DSBSC
cos
2
cos
2
cos
cos
)
(
t
E
t
v
m(
)
mcos
m
t
t
E
t
v
DSBSC(
)
mcos
mcos
cLet :
Therefore
v
DSBSC becomes :From trigonometry identity :
•
Frequency spectrum signal
am
DSBSC)
(
V
Amplitude
)
(
rads
1
c
c
mm
c
0
2
m
E
2
m
E
m
2
m
E
Jalur Sisi Bawah LSB
Jalur Sisi Atas USB
Modulating band
t
E
t
E
t
v
DSBSC
m
c
m
mcos
c
m2
cos
2
)
(
19
2.3.1.1 Power,
am
DSBSC
Components representation for amDSBSC signal:
)
(
V
Amplitud
) (rads1
c
c
mm c
0
2
m
E
2
m
E
t
E
t
E
t
am
DSBSC
m
c
m
mcos
c
m2
cos
2
)
(
Isyarat LSB Isyarat USB
LSB
R
E
R
E
R
E
R
E
R
E
R
V
R
V
P
P
P
m
m m
m m
USB LSB
USB LSB
T
rms rms
4
8
8
2
2
2
2
2
2 2
2 2
2 2
In DSBSC, all the power transmitted is sidebands power.
If R = 1 ohm.
4
2
m T
E
P
SB
T
P
P
21
2.3.2 SSB
• Both in amDSBFC and amDSBSC , the transmission bandwidth= 2 times the modulating signal bandwidth , vm(t).
• Both techniques transmit 2 sidebands i.e LSB and USB, which contain identical information - the wastage of energy still occur.
• Another technique to reduce the transmitted power is amSSB .
• In this technique of modulation only one sideband will be transmitted either LSB or USB signal.
Pemodulat SSB
am
SSBt
v
mt
ct
v
h(
t
)
sin
ct
2
1
cos
)
(
2
1
)
(
vm(t)
• To analyze, let vm(t) :
and
Therefore amSSB :
From trigonometry:
t
E
t
v
m(
)
mcos
m
t
E
t
E
t
E
t
E
t
am
m c m m c m m c m m c m SSB
cos
4
cos
4
cos
4
cos
4
)
(
t
t
E
t
t
E
t
am
SSB m
m
c msin
msin
c2
cos
cos
2
)
(
t
E
t
E
t
v
h m
m
msin
m2
cos
)
(
A B
kos
A B
kos B
kos A
kos
2 1 2 1 ) ( )
( A B kos
AB
kos
AB
23
• We can choose to transmit LSB or USB signal.
• Minus will have amSSB-LSB and plus will have amSSB-USB
t
E t E t E t E t E t t E t kos t E t am m c m m c m m c m m c m m c m c m m c m m USB SSB cos 2 cos 4 cos 4 cos 4 cos 4 sin sin 2 cos 2 ) (
t
E
t
am
SSB(
)
mcos
c
mIsyarat
am
SSB-LSB
t
E
t
25
•
Frequency spectrum isyarat
am
SSB
t
E
t
E
t
am
m c
m
m c
m
SSB
cos
2
cos
2
)
(
Isyarat amSSB-LSB
Isyarat amSSB-USB
)
(
V
Amplitud
) (rads1
c
c
mm c
0
2
m
A
2
m
A
m
m
A
Jalur Sisi Bawah LSB
Jalur Sisi Atas USB
2.3.2.1 Power
am
SSB
Mathematical representation for amSSB signal components:
)
(
V
Amplitud
) (rads1
c
c
mm
c
0
2
m
E
2
m
E
Isyarat LSB
Isyarat USB
LSB
V
USB
V
t
E
t
E
t
am
m c
m
m c
m
SSB
cos
2
cos
2
27
R
E
R
E
R
E
R
E
R
E
R
E
R
V
R
V
P
P
P
m m
m m
m m
USB LSB
USB LSB
T
rms rms
4
4
8
8
2
2
2
2
2 2
2 2
2 2
2 2
We therefore reduced thetransmitting power by 50%
compared to amDSB-SC . Assume, R
= 1 Ohm.
Therefore
4
2
m T
E
P
USB LSB
T
P
P
P
• Spektrum frekuensi isyarat amSSB
t A t A t am m c m m c m SSB cos 2 cos 2 ) (Isyarat amSSB-LSB
Isyarat amSSB-USB
m c m m c m m c m m c m SSBf
f
f
A
f
f
f
A
f
f
f
A
f
f
f
A
f
AM
2
2
2
2
)
(
Spektrum amSSB-LSB
Spektrum amSSB-USB
) (Hz f ) (V Amplitud c
f fc fm m
c f
f
0 fm
2
m
A
Jalur Memodulat
m
29
• VSB signal spectrum
( ) c ( ) cos(2 c ) c '( ) sin(2 c )
s t A m t f t A m t f t
Vestigal Sideband (VSB)
Vestigial sideband (VSB) transmission : Modified AM transmission in which one sideband, the carrier, and only a portion of the other sideband are
transmitted
VSB Signal, Spectrum
• VSB signal waveform
( ) c ( )cos(2 c ) c '( )sin(2 c )
s t A m t f t A m t f t
where: '( ) : the output of ( ) passing a filter
( ) : full upper sideband, with a partial lower sideband. ( ) : full lower sideband, with a partial upper sideband.
m t m t
2.4
AM Generation (DSBFC)
2 methods – Direct and Indirect methods.
(i) Direct - Kaedah terus
+
Ec
cosct
vs(t)cosct
v
AM
(
t
)
Balanced modulator Isyarat asal
vs(t)
mixer
E
v
t
t
t
t
v
t
E
t
v
c s
c
c s
c c
AM
cos
cos
cos
31
(ii) Indirect - Kaedah tidak terus
v
s(
t
)
v
c(
t
)
v
iv
k
v
operanti tidak linar
Penapis Lulus Jalur
(BPF)
t
E
t
v
t
E
t
v
c c
c
s s
s
cos
cos
t
v
t
v
t
v
i
s
cInput signal :
t
E
t
E
v
i
scos
s
ccos
c...
3 3 2
2 1
0
i i ik
E
m
v
m
v
m
v
v
cos
cos
....
cos
cos
cos
cos
....
cos
cos
2
cos
cos
cos
cos
....
cos
cos
cos
cos
2 2 2 2 2 2 2 1 1 0 2 2 2 2 2 2 2 1 1 0 2 2 1 0
t
t
E
E
m
t
E
m
t
E
m
t
E
m
t
E
m
E
t
t
E
E
m
t
E
m
t
E
m
t
E
m
t
E
m
E
t
E
t
E
m
t
E
t
E
m
E
v
s c s c c s c c s s c c s s c s c s c c s s c c s s c c s s c c s s k
Therefore:Isyarat
v
k(t) was then filtered using band pass filter
(BPF)
tuned at
the resonance (salun) frequency,
f
o= f
c.
t
t
E
m
m
E
m
t
t
E
E
m
t
E
m
v
c s s c s c s c c s c c o
cos
cos
2
1
cos
cos
cos
1 2 1 2 1
33
Compare the output signal:
t
E
m
ω
t
ω
t
v
AM
c1
cos
scos
ct
t
E
m
m
E
m
t
v
o(
)
c1
2
scos
scos
c1 2
1
Didapati isyarat terhasil adalah sama kerana komponen frekuensi yang terhasil adalah sama walaupun berlainan amplitud.
Spektrum frekuensi sebelum penapis Spektrum frekuensi selepas penapis
vk
0
sambutan frekuensi
penapis pembawa
fs 2fs (fc-fs) fc (fc+fs) 2fc f vo
f LSB USB
pembawa
2.5 Generation of DSBSC
Direct – menggunakan pemodulat terimbang/balanced modulator.
Fungsinya seperti pendarab/multiplier – menghasilkan isyarat LSB dan USB sahaja.
Isyarat asal
vs(t)
vc(t)
vs(t)cosct Pendarab
v
v
(a) Isyarat maklumat
t
t v
DSBSC
t
35
Isyarat pembawa,
v
cdiberi oleh siri Fourier sebagai ;
Mathematical Analysis
v
c(t)= { sin
ct
+ sin 3
ct
+ ………}
If
v
s(t)= E
scos
st
dan
k
is a multiplier sensitivity factor
Modulator output can be expressed:
t t kE t t kE t t kE t t kE t t t kE t v t kv v s c s c s s c s c s c s c s s c s s c c s s c s o
2 cos 2 cos 2 sin sin 2 sin sin 2 1 4 ... sin 4 cos 3 sin 3 1 sin 4 cosGeneration DSBSC – Indirect method
v
s(t))cos
ct
(Isyarat DSBSC)
E
ccos
ct
½
v
s(t)
-½
v
s(t)
(
E
c+½
v
s(t)
)
cos
ct
(
E
c-½
v
s(t)
)
cos
ct
+
+-
AM
modulator AM
modulator
Using 2 full AM modulator
The input signal are the same with different polarity but the same carrier frequencies
37
2.6 Generation of SSBSC
Can be realized in two ways :
(i) Generate first DSBSC signal dan
(ii) Then filtered DSBSC signal with band pass filter (BPF)
v
DSBSCv
SSBSCPemodulat terimbang
v
s(
t
)
cos
ct
BPF
BPF is a tuned circuit (litar tertala) that is very selective that will choose either LSB or USB to pass through.
Not important which sideband will be selected because both sidebands contain the same information.
Another method – using 2 balanced modulator that will produced 2 DSBSC signal with 180o phase difference (bezafasa).
The circuit is called litar anjakan fasa (phase shifting circuit).
Generation of SSBSC
Pemodulat terimbang 1
Anjakan fasa 900
+
v
SSBSCPemodulat Phase shift
900
t
ω
t
ω
mE
v
1
ccos
scos
ct
ω
E
t
v
s(
)
scos
st
ω
E
ssin
st ωc
cos
t ωc
sin
mixer + +
Phase Shift Method pg.176, B.P.Lathi
- /2
Which delays the phase of every
spectral component
39
Output balanced modulator 1 :
Mathematical Analysis
t
t
mE
t
v
1(
)
ccos
scos
ct
t
mE
t
v
2(
)
csin
ssin
cOutput balanced modulator 2 :
Hence output :
v
SSBSC=
v
1(t) + v
2(t)
cos
}
{cos
2
}
cos
{cos
2
sin
sin
cos
cos
t
t
mE
t
t
mE
t
t
mE
t
t
mE
s c
s c
c
s c
s c
c
c s
c c
s c
t
mE
• VSB signal spectrum
( ) c ( ) cos(2 c ) c '( ) sin(2 c )
s t A m t f t A m t f t
2.7 Generation of VSB
v
VSB
Penapis
VSB
v
s(
t
)
v
DSBSC2cos
ct
f (Hz)
v
VSBLSB USB
carrier
41
2.8 Demodulation/Penyahmodulatan
Information
signal
Information
signal
Rx
Tx
Modulated signal
(AM/FM)
Process to get beack the modulating signal or original signal. Done at the receiver part.
Demodulation done by demodulator circuit also called detector circuit.
Simple and economic detector for AM wave is envelope detector (pengesan sampul).
2.8.1 Demodulation AM
DSB-FC
(i) Envelope Detector Circuit – other name Rectifier
Detector
(Pengesan
Penerusuai)
or Diode Detector
(Pengesan Diod)
• Low cost
• Simple
• Does not need local carrier generator
Original signal
overlap with the envelope modulated
signal
+ C’
R’ R
a b c d
C
LPF
[Ec+ vs(t)] cos c t
43
(i)
Envelope Detector
IF RC is too large, voltage drop rate is slow and will cause diagonal clipping (perepangan pepenjuru) where parts of the peak input could not be detected at the output (Refer Rajah 2.18(a)) .
If RC is too small, output signal at the capacitor will have ripple (riak) and will cause distortion (wujud herotan) to the received information signal (Rujuk Rajah 2.18(b)) .
t
Rajah 2.18(a)
t
Rajah 2.18(b)
Discharge rate or voltage drop of the capacitor depends on RC time constant.
RC too
LPF Diode
Filter out DC component
R2 R1
C1
C2 Rs
m
ω
m
m
RC
2 / 1 2
1
To avoid that problem make sure the value of :
m – modulation index and
m – angle frequency of information signal45 1
1 RsC
When s(t) > vo(t)
Diode, D in forward biased condition Capacitor, C1will charging up to
where
When s(t) < vo(t)
Diode, D in reverse biased condition Capacitor, C1 will discharge up to where 2 R1C1
c
f
1
1
BW fc
1 1
2
s(t) v
o(t)
D
C1 R1 Rs
vo(t)
s(t)
D
C1 R1 Rs
Selection effect of RC value
Kesan pemilihan nilai RC right value
47
Mathematical Analysis
Assuming the function of the diode as a switch, output of the diode, Vd :
E
v
t
cos
ω
t
k
(
t
)
V
d
c
s cwhere k(t) is a representative of switching function of the diode
cos
3
...
3
1
cos
2
2
1
cos
t
t
t
t
v
E
V
d c s c
c
c
keranapemuat C menghalangarus terus melaluinya. 1 1 . pada salun frekuensi mempunyai LPF gi lebih ting frekuensi 1 ... 3 cos 3 1 cos 2 2 1 cos '
c s d titik s c c titik s s c c c c s c b titik d E t v V t v E V f t v E t t t t v E V V +a b c d
V pada titik a
t 0
[Ec+vs(t)] cos c t
Ec+vs(t)
1/ [Ec+vs(t)] V pada titik b
t
1/ [Ec+vs(t)] V pada titik c
t
1/ vs(t)
t V pada titik d
+
a b c d
49
amDSB-FC(t)
C
y(t)
Litar Kuasa Dua y =x2
Penapis Lulus Rendah
x(t)
A A m t m t A m t A m t kos t
t kos t m A t m A t kos t m t m t kos A A t kos t m A t kos t m t kos A t kos t m A t am t x c c c c c c c c c c c c c c c c c c c FC DSB
2 ] ) ( ) ( 5 . 0 5 . 0 [ ) ( 5 . 0 ) ( 5 . 0 2 ) ( ) ( 2 ) ( 5 . 0 ) ( 5 . 0 2 5 . 0 5 . 0 ) ( 2 ) ( } )] ( {[ )} ( { ) ( 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 DC component Information signal Harmonic signal)
(
)
(
t
A
m
t
y
cAfter passing through LPF the output is the required information signal ie:
(ii) Square Detector (Pengesan Kuasa Dua)
2.8.1 Demodulation AM
DSB-FC
2.9 Demodulation AM
DSB-SC
•
Due to the envelope modulated signal is not in the
same form of modulating signal,
m(t)
so the
envelope detection technique could not be used.
•
The detection of modulated signal could be done
using
pengesan segerak (
synchronous detector
)
also
51
2.9.1 Pengesan Segerak (Synchronous)
• Litar segerak, memerlukan sebuah penjana pembawa tempatan.
• Di mana isyarat penjana ini perlu disegerakkan dengan isyarat pembawa maklumat yang digunakan pada pemancar.
)
(
cos
)
(
)
cos(
)
cos(
)
(
)
cos(
)
(
)
(
2
t
t
m
t
t
t
m
t
t
am
t
x
c
c c
c SC
DSB
X
PenapisLulus Rendah
Penjana Pembawa Tempatan (LO)
c(t)=cos(ωct)
amDSB-SC(t) x(t) y(t)
Multiplier
Analisa matematik :
Analisa Matematik
• Keluaran pendarab adalah
• Identiti trigonometri
• Maka
• Selepas melalui LPF isyarat keluaran adalah isyarat maklumat asal
1
(
2
)
2
1
)
(
2
u
kos
u
kos
)
2
(
)
(
2
1
)
(
2
1
)
2
(
1
)
(
2
1
)
(
t
kos
t
m
t
m
t
kos
t
m
t
x
c c
)
(
2
1
)
(
t
m
t
y
)
(
)
(
)
(
t
m
t
kos
2t
53
2.9.1.1 Kesan Ralat Frekuensi Pembawa
• Masalah ini akan menyebabkan herotan berlaku di dalam proses penyahmodulatan isyarat amDSB-SC.
X
PenapisLulus Rendah
Penjana Pembawa Tempatan (LO)
c(t)=kos[(ωc+Δω)t]
amDSB-SC(t) x(t) y(t)
Multiplier
Analisa Matematik Ralat Frekuensi
• Keluaran pendarab adalah
• Identiti trigonometri :
• Maka
• Dengan melalukan isyarat x(t) ke dalam penapis lulus rendah, isyarat maklumat dapat diperolehi semula.
(
)
(
)
2
1
)
(
)
(
A
kos
B
kos
A
B
kos
A
B
kos
)
2
(
)
(
2
1
)
(
)
(
2
1
)
2
(
)
(
)
(
2
1
)
(
t
kos
t
m
kos
t
m
t
kos
kos
t
m
t
x
c c
)
(
)
(
2
1
)
(
t
m
t
kos
y
]
)
[(
)]
(
)
(
[
)
(
t
m
t
kos
t
kos
t
55
Implikasi Ralat Fasa Pembawa
• Kesan ralat fasa ini akan mewujudkan herotan, oleh yang
demikian penalaan isyarat pembawa tempatan perlulah tetap.
• Keluaran pada LPF mempunyai faktor kos(φ).
• Di mana jika
) ( )
( 2 1 )
(t m t kos
y
0
2
) ( 2 1 )
(t m t y
0
)
(
t
y
Untuk memastikan pengayun tempatan (LO) ditetapkan fasanya keada isyarat masukan supaya keluarannya isyarat maklumat/asal maksima, Gelung Costas / PLL digunakan.
2.9.2 Penyahmodulatan AM
SSBSC
X
PenapisLulus Rendah
vc(t)
amSSBSC(t) x(t) vo(t)
Multiplier
2.9.2.1 Pengesan Segerak SSBSC
Analisa Matematik :
asal
isyarat
komponen
cos
2
1
LPF,
Selepas
cos
2
cos
2
1
cos
cos
1
bersamaan
amplitud
dengan
cos
t
ω
v
t
ω
t
ω
ω
t
ω
t
ω
ω
v
v
v
t
ω
ω
v
S LPF
S s
c c
s c
c SSBSC
o
s c