SEE 3533
SEE 3533
COMMUNICATION PRINCIPLES
COMMUNICATION PRINCIPLES
Chapter III
3.1 Introduction
3.1 Introduction
•
Beside
AM technique
, there is another technique that
used modulating signal to change
frequency and
phase
of
carrier signal.
•
Both are known as
Angle Modulation
.
•
Also known as
Exponent Modulation
.
•
Introduced in 1931 (Edwin H. Armstrong).
•
Generally sinusoidal signal expression:
•
Therefore, we can change the
amplitude
and
angle
of
the
carrier signal
in order to send information signal.
)]
(
cos[
)
(
t
A
t
3.2 Basic Concept of Angle Modulation
3.2 Basic Concept of Angle Modulation
Graph shown the characteristic of sinusoidal signal
The angle of sinusoidal signal :
o c
t
t
(
)
Gradient for θ(t)=ωct+ois an angle frequency,
ωc for sinusoidal signal.
For nonlinear process,θ(t)=θx(t), the
gradient representsinstantaneous angle frequency, ωi for sinusoidal signal.
) ( )
( )
( t
dt t d t
i
t
i d
t
0
) ( )
(
and the instantaneous angle value is given by integration of:
Therefore, we can calculatethe instantaneous angle frequency,ωi at time t by calculating the gradient of graph θ(t) at time t i.e:
This can be seen at the time intervalt (t1 andt2) both signal are the same.
• Therefore, it is shown that information signal, vm(t) can be transmitted with the amplitude of the carrier signal is held constant and the angle
either the phase or frequency of the carrier is varied linearly with the information signal, vm(t).
• Let the carrier signal:
• And the instantaneous angle value:
)]
(
[
cos
)
(
t
E
t
t
v
c
c
c
c)
(
)
(
t
ct
ct
c
t
dt
t
d
t
c c ci
(
)
(
)
t
t
dt
t
c ct i
c
0
)
(
Ec
c(t)
ct
c(t)
i(t)
c(t)
c(t)
Therefore, the instantaneous angle frequency andinstantaneous angle value are given by:
Angle Modulation
Angle Modulation
t
dt
t
d
t
c c ci
3.3 Phase Modulation (PM)
3.3 Phase Modulation (PM)
)
(
)
(
t
ct
ct
c
)
(
)
(
t
ct
k
pv
mt
c
)]
(
[
)
(
t
E
kos
t
k
v
t
v
PM
c
c
p mdt
t
dv
k
dt
t
d
t
c c p mi
)
(
)
(
)
(
Pemodulatan Sudut
PM implies that the
phase deviation
of the carrier,
cis
proportional to the
modulating signal
,
v
m(
t
):
where
k
pis the phase deviation constant in radians/sec/volt
And
the instantaneous angle frequency:
3.4 Frequency Modulation (FM)
3.4 Frequency Modulation (FM)
c c f
t mFM
t
E
kos
t
k
v
t
dt
v
0
t c f m c f t mc
t
k
v
t
dt
t
k
v
t
dt
0 0
)
(
)
(
)
(
)
(
)
(
t
ck
fv
mt
i
t
dt
t
d
t
c c ci
(
)
(
)
FM implies that the
frequency deviation
of the carrier,
is proportional to the
modulating signal,
v
m(
t
):
t
c
where
k
fis the frequency deviation constant in radians per volt
Integrate:
3.5 Relationship between FM and PM
3.5 Relationship between FM and PM
• We can generate FM signal by using PM modulator and vice versa.
• From the above block diagrams, it can be shown that the generation of FM and PM signals are mutually related.
Differentiator
FM Modulator
v
m(
t
)
v
PM(t)
dt d
PM Modulator
v
m(
t
)
Integratorv
FM(t)
dt
Generation of FM
Generation of PM
Pemodulatan Sudut
)]
(
[
)
(
t
E
kos
t
k
v
t
v
PM
c
c
p m
c c f
t mFM t E kos t k v t dt
v
0
• Demodulation process is used to get back the information signal. • For FM demodulator in order to get back information signal from FM
signal : PM modulator is used and the signal is pass through differentiator.
• In contrast for PM demodulator : FM demodulator is used and the signal is pass through the integrator.
• This shows the close relationship between FM and PM.
• Hence we can discuss only either one technique in angle modulation.
Differentiator
dt d PM
Demodulator
v
m(
t
)
v
FM(t)
FM Demodulator
FM
Demodulator
v
m(
t
)
v
PM(t)
Integrator
dtPM Demodulator
c c f
t mFM t E kos t k v t dt
v
0
)]
(
[
)
(
t
E
kos
t
k
v
t
3.6 Analysis of AM signal
3.6 Analysis of AM signal
)
cos(
)
(
t
E
t
v
m
m
m]
sin
[
cos
]
)
cos(
[
cos
)
(
0
t
E
k
t
E
dt
t
E
k
t
E
t
v
m m
m f c
c
t
m m
f c
c FM
Pemodulatan Sudut
t
m f
c c
FM
t
E
t
k
v
t
dt
v
0
cos
Assuming that the modulating signal,
v
m(
t
)
:
Take:
m
m
f
f
m f
E
k
]
sin
[
cos
)
(
t
E
t
t
v
FM
c
c
m]
sin
[
cos
)
(
t
E
t
k
E
t
v
m mm f c
c
FM
rad/s, as a maximum frequency deviation
•
Define the modulation index
as a
ratio of maximum frequency
deviation to modulating signal frequency:
•
Trigonometric identities:
)]
(
sin
[
sin
)
sin(
)]
sin(
cos[
)
cos(
)
(
t
E
t
t
E
t
t
v
FM
c
c
m
c
c
m
genap n
m n
m
t
)]
J
(
)
2
J
(
)
cos(
n
t
)
sin(
cos[
0
ganjil n
m n
m
t
)]
2
J
(
)
sin(
n
t
)
sin(
sin[
n = even
n = odd
)
sin(
)
sin(
)
cos(
)
cos(
)
cos(
A
B
A
B
A
B
Pemodulatan Sudut
]
sin
[
cos
)
(
t
E
t
t
v
FM
c
c
m•
Hence :
Expand using Fourier series yields:
Where
cos
[
β
sin
(
ω
mt
)]
dan
sin
[
β
sin
(
ω
mt
)] is a trigonometric series called as
•
Using Bessel identities :
]
)
cos(
)
)[cos(
(
]
)
cos(
)
)[cos(
(
)
cos(
)
(
)
sin(
)
sin(
)
(
2
)
cos(
)
cos(
)
(
2
)
cos(
)
(
)
sin(
)
(
2
)
sin(
]
)
cos(
)
(
2
)
(
)[
cos(
)
(
0 0 0t
n
t
n
J
E
t
n
t
n
J
E
t
J
E
t
n
t
J
E
t
n
t
J
E
t
J
E
t
n
J
t
E
t
n
J
J
t
E
t
v
m c genap n m c n c m c ganjil n m c n c c c ganjil n m c n c genap n m c n c c c ganjil n m n c c genap n m n c c FM
Substitute inv
FM
odd
n
even
n
J
J
J
n n n
n n
n
J
•
Hence FM equation also known as WBFM:
Pemodulatan Sudut]}
)
cos[(
]
)
){cos[(
(
...
]}
)
4
cos[(
]
)
4
){cos[(
(
]}
)
3
cos[(
]
)
3
){cos[(
(
]}
)
2
cos[(
]
)
2
){cos[(
(
]}
)
cos[(
]
)
){cos[(
(
)
cos(
)
(
)
(
4 3 2 1 0t
n
t
n
J
E
t
t
J
E
t
t
J
E
t
t
J
E
t
t
J
E
t
J
E
t
v
m c m c n c m c m c c m c m c c m c m c c m c m c c c c FM
Sideband 1 Sideband 2 Sideband 3 Sideband 4 Sideband n Carrier band
(
)
cos[(
)
]
)
(
t
E
J
n
t
v
FM c n
c
m3.6.1 Frequency Spectrum of FM signal
3.6.1 Frequency Spectrum of FM signal
m c
c c m
β= 0.25
) (rads1
BW
m c
4 c c4m
β= 2
)
(
rads
1
BW=2nfm=8fm
m c
8 c c8m
β= 5
) (rads1
BW=2nfm=16fm
Bessel Function for n=0 to n=4
Bessel Function Plot
Pemodulatan Sudut
Bessel Function Table
•
Frequency spectrum consists of
carrier component at
f
cand also
sideband at
f
c±
nf
mwhere n is an integer
(
n
= 1,2,3,…)
•
The
number of sideband depends
on index
modulation value,
β
.
•
Magnitude of carrier signal
decreases as
β
increases.
•
Amplitude
of the frequency spectrum depends on
value of
J
n(
β
).
•
The
bandwidth
of modulated signal
increases
when
index modulation,
β
increases.
BW > 2
∆
f
mis expected
.
3.6.2 Carlson’s Rule
3.6.2 Carlson’s Rule
•
Even though
FM signal has infinite number of sidebands
but
from the experiment conducted, it is shown that errors
(herotan) due to the
band limited signal
of FM
can be neglected
if
98%
of the power of the signal has been
transmitted.
•
Based on Bessel function,
98% of signal power has been
transmitted
if the number of the sidebands transmitted equal
to
1+
β
.
•
Therefore the BW needed for FM was :
Pemodulatan Sudut
mm
f
f
f
BW
2
3.6.3 Narrow Band FM (NBFM)
3.6.3 Narrow Band FM (NBFM)
•
For FM signal with the small index modulation i.e
β
< 0.2, is
called
Narrow Band FM (FM jalur sempit)
•
For FM signal that we have studied previously also known as
WBFM
and the equation is given by :
•
Let :
•
Hence, the equation yields:
•
NBFM
with
β
= small , therefore;
)
sin(
)
(
t
mt
)]
(
sin
[
sin
)
sin(
)]
sin(
cos[
)
cos(
)
(
t
E
t
t
E
t
t
v
FM
c
c
m
c
c
m)]
(
[
sin
)
sin(
)]
(
cos[
)
cos(
)
(
t
E
t
t
E
t
t
v
FM
c
c
c
c
1
)
sin(
)
(
t
mt
Pemodulatan Sudut
]
)
cos[(
2
]
)
cos[(
2
)
cos(
)
sin(
)
sin(
)
cos(
)
sin(
)
(
)
cos(
)
(
t
E
t
E
t
E
t
t
E
t
E
t
t
E
t
E
t
v
m c c m c c c c c m c c c c c c c FM
1
)]
(
cos[
t
andsin[
(
t
)]
(
t
)
t
mE
kos
t
mE
kos
t
kos
E
t
am
c c mm c c c c FC
DSB
2
2
)
(
•
Therefore :
•
Hence NBFM equation yields :
•
Compared with
am
DSB-FCsignal:
•
It is shown from both equations for NBFM and
am
DSB-FCconsist of
one carrier component and two sidebands components. But
LSB
component for NBFM
the phase shift is varies for
90° (
quadrature
).
1
)
sin(
)
(
t
mt
3.7 Differences between FM and AM
3.7 Differences between FM and AM
• Frequency spectrum
• Phase diagram (Rajah pemfasa)
) (V Amplitud
) (rads 1
c
c m m c 0 c A 2 c mA 2 c mA 2 2 m c A mA Di mana ) (V Amplitud ) (rads 1
c
c m m c 0 c A 2 c A 2 c A 2 c A 2 c A c A m c m ) (t vFM ) (t 2 c mA 2 c mA c A m c m ) (t amDSBFC
3.8 Power in FM signal
3.8 Power in FM signal
•
Power signal
depends on the
amplitudes
and
not
on the
frequencies.
•
The
amplitude of the FM signal is constant
and therefore the
power transmitted depends only on the
amplitudes
of the
signal. It does not depends on the
modulation index.
•
For
AM
signal the power transmitted depends on the
modulation index
.
•
It can be seen from the Bessel equation:
•
In other word the
total power of FM signal
consists of the
power in carrier component
and
all the power in the sidebands.
Pemodulatan Sudut
12
...
2
0 3 2 1 0 n J J J J J J J T n nP
P
P
P
P
P
P
P
1 2 2 0 2 2 3 2 2 2 1 20
2
2
2
...
2
2
1
n
n
n
J
J
J
J
J
J
•
FM equation is given by:
•
And therefore the total power transmitted :
Ex. 1 :
A carrier with a peak value of 2000 V is frequency modulated with a
message signal of 5 kHz. The modulation index obtained is 2. Calculate the
average power in:
(i) Highest sideband (ii) Lowest sideband . Given R = 50
Ω
.
Solution :
For β= 2 from Bessel table :
The highest sideband is :
J
1
0
.
58
The lowest sideband is :J
5
0
.
01
2
0
.
01
58
.
0
2
5 1
J
J
=>
R
E
P
C1
2
58
.
0
21
(i)
kW
5
.
13
50
1
2
2000
58
.
0
2
50
1
2
2000
01
.
0
25
P
W
4
Ex. 2 :
(a) Determine the BW required to transmit FM signal when the modulating frequency, fm = 10 kHz and maximum frequency deviation is 20 kHz.
From Bessel table the components obtained is J0, J1, J2 , J3, J4 and J5 That means J1 will be at 10 kHz, J2 at 20 kHz, J3 at 30 kHz etc.
Therefore BW = BFM = 2nfm= 2 x 5 x 10 = 100 kHz
2
10
20
m
f
f
Amplitud
fc fc+fm fc+2fm J0
J1
J5
fc-fm f (kHz)
mm
f
f
f
BW
2
1
2
Carson Rule
(b) Repeat (a) with fm= 5 kHz
From Bessel table the highest component is J7 Therefore BW = 2 x 7 x 5 = 70 kHz
4
5
20
m
f
f
f
f
mm
f
BW
2
1
2
Carson Rule
Ex. 3 :
A FM signal, 2000 cos (2πx 108 t + 2 Sin πx 104t) is transmitted using an antenna with
the resistance of 50 Ω. Determine
(i) Carrier frequency (ii) Modulation index (iii) Information signal
(iv) Power transmitted (v) Bandwidth (vi) Power in highest and lowest sidebands
Penyelesaian :
]
sin
[
cos
)
(
t
E
t
t
v
FM
c
c
mBandingkan :
(i) fc = 108 Hz = 100 MHz
(ii) β= 2
(iii) fm = 104 / 2 = 5 kHz
i) (v) β= 2 => bilangan jalursisi 4
BW = BFM = 2nfm = 2 x 4 x 5 = 40 kHz Carson - BW = 2(β+ 1)fm = 2(2 + 1)5 = 30 kHz i) (iv)Ec = 2000 V => Ec(rms) = 2000 / 2
Kuasa dipancarkan PT = V2
(rms)/ R
= (2000 / 2)2 / 50
= 40 kW
(vi) Dari jadual J1 jalursisi amplitud tertinggi
Nilai puncak jalursisi = 0.58 x 2000 Kuasa P = (0.58 x 2000/2)2 / 50 Ω
= 13.27 kW untuk satu jalursisi Dua jalursisi = 2 x 13.27 kW = 26.54 kW Kedua-dua jalursisi berada pada
fc fm= 100 MHz 5 kHz Kuasa jalursisi terkecil J4
Contoh 3.1
Satu isyarat FM mempunyai persamaan berikut :
c c f
t mFM
t
E
t
k
v
t
dt
v
0
cos
di mana
v
m
t
E
msin
2
f
mt
,
100
V
,k
f
10
kHz
,c
E
kHz
5
dan
V
1
,
MHz
2
.
106
m mc
E
f
f
(i) Kirakan sisihan frekuensi (frequecy deviation)
(ii) BW menggunakan aturan Carson
(iii) Kuasa yang dipancarkan
Penyelesaian :
k
v
t
dt
f
t
E
t
f
E
v
R
E
P
f
f
BW
f
f
E
k
f
c m f c c c NBFM c FM m m m f
2
sin
2
2
cos
(iv)
1
R
anggapan
dengan
;
kW
5
1
2
100
2
(iii)
kHz
30
5
10
2
2
2
5
10
(ii)
kHz
10
1
10
(i)
2 2
)
sin(
)
(
sin
)
cos(
)
(
t
E
t
E
t
t
3.8.1
3.8.1
Isyarat
Isyarat
FM
FM
dan
dan
PM
PM
dalam
dalam
Domain
Domain
Masa
Masa
Pemodulatan Sudut
FM
3.9 Generation of FM signal
3.9 Generation of FM signal
2 techniques –
direct and indirect methods
(kaedah langsung dan
tidak angsung)
Require a system that able the frequency of the output signal to
vary in accordance to an information signal amplitude.
3.9.1 Direct method/Kaedah langsung
1. Varactor diode
2. Reactance modulation/Pemodulatan Regangan
3. Voltage Controlled Oscillator/Pengayun terkawal voltan (VCO)
Output frequency is proportional to the input voltage.
Ex: VCO manufactured by Signetics, SE/NE 566 or HCT
4046
http://www.see.ed.ac.uk/~gjrp/EE3/Comms/Lecture10/sld003.htmVaractor diode L
C
=
kv
mdimana
k
adalah
pemalar dan
v
madalah
voltan ketika isyarat
maklumat
1. Varactor diode
Varactor diode characteristic
C
C
L
o
2
1
C C
CT o
T o
LC
f
2
1
;Analisa matematik :
O C
LC
f
2
1
Bila vm= 0 ;
O O
O
C C LC
f
1 2
1
2 1
1
2
1
O
O
C
C
LC
Varactor diode’s capacitance depends on the voltage across it.
Audio signals placed across the diode cause its capacitance to change, which in turn,
Using Binomial expansion :
O C
O
C
C
f
f
2
1
O m C
C
kv
f
2
1
From the equation it can be seen
that the FM signal can be obtained
because the output frequency is
dependant to the information
signal amplitude,
v
m.
O
O
C
C
C
C
2
1
1
2 1
O
C
C
if
is small
A reactance modulator is a circuit in which
a transistor is made
to act like a variable reactance.
The reactance modulator is placed across the LC circuit of the
oscillator and
as the modulator’s reactance varies in response
to an applied audio signal, the oscillator frequency varies
as
well.
2. Reactance modulator
Frequency modulation using these techniques are not able to create
a signal with
large frequency deviation
. It means it is
not suitable for
WBFM
. To address this issue, the
Crosby modulator
was developed.
The Crosby circuit incorporates an automatic frequency control
(AFC).
The VCO’s output frequency is proportional to the voltage of the input signal.
If audio is applied to the input of a VCO, the output is an FM signal.
Direct method - Crosby circuit
AFC Circuit
To transmit and fed back an error control voltage to a modulator in
order to control frequency oscillator at 5 MHz (to prevent drift of the
carrier and frequency deviation).
This method is called Automatic
Frequency Control (Kawalan frekuensi automatic).
Let us look at an example. An
FM station operates at 106.5 MHz
with
a
maximum deviation of 75 KHz
. The FM signal is generated by a
reactance modulator that operates at 3.9444 MHz
, with a
maximum
deviation of 2.7778 KHz
. The resulting FM signal is fed through 3
frequency
triplers
,
multiplying the carrier frequency and deviation 27
times.
The final carrier frequency is 27*3.9444 = 106.5 MHz and the
final deviation is 27*2.7778 = 75 KHz.
3.9.2 Indirect method
Pemodulatan Sudut
~
vWBFM(t)
Mixer Penapis Lulus Jalur
Local Oscillator
cos(ωLOt) vz(t)
vy(t)
ωc1 Nωc1
Pemodulat NBFM
Pekali Frekuensi, N vm(t)
vNBFM(t)
Armstrong method
Armstrong method
First generate NBFM. Then multiplies NBFM frequency with multiplier
N
. This
frequency multiplication multiplies both the carrier frequency and the deviation.3.9.3 Generation of NBFM
3.9.3 Generation of NBFM
• FM modulation : The amplitude of the modulated carrier is held
constant and the time derivative of the phase of the carrier is varied linearly with the information signal.
• The instantaneous frequency of FM is given by:
• Hence
)
(
)
(
t
ck
fv
mt
i
)
(
)
(
t
k
fv
mt
c
t
dt
t
d
t
c c ci
(
)
(
)
where~
∫dt kf
vm(t)
c(
t
)
X ∑90°
vNBFM(t)
Eccos(ωct) Ecsin(ωct)
•
The angle of the FM signal can be obtained by integrating the
instantaneous frequency.
•
v
m(
t
)
is a sinusoidal signal, hence:
Pemodulatan Sudut
)
sin(
)
sin(
)
cos(
)
(
0t
t
E
k
dt
t
E
k
t
m m m m f t m m f c
t
t
dt
t
t
c ct
i
c
0)
(
)
(
f t mc
t
k
v
t
dt
0)
(
)
(
Notes:1
)
(
)
(
0
f
t mc
t
k
v
t
dt
Notes:
1
)
sin(
mt
• General equation for FM signal
)]
(
sin[
)
(
sin
)]
(
cos[
)
(
cos
)]
(
[
cos
)
(
t
t
E
t
t
E
t
t
E
t
v
c c
c c
c c
c c
c FM
)
(
sin
)
(
)
(
cos
)
(
t
E
t
t
E
t
v
NBFM
c
c
c c
c• Therefore NBFM signal can be generated using phase modulator circuit
as shown.
• To obtain WBFM signal, the output of the modulator circuit (NBFM) is fed
into frequency multiplier circuit and the mixer circuit.
• The function of the frequency multiplier is to increase the frequency deviation or modulation index so that WBFM can be generated.
• Hence :
1
)
(
t
c
For NBFM therefore
cos[
c(
t
)]
1
andsin[
c(
t
)]
c(
t
)
vWBFM(t)
~
Mixer Penapis Lulus Jalur
Penjana Tempatan
cos(ωLOt) vz(t)
vy(t)
ωc1 Nωc1
Pemodulat NBFM
Pekali Frekuensi, N vm(t)
vNBFM(t)
3.9.4 Generation of WBFM
3.9.4 Generation of WBFM
Analisa Matematik :
•
The instantaneous value of the carrier frequency is increased by
N
times.
)
(
)
(
)
(
t
1t
c ct
i
Let :
)
(
)]
(
[
)
(
)
(
2 1 2
t
N
t
N
t
N
t
c c
c c
Output of the
frequency multiplier :
c
c
N
And :
)
(
)
(
)
(
2 22
t
t
N
t
dt
d
t
c
c
c
c
N
Nota:2
)
sin(
)
sin(
)
(
2 1
t
t
N
t
N
m m c
1
2
N
•
It is proven that the modulation index was increased by
N
times following this equation.
) sin(
) sin(
) cos(
) (
0
t t E
k
dt t E
k t
m m m
m f
t
m m
f c
•
The output equation of the frequency multiplier :
•
Pass the signal through the mixer, then WBFM signal is
obtained :
•
BPF is used to filter the WBFM signal desired either at
ω
c2+
ω
LOor at
ω
c2-
ω
LO.
•
Hence the output equation :
)]
(
[
)]
(
[
cos
)
(
2 2t
N
t
kos
E
t
E
t
v
c c c c FM
Pemodulatan Sudut)]
(
)
cos[(
)]
(
)
cos[(
)
cos(
2
x
)]
(
[
cos
)
(
2 2 2t
N
t
E
t
N
t
E
t
t
N
t
E
t
v
c LO c c c LO c c LO c c c FM
)]
(
)
[(
)]
(
)
[(
)
(
2 2t
N
t
kos
E
t
N
t
kos
E
t
v
c LO c c c LO c cWBFM
3.9.5 Comparison between FM and AM
3.9.5 Comparison between FM and AM
•
Advantages
– SNR is much better than AM can be obtained, if the BW is greater enough.
– SNR can be increased by increasing the transmitted power.
– Constant amplitudes made the non linear preamplifier to be used effectively.
•
Disadvantages
3.10 Demodulation of FM signal
3.10 Demodulation of FM signal
• Demodulation process is done in order to recover/get back the information signal transmitted.
• Basic concepts of demodulation circuit is to detect the frequency variation.
• Two techniques can be used:
Pemodulatan Sudut
Penyahmodulatan FM
Secara Tak Terus Secara
Terus
3.10.1 Conversion circuit
3.10.1 Conversion circuit
-
-
FM to AM
FM to AM
(
(
Discriminator
Discriminator
)
)
–
–
K.
K.
Terus
Terus
• This technique is required to convert FM signal to AM signal and then by using AM demodulation circuit is to get back the information
signal.
• This technique is called pengesan kecerunan (slope detection) or
discriminator.
• Block diagram of the detection circuit is as shown below:
t t t
y(t)
Pengesan Sampul
dt d
v
FM(
t
)
vFM
t y(t)
t vFMPemodulatan Sudut
)
)
(
cos(
)
(
0
t m f
c c
FM
t
E
t
k
v
t
dt
v
)]
(
[
k
v
t
E
c
c
f mMathematical analysis :
Differentiate; yields : FM equation :
E
k
v
t
t
k
v
t
dt
dt
t
dv
m f
c m
f c
c
FM
sin
• From the above equation it can be seen that the amplitude of the signal contains the information signal.
•
For envelope detector to be used the frequency deviation,
Δ
ω
required must be smaller than the carrier frequency,
ω
cor otherwise an envelope detector cannot be used.
c m
f
v
t
k
(
)
0
]
[
c
c
E
for all t)
(
)
(
t
E
k
v
t
y
c f m•
In practice a limiter circuit (litar penghad amplitude) can be
used.
•
It is due to the FM signal received at the antenna was
influenced by the noise and therefore the amplitudes of the
signal were varied and not constant.
•
Hence the output equation of the envelope detector :
Pemodulatan Sudut
• For effective detection the constant amplitude of the FM signal is required. Therefore an amplitude limiter is used.
• Below is a block diagram of FM detection circuit with limiter circuits.
1
1
)
(
o
v
cos(θ) > 0cos(θ) < 0 v i(θ) vo(θ)
1 -1
Penghad BPF
)] ( cos[
)
(t t t
Ec c c
4
cos[
ct
c(
t
)]
Penghad Amplitud (Limiter) Penghad
Amplitud
Pengesan Sampul
dt d
v
FM(
t
)
y(t)Discriminator
