telecomunication

1. Fundamental of
Communication
System
Abdirahim Khalif Ali
M.Eng (Electrical-Electronics and Telcommunications)
Universiti Teknologi Malaysia (UTM)
B.Sc. (Honors), Electronic and Electrical Engineering.
International University of Africa (2009)
Email: abdirahim.kh@gmail.com

2. Ch 3– Angle
Modulation
FM Generation

3. Generation of FM signal
2 techniques – direct and indirect methods
Direct FM: the freq. of the carrier is varied/deviated
directly by the modulating signal.
Direct method
1. Varactor diode
2. Reactance modulation
3. Voltage Controlled Oscillator (VCO)
Output frequency is proportional to the input voltage.
3

4. Varactor Diode Modulator
Varactor Diode Schematic
Symbol
Varactor Diode is used to transform changes in the modulating signal
amplitude to changes in frequency 4

5. Varactor
diode
L C = kvm
1. Varactor diode
Varactor diode characteristic
C
C
C o
T 

 
C
C
L
LC
f
o
T
o





2
1
2
1
Mathematical analysis :
O
C
LC
f

2
1

If vm= 0
2
1
1
2
1
1
2
1



















O
O
O
O
O
C
C
LC
C
C
LC
f


 Varactor diode’s capacitance depends on the voltage
across it.
 Audio signals placed across the diode cause its
capacitance to change, which in turn, causes the
frequency of the oscillator to vary.
5

6. Using Binomial expansion :

















O
m
C
O
C
O
C
kv
f
C
C
f
f
2
1
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, vm .
O
O C
C
C
C
2
1
1
2
1










;
6
1. Varactor diode

7.  A reactance modulator is a
circuit in which a transistor is
made to act like a variable
reactance load to the LC
circuit
 The reactance modulator is
placed across the LC circuit of
the oscillator
 The modulating signal varies
the reactance , which causes a
corresponding change in the
resonant frequency of the
oscillator
Reactance modulator
7

8. 8
 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 and due to stability reason, 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.
Voltage Controlled Oscillator VCO
AFC circuit compares the freq. of the noncrystal carrier oscillator to a crystal
oscillator , the produces a correction voltage proportional to the difference
between the two freq.
The correction is fed back to the carrier oscillator to automatically compensate
for any drift that occured

9. Crosby Direct FM Modulator
fc is the carrier rest frequency = unmodulated output frequency from the master
oscillator
9

10. 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.
It is important to remember that frequency multiplication multiplies
both the carrier frequency and the deviation.
10

11. Indirect method
vWBFM(t)
vm(t)
Armstrong method
First generate NBFM. Then multiplies NBFM frequency with multiplier N. This
frequency multiplication multiplies both the carrier frequency and the deviation.
Then signal vy(t) is tuned at the frequency desired and is suitable to the ranges of
LO frequency, fLO . BPF is then used to filter the desired frequency components.
Mixer Band pass
filter
Local Oscillator
cos(ωLOt)
vz(t)
vy(t)
ωc1 Nωc1
NBFM
modulator
Freq.
multiplier, N
vNBFM(t)
~
Indirect FM: the frequency of the carrier is indirectly deviated by the
modulating signal, but the phase of the carrier is directly changed by the
modulating signal
11

12. 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
v
k
t m
f
c
i 
 

)
(
)
( t
v
k
t m
f
c 


 
t
dt
t
d
t c
c
c
i 


 



)
(
)
(
where
~
∫dt kf
vm(t)
)
(t
c

X ∑
90°
vNBFM(t)
Eccos(ωct)
Ecsin(ωct)
-
+
Phase modulator
12

13. • The angle of the FM signal can be obtained by integrating
the instantaneous frequency.
• vm(t) is a sinusoidal signal, hence:
)
sin(
)
sin(
)
cos(
)
(
0
t
t
E
k
dt
t
E
k
t
m
m
m
m
f
t
m
m
f
c








 
1
)
(
)
(
0

 
t
m
f
c dt
t
v
k
t

1
)
sin( 
t
m








t
m
f
c
t
m
f
c
c
dt
t
v
k
t
dt
t
v
k
t
0
0
)
(
)
(
)
(



 
t
t
dt
t
t c
c
t
i
c 


 

 
0
)
(
)
(


t
m
f
c dt
t
v
k
t
0
)
(
)
(

Notes:
Notes:
For NBFM
Therefore
13

14. • 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 c
c
c
c
c
NBFM 

 

• 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 1
)]
(
cos[ 
t
c
 )
(
)]
(
sin[ t
t c
c 
 
and
Summary:
14
Generation of NBFM

15. vWBFM(t)
~
Mixer
Band pass
filter
LO
cos(ωLOt)
vz(t)
vy(t)
ωc1 Nωc1
NBFM
modulator
Freq.
multiplier, N
vm(t)
vNBFM(t)
Generation of WBFM
Mathematical analysis
• The instantaneous value of the carrier frequency is increased by N
times. Let:
)
(
)
(
)
( 1 t
t
t c
c
i 


 



)
(
)]
(
[
)
(
)
(
2
1
2
t
N
t
N
t
N
t
c
c
c
c













Output of the frequency
multiplier :
c
c N
 
2
Notes
15

16. And :
)
(
)
(
)
( 2
2
2 t
N
t
t
dt
d
t c
c 


 


c
c N
 
2
Note:
)
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








 
16
Generation of WBFM

17. • 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 ωc2+ ωLO or at
ωc2- ωLO .
• Hence the output equation :
)]
(
[
)]
(
[
cos
)
(
2
2
t
N
t
kos
E
t
E
t
v
c
c
c
c
FM






)]
(
)
cos[(
)]
(
)
cos[(
)
cos(
2
x
)]
(
[
cos
)
(
2
2
2
t
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
2
t
N
t
kos
E
t
N
t
kos
E
t
v
c
LO
c
c
c
LO
c
c
WBFM






17

18. 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
– BW is usually larger than AM.
– Circuitry is more complex.
18

19. PREEMPHASIS/DEEMPHASIS
In an FM system the higher frequencies contribute more to the noise than
the lower frequencies. The situation become more complex due to the
amplitude of the signal at higher frequencies are smaller than at the lower
frequencies.
Because of this all FM systems adopt a system of preemphasis at the
transmitter and deemphasis at the receiver.
Preemphasis (before the modulation process)– The higher
frequencies are increased in amplitude before being used to
modulate the carrier and therefore will be less affected to
noise.
Deemphasis (after the demodulation process)– is the mirror of
pre-emphasis process.
19

20. FM Transmission system
preemphasis
FM
modulator
Channel
FM
demodulator
deemphasis
vM (t)
vM (t)
Preemphasis: allow the high-freq modulating
signal to modulate the carrier at higher level
Deemphasis: restores the original amplitude
vs freq the information signal
20

21. 21

22. IF Bandwidth
200 kHz
FM Radio Receiver
Preemphasis
FM
FM
modulation
fc
88 – 108 MHz
RF amplifier
(Mixer) Limiter
FM
detector
deemphasis
Audio
amplifier
LO : fLO = fc +
10.7 MHz
Talaan sepunya
(common tuning)
fIF = 10.7 MHz
A
FM transmitter
22

23. Pemodulatan Sudut
FM Radio Channel
CH
1
CH
2
CH
3
CH
99
CH
100
88MHz 108MHz
20MHz Radio FM
BW=200kHz
fc1=88.1MHz fc2=88.3MHz
25kHz
Guard
Band
25kHz
Guard
Band
25kHz
Guard
Band
25kHz
Guard
Band
BW=200kHz
150kHz
(Δf=±75kHz)
150kHz
(Δf=±75kHz)
Channel 1 Channel 2
Modulating signal freq. range
fm = 50Hz – 15kHz
Maximum freq. deviation
Δf = ±75kHz
Range of modulation index
βmin = (75kHz/15kHz) = 5
βmax = (75kHz/50Hz) = 1500
BW for each channel
BW = 200kHz
No. of channel
N = 5(f-47.9)
23