1. Communication System
Ass. Prof. Ibrar Ullah
BSc (Electrical Engineering)
UET Peshawar
MSc (Communication & Electronics Engineering)
UET Peshawar
PhD (In Progress) Electronics Engineering
(Specialization in Wireless Communication)
MAJU Islamabad
E-Mail: ibrar@cecos.edu.pk
Ph: 03339051548 (0830 to 1300 hrs)
1
2. Chapter-5 Angle Modulation
•
What is Angle modulation
•
What is the difference between frequency and phase
modulation
•
What is direct and indirect modulation
•
Deviation sensitivity, phase deviation, modulation
index
•
Bandwidth of angle-modulated wave
2
3. Angle Modulation
• Idea: The angle θ (t) of the carrier A Cos (Wc + θ (t))is
modulated according to the modulating signal m(t):
• The amplitude A remains constant.
• This modulation type is called Angle modulation
3
4. Angle Modulation
Generalized sinusoidal function is given by:
ϕ (t ) = A cos θ (t )
θ (t) = instantaneous phase (radians)
Question:
What is the instantaneous frequency?
4
5. Angle Modulation
A carrier can be represented as:
ϕ (t ) = A cos θ (t )
dθ
wi (t ) =
dt
t
θ i (t ) = ∫ wi (t )dt
0
ϕ (t ) = angle modulated wave (Volt)
A
= peak carrier amplitude (Volt)
wi = instantaneous angular frequency (rad/sec)
θ i = instantaneous phase (radians)
5
6. Phase Modulation (PM)
The instantaneous phase of a harmonic carrier signal
is varied in such a way that the instantaneous phase
deviation i.e. the difference between the instantaneous
phase and that of the carrier signal is linearly related to
the size of the modulating signal at a given instant of
time.
In PM the angle θ (t ) varies linearly with m(t)
θ i (t ) = wc t + k p m(t )
[
ϕ PM = A cos wc t + k p m(t )
wi (t ) =
[
]
]
dθ i (t ) d wc t + k p m(t )
dm(t )
=
= wc + k p
dt
dt
dt
Kp is the phase deviation sensitivity (rad/Volt)
6
7. Frequency Modulation (PM)
The frequency of a harmonic carrier signal is varied in such a
way that the instantaneous frequency deviation i.e. the
difference between the instantaneous frequency and the
carrier frequency is linearly related to the size of the
modulating signal at a given instant of time.
If wi is varied linearly with the modulating signal we have FM
and instantaneous frequency wi is given by:
wi (t ) =
wc + k f m(t )
t
θ i (t ) =
∫ w (t )dt = w t + ∫ k
i
0
ϕ FM =
t
c
f
m(t )dt
0
t
A cos wc t + ∫ k f m(t )
0
Kf is the frequency deviation sensitivity
rad / s
Volt
7
8. Frequency Modulation (PM)
PM
θi (t ) = wc t + k p m(t )
ϕPM =
A cos wc t + k p m(t )
[
]
wi (t ) =
dθi (t ) d wc t + k p m(t )
dm(t )
=
= wc + k p
dt
dt
dt
[
]
FM
wi (t ) =
wc +k f m(t )
t
θi (t ) =
∫ w (t )dt = w t +∫ k
i
0
ϕFM =
t
c
f
m(t ) dt
0
t
A cos wc t + ∫ k f m(t )
0
TASK: Make block diagrams of PM and FM modulators
8
9. PM Modulator
θi (t ) =
wc t +k p m(t )
ϕPM =
A cos wc t +k p m(t )
wi (t ) =
PM
d wc t +k p m(t )
dθi (t )
dm(t )
=
= wc +k p
dt
dt
dt
[
Modulating
signal
source
[
Phase
modulator
]
]
PM wave
Direct
A cos wc t
Modulating
signal
source
Differentiato
r
Frequency
modulator
A cos wc t
PM wave
Indirect
9
10. FM Modulator
FM
wi (t ) =
wc +k f m(t )
t
θ (t ) =
i
t
∫w (t )dt =w t +∫k
i
c
0
ϕ =
FM
f
m(t ) dt
0
A cos c t +∫k f m(t )
w
0
Modulating
signal
source
t
Frequency
modulator
FM wave
Direct
A cos wc t
Modulating
signal
source
Integrator
Phase
modulator
A cos wc t
FM wave
Indirect
10
11. Frequency modulation of single frequency signal
PM:
m(t ) = Am cos( wmt )
ϕ PM (t ) = A cos( wc t + k p Am cos( wmt ))
FM:
m(t ) = Am cos( wmt )
t
ϕ FM (t ) = A cos wc t + ∫ k f Am cos( wmt )dt
0
k f Am
= A cos wc t +
sin( wmt )
wm
11
