1. Angle Modulation
BY
Muhammad Uzair Rasheed
2009-CPE-03
UCE&T BZU MULTAN
2. Contents
Properties of Angle (exponential) Modulation
Types
Phase Modulation
Frequency Modulation
3. Properties
Angle Modulation: A non-linear process:-
– Modulated wave does not look like message wave
– Amplitude of an exponentially modulated wave is constant
Therefore, regardless of message signal the average transmitted power is
1 2
P Ac
2
– It is less sensitive to noise
4. Basic Concept
First introduced in 1931
A sinusoidal carrier signal is defined as: c(t ) Ac cos [ c t c (t )]
For un-modulated carrier signal the total instantaneous angle is:
c (t ) ct c (t )
Thus one can express c(t) as: c(t ) Ac cos c (t ) Ac Re [e j c (t )
]
Thus:
• Varying the frequency fc Frequency modulation
• Varying the phase c Phase modulation
5. Basic Concept - Cont’d.
In angle modulation: Amplitude is constant, but angle
varies (increases linearly) with time
c(t)
(red)
Frequency-modulated Unmodulated
angle carrier
Unmodulated 47 /2
carrier 35 /2
Phase-modulated
Amplitude 23 /2 angle
Ac 11 /2
Slope = - /2
c/ t t
Initial
phase c 0 1 2 3 4 (ms)
t=0 t
2 m(t)
0
-1
6. Phase Modulation (PM)
PM is defined If c (t ) K p m(t ) K p 1800
Thus c(t ) PM Ac cos [ c t K p m(t )]
Where Kp is known as the phase modulation index
Instantaneous phase i (t ) K p m(t )
i(t
Ac )
Instantaneous frequency
c(t)
c(t)
d c (t )
c(t) i (t ) c c (t )
dt
Rotating Phasor diagram
7. Frequency Modulation (FM)
The instantaneous frequency is; i (t ) c K f m(t )
Where Kf is known as the frequency modulation index.
Instantaneous phase
Note that
c (t ) K f m (t )
t
Integrating
i (t ) c c (t ) c (t ) ct K f m(t ) dt 0
0
t
Substituting c(t) in c(t) results in: c(t ) FM Ac cos[ ct K f m(t ) dt ]
0
8. Bandwidth of Angle modulation
• For FM:-
1
BFM 2k f m p 8 B
2
BFM 2 f 2B
k f mp
Frequency deviation= f
2
k f mp
9. • Deviation Ratio:-
f
B
• Carson’s Rule:-
BFM 2B 1
Note : Deviation ratio is also called modulation index
10. • For PM:-
k f mp '
Where, mp ' m t max
Now,
k pmp '
BPM 2 B
2
