L#3: Amplitude Modulation
Dr. Jayanta K Rakshit
Conventional Amplitude Modulation (Full AM)
AM is the process of varying the instantaneous amplitude
of carrier signal accordingly with instantaneous amplitude
of message signal.
• If sm(t) is the message signal and
carrier signal, then AM signal is:
S (t ) Ac . cos(ct ) sm (t ). cos(ct )
Conventional Amplitude Modulation (Full AM)
Conventional Amplitude Modulation (Full AM)
Modulating signal (information signal) can also be expressed as:
The amplitude-modulated wave can be expressed as
By substitution
Therefore The full AM signal may be written as
Where,
- modulation index
Using,
Frequency spectrum of Amplitude Modulation
Fourier transform of a cosine signal cos (ωct) consists of
two impulses at ωc and –ωc as
cos(ct ) [ ( c ) ( c )]
So, Ac cos(ct ) Ac [ ( c ) ( c )]
In general, AM wave :
S (t ) Ac . cos(ct ) sm (t ). cos(ct )
sm (t ) Sm ( )
1 jct
sm (t ). cos(ct ) sm (t ) e e
jct
2
sm (t ). cos(c t ) S m ( c ) S m ( c )
1
2
Frequency spectrum of Amplitude Modulation
So, the Fourier transform of AM wave is:
S ( ) S m ( c ) S m ( c ) Ac [ ( c ) ( c )
1
2
Considering baseband signal as,
mAc
S ( ) Ac [ ( c ) ( c ) { (c m )} { (c m )}
2
mAc
{ (c m )} { (c m )}
2
Frequency spectrum of Amplitude Modulation
S(ω)
πAc
mπAc/2 BW=2fm
LSB
USB
-(ωc+ ωm) ω= -ωc -(ωc- ωm) ω=0 ωc- ωm ω= ωc ωc+ ωm
BW
• Frequency spectrum of AM comprises of:
• Carrier frequency ωc .
• A lower side band whose highest frequency component is present at ωc-ωm
• An upper side band whose highest frequency component is present at ωc+ωm
Because of the two side bands in the frequency spectrum it is often called Double
Sideband -full carrier(DSB-FC)
The information in the base band (information) signal is duplicated in the LSB and USB and
the carrier conveys no information.
Modulation index or percentage of modulation
• m is merely defined as a parameter, which determines
the amount of modulation.
• What is the degree of modulation required to establish a
desirable AM communication link?
Answer is to maintain m<1.0 (m<100%).
• This is important for successful retrieval of the original
transmitted information at the receiver end.
Modulation index (m) is defined as: Am
m
Ac
Modulation index
Amax Amin
Am
2
Amax Amin Amax Amin
Ac Amax Am Amax
2 2
Amax Amin
m
Amax Amin
Effect of Modulation Index
m=0.5, called under modulation
m=1.0, called 100% modulation
If the amplitude of the
modulating signal is
higher than the carrier
m>1, amplitude, severe
Called over distortion to the
modulation modulated signal will
occurs.
Power distribution in AM
2
Acar ( Ac / 2 ) 2 Ac2
Pc
R R 2R 2
ASB (mAc / 2 2 ) 2 m 2 Ac2
PLSB / USB
R R 8R
Power distribution in AM
Now, the information are
contained in AM sidebands only.
Thus the fraction of total power
is used to transmit the
information.
m12 m22 m32
For multi tone modulation: Pt Pc 1
2 2 2
The percentage of total power carried by the sidebands is called the transmission efficiency.
For single tone modulation
Observations
1. If m=0 Pt=Pc no modulation occurs
2. As m PSB ( m P )
2
c , But Pc remain same as it is
4
independent of m
3. If m=1, Pt=1.5Pc and efficiency will be 33.33 %
4. Over-modulation, i.e. Am>Ac , should be avoided
because it will create distortions.
In terms of power efficiency, for m=1 modulation, only 33% power
efficiency is achieved which tells us that only one-third of the
transmitted power carries the useful information.
Numerical Problems
P1. An unmodulated AM transmitted power=100W. Find
AM transmitted power with 100% modulation.
Solution:
PC=100 W, m=1, Pt=?
Pt=(3/2)*100=150
Pt=150 W
Numerical Problems
P2. For an AM signals, total side band power=200 W with
50 % of modulation. Find the total transmitted AM power.
Solution:
m=0.5
Pt=PC+PSB
=0.2
200
0.2
PT
Pt=1000 W
THANK YOU
