2. Content
• What is Modulation
• Amplitude Modulation (AM)
• Angle Modulation
3. What is Modulation
• Modulation
– In the modulation process, some characteristic of a high-
frequency carrier signal (bandpass), is changed according
to the instantaneous amplitude of the information
(baseband) signal.
• Why Modulation
– Suitable for signal transmission (distance…etc)
– Multiple signals transmitted on the same channel
– Capacitive or inductive devices require high frequency AC
input (carrier) to operate.
– Stability and noise rejection
8. AM Modulation/Demodulation
Modulator Demodulator
Baseband Signal
with frequency
fm
(Modulating Signal)
Bandpass Signal
with frequency
fc
(Modulated Signal)
Channel
Original Signal
with frequency
fm
Source Sink
fc >> fm
Voice: 300-3400Hz GSM Cell phone: 900/1800MHz
9. Amplitude Modulation
• The amplitude of high-carrier signal is
varied according to the instantaneous
amplitude of the modulating message
signal m(t).
Carrier Signal: or
Modulating Message Signal: or
The AM Signal:
cos(2 ) cos( )
( ): cos(2 ) cos( )
( ) [ ( )]cos(2 )
c c
m m
AM c c
f t t
m t f t t
s t A m t f t
10. * AM Signal Math Expression*
• Mathematical expression for AM: time domain
• expanding this produces:
• In the frequency domain this gives:
( ) (1 cos ) cos
AM m c
S t k t t
( ) cos cos cos
c c
AM m
S t t k t t
)
cos(
)
cos(
cos
cos
:
using 2
1 B
A
B
A
B
A
2 2
( ) cos cos( ) cos( )
c c c
k k
AM m m
S t t t t
frequency
k/2
k/2
Carrier, A=1.
upper sideband
lower
sideband
Amplitude
fc
fc-fm fc+fm
11. AM Power Frequency Spectrum
• AM Power frequency spectrum obtained by
squaring the amplitude:
• Total power for AM:
.
2 2
2
2
4 4
1
2
k k
A
k
freq
k2/4
k2/4
Carrier, A2=12 = 1
Power
fc
fc-fm fc+fm
12. Amplitude Modulation
• The AM signal is generated using a
multiplier.
• All info is carried in the amplitude of the
carrier, AM carrier signal has time-varying
envelope.
• In frequency domain the AM waveform are
the lower-side frequency/band (fc - fm),
the carrier frequency fc, the upper-side
frequency/band (fc + fm).
13. AM Modulation – Example
• The information signal is usually not a single
frequency but a range of frequencies (band). For
example, frequencies from 20Hz to 15KHz. If we
use a carrier of 1.4MHz, what will be the AM
spectrum?
• In frequency domain the AM waveform are the
lower-side frequency/band (fc - fm), the carrier
frequency fc, the upper-side frequency/band (fc +
fm). Bandwidth: 2x(25K-20)Hz.
frequency
1.4 MHz
1,385,000Hz to
1,399,980Hz
1,400,020Hz to
1,415,000Hz
fc
14. Modulation Index of AM Signal
m
c
A
k
A
)
2
cos(
)
( t
f
A
t
m m
m
Carrier Signal: cos(2 ) DC:
c C
f t A
For a sinusoidal message signal
Modulation Index is defined as:
Modulated Signal: ( ) [ cos(2 )]cos(2 )
[1 cos(2 )]cos(2 )
AM c m m c
c m c
S t A A f t f t
A k f t f t
Modulation index k is a measure of the extent to
which a carrier voltage is varied by the modulating
signal. When k=0 no modulation, when k=1 100%
modulation, when k>1 over modulation.
15. Modulation Depth
Ac
Am
2Amax
2Amin
2Amax = maximum peak-to-peak of waveform
2Amin = minimum peak-to-peak of waveform
This may be shown to equal
m
C
A
k
A
as follows:
2 2 2
max C m
A = A + A 2 2 2
min C m
A = A A
max min max min
max min
2 2
2 2
m
C C
A A A A A
k
A A A A
16. High Percentage Modulation
• It is important to use as high percentage of
modulation as possible (k=1) while ensuring
that over modulation (k>1) does not occur.
• The sidebands contain the information and
have maximum power at 100% modulation.
• Useful equation
Pt = Pc(1 + k2/2)
Pt =Total transmitted power (sidebands and
carrier)
Pc = Carrier power
