2. Principles of AM
Definitions:
The process of changing the amplitude of
a relatively high frequency carrier signal in
proportion with the instantaneous value of
modulating signal (information)
A process of translating information signal
from low band frequency to high band
frequency.
3. Cont’d…
Information signal cannot travel far. It
needs carrier signal of higher frequency
for long distance destination.
Inexpensive, low quality form of
modulation
4. Cont’d…
Amplitude of the carrier signal varies with the
information signal.
The modulated signal consist of carrier signal,
upper sideband and lower sideband signals
The modulated AM signal (figure 1 & figure 2)
needs to go through demodulation process to
get back the information signal.
6. The AM Envelope
AM double-sideband full carrier (AM DSBFC)
is the most commonly used and the oldest
and simplest form of AM modulation.
Sometimes called conventional AM or simply
AM.
The outline of the positive and negative
peaks of the carrier frequency re-create the
exact shape of the modulating signal known
as envelope.
Note that the repetition rate of the envelope
is equal to the frequency of the modulating
signal.
8. AM Frequency Spectrum and
Bandwidth
An AM modulator is a non-linear device.
Nonlinear mixing results in a complex output
envelope consists of the carrier frequency
and the sum (fc + fm) and difference (fc – fm)
frequencies (called cross-products).
The cross-products are displaced from the
carrier frequency by fm on both sides of it.
AM modulated wave contains no frequency
component of fm.
10. Bandwidth (BW)
The BW of an AM DSBFC wave is equal
to the difference between the highest
upper side frequency and lowest lower
side frequency:
BW = [fc + fm(max)] – [fc – fm(max)]
= 2fm(max)
For efficiency transmission the carrier
and sidebands must be high enough to
be propagated thru earth’s atmosphere.
11. Example 1
For a conventional AM modulator with a
carrier freq of fc = 100 kHz and the
maximum modulating signal frequency of
fm(max = 5 kHz, determine:
a) Freq limits for the upper and lower
sidebands.
b) Bandwidth.
c) Upper and lower side frequencies produced
when the modulating signal is a single-freq
3-kHz tone.
d) Draw the output freq spectrum.
12. Modulation Index and Percent of
Modulation
Used to describe the amount of amplitude
change (modulation) present in an AM
waveform.
Percentage modulation (%m) is simply the
modulation index (m) stated as a percentage.
More specifically percent modulation gives
the percentage change in the amplitude of
the output wave when the carrier is acted on
by a modulating signal.
13. Cont’d…
Mathematically, the modulation index is
And the percentage of modulation index is
c
m
E
E
m
m = modulation index
Em = peak change in the amplitude output
waveform (sum of voltages from upper and
lower side frequencies)
Ec = peak amplitude of the unmodulated
carrier
%
100
% x
E
E
m
c
m
15. Cont’d…
If the modulating signal is a pure, single-freq
sine wave and the process is symmetrical then
the modulation index can be derived as follows:
Therefore,
)
(
2
1
)
(
2
1
min
max
min
max
V
V
E
V
V
E
c
m
)
(
)
(
)
(
2
1
)
(
2
1
min
max
min
max
min
max
min
max
V
V
V
V
V
V
V
V
m
16. Cont’d…
Since the peak change of modulated output
wave Em is the sum of the usf and lsf
voltages hence,
Then
lsf
usf
lsf
usf
m
E
E
where
E
E
E
)
(
4
1
2
)
(
2
1
2
min
max
min
max
V
V
V
V
E
E
E m
lsf
usf
Eusf = peak amplitude
of the upperside
frequency (volts)
Elsf = peak amplitude
of the lower side
frequency (volts)
17. Cont’d…
From the modulated wave displayed in
the previous slide, the maximum and
minimum values of the envelope occurs
at
+Vmax = Ec + Eusb + Elsb
+Vmin = Ec – Eusb – Elsb
-Vmax = -Ec - Eusb - Elsb
-Vmin = -Ec + Eusb + Elsb
18. Modulation Index for
trapezoidal patterns
Modulation index, m can be calculated using
the equation:
m = Vmax – Vmin/ Vmax + Vmin
= Em / Ec
= (A - B) / (A + B)
21. Cont’d…
For proper AM operation, Ec > Em
means that 0≤ m ≤ 1.
If Ec < Em means that m > 1 leads to
severe distortion of the modulate wave.
If Ec = Em the percentage of modulation
index goes to 100%, means the
maximum information signal is
transmitted. In this case, Vmax = 2Ec
and Vmin = 0.
22. Example 2
Suppose that Vmax value read from the
graticule on an oscilloscope screen is
4.6 divisions and Vmin is 0.7 divisions.
Calculate the modulation index and
percentage of modulation.
23. Example 3
For the AM waveform shown in Figure
below, determine
a) Peak amplitude of the upper and lower side
frequencies.
b) Peak amplitude of the unmodulated carrier.
c) Peak change in the amplitude of the
envelope.
d) Modulation index.
e) Percent modulation.
25. The Mathematical Representation
and Analysis of AM
Representing both the modulating signal Vm(t) and the
carrier signal Vc(t) in trigonometric functions.
The AM DSBFC modulator must be able to produce
mathematical multiplication of these two analog signals
)
2
(
sin
)
( t
f
V
t
v m
m
m
)
2
(
sin
)
( t
f
V
t
v c
c
c
)
2
(
sin
)]
2
(
sin
[
)
( t
f
t
f
V
V
t
v c
m
m
c
am
26. Cont’d…
Substituting Em = mEc gives:
)
2
(
sin
)]
2
(
sin
1
[
)
2
(
sin
)]
2
(
sin
[
)
(
t
f
V
t
f
m
t
f
t
f
mV
V
t
v
c
c
m
c
m
c
c
am
Constant +
mod. signal
Unmodulated
carrier
27. Cont’d…
The constant in the first term produces the carrier
freq while the sinusoidal component in the first term
produces side bands frequencies
]
)
(
2
[
cos
2
]
)
(
2
[
cos
2
)
2
(
sin
)]
2
(
[sin
)]
2
(
sin
[
)
2
(
sin
)
(
t
f
f
V
m
t
f
f
V
m
t
f
V
t
f
t
f
mV
t
f
V
t
v
m
c
c
m
c
c
c
c
c
m
c
c
c
am
Upper side frequency
signal (volts)
Lower side frequency
signal (volts)
Carrier frequency
signal (volts)
28. Cont’d…
From the equation it is obvious that the
amplitude of the carrier is unaffected by
the modulation process.
The amplitude of the side frequencies
depend on the both the carrier
amplitude and modulation index.
At 100% modulation the amplitudes of
side frequencies are each equal to one-
half the amplitude of the carrier.
29. Generation of AM DSBFC envelope
showing the time-domain of the
modulated wave, carrier&sideband signals
31. Example 4
One input to a conventional AM modulator is a 500-
kHz carrier with an amplitude of 20 Vp. The second
input is a 10-kHz modulating signal that is of
sufficient amplitude to cause a change in the
output wave of ±7.5 Vp. Determine
a) Upper and lower side frequencies.
b) Modulation index and percentage modulation.
c) Peak amplitude of the modulated carrier and the
upper and lower side frequency voltages.
d) Maximum and minimum amplitudes of the
envelope.
e) Expression for the modulated wave.
32. AM Power Distribution
In any electrical circuit, the power dissipated
is equal to the voltage squared (rms) divided
by the resistance.
Mathematically power in unmodulated carrier
is
Pc = carrier power (watts)
Vc = peak carrier voltage (volts)
R = load resistance i.e antenna (ohms)
R
V
R
V
P c
c
c
2
)
2
/
(
2
2
33. Cont’d
The upper and lower sideband powers will
be
Rearranging in terms of Pc,
R
V
m
R
mV
P
P c
c
lsb
b
us
8
2
)
2
/
(
2
2
2
c
c
lsb
b
us P
m
R
V
m
P
P
4
2
4
2
2
2
34. Cont’d…
The total power in an AM wave is
Substituting the sidebands powers in terms of PC yields
Since carrier power in modulated wave is the same as
unmodulated wave, obviously power of the carrier is
unaffected by modulation process.
lsb
usb
c
t P
P
P
P
]
2
1
[
2
4
4
2
2
2
2
m
P
P
m
P
P
m
P
m
P
P
c
c
c
c
c
c
t
35. Power spectrum for AM DSBFC wave with
a single-frequency modulating signal
36. Cont’d…
With 100% modulation the maximum power
in both sidebands equals to one-half the
carrier power.
One of the most significant disadvantage of
AM DSBFC is with m = 1, the efficiency of
transmission is only 33.3% of the total
transmitted signal. The less wasted in the
carrier which brings no information signal.
The advantage of DSBFC is the use of
relatively simple, inexpensive demodulator
circuits in the receiver.
37. Example 5
For an AM DSCFC wave with a peak
unmodulated carrier voltage Vc = 10
Vp, a load resistor of RL = 10 and m
= 1, determine
a) Powers of the carrier and the upper
and lower sidebands.
b) Total sideband power.
c) Total power of the modulated wave.
d) Draw the power spectrum.
39. Modulation by a complex
information signal
Previous examples are all using a single frequency modulation
signal. In practice, however, modulating signal is very often a
complex waveform made up from many sine waves with
different amplitudes and frequencies.
Example: if a modulating signal contains three frequencies(fm1,
fm2, fm3), the modulated signal will contain the carrier and three
sets of side frequencies, spaced symmetrically about the carrier:
]
)
(
2
[
cos
2
]
)
(
2
[
cos
2
]
)
(
2
[
cos
2
]
)
(
2
[
cos
2
]
)
(
2
[
cos
2
]
)
(
2
[
cos
2
)
2
(
sin
)
(
3
3
2
2
1
1
t
f
f
V
m
t
f
f
V
m
t
f
f
V
m
t
f
f
V
m
t
f
f
V
m
t
f
f
V
m
t
f
V
t
v
m
c
c
m
c
c
m
c
c
m
c
c
m
c
c
m
c
c
c
c
am
41. Cont’d..modulation index for
complex information signal
When several frequencies simultaneously
amplitude modulate a carrier, the combined
coefficient of modulation is defined as:
mt=total modulation index/coefficient of modulation
m1, m2, m3, mn= modulation index/coefficient of
modulation for input 1, 2 ,3 , n
2
2
3
2
2
2
1
t
... n
m
m
m
m
m
42. Cont’d..Power calculation for
complex information signal
The combined coefficient of modulation
can be used to determine the total
sideband power and transmitted power,
using:
2
1
2
4
2
2
2
t
c
t
t
c
sbt
t
c
lsbt
usbt
m
P
P
m
P
P
m
P
P
P
43. Example 6
For an AM DSBFC transmitter with an unmodulated carrier
power, Pc= 100W that is modulated simultaneously by three
modulating signals, with coefficients of modulation m1=0.2,
m2= 0.4, m3=0.3, determine:
a) Total coefficient of modulation
b) Upper and lower sideband power
c) Total transmitted power
