Suggested Text Books
An introduction to Analogue and Digital communication, Haykin (Wiley)
Communication Systems, Carlson (McGraw & Hill)
Information, Transmission, Modulation and Noise, Schwartz (McGraw &
Hill)
Analogue and Digital Communication Systems, Raden (Prentice-Hall)
Communication Systems, Haykin (Wiley)
Electronic Communication Techniques, Young (Merril-Publ)
Analogue Modulation Amplitude Modulation
Consider a 'sine wave' carrier.
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vc(t) = Vc cos(ct), peak amplitude = Vc, carrier frequency c radians per second.
Since c = 2fc, frequency = fc Hz where fc = 1/T.
Amplitude Modulation AM
Is defined as a process in which the amplitude of the carrier
wave is varied about a mean value, linearly with the message
signal m(t).
Message Signal m(t)
In general m(t) will be a band of signals, for example speech or video signals. A
notation or convention to show baseband signals for m(t) is shown below
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Message Signal m(t)
In general m(t) will be band limited. Consider for example, speech via a microphone.
The envelope of the spectrum would be like:
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Message Signal m(t)
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In order to make the analysis and indeed the testing of AM systems easier, it is common to
make m(t) a test signal, i.e. a signal with a constant amplitude and frequency given by
m t
V m cos
Schematic Diagram for Amplitude
Modulation
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VDC is a variable voltage, which can be set between 0 Volts and +V Volts. This
schematic diagram is very useful; from this all the important properties of AM
and various forms of AM may be derived.
Equations for AM
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Equations for AM
Components:
Carrier upper sideband USB
lower sideband LSB
Amplitude:
VDC
Vm/2
Vm/2
Frequency:
c
fc
c + m
fc + fm
c m
fc - fm
This equation represents Double Amplitude Modulation DSBAM
Spectrum and Waveforms
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The following diagrams
represent the spectrum
of the input signals,
namely (VDC + m(t)),
with m(t) = Vm cos mt,
and the carrier cos ct
and corresponding
waveforms.
Spectrum and Waveforms
The above are input signals. The diagram below shows the spectrum and
corresponding waveform of the output signal, given by
vs t
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V DC cos
Vm
2
cos
Vm
2
cos
Double Sideband AM, DSBAM
The component at the output at the carrier frequency fc is shown as a broken line
with amplitude VDC to show that the amplitude depends on VDC. The structure of
the waveform will now be considered in a little more detail.
Waveforms
Consider again the diagram
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VDC is a variable DC offset added to the message; m(t) = Vm cos mt
Double Sideband AM, DSBAM
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This is multiplied by a carrier, cos ct. We effectively multiply (VDC + m(t)) waveform
by +1, -1, +1, -1, ...
The product gives the output signal
vs t
V DC m t cos
Double Sideband AM, DSBAM
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Modulation Depth
From an oscilloscope display the modulation depth for Double Sideband AM may be
determined as follows:
Vm
2Emax
VDC
2Emin
Modulation Depth
The ratio
Vm
VDC
is defined as the modulation depth, m, i.e.
Modulation Depth
m=
Vm
VDC
From an oscilloscope display the modulation depth for Double Sideband AM may be
determined as follows:
Vm
2Emax
VDC
2Emin
Modulation Depth cont
m=0.5, corresponding to undermodulation
m=1.0, corresponding to 100% modulation
m=2.0, corresponding to overmodulation
Double Sideband Modulation 'Types'
There are 3 main types of DSB
Double Sideband Amplitude Modulation, DSBAM with carrier
Double Sideband Diminished (Pilot) Carrier, DSB Dim C
Double Sideband Suppressed Carrier, DSBSC
The type of modulation is determined by the modulation depth,
which for a fixed m(t) depends on the DC offset, VDC. Note, when a
modulator is set up, VDC is fixed at a particular value. In the
following illustrations we will have a fixed message, Vm cos mt and
vary VDC to obtain different types of Double Sideband modulation.
Graphical Representation of Modulation
Depth and Modulation Types.
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Graphical Representation of Modulation
Depth and Modulation Types 2.
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Graphical Representation of Modulation
Depth and Modulation Types 3
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Note then that VDC may be set to give
the modulation depth and modulation
type.
DSBAM VDC >> Vm, m 1
DSB Dim C 0 < VDC < Vm,
m > 1 (1 < m < )
DSBSC VDC = 0, m =
The spectrum for the 3 main types of
amplitude modulation are summarised
Bandwidth Requirement for
DSBAM
In general, the message signal m(t) will not be a single 'sine' wave, but a band of
frequencies extending up to B Hz as shown
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Remember the 'shape' is used for convenience to distinguish low frequencies from high
frequencies in the baseband signal.
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Bandwidth Requirement for
DSBAM
Amplitude Modulation is a linear process, hence the principle of superposition applies. The
output spectrum may be found by considering each component cosine wave in m(t)
separately and summing at the output.
Note:
Frequency inversion of the LSB
the modulation process has effectively shifted or frequency translated the baseband m(t)
message signal to USB and LSB signals centred on the carrier frequency fc
the USB is a frequency shifted replica of m(t)
the LSB is a frequency inverted/shifted replica of m(t)
both sidebands each contain the same message information, hence either the LSB or USB
could be removed (because they both contain the same information)
the bandwidth of the DSB signal is 2B Hz, i.e. twice the highest frequency in the baseband
signal, m(t)
The process of multiplying (or mixing) to give frequency translation (or up-conversion)
forms the basis of radio transmitters and frequency division multiplexing which will be
discussed later.
Power Considerations in DSBAM
we may tabulate AM components as follows:
v s t = VDC cosc t +
Vm
V
cosc + m t + m cosc m t
2
2
Component
Carrier
USB
Amplitude pk
VDC
Vm
2
Power
Power
Vm
2
V
Vm
= m
8
2 2
m VDC
8
VDC
2
VDC
2
LSB
V
Vm
= m
8
2 2
m 2VDC
8
Total Power PT =
Carrier Power Pc
+ PUSB
+ PLSB
Power Considerations in DSBAM
From this we may write two equivalent equations for the total power PT, in a DSBAM signal
The carrier power
m2
PT = Pc 1+
2
Either of these forms may be useful. Since both USB and LSB contain the same information a
useful ratio which shows the proportion of 'useful' power to total power is
m2
Pc
PUSB
4
=
PT
m2
Pc 1 +
2
m2
=
4 + 2m 2
Power Considerations in DSBAM
For DSBAM (m 1), allowing for m(t) with a dynamic range, the average value of m
may be assumed to be m = 0.3
Hence,
0.3 = 0.0215
m2
=
4 + 2m 2 4 + 20.32
2
Hence, on average only about 2.15% of the total power transmitted may be regarded
as 'useful' power. ( 95.7% of the total power is in the carrier!)
1
m2
=
Even for a maximum modulation depth of m = 1 for DSBAM the ratio
4 + 2m 2 6
i.e. only 1/6th (or 16.7%) of the total power is 'useful' power (with 83.3%
of the total power in the carrier).
Example
Suppose you have a portable (for example you carry it in your ' back pack') DSBAM transmitter
which needs to transmit an average power of 10 Watts in each sideband when modulation depth
m = 0.3. Assume that the transmitter is powered by a 12 Volt battery. The total power will be
m2
m2
PT = Pc + Pc
+ Pc
4
4
m2
where Pc
4
= 10 Watts, i.e.
Pc =
410
40
=
m2
0.32
= 444.44 Watts
Hence, total power PT = 444.44 + 10 + 10 = 464.44 Watts.
Hence, battery current (assuming ideal transmitter) = Power / Volts = 464.44
i.e. a large and heavy 12 Volt battery.
amps!
12
Suppose we could remove one sideband and the carrier, power transmitted would be
10 Watts, i.e. 0.833 amps from a 12 Volt battery, which is more reasonable for a
portable radio transmitter.
Single Sideband Amplitude Modulation
One method to produce signal sideband (SSB) amplitude modulation is to produce
DSBAM, and pass the DSBAM signal through a band pass filter, usually called a
single sideband filter, which passes one of the sidebands as illustrated in the diagram
below.
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The type of SSB may be SSBAM (with a 'large' carrier component), SSBDimC or
SSBSC depending on VDC at the input. A sequence of spectral diagrams are shown
on the next page.
Single Sideband Amplitude Modulation
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Single Sideband Amplitude Modulation
Note that the bandwidth of the SSB signal B Hz is half of the DSB signal bandwidth.
Note also that an ideal SSB filter response is shown. In practice the filter will not be
ideal as illustrated.
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As shown, with practical filters some part of the rejected sideband (the LSB in this
case) will be present in the SSB signal. A method which eases the problem is to
produce SSBSC from DSBSC and then add the carrier to the SSB signal.
Single Sideband Amplitude Modulation
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with m(t) = Vm cos mt, we may write:
v s t = VDC cosc t +
Vm
V
cosc + m t + m cosc m t
2
2
The SSB filter removes the LSB (say) and the output is
Vm
cosc + m t
2
Again, note that the output may be
For SSBSC, output signal =
v s t = VDC cosc t +
SSBAM, VDC large
SSBDimC, VDC small
SSBSC, VDC = 0
v s t =
Vm
cosc + m t
2
Power in SSB
From previous discussion, the total power in the DSB signal is
m2
m2
= PT = Pc + Pc
+ Pc
4
4
m2
PT = Pc 1+
2
for DSBAM.
Hence, if Pc and m are known, the carrier power and power in one sideband may be
determined. Alternatively, since SSB signal =
Vm
v s t = VDC cosc t + cosc + m t
2
then the power in SSB signal (Normalised Average Power) is
2
PSSB
V
V
V
V
= DC + m = DC + m
2
2
8
2 2
2
Power in SSB signal =
VDC
V
+ m
2
8
