Principles of analogue modulation

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Principles of analogue modulation

• Lecture 3

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Analogue Modulation Techniques

• Theory of amplitude modulation
• Representation of AM
• Power relations in the AM wave
• Single-sideband techniques

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Amplitude Modulation

• This is the simplest and oldest form of
  modulation. In this type, the information signal
  (intelligence) causes the amplitude of the
  carrier to vary in time, in proportion to the
  instantaneous magnitude of their sum

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Amplitude Modulation

• Apart from transforming the signal into a form
  suitable for transmission, modulation allows many
  signals originally at the same frequency to be
  transferred to other parts of the electromagnetic
  spectrum.

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Mathematical description

• To describe amplitude modulation mathematically,
  consider the carrier wave given as a sinusoidal
  wave , with a frequency of and
  amplitude . This can be written as

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Amplitude Modulation

• Without modulation this sine wave will convey no
  information.
• Reason We can calculate its value at anytime
  from previously known values.
• What modulation does is to modify the constant
  value with the signal, which carries the
  information. This results in the amplitude of the
  modulated carrier varying in proportion to the
  amplitude of the information signal.

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Derivation of the AM equation

• Let the information signal be given by
• Let and
• then
• and

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Derivation of the AM equation

• The amplitude of the resulting modulation is the
  sum of the amplitude of the carrier and the
  signal.
• Substituting for

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• where this is index of
  modulation
• The resulting AM wave will thus be

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• Expanding the brackets
• but
• such that

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If we rewrite this in terms of frequencies
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Examples

• In an AM radio broadcast the tone has a frequency
  of 1000Hz and the carrier frequency is 1500kHz.
  What are the resulting sidebands.
• What will be the frequency of the sidebands if
  the carrier is at 1250kHz?
• If the tone has a spectrum of 300 to 3000Hz and
  the carrier is at 100kHz then one of the
  sidebands will range from 100.3 to 103 and the
  other will be from 97 to 99.7kHz.

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Modulating with different carriers

• Modulation can be used to translate signals
  originally at the same frequency to different
  parts of the frequency spectrum.
• Assume that AM radio stations have a voice and
  music spectrum from 0 to 5kHz.
• Assume that they are spaced 10kHz apart in the
  broadcast band.
• If the broadcast from each station is then
  modulated with a different carrier frequency,
  then the broadcast will not overlap. Reason the
  signal is less than half the difference between
  adjacent carriers.
• Example Stations broadcast at 1000, 1010 and
  1020kHz. Draw the frequency spectrum of the
  stations if the signal bandwidth is 5kHz
• What happens if the modulating signal bandwidth
  is now 8kHz?

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Modulation Index and Signal Power

• It is a measure of how fully the carrier has been
  modulated.
• Examples The modulated peak value of a signal is
  10 V and the unmodulated carrier is 8 V. Find the
  modulation index.
• A modulated signal seen on an oscilloscope has a
  maximum span of 5 V and a minimum of 1 V. What is
  the modulation index?

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Signal Power

• The power in a system can be defined through
  voltage as
• and through current as
• Assume that R 1 ohm
• The carrier power is then
• Power in each side band is the given as

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• The power in both side-bands
• The total transmitted power is
• since

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Comment
The maximum power in the sidebands is 50 of the
carrier power at m 1. The carrier and one
sideband may be suppressed without destroying the
information Examples A carrier of 1000W is
modulated with an index of 0.8. What is the total
power? For a carrier of 250W and 90 modulation,
what is the total power? What is the carrier
power if the total power is 1000W and the
modulation index is 0.95.
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Single-sideband techniques

• Conventional AM systems have two main
  disadvantages
• Two thirds or more of the total transmitted power
  is in the carrier
• The bandwidth required is twice that which will
  be needed in SSB
• Such systems are therefore both power and
  bandwidth inefficient.
• The mathematical foundation for single sideband
  systems was laid in 1914.
• There are many variations of the single sideband
  systems

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AM SSB Full carrier (SSBFC)
Carrier is transmitted at full power with only
one of the sidebands. In this only half as much
bandwidth will be required The power relations
will be as follows Power in carrier Power in
lower sideband 0 Power in upper sideband
Total power What is the ratio of sideband
power to carrier power at 100 modulation?
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AM Single sideband suppressed carrier (SSBSC)
In this the carrier is totally removed together
with one of the sidebands. Only half the bandwith
is required. Power Relations The sideband power
will constitute 100 of the total transmitted
power. Power in carrier, Power in lower
sideband 0 Power in upper sideband
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AM SSB Reduced carrier (SSBRC)
In this one sideband is removed and the carrier
reduced to about 10 of the unmodulated
amplitude. The carrier will have to be reinserted
at reduced amplitude for the purpose of
demodulation Power relations Power in carrier,
Power in lower sideband 0 Power in upper
sideband Total power
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Comparison of SSB to Double sideband AM
Advantages of SSB Bandwidth conservation Only
half the bandwidth is required Power
conservation Only one sideband with carrier
removed or suppressed. Hence total transmitted
power will be less. This allows smaller
transmitters to be used. Selective fading In
double sideband, the two sidebands may experience
different impairments as the propagate along
different paths in the medium. This could result
in carrier phase shift. This cannot happen if
only one sideband is transmitted. Noise
Reduction Thermal noise is reduced to half,
because the bandwidth is also half.
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Disadvantages
Complex receivers Tuning Difficulties More
difficult to tune than conventional AM receivers.
More expensive tuning circuits can be
used. Examples A double sideband AM radio
transmitter gives a power output of 5 kW when the
carrier is modulated to a depth of 95. A speech
signal is then used to modulate the carrier with
a depth of 20 and the carrier and one sideband
are suppressed. Find the output power in the
other sideband.