Amplitude Modulation

1
Amplitude Modulation

• Lecture 2

2
Amplitude Modulation

• The AM waveform is composed entirely of spectral
  components related to the carrier and information
  signal frequencies.
• It can be expressed by
• is the angular frequency of the information
  signal when the information signal is a single
  test frequency.

3
Proof

• Substituting a single test tone for the
  modulating function and adding a separate carrier
  component yields the AM formula
• When the modulating function f(t) is a single
  test tone,
• results
• The carrier term, is inserted into
  this AM waveform for use in demodulation at the
  receiver

results
Applying the half-wave identity
.
4

• Since the modulation process is based on
  frequency multiplication, the waveform contains
  two components derived from the sum and
  difference frequencies of the carrier and the
  information signal.
• The third component is the carrier frequency,
  , which is included in the waveform solely for
  use in the demodulation process (the process of
  recovering separating an information signal
  from a modulated carrier).
• The three sine wave terms in the AM equation can
  be represented by three rotating vectors.

5
Sidebands contain the frequency of the
information signals produced by the process of
modulation. The upper sideband has a frequency
higher than the carrier signal frequency. The
sideband vectors each rotate in opposite
directions at the modulation frequency,

- when viewed from the
perspective of the rotating carrier. The upper
sideband vector rotates at a faster rate than the
carrier. The resultant of the carrier and the
side band component vectors traces out the
envelope of the modulated carrier signal. This AM
signal with a carrier and two sideband components
is called double sideband DSB (or full carrier ?
transmits the carrier and both sidebands).
- when viewed from the perspective of the
rotating carrier.
6
In the frequency domain, the three components of
the DSB signal appear as spectral lines that
correspond in amplitude and frequency to the
rotating vectors in the time domain.
The information signal frequency, , is the
difference between the carrier and either
sideband.
7
On a spectrum analyzer
The modulation index, m, represents the amount
of modulation or the degree to which the
information signal modulates the carrier
signal. As the information signal varies in
amplitude, the sidebands vary in amplitude and m
ranges between its limits of 0 and 1. Since
signal power is proportional to signal amplitude,
maximum signal power increases as modulation
increases.
8
50 modulation (m 0.5)
For m 1 is the greatest possible modulation
method without distortion (is undesired
alterations to the shape of the waveform) to the
modulated carrier. Sidebands are 6 dB down from
carrier. m 1 ? in the time domain, the modulated
carrier signal varies in amplitude from 0 to
twice the amplitude of the unmodulated carrier.
9
The modulated carriers signal waveform goes to 0
at the point the information signal reaches its
minimum value. Generally, the information signal
amplitude should be as long as possible to make
signal detection easier at the receiver. However,
when information signal amplitude increases above
the level required for 100 modulation, over
modulation results (is a condition where the
modulation index exceeded its maximum).
10
Overmodulating

• Generates Harmonics -gt
• Distorts the waveform -gt
• Causes adjacent channel interference

11
DSB bandwidth

• In Digital Sound Broadcasting

12
Sidebands

• Hold the information that can vary in amplitude
  and frequency (the carrier signal doesnt vary at
  all)
• Increase in amplitude up to 100 of the carrier
  frequency

13
Signal Power

• Even at 100 modulation, 2/3 of the power is
  needed for transmitting the carrier

14
Modulation Index (m) 1/4

• Only for signals modulated by a single text
  frequency

15
Modulation Index (m) 2/4
16
Modulation Index (m) 3/4

• When m is very small (down to 0.1)

17
Modulation Index (m) 4/4

• Finding m
• Converting to dB