ContinuousWave Modulation

1

• Chapter 2
• Continuous-Wave Modulation
• Amplitude Modulation (AM)
• Double Sideband Suppressed carrier (DSSC)
• Assymetric Sideband Signals
• Single sideband signals (SSB)
• Vestigial-Sideband AM
• Frequency Division Multiplexing (FDM)

2
Bandpass Signaling Review

• The modulated bandpass signal can be described by

Modulation Mapping function Convert m(t)
?g(t)

• The voltage spectrum of the bandpass signal is

• The PSD of the bandpass signal is

3
Amplitude Modulation

• The Complex Envelope of an AM signal is given by

Ac indicates the power level of AM and m(t) is
the Modulating Signal

• Representation of an AM signal is given by

• Ac1m(t) In-phase component x(t)

• If m(t) has a peak positive values of 1 and a
  peak negative value of -1

AM signal ? 100 modulated

• Envelope detection can be used if modulation
  is less than 100.

4
Amplitude Modulation
An Example of a message signal m(t)
Waveform for Amplitude modulation of the message
signal m(t)
5
Amplitude Modulation
B
An Example of message energy spectral density.
Carrier component together with the message
2B
Energy spectrum of the AM modulated message
signal.
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AM Percentage Modulation

• Definition The percentage of positive
  modulation on an AM signal is

• The percentage of negative modulation on an AM
  signal is

• The percentage of overall modulation is

If m(t) has a peak positive values of 1 and a
peak negative value of -1 AM signal ? 100
modulated
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AM Signal Waveform
Positive modulation 50 Negative
modulation 50 Overall Modulation 50
Amax 1.5Ac Amin 0.5 Ac
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AM Percentage Modulation
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AM Normalized Average Power
The normalized average power of the AM signal is
If the modulation contains no dc level, then
The normalized power of the AM signal is
Discrete Carrier Power
Sideband power
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AM Modulation Efficiency

• Definition The Modulation Efficiency is the
  percentage of the total power of the modulated
  signal that conveys information.

Only Sideband Components Convey information
Modulation Efficiency
Highest efficiency for a 100 AM signal 50 -
square wave modulation
Normalized Peak Envelope Power (PEP) of the AM
signal
Voltage Spectrum of the AM signal
Translated Message Signal
Unmodulated Carrier Spectral Component
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Double Side Band Suppressed Carrier (DSBSC)

• Power in a AM signal is given by

• DSBSC is obtained by eliminating carrier
  component
• If m(t) is assumed to have a zero DC level, then

Power ?

• Disadvantages of DSBSC
• Less information about the carrier will be
  delivered to the receiver.
• Needs a coherent carrier detector at receiver

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DSBSC Modulation
B
An Example of message energy spectral density.
No Extra Carrier component
2B
Energy spectrum of the DSBSC modulated message
signal.
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Carrier Recovery for DSBSC Demodulation

• Coherent reference for product detection of
  DSBSC can not be obtained by the use of ordinary
  PLL because there are no spectral line components
  at fc.

sin?c
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Carrier Recovery for DSBSC Demodulation

• A squaring loop can also be used to obtain
  coherent reference carrier for product detection
  of DSBSC. A frequency divider is needed to bring
  the double carrier frequency to fc.

15
Single Sideband (SSB) Modulation

• An upper single sideband (USSB) signal has a
  zero-valued spectrum for

• A lower single sideband (LSSB) signal has a
  zero-valued spectrum for

• SSB-AM popular method BW is same as that of
  the modulating signal.

Note Normally SSB refers to SSB-AM type of
signal
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Single Sideband Signal

• Theorem A SSB signal has Complex Envelope and
  bandpass form as

Upper sign (-) ? USSB Lower sign ()
? LSSB
Hilbert Transform corresponds to a -900 phase
shift
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Single Sideband Signal
Proof Fourier transform of the complex envelope
Upper sign ? USSB Lower sign ? LSSB
Upper sign ? USSB
If lower signs were used ? LSSB signal would have
been obtained
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Single Sideband Signal
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SSB - Power
The normalized average power of the SSB signal
Hilbert transform does not change power.
SSB signal power is
Power of the modulating signal
Power gain factor
The normalized peak envelope (PEP) power is
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Generation of SSB
SSB signals have both AM and PM.
The complex envelope of SSB
For the AM component,
For the PM component,
Advantages of SSB

• Superior detected signal-to-noise ratio compared
  to that of AM
• SSB has one-half the bandwidth of AM or DSB-SC
  signals

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Generation of SSB

• SSB Can be generated using two techniques
• Phasing method
• Filter Method
• Phasing method
• This method is a special modulation type of IQ
  canonical form
• of Generalized transmitters discussed in Chapter
  4 ( Fig 4.28)

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Generation of SSB

• Filter Method
• The filtering method is a special case in which
  RF processing (with a
• sideband filter) is used to form the equivalent
  g(t), instead of using
• baseband processing to generate g(m) directly.
  The filter method is the
• most popular method because excellent sideband
  suppression can be
• obtained when a crystal oscillator is used for
  the sideband filter.
• Crystal filters are relatively inexpensive when
  produced in quantity at
• standard IF frequencies.

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Vestigial-Sideband AM

• In the time domain the VSB can be expressed as

where h(t) is the impulse response of the VSB
filter.

• In the frequency domain we have

• The demodulation can be done by multiplying the
  modulated signal with the carrier and passing it
  through a LPF

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Vestigial-Sideband AM

• The expression for u(t) in the frequency domain
  becomes

• After passing u(t) through a LPF we have

• Hence to retrieve the message after demodulation
  the VSB filter must satisfy the following equation

where W is the bandwidth of the message.
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Frequency Divison Multiplexing