Chapter 3 Analog Signal Transmission and Reception

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Chapter 3Analog Signal Transmission and Reception
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CONTENTS

• Introduction to Modulations
• Amplitude Modulation
• Angle Modulation
• Radio and Television Broadcasting
• Mobile Radio Systems

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3.1 INTRODUCTION TO MODULATION

• Denote m(t) as the analog signal to be
  transmitted.
• The signal m(t) is assumed to be a lowpass signal
  of bandwidth W and is a power-type signal with
• The message signal m(t) is transmitted through
  the communication channel by putting it on a
  carrier signal of the form

carrier amplitude
carrier amplitude
carrier phase
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• The signal m(t) modulates the carrier signal c(t)
  in three forms
• Amplitude Modulation (AM)
• Frequency Modulation (FM)
• Phase Modulation (PM)
• Objectives of modulation
• Translate the low pass signal m(t) to bandpass
  signal to match the passband characteristics of
  the channel.
• Accommodate for simultaneous transmission -
  frequency-division multiplexing (FDM).
• Increase the noise immunity in transmission by
  expanding the bandwidth of the transmitted
  signal.

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3.2 AMPLITUDE MODULATION (AM)

• The message signal m(t) is impressed on the
  amplitude of the carrier signal c(t).
• Types of amplitude modulation
• Double-sideband, suppressed carruer AM (DSB-SC
  AM)
• Conventional double-sideband AM
• Single-sideband AM (SSB AM)
• Vestigial-sideband AM (VSB AM)

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3.2.1 Double-Sideband Suppressed Carrier AM

• A double-sideband, suppressed carrier (DSB-SC) AM
  signal is obtained by multiplying the message
  signal m(t) with the carrier signal c(t).
• Amplitude modulated signal
• The spectrum of the modulated signal can be
  obtained by taking the Fourier transform of u(t).

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upper sideband
upper sideband
lower sideband
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• The magnitude of the spectrum of the message
  signal m(t) has been translated or shifted in
  frequency by an amount
• The phase of the message signal has been
  translated in frequency and offset by the carrier
  phase
• The bandwidth of the AM signal is 2W, where W is
  the bandwidth of m(t).
• The upper sideband of U(f) contains all the
  frequency contain of the message signal M(f).
• u(t) does not contain carrier components - u(t)
  is called a suppressed-carrier signal (DSB-SC AM
  signal)

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• To compute power content of DSB-SC signal, we
  first evaluate the time-average autocorrelation
  function of the signal u(t)
• We may show that the following equation equals to
  zero.

Parsevals relation
No frequency overlap
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• Finally, we have
• Taking Fourier transform of both sides
• The power spectral density of the DSB-SC signal
  is the power spectral density of the message
  shifted upward and downward by and scaled
  by
• The power of the modulated signal
• where is the power of the
  message signal

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Demodulation of DSB-SC AM Signal

• In the absence of noise, and with the assumption
  of an ideal channel, the received signal can be
  expressed as
• Demodulation of DSB-SC AM signal
• Multiply r(t) by a locally generated sinusoid
• Pass the product signal through an ideal lowpass
  filter having a bandwidth W.
• Multiplication

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• The lowpass filter rejects the high frequency
  components and pass only the low frequency
  component. Hence, the output of the filter is
• Note that m(t) is multiplied by
  . Thus the desired signal is scaled by a factor
  that depends on the phase difference between the
  pahse of the carrier and the phase of
  the locally generated sinusoid.
• If the amplitude of the
  desired signal is reduced by
• If the desired signal
  component vanishes.
• For perfect demodulation, (Phase
  coherent)

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Pilot Tone for Carrier Recovery in DSB AM

• Addition a pilot tone to a DSB AM signal-
  additional power requirement
• Carrier recovery by a narrow band filter

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3.2.2 Conventional Amplitude Modulation

• A conventional AM signal consists of a large
  carrier component in addition to the double
  sideband AM modulated signal. The transmitted
  signal can be expressed as
• Advantage easy to demodulate

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• It is convenient to express m(t) as
• where is normalized such that
• The above equation can be done by using
• The scale factor a is called the modulation
  index. The modulated signal can be expressed as

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Overmodulated (a gt 1)
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• The spectrum of the amplitude modulated signal
  u(t) is
• The spectrum of a conventional AM signal occupies
  bandwidth twice the bandwidth of the message
  signal.

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• Example Suppose that the modulating signal
  is a sinusoid of the form
• Determine the DSB AM signal, its upper and
  lower sidebands, and its spectrum, assuming a
  modulation index of a.
• Solution The DSB AM signal

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• The spectrum of the DSB AM signal

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• We have already proved in the DSB-SC case, the
  power in the modulated signal is
• For the conventional AM
• Finally, we have

contains no DC component
Message power
Carrier power
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• Advantage of conventional AM signal easy to be
  demodulated
• Envelope detector

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• Output of the envelope detector

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3.2.3 Single-Sideband AM

• DSB-SC AM signal requires a channel bandwidth
• of
• The transmission of either sideband is sufficient
  to reconstruct the message signal m(t) at the
  receiver.
• We may reduce the transmitted bandwidth to W Hz
  by transmitting only the upper sideband or the
  lower sideband.
• A single sideband AM signal can be represented
  mathematically as
• Hilbert transform of m(t).

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• Generation of a single-sideband AM signal by
  Hilbert transform

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• Generation of a single-sideband AM signal by
  bandpass filter

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• Let m(t) be a signal with Fourier transform M(f).
• An upper sideband AM signal is obtained by
  eliminating the lower sideband of a DSB AM
  signal.
• We may pass the DSB AM signal through a highpass
  filter whose transfer function is given by
• Obviously H(f) can be written as

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• The spectrum of the USSB AM signal is given by
• Taking the inverse Fourier transform of both
  sides, we obtain

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• For lower sideband (LSSB) AM signal, notice
• We have
• Finally, we have proved

USSB AM
LSSB AM
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• To recover the message signal from SSB AM signal,
  we require a phase coherent or synchronous
  demodulator.
• First multiply the received signal with the local
  generated carrier , we have
  
• By passing the above signal through an ideal
  lowpass filter, we have the output
• For perfect demodulation, we must have .

desired signal
interference
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3.2.4 Vestigial-Sideband AM

• Relaxing the SSB AM by allowing a part called
  vestige to appear at the output of the modulator.
  The resulting signal is called vestigial-sideband
  (VSB) AM.
• Generation of VSB AM
• generate a DSB-SC AM signal
• pass the DSB-SC AM signal through a sideband
  filter with frequency response H(f)

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• In the time-domain the VSB signal may be
  expressed as
• impulse response of the VSB
  filter
• In frequency domain
• Consider the demodulation of the VSB signal

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• We have the product signal
• The lowpass filter rejects the double-frequency
  terms and pass only the components in the
  frequency range
• The signal spectrum at the output of the lowpass
  filter is
• Undistirtion requirement

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3.2.5 Implementation of AM Modulator and
Demodulator

• Power-Law Modulation
• Nonliear device
• voltage-current characteristic of P-N diode
• input is the sum of the message signal and the
  carrier
• Let be the input signal. The output of
  the nonlinear device can be expressed as

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• Power-Law AM modulator
• Suppose that the nonlinear device is approximated
  by a second order polynomial.

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• Input to the nonlinear device
• Output of the nonlinear device
• The band pass filter with bandwidth 2W centered
  at yields
• where by design

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• Switching Modulator

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• Assume that
• Let
• The diode will turn on if and will
  turn off if
• The output across the load resistor is
• Since s(t) is a periodic rectangular function,
  the Fourier series is

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• Hence
• Passing through a bandpass filter, we
  have

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• Balanced Modulator for DSB-SC AM signal

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• Ring modulator for DSB-SC AM
• If c(t) gt 0, 1, 4 on, and 2, 3 off,
• If c(t) lt 0, 1,4 off, and 2,3 on,

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2
3
4
C(t)
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• Therefore, we have
• Since c(t) is a periodic function, the Fourier
  series can be expressed as
• The desired DSB-SC AM signal is obtained by
  passing through a bandpass filter with center
  frequency and bandwidth 2W.

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• Demodulation of DSB-SC AM Signals

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• Demodulation of SSB Signals with pilot tone

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3.2.6 Signal Multiplexing

• Multiplexing The process of combining a number
  of separate message signals into a composite
  signal for transmission over a common channel.
• All message signals can be recovered at the
  receivers.
• Three common methods
• Time-division multiplexing (TDM)
• Frequency-division multiplexing (FDM)
• Code-division multiplexing (CDM)

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• FDM system

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• Quadrature-Carrier Multiplexing
• Two message signal and .
• Transmit two message signals on the same carrier
  frequency
• Two signals are modulated into u(t) by
• The two message signals are demodulated by

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3.3 ANGLE MODULATION

• Angle modulation
• Frequency modulation (FM) Frequency is changed
  by the message signal.
• Phase modulation (PM) Phase is changed by the
  message signal.
• High degree of noise immunity by bandwidth
  expansion.
• They are widely used in high-fidelity music
  broadcasting.

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3.3.1 Presentation of FM and PM Signal

• An angle-modulated signal
• the phase of the signal.
• Instantaneous frequency is given by
• Since u(t) is a bandpass signal, it can be
  represented as

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• If m(t) is the message signal, then in a PM
  system we have
• In an FM system
• From the above relationships we have
• On the other hand

phase deviation constant
frequency deviation constant
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• The maximum phase deviation in a PM system
• The maximum frequency-deviation in an FM system

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• The message signal
  is used to either FM or PM for the carrier
  . Find the modulated signal in
  each case.
• Solution
• we have
• Modulation index for a general m(t)

PM
FM
Modulation index
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• Narrowband Angle Modulation If for all , we
  have
• then we can use the approximation
• The modulation is very similar to conventional AM

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3.3.2 Spectral Characteristics of Angle-Modulated
Signals

• Assume that the message is a sinusoidal signal
• The signal is periodic with
  period . The same is also true
  for the complex exponential signal
• Fourier series representation

Bessel function of the first kind of
order n
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• Therefore, we have
• Finally we obtain
• The actual bandwidth of the modulated signal is
  infinite. However, the amplitude of the
  sinusoidal components of frequencies
  for large n is very small.
• Property

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• Example
• Find the expression for the modulated signal
  and determine how many harmonics should be
  selected to contain 99 of the modulated signal
  power.
• Solution The total power
• The modulated signal

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• The modulation index is given by
• Therefore
• We have to choose k large enough such that
• The solution k6.

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• In general the effective bandwidth of an
  anglr-modulated signal, which contains at least
  98 of the signal power, is given by
• Let the message signal be given by
• The bandwidth of the modulated signal is given by
• FM occupies less bandwidth then PM .
• Carsons rule For general message signal, the
  bandwidth of the angle-modulated signal is given
  by

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3.3.3 Implementation of Angle Modulators and
Demodulators

• Design an oscillator whose frequency changes with
  the input voltage.
• Voltage-controlled oscillator
• Varactor diode - capacitance changed with the
  applied voltage.
• A inductor with the varactor diode is used
  in the oscillator circuit.

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• Let the capacitance of the varactor diode is
  given by
• When m(t) 0, the frequency of the tuned circuit
  is given by
• In general for nonzero m(t), we have
• Assuming that
• We have

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• Indirect method for generation of FM and PM
  signals
• generate a narrow a narrow band angle-modulated
  signal
• change the narrow band signal to wideband signal

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• Generate wideband angle-modulated signals from
  narrow band angle-modulated signals
• frequency multiplier
• implemented by nonlinear device and bandpass
  filters
• Using down converter

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• FM demodulation
• generate an AM signal
• use AM demodulator to recover the message signal
• Pass the FM signal through an filter with
  response
• If the input to the system is
• the output
• The above signal is an AM signal.

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• Balanced discriminator
• use two tuned circuits
• connect in series to form a linear frequency
  response region.

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• FM demodulator with feedback

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• FM demodulator with phase-locked loop (PLL)
• Input
• VCO output
• Phase Comparator

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• Linearized model of the PLL
• or

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• By taking the Fourier transform
• Suppose that we design G(f) such that

v(t) is the demodulated signal
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3.4 RADIO AND TELEVISION BROADCASTING

• AM Radio
• FM Radio
• Television

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3.4.1 AM Radio Broadcasting

• AM Radio Broadcasting
• 535-1605 kHz
• 10kHz spacing
• bandwidth of m(t) is 5kHz.
• Superheterodyne receiver with intermediate
  frequency
• two frequency components and
  are produced after the mixer
  

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• Rejection of the radio signal at the image
  frequency
• Assume there are two received signal
• The mixer output consists of the two signals
• The RF amplifier bandwidth is designed to be
  sufficiently narrow so that the image frequency
  signal is rejected
• The IF amplifier has bandwidth of 10kHz to reject
  signal from adjacent channels.
  

Desired signal
Interference from image channel
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3.4.2 FM Radio Broadcasting

• FM Radio Broadcasting
• 88 - 108 MHz
• 100kHz spacing
• peak-frequency deviation 75kHz
• Superheterodyne receiver with intermediate
  frequency

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FM Stereo Transmitter
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FM Stereo Receiver
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3.4.3 Television Broadcasting

• 1936 BBC black-and-white picture transmission
• Black-and-white TV Signal.
• The two dimensional image is converted to a
  one-dimensional electrical signal by sequentially
  scanning the image.
• The scanning of the electron beam in the CRT is
  controlled by two voltage applied across the
  horizontal and vertical deflection plates.
• In commercial TV broadcasting, the bandwidth of
  the video signal is is limited to W 4.2Mhz.
• VSB modulation is employed, the total
  transmission bandwidth is around 6Mhz.

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Interlaced pattern with rate 1/60 sec
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A typical video signal
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3.5 Mobile Radio Systems

• Cellular concept