Amplitude Modulation

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Chapter 2

• Amplitude Modulation

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In this chapter you will learn..

• Definition of amplitude modulation
• Type of AM modulation
• Voltage and power analysis
• Time and frequency domain waveform
• Double side band, single side band and vestigial
  side band
• AM, DSB, and SSB modulator and demodulator
• Advantage and disadvantage of single side band
  over double side band
• Applications of AM

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Revision..

• Why do we need modulation?
• What are the types of modulation?
• What is AM?
• Why use AM?

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Introduction

• Amplitude Modulation is the process of changing
  the Amplitude of a relatively high frequency
  carrier signal in accordance with the amplitude
  of the modulating signal (Information).
• It is a low quality form of modulation and often
  used for commercial broadcasting of both audio
  and video signals.
• AM Modulators are nonlinear devices with 2 inputs
  and 1 output a single, high frequency of carrier
  signal of constant-amplitude carrier signal and
  the low frequency information signal.
• The Output of AM Modulator is called Modulated
  Wave and the shape of the Modulated Wave is
  called AM Envelope.

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An example of amplitude modulator circuit using a
transformer
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Types of AM

• 1) Double sideband full carrier (DSBFC)
• - Contains USB, LSB and Carrier
• 2) Double sideband suppressed carrier (DSBSC)
• - Contains only USB LSB
• - A circuit that produces DSBSC is
  Balanced modulator
• 3) Single sideband (SSB)
• - Contains either LSB or USB
• - Produce efficient system in term or
• power consumption and bandwidth

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AM Waveform

• Generally.
• Carrier Signal gt VCsin(2?fct)
• Modulating Signal gt Vmsin(2?fmt)
• Modulated Wave gt Vam(t)
• For Double sideband full carrier (DSBFC) AM
  waveform consists of
• DC voltage
• The carrier frequency fc
• Lower side frequency (fc - fm)
• Upper side frequency (fc fm)
• ? Known as AM envelope
• Then the AM waveform is shown in the next figure

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• The AM waveform reaches maximum value when the
  modulating signal amplitude is at maximum value.
• The AM waveform reaches minimum value when the
  modulating signal amplitude is at maximum
  negative.
• The repetition rate of the envelope is equal to
  the frequency of the modulating signal, and the
  shape of the envelope is identical to the shape
  of the modulating signal.

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Frequency Spectrum

• The Frequency Spectrum of AM DBSFC is shown
  below
• Frequencies between and fc is called
  lower side band (LSB)
• Frequencies between fc and is called upper
  side band (USB)
• The Bandwidth of AM DBSFC is FB 2fm (max)
• AM signal does not contain modulating signal
  frequency

Carrier
Lower side band
Upper side band
Amplitude
Upper side frequencies
Lower side frequencies
fcfm(max)
Frequency
fc-fm(max
fc
fc-fm(max)
fcfm(max)
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EXAMPLE 1

• AM DBSFC Modulator with a carrier frequency, fc
  100 kHz and maximum modulating signal frequency,
  fm of 10 kHz, determine the following
• a. LSB USB
• b. Bandwidth
• c. Upper and Lower side frequencies if the
  modulating signal is a single frequency of 5kHz.
• d. Draw the output frequency spectrum

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Solution
Lower side band
Upper side band
Carrier
Frequency
100kHz
95kHz
105kHz
90kHz
110kHz
fc
fUSF
fc-fm(max
fcm(max
fLSF
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Modulation Output

• The output voltage of the modulated wave can be
  described as below
• 1. Vmax Vc Vusf Vlsf
• 2. - Vmax -(Vc Vusf Vlsf)
• 3. Vmin Vc -Vusf - Vlsf
• 4. - Vmin -Vc Vusf Vlsf

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Modulation Index

• Modulation index or coefficient is an indicator
  to describe the amount of amplitude change
  (modulation) present in an AM waveform (depth of
  modulation), basically stated in form of
  percentage.It is defined mathematically as
• Where mmodulation coefficient (unitless)
• Em peak change in the amplitude of the output
  waveform voltage
• Ec peak change in the amplitude of the
  unmodulated carrier voltage
• Percent modulation

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• The relationship between Em , Ec , Vmax or Vmin
  are shown in the diagram below

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• If the modulating signal is pure, single
  frequency sine wave and the modulation process is
  symmetrical, then
• Em ½ (Vmax - Vmin) , and Ec ½
  (Vmax Vmin)
• Thus we can obtain M from
• Where Vmax Ec Em , and Vmin Ec - Em
• Since Em Eusf Elsf and Eusf Elsf ,
  then
• Where Eusf peak amplitude of the upper side
  frequency (V)
• Elsf peak amplitude of the lower side
  frequency (V)

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• 50 Modulated Wave gt Em Ec / 2
• 100 Modulated Wave gt Em Ec (Vmin 0V)

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Voltage Distribution

• An unmodulated carrier (carrier signal) is
  described by the following equation -
• Vc (t) Ec sin (2?fct)
• The Amplitude of the AM Wave varies proportional
  to the amplitude of the modulation signal, and
  the maximum of the modulated wave equal to Ec
  Em.
• Thus the amplitude of the modulated wave can be
  expressed as -
• Vam(t) Ec Emsin(2?fmt) sin (2?fct)
• Ec Emsin(2?fmt) ? Amplitude of modulated wave.
• Em Peak Change in the Amplitude of Envelope
• fm Frequency of Modulating signal

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Voltage Modulation

• Since Em mEc and by developing the equation
  for modulated wave, the final equation of the
  modulated wave can be expressed in term of its
  Carrier Component and Side Frequencies Component
  (usf lsf)-
• Where Ecsin(2?fct)? carrier signal (V)
• ? upper side frequency signal (V)
• ? lower side frequency signal (V)
• Carrier wave is 90 out of phase with the upper
  and lower side frequencies
• The upper and lower side frequencies are 180
  out of phase with each other

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EXAMPLE 2

• Given the first input to AM Modulator is 500 kHz
  Carrier signal with Amplitude of 20V. The second
  input to AM Modulator is the 10kHz modulating
  signal which cause a change in output signal of
• 7.5 Vp. Determine the following -
• a. USF LSF
• b. Modulation Index or Coefficient, M
• c. Peak Amplitude of modulated carrier
• d. Upper Lower side frequency voltage
• e. Maximum Minimum Amplitude of the
• envelope, Vmax and Vmin
• f. Expression of Modulated Wave
• g. Output Spectrum Envelope

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Power Distribution

• The Average power dissipated in a load by carrier
  signal (unmodulated carrier) is equal to the rms
  carrier voltage squared divided by the load
  resistance. It is expressed mathematically as
  below
• Pc (Ec)2 / 2R
• where Pc carrier power (W)
• Ec peak carrier voltage(V)
• R load resistance (Ohm)
• The total power, PT distribution during a
  modulation process is affected by modulation
  index (depth) and defined mathematically as
• PT Pc1 (m2 /2)
• A power at sideband frequencies (LSF USF) is
  defined as
• Plsf Pusf m2 Pc/4

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• EXAMPLE 3
• For AM DSBFC wave with an unmodulated carrier
  voltage, Vc 10 Vp , a load resistance of 10 ?
  and modulation index of 1, determine the
  following
• a. Power of the carrier, and sideband
  frequencies (Plsf Pusf)
• b. Total Power of sideband, PT
• c. Draw Power Spectrum

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• EXAMPLE 4
• An AM Transmitter has a carrier power output
  of 50W. Determine the total power that produced
  80 modulation.
• SOLUTION
• 1. Total Power is defined as
• PT Pc1 (m2 /2)
• Thus,
• PT (50 W)1 ((0.8)2 /2)
• 66 W

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Modulation of complex signal

• The modulating signal (information signal) is
  often a complex form consists of many sinusoidal
  wave with different Amplitude and Frequencies
• v(t) V1sin(2?f1t) V2sin(2?f2t)
  V3sin(2?f3t)
• V4sin(2?f4t) V5sin(2?f5t) .
• Thus, after modulation, the output wave will be
  in the form of
• vam(t) Ecsin(2?fct) - ½ m1Ec
  cos2?(fcfm1)t ½
• m1Ec cos2?(fc-fm1)t - ½ m2Ec
  cos2?(fcfm2)t
• ½ m2Ec cos2?(fc-fm2)t - ½
  m3Ec cos2?(fcfm3)t
• ½ m3 Ec cos2?(fc-fm3)t -
• The Total Modulation Index will be
• m sqrt (m12 m22 m32
  mn2)

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• EXAMPLE
• For AM DSBFC transmitter with an unmodulated
  carrier Power, Pc 100 W is modulated
  simultaneously with 3 other modulating signals
  with coefficient index of m1 0.2, m1 0.4, m1
  0.5,
• determine the following -
• a. Total Modulation Index or Coefficient
• b. Upper and Lower sideband power
• c. Total transmitted power

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AM Modulator

• Modulation circuit designs can be broadly divided
  into low and high level. It is determined from
  the location where modulation occurs in
  transmitter.
• The Low-Level AM Modulator
• Modulation takes place prior to the output
  element of the final stage of the transmitter
• It can be a Class A or Class AB or Class B
  Amplifier.
• It is an 2 input Modulator.
• It is also called as Emitter Modulator.
• The High-Level AM Modulator
• Modulation occurred in the final element of the
  final stage where carrier signal is at maximum
  amplitude
• A Class C Amplifier which is also called
  Collector Modulator because a modulating signal
  is applied directly to the Modulator.

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Low-Level AM Modulator

• Advantages
• Less modulating signal power is required to
  achieve high percentage of modulation
• The advantage of using a linear RF amplifier is
  that the smaller early stages can be modulated,
  which only requires a small audio amplifier to
  drive the modulator.
• Disadvantages
• The great disadvantage of this system is that the
  amplifier chain is less efficient, because it has
  to be linear to preserve the modulation.

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Low-Level AM Modulator Voltage Gain

• The voltage gain for emitter modulator is
  obtained from
• Av Aq 1 m sin(2?fmt)
• Where Av amplifier voltage gain with modulation
• Aq amplifier quiescent (without modulation)
  voltage gain with
• Since sin(2?fmt) always goes from 1 to -1
• Av Aq(1 m)
• For 100 modulation (m1),
• Av(max) 2Aq
• Av(min) 0

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High-Level AM Modulator

• Advantages
• One advantage of using class C amplifiers in a
  broadcast AM transmitter is that only the final
  stage needs to be modulated, and that all the
  earlier stages can be driven at a constant level.
  
• These class C stages will be able to generate the
  drive for the final stage for a smaller DC power
  input.
• Disadvantages
• A large audio amplifier will be needed for the
  modulation stage, at least equal to the power of
  the transmitter output itself.
• Traditionally the modulation is applied using an
  audio transformer, and this can be bulky.

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AM Demodulator

• It is a circuit that accepts a modulated signal
  and recovers the original modulating signal.
• It is a key circuit in Receiver and also called
  as DETECTOR.
• The widely used AM Demodulator is DIODE DETECTOR,
  by means of a diode rectifier, which may be
  either a vacuum tube or a semiconductor diode.
• The demodulator must meet three requirements
• It must be sensitive to the type of modulation
  applied at the input,
• it must be nonlinear
• it must provide filtering.

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• Remember that the AM waveform contains only three
  RF frequencies the carrier frequency, the sum
  frequency, and the difference frequency.
• The modulating signal is contained in the
  difference between these frequencies.
• The vector addition of these frequencies
  provides the modulation envelope which
  approximates the original modulating waveform.
• Thus it is this modulation envelope that the
  DIODE DETECTORS use to reproduce the original
  modulating frequencies.

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Diode rectifier
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AM Transmitters
Modulating signal driver amplifier
Modulating signal source
Preamplifier
Bandpass filter
AM modulator and output power amplifier
Linear intermediate power amplifier
Linear final power amplifier
Bandpass filter
Antenna
RF carrier oscillator
Buffer amplifier
Carrier driver
Low level
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AM Transmitters
Modulating signal driver amplifier
Modulating signal power amplifier
Modulating signal source
Preamplifier
Bandpass filter
AM modulator and output power amplifier
Matching network
Bandpass filter
Antenna
RF carrier oscillator
Carrier power amplifier
Buffer amplifier
Carrier driver
High level
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AM receiver Block Diagram
RF section
Bandpass Filter
Mixer/ converter section
Bandpass filter
IF section
Bandpass filter
AM detector
Bandpass filter
Audio section
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Receiver parameters

• Selectivity measure the ability of receiver to
  accept a given band of frequencies and reject
  others
• Bandwidth improvement reducing bandwidth in
  receiver is needed in order to reduce noise
• Sensitivity threshold value-minimum RF signal
  that can be detected by the receiver
• Dynamic range input power range over which the
  receiver is useful
• Fidelity a measure of the ability of a
  communication system to produce output signal
  that is a replica of the original source
  information

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Noncoherent Tuned Radio-Frequency Receiver
Antenna coupling network
RF amp.
RF amp.
RF amp.

• AM 535 1605 kHz
• Channel BW 10 kHz
• Difficult to tune
• Q remains constant ? filter bandwidth varies

Audio detector
Audio amplifier
Nonuniform selectivity
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Superheterodyne Receiver
RF-section
Mixer
Preselector
RF amplifier
oscillator
IF-section
Bandpass filter
IF amplifier
Audio detector
Audio amplifier
Fixed BPF at lower frequencies than RF
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What Heterodyning is

• To heterodyne means to mix to frequencies
  together so as to produce a beat frequency,
  namely the difference between the two.
• Amplitude modulation is a heterodyne process the
  information signal is mixed with the carrier to
  produce the side-bands.
• The side-bands occur at precisely the sum and
  difference frequencies of the carrier and
  information.
• These are beat frequencies (normally the beat
  frequency is associated with the lower side-band,
  the difference between the two).

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What Superheterodyning is

• When you use the lower side-band (the difference
  between the two frequencies), you are
  superheterodyning.
• Strictly speaking, the term superheterodyne
  refers to creating a beat frequency that is lower
  than the original signal.
• Although we have used the example of amplitude
  modulation side-bands as an example, we are not
  talking about encoding information for
  transmission.
• What superheterodying does is to purposely mix in
  another frequency in the receiver, so as to
  reduce the signal frequency prior to processing.
  Why and how this is done will be discussed below.
  

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RF-section

• Preselector
• Broad-tuned bandpass filter with adjustable
  center frequency that is tuned to the desired
  frequency
• Provide enough initial bandlimiting to prevent
  unwanted radio frequency (image frequency)
• Reduce noise bandwidth of the receiver and
  initial step to reducing the whole bandwidth
• RF amplifier
• Sets the signal threshold
• Advantages
• Greater gain, thus better sensitivity
• Improved image-frequency rejection
• Better signal to noise ratio
• Better selectivity

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RF-to-IF conversion
Receiver RF input (535 1605 kHz)
Channel 1
Channel 2
Channel 3
Preselector 535 - 565 kHz
565 kHz
535
545
555
550
540
560
Mixer
Oscillator 1005 kHz
470 kHz
440
450
460
445
455
465
high-side injection (fLO gt fRF)
Channel 1
Channel 3
Channel 2
IF filter 450 460 kHz
Channel 2
IF Filter output
450
460 kHz
455
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Envelope detection
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t1
t2
t3
t0
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Highest modulating frequency
The highest modulating signal frequency that can
be demodulated by a peak detector without
attenuation
RCtime constant (s)
for m70.7
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Single Side Band

• In conventional AM double-sideband system, the
  carrier signal does not carry information the
  information is contained in the sidebands.
• Due to the nature of this system these are the
  setbacks
• Carrier power constitutes two-thirds or more of
  the total transmitted power
• Both sidebands contained the same information.
  Transmitting both sidebands is redundant and thus
  causes it to utilize twice as much bandwidth as
  needed with single sideband system.
• ?Conventional AM is both power and bandwidth
  inefficient.

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AM Single Sideband Full Carrier (SSBFC)

• Carrier signal is transmitted at full power
• Only one of the sidebands is transmitted
• Require only half as much bandwidth as
  conventional AM
• However, this type of single sideband, the
  information-carrying portion still utilize small
  percentage from the total power transmitted.

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AM Single Sideband Suppressed Carrier (SSBSC)

• In this system, the carrier signal is totally
  suppressed and one of the sideband removed
• The sideband power makes up 100 of the total
  transmitted power
• As the results of SSBSC, the transmitted waveform
  is not an envelope, it is simply a sine-wave
  which frequency is either
• fcfm or fc-fm
• depending on which sideband to be transmitted

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AM Single Sideband Reduced Carrier (SSBRC)

• The carrier amplitude is reduced to approximately
  10 of its unmodulated amplitude.
• One sideband is totally suppressed
• Sideband takes up to 96 of the total power
• Also known as
• reinserted carrier because carrier is suppressed
  during modulation and reinserted at a reduced
  amplitude
• Exalted carrier because the carrier is elevated
  in the receiver prior to demodulation

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AM Independent Sideband (ISB)

• A single carrier frequency is independently
  modulated by two different information signals by
  two different suppressed carrier modulators.
• One modulator produced lower sideband and the
  other one produced upper sideband.
• The transmitted wave therefore consists of two
  independent single sidebands which are
  symmetrical about the carrier frequency.
• Conserves both transmit power and bandwidth

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AM Vestigial Sideband (VSB)

• Carrier is transmitted with full power
• One complete sideband is also transmitted
• Only part of the second sideband is transmitted
• Lower modulating signal frequencies are
  transmitted double sideband and the higher
  modulating signals are transmitted single
  sideband
• Thus lower sideband experience 100 modulation
  while the upper sideband cannot achieve more than
  50 modulation

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Pc Vc2 /R
PT Pc1 (m2 /2)
Plsb (m2 Pc /4)
Pusb (m2 Pc /4)
DSBFC AM
USB
LSB
Pc Vc2 /R
SSBFC AM
PT Pc (m2 Pc /4)
Pusb (m2 Pc /4)
Plsb 0
USB
Pc 0
SSBSC AM
Pusb (m2 Pc /4) Pt
USB
Plsb 0
Pc (0.1Vc)2 /R
PT 0.01Pc m2 Pc /2
Plsb (m2 Pc /4)
Pusb (m2 Pc /4)
ISB AM
Ch A
Ch B
PT Pc m2 Pc /4 Plsb
Plsblt Pusb
Pusb (m2 Pc /4)
VSB AM
USB
LSB
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Mathematical Analysis
Constant modulating signal
Unmodulated carrier

• If the constant component is removed, then
• where

? upper side frequency signal (V) ? lower side
frequency signal (V)
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SSB Modulator
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Balanced Ring modulator

• Constructed with diodes and transformers
• Has 2 inputs carrier frequency and modulating
  signal. Amplitude of carrier signal is grater
  than modulating signal so that it controls the on
  off of the four diode switches
• D1 to D4 control whether the modulating signal is
  passed from input transformer T1 to output
  transformer T2 as is or with 180 phase shift.

T1
T2
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D1 on
T1
T2




Output signal modulating signal
Modulating signal input
-

D2 on
-
-
-
-
Carrier input

-

• When the polarity of carrier signal is as shown
  above
• D1 and D2 are forward biased ON
• D3 and D4 are reverse biased OFF
• ? The output signal at T2 is the modulating
  signal without phase reversal

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T1
T2


-
D3on
-
Output signal modulating signal reversed
Modulating signal input

-
-
-


D4on
Carrier input

-

• When the polarity of the carrier is reversed
• D1 and D2 are reverse biased OFF
• D3 and D4 are forward biased ON
• ?Modulating signal undergoes 180 phase reversal
  before reaching T2

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• Carrier current flows from its source to the
  center taps of T1 and T2 where it splits and goes
  in opposite directions through the upper and
  lower halves of the transformer.
• Thus their magnetic fields cancel in the
  secondary windings of the transformer and the
  carrier is suppressed
• If the diodes are not perfectly matched or the
  transformer are not exactly center tapped, the
  circuit is not balanced and carrier is not
  totally suppressed
• Perfect balanced is impossible. Small amount of
  carrier is always present? carrier leak
• The amount of carrier suppression between 40dB
  to 60dB

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DSBSC
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Single-Sideband Transmitter

• Filter method
• Phase-Shift Method

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SSB Transmitter Filter Method (3 Stages)
Balanced modulator
BPF1
?
Next slide
Carrier 100 kHz
Carrier 2 MHz
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SSB Transmitter Filter Method
17.9M
22.1M
17.895M
22.105M
2M
1.9M
2.1M
1.895M
2.105M
20M
BPF2
BPF3
Previous slide
Carrier 20 MHz
22.105M
22.1M
2.105M
2.1M
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Single conversion

• Need a multi-pole BFP filter with high quality
  factor- difficult to construct
• Tunable BPF filter in MHz range of frequencies
  with passband of only 5MHz is not economic

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Single-Sideband Filter

• The quality factor (Q) of a single-sideband
  filter can be obtained using the following
  equation

• Q quality factor
• fc center of carrier frequency
• S dB level of unwanted sideband
• ?f frequency separation between the highest
  lower sideband frequency and the lowest upper
  sideband frequency

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Example

• Determine the quality factor (Q) necessary for a
  single-sideband filter with a 1-MHz carrier
  frequency, 80-dB unwanted sideband suppression
  and the following frequency spectrum
• Solution

Filter response
LSB
USB
0.997 MHz
1.003 MHz
1MHz ?f 200kHz
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Types of Filter
Surface acoustic wave filters

• Crystal filter
• Mechanical filter

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Single-Sideband Transmitter Phase-Shift Method

• Undesired sideband is cancelled at the modulator?
  sharp filtering is unnecessary

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SSB Receiver
Noncoherent Beat Frequency Oscillator (BFO)
Receiver
71

• RF local oscillator and beat frequency oscillator
  are not synchronized with each other or the
  oscillator in the transmitter
• Output from IF amplifier is mixed (heterodyned)
  with the output of BFO
• The difference between IF and BFO signal is
  information signal
• Demodulation is done through several mixing and
  filtering stages
• Because the system is noncoherent, any different
  between transmit and receive local oscillator
  frequencies produces a frequency offset error in
  the demodulated information signal

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Coherent BFO Receiver
73

• LO and BFO frequencies are synchronized to the
  carrier oscillator in the transmitter
• Carrier recovery circuit a narrowband PLL that
  tracks the pilot carrier in the composite SSBRC
  received signal
• The recovered signal is used to regenerate
  coherent local oscillator frequencies in the
  synthesizer
• Synthesizer circuit produces a coherent RF local
  oscillator and BFO frequency
• Minor changes in the carrier frequency in the
  transmitter are compensated for in the receiver,
  thus eliminating offset error.

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SSB envelope detection
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Advantage Disadvantage of SSB

• ADVANTAGE OF SSB
• 1. SSB Amplitude Modulation is widely used by
  military or radio amateurs in high-frequency
  communication. It is because the bandwidth is the
  same as bandwidth of
• modulating signals.
• 2. Occupy one half of the spectrum space.
• 3. Efficient in terms of Power Usage
• 4. Less Noise on the signal
• DISADVANTAGE OF SSB
• 1. When no information or modulating signal
  is present,
• no RF signal is transmitted.
• 2. Most information signals transmitted by
  SSB are not
• pUre sine waves.
• 3. A voice signal will create a complex SSB
  signal.

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Advantage Disadvantage of DSB

• Advantage of DSB
• Efficient in terms of Power Usage
• Modulation Efficiency is 100.
• Large Bandwidth

• Disadvantage of DSB
• Product Detector is required for demodulation of
  DSB signal which is quite expensive.
• Signal is rarely used because the signal is
  difficult to recover at the receiver.

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AM Application

• The AM SSB is used in telephone systems and 2 way
  radio and also in Military communication.
• The AM DSB is used in FM and TV Broadcasting