Amplitude Modulation

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Chapter 2

• Amplitude Modulation

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Learning Outcomes

• Define AM concepts
• Calculate the AM voltage distribution modulation
  index voltage power distribution
• Calculate and draw AM in time and frequency
  domain bandwidth

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Revision..

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

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Basic Amplitude Modulation

• 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
• Amplitude Modulation is the simplest and earliest
  form of transmitters

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Basic Amplitude Modulation
Envelope
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AM Envelope

• Wave and the shape of the Modulated Wave is
  called AM Envelope.

Envelope is the original modulating signal
Carrier
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Amplitude Modulation What really happened
(you are not required to memorized this)
carrier
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• We now know how AM wave looks like but how do we
  represent it mathematically
• Can you write the general equation of a sinusoid
  wave

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AM wave equation

• The expression of voltage in the electric circuit
  is given by
• or
• V Amplitude of the signal in Volts
• f The signal frequency in Herzt
• (2ft ) The phase of the signal in radian

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AM wave equation

• An unmodulated modulating signal
• vm (t) Em sin (2fmt)
• Or vm (t) Vm sin (2fmt)

Em Vm peak modulating signal amplitude(volts)
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• Envelope of the modulating signal varies above
  below the peak carrier amplitude
• In general Em lt Ec otherwise distortion will
  occur. The modulating signal values adds or
  subtracts from the peak value of the carrier.
• This instantaneous value either top or bottom
  voltage envelope (new expression for Vm)

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AM wave equation

• An unmodulated carrier (carrier signal) is
  described by the following equation -
• vc (t) Ec sin (2fct)
• Or vc (t) Vc sin (2fct)

Ec Vc peak carrier amplitude (volts)
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AM Concepts
(Low frequency)
carrier
(nonlinear devices)
Modulation x carrier
(High frequency)
Figure 3-3 Amplitude modulator showing input and
output signals.
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AM wave equation

• The modulated wave can be
• expressed as -
• Vam(t) Ec Em sin (2fmt) (sin 2fct)
  .........(1)
• WHERE
• Ec Em sin (2fmt) Amplitude of the modulated
  wave
• Em peak change in the amplitude of the envelope
  
• fm frequency of the modulating signal

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AM wave equation

• Expanding eq (1) we get

Carrier signal
Modulating signal
Later we will see how this equation can be
further improved to make it more meaningful
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AM wave equation
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AM Concepts

• In AM it is particularly important that the peak
  value of the modulating signal be less than the
  peak value of the carrier.
• Vm lt Vc
• Distortion occurs when the amplitude of the
  modulating signal is greater than the amplitude
  of the carrier.

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Modulation Index and Percentage of Modulation

• modulation index (m) is a value that describes
  the relationship between the amplitude of the
  modulating signal and the amplitude of the
  carrier signal.
• Percentage of modulation.

modulating factor or coefficient or degree of
modulation.
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Modulation Index and Percentage of Modulation

• modulation index (m) can also calculate it using

where
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Modulation Index for Multiple Modulating
Frequencies
Modulation Index for Multiple Modulating
Frequencies

• Two or more sine waves of different uncorrelated
  frequencies modulating a single carrier is
  calculated by the equation

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• Consider these envelopes
• Do they look the same

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Modulation Index and Percentage of Modulation

• Overmodulation and Distortion
• The modulation index should be a number between 0
  and 1.
• If the amplitude of the modulating voltage is
  higher than the carrier voltage m will be
  greater than 1 causing distortion.
• If the distortion is great enough the
  intelligence signal becomes unintelligible.

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Modulation Index and Percentage of Modulation

• Overmodulation and Distortion
• Distortion of voice transmissions produces
  garbled harsh or unnatural sounds in the
  speaker.
• Distortion of video signals produces a scrambled
  and inaccurate picture on a TV screen.

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http//www.williamson-labs.com/480_am.htm
Over Modulation
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Modulation Index and Percentage of Modulation
Figure Distortion of the envelope caused by
overmodulation where the modulating signal
amplitude Vm is greater than the carrier signal
Vc.
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• Draw AM wave in time domain and frequency domain

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Frequency Domain

• The frequency domain provides an alternative
  description of signal in which the time axis is
  replaced by a frequency axis.

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The relationship between the time and frequency
domains
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Sidebands and the Frequency Domain

• Side frequencies or sidebands are generated as
  part of the modulation process and occur in the
  frequency spectrum directly above and below the
  carrier frequency.
• Single-frequency sine-wave modulation generates
  two sidebands.
• Complex wave (e.g. voice or video) modulation
  generates a range of sidebands.

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Sidebands and the Frequency Domain
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Sidebands and the Frequency Domain

• Figure The AM wave is the algebraic sum of the
  carrier and upper and lower sideband sine waves.
• Intelligence or modulating signal.
• (b) Lower sideband.
• (c ) Carrier.
• (d ) Upper sideband.
• (e ) Composite AM wave.

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Bandwidth

• Signal bandwidth is an important characteristic
  of any modulation scheme
• In general a narrow bandwidth is desirable
• Bandwidth is calculated by

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Bandwidth

• Bandwidth is the difference between the upper and
  lower sideband frequencies.
• BW fUSB-fLSB

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Sidebands and the Frequency Domain

• Example
• A standard AM broadcast station is allowed to
  transmit modulating frequencies up to 5 kHz. If
  the AM station is transmitting on a frequency of
  980 kHz what are sideband frequencies and total
  bandwidth

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Solution to Example 1
fm
1. Highlight and identify important information
in the question

• A standard AM broadcast station is allowed to
  transmit modulating frequencies up to 5 kHz. If
  the AM station is transmitting on a frequency of
  980 kHz what are sideband frequencies and total
  bandwidth

fc
2. Use the formulas to solve the problem
fUSB fc fm 980 5 985 kHz fLSB fc -fm
980 5 975 kHz BW fUSB fLSB 985 975
10 kHz Or BW 2 (5 kHz) 10 kHz
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EXAMPLE

• 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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Group Activity

• 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 with 7.5 Vp. Determine the following -
•  
• USB LSB
• Modulation Index and percent modulation M
• Peak Amplitude of modulated carrier and Upper
  Lower side frequency voltage
• Maximum Minimum Amplitude of the envelope Vmax
  and Vmin
• Draw output in frequency domain time domain
•  

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Solution

• Upper and lower side frequencies
• Modulation Index and percent modulation M

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Solution (c)-method 1

• (c) Peak Amplitude of modulated carrier and Upper
  Lower side frequency voltage
• We can find Elsb and Eusb by using equation
• Thus

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Solution (c)- method 2

• (c) Peak Amplitude of modulated carrier and Upper
  Lower side frequency voltage
• Lets say Em is unknown. Em can be found from
• Thus

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Solution

• (d) Maximum Minimum Amplitude of the envelope
  Vmax and Vmin

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Solution

• (e) frequency domain

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3.75
3.75
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Solution

• (e) time domain

Vmax27.5 Vp
Vmin 12.5 Vp
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How to calculate AM power
Pc
PT
PUSB
PLSB
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AM Power

• The AM signal is a composite of the carrier and
  sideband signal voltages.
• Each signal produces power in the antenna.
• Total transmitted power (PT) is the sum of
  carrier power (Pc ) and power of the two
  sidebands (PUSB and PLSB).

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AM Power

• Power in a transmitter is important but the most
  important power measurement is that of the
  portion that transmits the information
• Power in an AM transmitter is calculated
  according to the formula at the right

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Measuring AM signal power

• The greater the percentage of modulation the
  higher the sideband power and the higher the
  total power transmitted.
• Power in each sideband is calculated
• PSB PLSB PUSB Pcm2 / 4
• Maximum power appears in the sidebands when the
  carrier is 100 percent modulated.
• Pc (Vc )2 / 2R
• where Pc carrier power (W)
• Vc peak carrier voltage(V)
• R load resistance (Ohm)

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Measuring AM signal power

• In reality it is difficult to determine AM power
  by measuring the output voltage.
• However antenna current is easy to measure and
  output power can be expressed
• where IT is measured RF current and R is antenna
  impedance

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AC average power dissipation

• Recall that the average power dissipated by
  resistor R is with a sinusoidal source of
  amplitude Vpk is given

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AM signal power

• Since the vAM is composed of three sinusoids
  the total average power dissipated by the
  antenna R is given

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AM signal power

• Remembering that the modulation index m Vm /Vc
  we can write
• The common term is the just the carrier power
  thus the total power can also be written

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AM power efficiency

• Therefore given the equation for power of an AM
  waveform the efficiency is
• It can be seen from this equation that the
  efficiency of AM modulation increases as the
  modulation index µ increases.

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Example Problem 1

• An AM transmitter has a carrier power of 30 W.
  The percentage modulation is 85. Calculate (a)
  the total power and (b) the power in one
  sideband.

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AM power efficiency

• From the previous example what percentage of the
  total power was dedicated to transmitting the
  carrier
• Is any information conveyed by the carrier
  itself
• How could we maximize the power in the sidebands

PT 42.75 W
Pc 30 W
PUSB 5.4 W
PLSB 5.4 W
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AM power efficiency

• Sideband power is maximized by setting m 1.
• For m 1 what percentage of the total power is
  dedicated to the sidebands

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AM power efficiency

• At maximum modulation the sideband power is at
  most 33 of the total transmitted power.

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AM power efficiency

• Two-thirds of the power is wasted in the carrier.
• Further 100 modulation only occurs at peaks in
  the modulating signal thus the average sideband
  power is considerably worse than the ideal.

100 modulation only occursat peaks
Speech as a modulating signal
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Improving on AM

• Besides the 67 power loss due to the carrier
  the sidebands contain redundant information.
• To maximize the efficiency of AM we need to
• Suppress the carrier
• Eliminate one of the sidebands

Upper and lower sidebands contain the same
information.
AM modulated speech signal
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Why is still widely used

• AM is still widely used because it is simple and
  effective.
• AM broadcast radio
• CB radio (11m range)
• TV broadcasting
• Air traffic control radios
• Garage door opens keyless remotes

Aircraft VHF Communications Transceiver
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Types of AM

• 1) Double sideband full carrier (DSBFC)
• - Contains USB LSB and Carrier
• - This is the most widely used type of
  AM modulation. In fact all radio channels in the
  AM band use this type of modulation.
• 2) Double sideband suppressed carrier (DSBSC)
• - Contains only USB LSB
• - A circuit that produces DSBSC is
  Balanced modulator
• 3) Single sideband (SSB)
• - In this modulation only half of the
  signal of the DSBSC is used
• - Contains either LSB or USB
• - Produce efficient system in term of
  power consumption and bandwidth
• 4) Vestigial Sideband (VSB)
• - This is a modification of the SSB to ease
  the generation and reception of the signal.

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EXAMPLE

• 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

• 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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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