Amplitude Modulation

• 2-1: AM Concepts
• 2-2: Modulation Index and Percentage of
Modulation
• 2-3: Sidebands and the Frequency Domain
• 2-4: Single-Sideband Modulation
• 2-5: AM Power

• In the modulation process, the voice, video, or digital signal modifies another signal called the carrier.
• In amplitude modulation (AM) the information signal varies the amplitude of the carrier sine wave.
• The instantaneous value of the carrier amplitude changes in accordance with the amplitude and frequency variations of the modulating signal.
• An imaginary line called the envelope connects the positive and negative peaks of the carrier waveform.

Figure 1-1: Amplitude modulation. (a) The modulating or information signal.

Figure 1-2: Amplitude modulation. (b) The modulated carrier.

• In AM, it is particularly important that the peak value of the modulating signal be less than the peak value of the carrier.
V m
< V c
• Distortion occurs when the amplitude of the modulating signal is greater than the amplitude of the carrier.
• A modulator is a circuit used to produce AM.
Amplitude modulators compute the product of the carrier and modulating signals.

Figure 1-3: Amplitude modulator showing input and output signals.

2-2: Modulation Index and Percentage of
Modulation
Figure 1-5: AM wave showing peaks (V max
) and troughs (V min
).

2-2: Modulation Index and Percentage of
Modulation
• The modulation index (m) is a value that describes the relationship between the amplitude of the modulating signal and the amplitude of the carrier signal.
m = V m
/ V c
• This index is also known as the modulating factor or coefficient, or the degree of modulation.
• Multiplying the modulation index by 100 gives the percentage of modulation.

2-2: Modulation Index and Percentage of
Modulation
Percentage of Modulation
– The modulation index is commonly computed from measurements taken on the composite modulated waveform.
– Using oscilloscope voltage values:
Vm =
V max
− V min
2
 The amount, or depth, of AM is then expressed as the percentage of modulation (100 × m) rather than as a fraction.

max
min
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• Mathematically, the modulation index is
m = modulation index
E m
= peak change in the amplitude output waveform (sum of voltages from upper and lower side frequencies)
E c
= peak amplitude of the unmodulated carrier m

E m
E c
• And the percentage of modulation index is
% m

E m x 100 %
E c
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• If the modulating signal is a pure, single-freq sine wave and the process is symmetrical then the modulation index can be derived as follows:
• Therefore
,
E m

1
2
E c

1
2
( V max

V min
( V max

V min
)
)
1 m
 2
1
2
(
( V
V m ax m ax


V m in
)
V m in
)
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
(
( V m ax
V m ax

V m in
)

V m in
)
14

• Since the peak change of modulated output wave E m voltages hence,
E m

E usf

E lsf is the sum of the u sf and l sf where E usf

E lsf
• Then
E usf

E lsf

E
2 m


1
4
( V max
1
2
( V max
2

V min
)

V min
)
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E usf
= peak amplitude of the upper side frequency (volts)
E lsf
= peak amplitude of the lower side frequency (volts)
15

2-2: 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.

2-2: 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.

2-2: Modulation Index and Percentage of
Modulation
Figure 1-4: Distortion of the envelope caused by overmodulation where the modulating signal amplitude V m is greater than the carrier signal V c
.

2-3: 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.

2-3: Sidebands and the Frequency Domain
Sideband Calculations
– Single-frequency sine-wave modulation generates two sidebands.
– Complex wave (e.g. voice or video) modulation generates a range of sidebands.
– The upper sideband (f
USB
) and the lower sideband (f
LSB
) are calculated: f
USB
= f c
+ f m and f
LSB
= f c
− f m

2-3: Sidebands and the Frequency Domain
Figure 1-6: The AM wave is the algebraic sum of the carrier and upper and lower sideband sine waves. (a)
Intelligence or modulating signal. (b)
Lower sideband. (c ) Carrier. (d ) Upper sideband. (e ) Composite AM wave.

2-3: Sidebands and the Frequency Domain
Frequency-Domain Representation of AM
– Observing an AM signal on an oscilloscope, you see only amplitude variations of the carrier with respect to time.
– A plot of signal amplitude versus frequency is referred to as frequency-domain display.
– A spectrum analyzer is used to display the frequency domain as a signal.
– Bandwidth is the difference between the upper and lower sideband frequencies.
– BW = f
USB
−f
LSB
=
[f c
= 2f
+ f m(max) m(max)
] – [f c
–f m(max)
]

2-3: Sidebands and the Frequency Domain
Figure 1-8: The relationship between the time and frequency domains.

2-3: Sidebands and the Frequency Domain
•
Frequency-Domain Representation of AM
• Example 1: f
For a conventional AM modulator with a carrier freq of f c
= 100 kHz and the maximum modulating signal frequency of m(max)
= 5 kHz, determine: a) Freq limits for the upper and lower sidebands.
b) Bandwidth.
c) Upper and lower side frequencies produced when the modulating signal is a single-freq 3-kHz tone.
d) Draw the output freq spectrum.

• Suppose that V max value read from the graticule on an oscilloscope screen is 4.6 divisions and V min is 0.7 divisions. Calculate the modulation index and percentage of modulation.
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• For the AM waveform shown in Figure below, determine a) Peak amplitude of the upper and lower side frequencies.
b) Peak amplitude of the unmodulated carrier.
c) Peak change in the amplitude of the envelope.
d) Modulation index.
e) Percent modulation.
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The Mathematical Representation and Analysis of
AM
• Representing both the modulating signal V m
(t) and the carrier signal V c
(t) in trigonometric functions.
• The AM DSBFC modulator must be able to produce mathematical multiplication of these two analog signals v m
( t )

V m sin ( 2
 f m t ) v am
( t )

[ V c

V m sin ( 2
 f m t )] sin ( 2
 f c t ) v c
( t )

V c sin ( 2
 f c t )
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• Substituting V m
= mV c gives: v am
( t )


[ V c
[ 1

 m mV c sin sin
( 2
 f
( 2
 f m t )] m t )] V c sin sin
( 2
 f c t )]
( 2
 f c t )]
Constant + mod. signal
Unmodulated carrier
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• The constant in the first term produces the carrier freq while the sinusoidal component in the first term produces side bands frequencies v am
( t )

V c sin ( 2
 f c t )

[ mV c sin ( 2
 f m t )] [sin ( 2
 f c t )]
Carrier frequency signal (volts)

V c sin ( 2
 f c t )
 m V c cos [ 2

( f c

2
 m V c
2 cos [ 2

( f c
 f m
) t ] f m
) t ]
Upper side frequency signal (volts)
Lower side frequency signal (volts)
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• From the equation it is obvious that the amplitude of the carrier is unaffected by the modulation process.
• The amplitude of the side frequencies depend on the both the carrier amplitude and modulation index.
• At 100% modulation the amplitudes of side frequencies are each equal to one-half the amplitude of the carrier.
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Generation of AM DSBFC envelope showing the timedomain of the modulated wave, carrier & sideband signals
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• One input to a conventional AM modulator is a 500-kHz carrier with an amplitude of 20 V p
. The second input is a
10-kHz modulating signal that is of sufficient amplitude to cause a change in the output wave of ±7.5 V p
. Determine a) Upper and lower side frequencies.
b) Modulation index and percentage modulation.
c) Peak amplitude of the modulated carrier and the upper and lower side frequency voltages.
d) Maximum and minimum amplitudes of the envelope.
e) Expression for the modulated wave.
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2-3: Sidebands and the Frequency Domain
Pulse Modulation
– When complex signals such as pulses or rectangular waves modulate a carrier, a broad spectrum of sidebands is produced.
– A modulating square wave will produce sidebands based on the fundamental sine wave as well as the third, fifth, seventh, etc. harmonics.
– Amplitude modulation by square waves or rectangular pulses is referred to as amplitude shift keying (ASK).
– ASK is used in some types of data communications.

2-3: Sidebands and the Frequency Domain
Figure 1-11: Frequency spectrum of an AM signal modulated by a square wave.

2-3: Sidebands and the Frequency Domain
Figure 1-12: Amplitude modulation of a sine wave carrier by a pulse or rectangular wave is called amplitude-shift keying. (a) Fifty percent modulation. (b) One hundred percent modulation.

2-3: Sidebands and the Frequency Domain
Pulse Modulation
– Continuous-wave (CW) transmission can be achieved by turning the carrier off and on, as in
Morse code transmission.
– Continuous wave (CW) transmission is sometimes referred to as On-Off keying (OOK).
– Splatter is a term used to describe harmonic sideband interference.

2-4: Single-Sideband Modulation
• In amplitude modulation, two-thirds of the transmitted power is in the carrier, which conveys no information.
• Signal information is contained within the sidebands.
• Single-sideband (SSB) is a form of AM where the carrier is suppressed and one sideband is eliminated.

2-4: Single-Sideband Modulation
DSB Signals
– The first step in generating an SSB signal is to suppress the carrier, leaving the upper and lower sidebands.
– This type of signal is called a double-sideband
suppressed carrier (DSSC) signal. No power is wasted on the carrier.
– A balanced modulator is a circuit used to produce the sum and difference frequencies of a DSSC signal but to cancel or balance out the carrier.
– DSB (or DSSC) is not widely used because the signal is difficult to demodulate (recover) at the receiver.

2-4: Single-Sideband Modulation
Figure 1-16: A frequency-domain display of DSB signal.

2-4: Single-Sideband Modulation
SSB Signals
– One sideband is all that is necessary to convey information in a signal.
– A single-sideband suppressed carrier (SSSC) signal is generated by suppressing the carrier and one sideband.

2-4: Single-Sideband Modulation
SSB Signals
– SSB signals offer four major benefits:
1. Spectrum space is conserved and allows more signals to be transmitted in the same frequency range.
2. All power is channeled into a single sideband. This produces a stronger signal that will carry farther and will be more reliably received at greater distances.
3. Occupied bandwidth space is narrower and noise in the signal is reduced.
4. There is less selective fading over long distances.

2-4: Single-Sideband Modulation
Disadvantages of DSSC and SSBSC
– Single and double-sideband SC’s are not widely used because the signals are difficult to recover
(i.e. demodulate) at the receiver.
– A low power, pilot carrier is sometimes transmitted along with sidebands in order to more easily recover the signal at the receiver.

2-4: Single-Sideband Modulation
Signal Power Considerations
– In SSB, the transmitter output is expressed in terms of peak envelope power (PEP), the maximum power produced on voice amplitude peaks.
Applications of DSB and SSB
– A vestigial sideband signal (VSB) is produced by partially suppressing the lower sideband. This kind of signal is used in TV transmission.

• In radio transmission, the AM signal is amplified by a power amplifier.
• A radio antenna has a characteristic impedance that is ideally almost pure resistance.
• The AM signal is a composite of the carrier and sideband signal voltages.
• Each signal produces power in the antenna.
• Total transmitted power (P power (P and P
LSB
).
c
T
) is the sum of carrier
) and power of the two sidebands (P
USB

• When the percentage of modulation is less than the optimum 100, there is much less power in the sidebands.
• Output power can be calculated by using the formula
P
T
= (I
T
) 2 R where I
T is measured RF current and R is antenna impedance

• The greater the percentage of modulation, the higher the sideband power and the higher the total power transmitted.
• Power in each sideband is calculated
P
SB
= P
LSB
= P
USB
= P c m 2 / 4
• Maximum power appears in the sidebands when the carrier is 100 percent modulated.

Review: conventional AM(DSB-FC)
Frequency spectrum: f c
-f m f c f c
+f m
Bandwidth=2 x f mmax
Total Power=P carrier
+P usb
+P lsb
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• Large power consumption, where carrier power constitutes
>2/3 transmitted power.{ remember : carrier does not contain any information }
• Utilize twice as much bandwidth – both the upper and lower sideband actually contains same information (redundant).
Thus, DSBFC is both power and bandwidth inefficient
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• Frequency spectrum: f c
-f m f c
• Bandwidth:2 x f mmax
• Total Power= P usb
+ P lsb
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+f m
52

•
The carrier is transmitted at full power but only one sideband is transmitted
– requires half the bandwidth of DSBFC AM
–
Carrier power constitutes 80% of total transmitted power, while sideband power consumes 20%
–
SSBFC requires less total power but utilizes a smaller percentage of the power to carry the information
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Frequency spectrum: f c
-f m f c f c
+f m
Bandwidth=f mmax
Total Power=P carrier
+P usb
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AM Single-Sideband Suppressed Carrier (SSBSC)
•
The carrier is totally suppressed and one sideband is removed
– requires half the bandwidth of DSBFC AM
– Considerably less power than DSBFC and SSBFC schemes
–
Sideband power makes up 100% of the total transmitted power
–
The wave is not an envelope but a sine wave at frequency equal to the carrier frequency
± modulating frequency (depending on which sideband is transmitted)
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Frequency spectrum: f c
-f m f c
+f m f c
Bandwidth=f mmax
Total Power=+P usb
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AM Single-Sideband Reduced Carrier (SSBRC)
• One sideband is totally removed and the carrier voltage is reduced to approximately 10% of its unmodulated amplitude
– requires half the bandwidth of DSBFC AM
– Less transmitted power than DSBFC and SSBFC but more power than
SSBSC
– As much as 96% of the total transmitted power is in the sideband
–
The output modulated signal is similar to SSBFC but with reduced maximum and minimum envelope amplitudes
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Comparison of time domain representation of three common AM transmission systems:
Tomasi
Electronic Communications Systems, 5e
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For an AM DSCFC wave with a peak unmodulated carrier voltage Vc
= 10Vp, frequency of 100kHz, a load resistor of RL = 10

, frequency of modulating signal of 10kHz and m = 1, determine the following i) Powers of the carrier and the upper and lower sidebands.
ii) Total power of the modulated wave.
iii) Bandwidth of the transmitted wave.
iv) Draw the power and frequency spectrum.
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ii) i)
• Solution for DSBFC;
P c

( V c
/
R
2 ) 2
P usb

P lsb
 m 2 P c
4

V c
2 R
2

( 10 ) 2
2

10

5 W

1 .
25 W
P t

P c
 m
2
4
P c
 m
4
2
P c

5

1
2
4
( 5 )

1
2
4
( 5 )

7 .
5 W iii) Bandwidth=2xf mmax
=2(10kHz)=20kHz
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• For the same given values, determine questions (ii)-(iv) for a AM DSB-SC, AM SSB-FC and AM SSB-SC systems. Determine also the
percentage of power saved in each of the system design.
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• Solution: For DSB-SC ii) P t
 m 2
4
P c
 m
4
2
P c

1 2
4
( 5 )

1 2
4
( 5 )

2 .
5 W
Power saved

5 W

7 .
5 W

2 .
5 W
% Power saved

5 W
7 .
5 W x 100 %

66 .
67 % iii)
Bandwidth=2xf mmax
=2(10kHz)=20kHz iv)
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90kHz 110kHz
62

• Solution:For SSB-FC ii) P t

P c
 m 2
4
P c

5

1 2
4
( 5 )

6 .
25 W iii)
Bandwidth=f mmax
=10kHz iv)
Power saved

1 .
25 W

7 .
5 W

6 .
25 W
% Power saved

1 .
25 W
7 .
5 W

16 .
67 % x 100 % f c
-f m
100kHz 110kHz
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• Solution:For SSB-SC ii)
P t
 m 2
4
P c

1 2
4
( 5 )

1 .
25 W
Power saved

6 .
25 W

7 .
5 W

1 .
25 W
% Power saved

6 .
25 W
7 .
5 W

83 .
33 % x 100 % iii)
Bandwidth=f mmax
=10kHz iv) f c
-f m f c
110kHz
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1. An audio signal 15sin2π (1500t ). Amplitude modulates a carrier 60sin2π (100000t).
a) Sketch the audio signal b) Sketch the carrier c) Construct the modulated wave d) Determine the modulation index and percent modulation e) What are the frequencies of the audio signal and the carrier f) What frequencies would show up in the spectrum analysis of the modulated wave.

2. The total power content of an AM wave is
600W. Determine the percent modulation of the signal if each of the sidebands contains
75W.
3. Determine the power content of the carrier and each of the sidebands for an AM signal having a percent modulation of 80% and the total power of 2500W

• 2 methods,
•
• i) Filtering method
A filter removes the undesired sideband producing SSB.
Quartz crystal filters are the most widely used sideband filters since they are very selective and inexpensive .
ii) Phasing method
 A balanced modulator eliminates the carrier and provides DSB.
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Carrier oscillator
Microphone
Antenna
Balanced modulator
DSB signal
Sideband filter
SSB signal
Linear amplifier
Audio amplifier
Lower Upper sidebands sidebands
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Filter response curve
68

• Another way to produce SSB uses a phase shift method to eliminate one sideband.
• Two balanced modulators driven by carriers and modulating signals 90º out of phase produce DSB.
• Adding the two DSB signals together results in one sideband being cancelled out.
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Information signal
Am cos wmt A
1
(t)
Balanced
Modulator 1
Ac cos (wct + 90)
Phase shifter
+
Output Signal, a o t
Carrier signal
Phase shifter Balanced
Modulator 2
Am cos (wmt + 90)
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A
2
(t)
70

a
0
( t )
 a
1
( t )
 a
1
( t )
 a
2
( t )
   
A c cos( w c t

90 0 ) * A m

( 1 ) cos w m t

1
2

A c
A m cos( w c t

90 0
 w m t )

A c
A m cos( w c t

90 0
 w m t )

  
( 2 ) a
2
( t )

A c cos( w c t ) * A m cos( w m t

90 0 )

1
2

A c
A m cos( w c t

90 0
 w m t )

A c
A m cos( w c t

90 0 a
0

( t

A c
)

A m
( 2 )

( 3 ) cos( w c t

90 0
 w m t )

  
( 3 )
 w m t )

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Advantages
• Power consumption -
Much less total transmitted power is necessary to produce the same quality signal as achieved with DSBFC AM
• Bandwidth conservation
• Selective fading carrier phase shift and carrier fading can not occur, thus smaller distortion is expected.
• Noise reduction
thermal noise power is reduced
Disadvantages
• Complex receivers
• Tuning difficulties – requires more complex and precise than DSB
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• VSB is similar to SSB but it retains a small portion (a vestige) of the undesired sideband to reduce DC distortion.
• VSB signals are generated using standard AM or DSBSC modulation, then passing modulated signal through a sideband shaping filter.
• Demodulation uses either standard AM or
DSBSC demodulation.
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 Also called asymmetric sideband system.
 Compromise between DSB & SSB.
 Easy to generate.
 Bandwidth is only ~ 25% greater than SSB signals.
 Derived by filtering DSB, one pass band is passed almost completely while just a trace or vestige of the other sideband is included.
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 AM wave is applied to a vestigial sideband filter, producing a modulation scheme – VSB +
C
 Mainly used for television video transmission.
 VSB Frequency Spectrum
VSB
Carrier
LSB MSB
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