Chapter 2 Amplitude Modulation. Topics Covered in Chapter 2 2-1: AM Concepts 2-2: Modulation Index and Percentage of Modulation 2-3: Sidebands and the.
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Chapter 2
Amplitude Modulation
Topics Covered in Chapter 2
• 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
2-1: AM Concepts
• 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.
2-1: AM Concepts
Figure 1-1: Amplitude modulation. (a) The modulating or information signal.
2-1: AM Concepts
Figure 1-2: Amplitude modulation. (b) The modulated carrier.
2-1: 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 < Vc
• 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.
2-1: AM Concepts
Figure 1-3: Amplitude modulator showing input and output signals.
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 = Vm / Vc
• 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
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 Vm is greater than the carrier signal Vc.
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 =Vmax − Vmin
2
The amount, or depth, of AM is then expressed as the percentage of modulation (100 × m) rather than as a fraction.
2-2: Modulation Index and Percentage of Modulation
Figure 1-5: AM wave showing peaks (Vmax) and troughs (Vmin).
Determining modulation index from Vmax and Vmin
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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 (fUSB) and the lower sideband (fLSB) are
calculated:fUSB = fc + fm and fLSB = fc − fm
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 = fUSB−fLSB
= [fc + fm(max)] – [fc – fm(max)
= 2fm(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:• For a conventional AM modulator with a carrier freq
of fc = 100 kHz and the maximum modulating signal frequency of fm(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.
Example 2
• Suppose that Vmax value read from the graticule on an oscilloscope screen is 4.6 divisions and Vmin is 0.7 divisions. Calculate the modulation index and percentage of modulation.
EKT343 –Principle of Communication Engineering 21
Example 3• For the AM waveform shown in Figure
below, determinea) 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.
EKT343 –Principle of Communication Engineering 22
AM Envelope for Example 3
EKT343 –Principle of Communication Engineering 23
The Mathematical Representation and Analysis of AM
• Representing both the modulating signal Vm(t) and the carrier signal Vc(t) in trigonometric functions.
• The AM DSBFC modulator must be able to produce mathematical multiplication of these two analog signals
)2(sin)( tfVtv mmm
)2(sin)( tfVtv ccc
)2(sin)]2(sin[)( tftfVVtv cmmcam
EKT343 –Principle of Communication Engineering 24
Cont’d…
• Substituting Vm = mVc gives:
)]2(sin)]2(sin1[
)]2(sin)]2(sin[)(
tfVtfm
tftfmVVtv
ccm
cmccam
Constant + mod. signal
Unmodulated carrier
EKT343 –Principle of Communication Engineering 25
Cont’d…• The constant in the first term produces the
carrier freq while the sinusoidal component in the first term produces side bands frequencies
])(2[cos2
])(2[cos2
)2(sin
)]2([sin)]2(sin[)2(sin)(
tffVm
tffVm
tfV
tftfmVtfVtv
mc
c
mc
c
cc
cmcccam
Upper side frequency signal (volts)
Lower side frequency signal (volts)
Carrier frequency signal (volts)
EKT343 –Principle of Communication Engineering 26
Cont’d…
• 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.
EKT343 –Principle of Communication Engineering 27
Generation of AM DSBFC envelope showing the time-domain of the modulated wave, carrier & sideband signals
28EKT343 –Principle of Communication Engineering
Voltage spectrum for an AM DSBFC wave
EKT343 –Principle of Communication Engineering 29
Example 4• One input to a conventional AM modulator is a 500-kHz
carrier with an amplitude of 20 Vp. 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 Vp. 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.
EKT343 –Principle of Communication Engineering 30
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 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 DSB and SSB– Single and double-sideband 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.
EKT343 –Principle of Communication Engineering
42
VESTIGIAL SIDEBAND (VSB)
• 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.
43
Cont’dAlso 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.
EKT343 –Principle of Communication Engineering
44
Cont’d
AM wave is applied to a vestigial sideband filter, producing a modulation scheme – VSB + C
Mainly used for television video transmission.VSB Frequency Spectrum
EKT343 –Principle of Communication Engineering
fcfc
LSB MSB
Carrier
VSB
AM Power Distribution
2-5: AM Power
• 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 (PT) is the sum of carrier
power (Pc ) and power of the two sidebands (PUSB and PLSB).
2-5: AM Power
• 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
PT = (IT)2R
where IT is measured RF current and R is antenna impedance
2-5: AM Power
• The greater the percentage of modulation, the higher the sideband power and the higher the total power transmitted.
• Power in each sideband is calculatedPSB = PLSB = PUSB = Pcm2 / 4
• Maximum power appears in the sidebands when the carrier is 100 percent modulated.
2-5: AM Power • In any electrical circuit, the power
dissipated is equal to the voltage squared (rms) divided by the resistance.
• Mathematically power in unmodulated carrier is
R
V
R
VP cc
c 2
)2/( 22
EKT343 –Principle of Communication Engineering 49
Pc = carrier power (watts)
Vc = peak carrier voltage (volts)
R = load resistance i.e antenna (ohms)
Cont’d
• The upper and lower sideband powers will be
• Rearranging in terms of Pc,
R
Vm
R
mVPP cc
lsbbus 82
)2/( 222
cc
lsbbus Pm
R
VmPP
424
222
EKT343 –Principle of Communication Engineering 50
Cont’d…• The total power in an AM wave is
• Substituting the sidebands powers in terms of PC yields
• Since carrier power in modulated wave is the same as unmodulated wave, obviously power of the carrier is unaffected by modulation process.
lsbusbct PPPP
]2
1[2
4422
22
mPP
mP
Pm
Pm
PP
ccc
ccct
EKT343 –Principle of Communication Engineering 51
Power spectrum for AM DSBFC wave with a single-frequency modulating signal
EKT343 –Principle of Communication Engineering 52
Cont’d…• With 100% modulation the maximum power in both
sidebands equals to one-half the carrier power.
• One of the most significant disadvantage of AM DSBFC is with m = 1, the efficiency of transmission is only 33.3% of the total transmitted signal. The less wasted in the carrier which brings no information signal.
• The advantage of DSBFC is the use of relatively simple, inexpensive demodulator circuits in the receiver.
EKT343 –Principle of Communication Engineering 53
54
AM PowerReview: conventional AM(DSB-FC)Frequency spectrum:
Bandwidth=2Xfmmax
Total Power=Pcarrier +Pusb +PlsbEKT343 –Principle of Communication Engineering
fc
fc+fmfc-fm
55
Two major Drawbacks of DSBFC
• 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
EKT343 –Principle of Communication Engineering
56
Double side band suppressed carrier(DSB-SC)
• Frequency spectrum:
• Bandwidth:2 x fmmax
• Total Power= Pusb + PlsbEKT343 –Principle of Communication Engineering
fc
fc+fmfc-fm
EKT343 –Principle of Communication Engineering
Single-Sideband (SSB)
• 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
57
58
Single Side Band Full Carrier (SSB-FC)
Frequency spectrum:
Bandwidth=fmmax
Total Power=Pcarrier +PusbEKT343 –Principle of Communication Engineering
fc fc+fmfc-fm
EKT343 –Principle of Communication Engineering
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) 59
60
Single Side band Suppress Carrier (SSB-SC)
Frequency spectrum:
Bandwidth=fmmax
Total Power=+PusbEKT343 –Principle of Communication
Engineering
fc
fc+fmfc-fm
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 amplitudesEKT343 –Principle of Communication
Engineering 61
62
Comparison of time domain representation of three common AM transmission systems:
EKT343 –Principle of Communication EngineeringTomasi
Electronic Communications Systems, 5e
Example 5
• For an AM DSBFC wave with a peak unmodulated carrier voltage Vc = 10 Vp, a load resistor of RL = 10 and m = 1, determine
a) Powers of the carrier and the upper and lower sidebands.
b) Total sideband power.c) Total power of the modulated wave.d) Draw the power spectrum.
EKT343 –Principle of Communication Engineering 63
Transmitter Efficiency
Transmitter efficiency, average power from sideband/total = ּת
power absorbed. = m²/ ( 2+m² )
EKT343 –Principle of Communication Engineering 64
Modulation by a complex information signal
• Previous examples are all using a single frequency modulation signal. In practice, however, modulating signal is very often a complex waveform made up from many sine waves with different amplitudes and frequencies.
• Example: if a modulating signal contains three frequencies(fm1, fm2, fm3), the modulated signal will contain the carrier and three sets of side frequencies, spaced symmetrically about the carrier:
EKT343 –Principle of Communication Engineering 65
])(2[cos2
])(2[cos2
])(2[cos2
])(2[cos2
])(2[cos2
])(2[cos2
)2(sin)(
332
21
1
tffVm
tffVm
tffVm
tffVm
tffVm
tffVm
tfVtv
mcc
mcc
mcc
mcc
mcc
mcc
ccam
frequency spectrum for complex information signal
EKT343 –Principle of Communication Engineering 66
fcFc-fm1Fc-fm2Fc-fm3 Fc+fm1 Fc+fm2 Fc+fm3
Index modulation for complex signal
• When several frequencies simultaneously amplitude modulate a carrier, the combined coefficient of modulation is defined as:
mt=total modulation index/coefficient of modulationm1, m2, m3, mn= modulation index/coefficient of modulation for
input 1, 2 ,3 , n
EKT343 –Principle of Communication Engineering 67
22
3
2
2
2
1t...
nmmmmm
Power calculation for complex information signal
• The combined coefficient of modulation can be used to determine the total sideband power and transmitted power, using:
EKT343 –Principle of Communication Engineering 68
21
2
4
2
2
2
t
ct
tc
sbt
tc
lsbtusbt
mPP
mPP
mPPP
Example 6• For an AM DSBFC transmitter with an unmodulated carrier
power, Pc= 100W that is modulated simultaneously by three modulating signals, with coefficients of modulation m1=0.2, m2= 0.4, m3=0.3, determine:
a) Total coefficient of modulationb) Upper and lower sideband powerc) Total transmitted power
EKT343 –Principle of Communication Engineering 69
70
Example 7
EKT343 –Principle of Communication Engineering
For an AM DSBFC 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.
71
Example 7..cont’d• Solution for DSBFC;
i)
ii)
iii) Bandwidth=2xfmmax=2(10kHz)=20kHzEKT343 –Principle of Communication
Engineering
W
Pm
Pm
PP ccct
5.7)5(4
1)5(
4
15
4422
22
WPm
PP
WR
V
R
VP
c
lsbusb
cc
c
25.14
5102
)10(
2
)2/(
2
222
72
Example 7..cont’d• Solution:For DSB-SC
ii)
iii)Bandwidth=2xfmmax=2(10kHz)=20kHz
iv)
%67.66
%1005.7
5%
5
5.25.7
xW
WPower
W
WWPower
saved
saved
EKT343 –Principle of Communication Engineering
W
Pm
Pm
Pcct
5.2)5(4
1)5(
4
14422
22
110kHz90kHz
73
Example 7..cont’d
• 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.
EKT343 –Principle of Communication Engineering
Example 7..cont’d• Solution:For SSB-FC
ii)
iii)Bandwidth=fmmax=10kHz
iv)
%67.16
%1005.7
25.1%
25.1
25.65.7
xW
WPower
W
WWPower
saved
saved
EKT343 –Principle of Communication Engineering 74
W
Pm
PPcct
25.6)5(4
15
42
2
100kHz 110kHzfc-fm
Example 7..cont’d• Solution:For SSB-sC
ii)
iii)Bandwidth=fmmax=10kHz
iv)
%33.83
%1005.7
25.6%
25.6
25.15.7
xW
WPower
W
WWPower
saved
saved
EKT343 –Principle of Communication Engineering 75
W
Pm
Pct
25.1)5(4
14
2
2
fc 110kHzfc-fm
Exercises
1. An audio signal 15sin2π (1500t ) Amplitude modulates a carrier 60sin2π (100000t)a) Sketch the audio signalb) Sketch the carrierc) Construct the modulated waved) Determine the modulation index and percent modulatione) 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.
Exercises
2. The total power content of an AM wave is600W. Determine the percent modulation ofthe signal if each of the sidebands contains75W.3. Determine the power content of the carrierand each of the sidebands for an AM signalhaving a percent modulation of 80% and thetotal power of 2500W
Advantages/Disadvantages of SSB
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 DSBEKT343 –Principle of Communication
Engineering 78
Methods of Generating SSB• 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.
EKT343 –Principle of Communication Engineering 79
Filtering method
Filterresponsecurve
Sidebandfilter
Balancedmodulator
Carrieroscillator
MicrophoneAudioamplifier
Linearamplifier
Antenna
Uppersidebands
DSBsignal
SSBsignal
Lowersidebands
EKT343 –Principle of Communication Engineering 80
Phasing methods-using two balance modulator
• 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.
EKT343 –Principle of Communication Engineering 81
Phasing method..cont’d
BalancedModulator 1
Balanced Modulator 2
Phase shifter
Phase shifter
+
Information signal
Carrier signal
Output Signal, aot
Am cos wmt
Am cos (wmt + 90)
Ac cos (wct + 90)
A2(t)
A1(t)
EKT343 –Principle of Communication Engineering 82
Phasing method..cont’d
)2()90cos()90cos(2
1
cos*)90cos()(
)1()()()(
00
0
1
210
twtwAAtwtwAA
twAtwAta
tatata
mcmcmcmc
mmcc
)3()90cos()90cos(2
1
)90cos(*)cos()(
00
0
2
twtwAAtwtwAA
twAtwAta
mcmcmcmc
mmcc
)90cos(
)3()2()(0
0
twtwAA
ta
mcmc
EKT343 –Principle of Communication Engineering 83
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