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.

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.


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.


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.


Figure 1-4: Distortion of the envelope caused by overmodulation where the modulating signal amplitude Vm is greater than the carrier signal Vc.


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.


Figure 1-5: AM wave showing peaks (Vmax) and troughs (Vmin).

Determining modulation index from Vmax and Vmin

EKT343 –Principle of Communication Engineering 14

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.


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


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.


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)


Figure 1-8: The relationship between the time and frequency domains.


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.


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.


AM Envelope for Example 3


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


Cont’d…

• Substituting Vm = mVc gives:

)]2(sin)]2(sin1[

)]2(sin)]2(sin[)(

tfVtfm

tftfmVVtv

ccm

cmccam

Constant + mod. signal

Unmodulated carrier


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)


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.


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


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.



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.


Figure 1-11: Frequency spectrum of an AM signal modulated by a square wave.


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.


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.


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.


Figure 1-16: A frequency-domain display of DSB signal.


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.


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.


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.


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.


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


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


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


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


Power spectrum for AM DSBFC wave with a single-frequency modulating signal


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.


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


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


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


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.


Transmitter Efficiency

Transmitter efficiency, average power from sideband/total = ּת

power absorbed. = m²/ ( 2+m² )


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:


])(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


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


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:


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


70

Example 7


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


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.


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


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


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.


Filtering method

Filterresponsecurve

Sidebandfilter

Balancedmodulator

Carrieroscillator

MicrophoneAudioamplifier

Linearamplifier

Antenna

Uppersidebands

DSBsignal

SSBsignal

Lowersidebands


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.


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)


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


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.

Documents

modulation index

amplitude modulation

modulation process

degree of modulation

modulating signal amplitude

carrier signal v

singlesideband modulation

v max v