EKT358 Communication Systemsportal.unimap.edu.my/portal/page/portal30/Lecture...cause a change in the output wave of ±7.5 V p. Determine a) Upper and lower side frequencies. b) Modulation

EKT358 Communication Systems

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

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.

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 10

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.


2-2: Modulation Index and Percentage of Modulation

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


• 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. It is the term used to describe the amount of amplitude change(modulation) present in the an AM waveform.

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.


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.

Determining modulation index from Vmax and Vmin

EKT343 –Principle of Communication Engineering

17

Cont’d…

• Mathematically, the modulation index is

• And the percentage of modulation index is

c

m

E

Em


m = modulation index

Em = peak change in the amplitude output

waveform (sum of voltages from upper and

lower side frequencies)

Ec = peak amplitude of the unmodulated

carrier

%100% xE

Em

c

m

Cont’d…

• 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,

)(2

1

)(2

1

minmax

minmax

VVE

VVE

c

m

)(

)(

)(2

1

)(2

1

minmax

minmax

minmax

minmax

VV

VV

VV

VV

m


Cont’d…

• Since the peak change of modulated output wave Em is the sum of the usf and lsf voltages hence,

• Then

lsfusflsfusfmEEwhereEEE

)(4

1

2

)(2

1

2

minmax

minmax

VV

VVE

EE m

ls fus f


Eusf = peak amplitude

of the upper side

frequency (volts)

Elsf = peak amplitude

of the lower side

frequency (volts)


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.

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.

Solution: Example 1

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, 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.


AM Envelope for Example 3


Generation of AM DSBFC envelope showing the time-domain of the modulated wave, carrier & sideband

signals


37

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 (or DSSC) 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 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.


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.

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 calculated

PSB = PLSB = PUSB = Pcm2 / 4

• Maximum power appears in the sidebands when the carrier is 100 percent modulated.

AM Power

Review: conventional AM(DSB-FC) Frequency spectrum: Bandwidth=2 x fmmax Total Power=Pcarrier +Pusb +Plsb


fc

fc+fm fc-fm

DSB FULL CARRIER

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


Double side band suppressed carrier(DSB-SC)

• Frequency spectrum:

• Bandwidth:2 x fmmax

• Total Power= Pusb + Plsb


fc

fc+fm fc-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


60

Single Side Band Full Carrier (SSB-FC)

Frequency spectrum: Bandwidth=fmmax

Total Power=Pcarrier +Pusb EKT343 –Principle of Communication

Engineering 61

fc fc+fm fc-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)


62

Single Side band Suppress Carrier (SSB-SC)

Frequency spectrum: Bandwidth=fmmax

Total Power=+Pusb EKT343 –Principle of Communication

Engineering 63

fc

fc+fm fc-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 amplitudes


64

Comparison of time domain representation of three common AM transmission systems:

EKT343 –Principle of Communication Engineering 65 Tomasi

Electronic Communications Systems, 5e

Example 5


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.

Example 5..cont’d • Solution for DSBFC; i) ii) iii) Bandwidth=2xfmmax=2(10kHz)=20kHz


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

Example 5..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 5..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

1

4422

22

110kHz 90kHz

Example 5..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 110kHz fc-fm

Example 5..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

1

42

2

fc 110kHz fc-fm

Exercises 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.

Exercises

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

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


Filter

response

curve

Sideband

filter

Balanced

modulator

Carrier

oscillator

Microphone Audio

amplifier

Linear

amplifier

Antenna

Upper

sidebands

DSB

signal

SSB

signal

Lower

sidebands

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


Balanced

Modulator 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

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 DSB


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.


80

Cont’d

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.


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


fc fc

LSB MSB

Carrier

VSB

Documents

EKT358 Communication Systemsportal.unimap.edu.my/portal/page/portal30/Lecture...cause a change in the output wave of ±7.5 V p. Determine a) Upper and lower side frequencies. b) Modulation