Chapter 4

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Communication Systems

Instructor: Engr. Dr. Sarmad Ullah Khan

Assistant ProfessorAssistant ProfessorElectrical Engineering Department

CECOS University of IT and Emerging [email protected]

Chapter 4

Dr. Sarmad Ullah Khan

Amplitude Modulations and Demodulations

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Outlines

• Baseband versus Carrier Communication

D bl id b d A lit d M d l ti


• Double sideband Amplitude Modulation

• Amplitude Modulation

• Bandwidth Efficient Amplitude Modulation

• Amplitude Modulation: VESTIGIAL Sideband

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Outlines








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Baseband versus Carrier Communication

• Modulation is a process that moves signal into aspecific frequency band


specific frequency band• The bandwidth B represents a measure of frequency

range.• It is typically measured in Hz with 1 Hz = 1/sec.• The bandwidth of a signal indicates the frequency

range in which the signal‘s Fourier transform has ag gpower above a certain threshold (typically half ofthe maximum power)

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• Communication systems that do not use modulationare called baseband communication


are called baseband communication• Communication systems that use modulation are

called carrier communication• Baseband is original message frequency band• In telephony, baseband is audio band (0 – 3.5 kHz)• In NTSC television, video baseband is 0 – 4.3 MHzIn NTSC television, video baseband is 0 4.3 MHz

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• Baseband CommunicationMessage signals are directly transmitted without any


Message signals are directly transmitted without anymodulation

Dedicated user channels are assigned to each long distancecommunication

Baseband signals have overlapping bandsSevere interferenceWaste of channel resourcesWaste of channel resourcesModulation and shifting to non overlapping bands save

channel resources

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• Carrier CommunicationModulation techniques is used to shift the frequency


Modulation techniques is used to shift the frequencyspectrum of message signal

Modulation changes one of the basic parameter of carriersignal (Amplitude, Frequency, Phase)

Carrier signal is a sinusoidal signal of high frequency fc

Parameter variation is proportional to message signal m(t)Amplitude modulation is linearAmplitude modulation is linearFrequency and Phase modulations are non linearsPAM, PWM, PPM, PCM and DM are baseband signals

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• Amplitude Modulation and Angle ModulationAmplitude modulation (AM) varies the amplitude of a


Amplitude modulation (AM) varies the amplitude of acarrier signal according to a modulatingsignal m(t).

The modulated signal is

)cos(c

tc

wA

)cos()( twtm c

Source signal m(t) and its Fourier transform M(f)

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• Amplitude Modulation and Angle Modulation


Frequency Shifting Property

10 )()(

2

1cos)( ccc wwMwwMtwtm

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Outlines








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Double Sideband Amplitude Modulation

• Amplitude Modulation and Angle Modulation


1

M(f - fc) is M(f) shifted to the right of fc

M(f + fc) is M(f) shifted to the left of fc

The bandwidth changed from B to 2B The modulated signal is composed of two parts, above

)()(2

12cos)( ccc ffMffMtftm

The modulated signal is composed of two parts, abovefc and below fc

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• Amplitude Modulation and Angle ModulationThe upper sideband (USB) containing the frequencies


The upper sideband (USB) containing the frequencies|f| > |fc|The lower sideband (LSB) containing the frequencies

|f| < |fc|The modulated signal in this scheme does not have a

discrete component of the carrier frequency fc. For thisreason this is called double sideband suppressedreason this is called double-sideband suppressedcarrier (DSB-SC) modulation

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• Amplitude Modulation and Angle ModulationB vs f


B vs fc

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Spectrum

Spectrum of the DSB-SC signal m(t)cos10,000t

)cos()cos(1

coscos

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)cos()cos(2

coscos

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Spectrum



Spectrum


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Spectrum



Spectrum


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• Modulation and Demodulation


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• Modulation and Demodulation


)2cos()()(21cos)()( 2 twtmtmtwtmte

cc

20 )2()2(4

1)(21)(

ccwwMwwMwMwE

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• ModulatorsMultiplier Modulators


Multiplier ModulatorsModulation is achieved directly by multiplying m(t) by

cos(wct) using an analog multiplier.The output is proportional to the product of two input

signals.Difficult to maintain linearity and are expansive.

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Better to avoid


• ModulatorsNon Linear Modulators


Non Linear ModulatorsModulation can be achieved by using non linear deviceFor example, diodes or transistors

Input-output characteristics of NL element is approx. bypower series as

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Non Linear Modulators

The summer output z(t) is given by

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Substitution of x1(t)=coswct+m(t) and x2(t)=coswct-m(t)

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Spectrum of m(t) is centered at originSpectrum of m(t) coswct is centered at ±ωThe signal is ready for transmission but we do not need the

m(t) part of z(t)m(t) part of z(t)Z(t) passed through band pass filter tuned to ωc

am(t) is suppressed and desire modulated signal4bm(t)coswct pass without distortion

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• ModulatorsNon Linear Modulators (summary)


Non Linear Modulators (summary)

Two inputs m(t) and coswctThe summer output does not contain one of the input coswctCircuits which have this characteristic are called balanced

circuits.circuits.The previous circuitry is an example of balanced modulators.

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This circuit is balanced to only one input carrier, the other input m(t) stillappear at the filter input, which must reject it…….for that reason it iscalled a single balanced modulator

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• ModulatorsModulation through any periodic signal


Modulation through any periodic signalModulated signal can not only be obtained by a pure sinusoid but

by any periodic signal of fundamental frequency wc

Periodic signal can be expresses by trigonometric FourierSeries

Spectrum of the modulated signal is the spectrum M(w) shifted to±fc , ±2fc , ±3fc , ±4fc , …… ±nfc ,……

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• ModulatorsModulation through any periodic signal


Modulation through any periodic signalIf we pass this modulated signal through band-pass filter of

bandwidth 2B tuned to wc

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• ModulatorsSwitching Modulators


Switching ModulatorsMultiplication operation of modulation can be replaced by

switching operation. If a periodic signal having Fourier series as:

carrier

Modulated signal

Now consider a periodic square pulse train with Fourier series as

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Modulated signal

....7cos

7

15cos

5

13cos

3

1cos

2

2

1)( twtwtwtwtw cccc

From example 2.8


• ModulatorsSwitching Modulators


Switching ModulatorsThe modulated signal m(t)w(t) is given by

....7cos)(

7

15cos)(

5

13cos)(

3

1cos)(

2)(

2

1)()( twtmtwtmtwtmtwtmtmtwtm cccc

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Modulated signal m(t)w(t) consists of the component m(t) plus infinite numbers of modulated signals with carrier frequencies ,.....5,3,

cccwww

Th f ( ) ( ) i f M( ) d M( ) hif d



The spectrum of m(t)w(t) consists of M(w) and M(w) shifted to,.....5,3,

cccwww

As we are interested in modulated component only. To separate this component from others we pass m(t)w(t) through a bandpass filter of bandwidth 2BHz, centered at

twtmc

cos)(

cw

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gives the required modulated signal twtmc

cos)(2

Therefore the multiplication of a signal by a square pulse train is is reality a switching operation means turning off and on signal m(t)periodically and can be accomplished by switching element controlled by w(t)


• ModulatorsDiode Bridge Modulator


Diode Bridge ModulatorConsider the following electronic switch circuit driven by

to produce the switching action

4321 ,, DDDD and

are matched pairs

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During the next half cycle d is positive with respect to c, all the diodes open, terminal a & b are open.

When terminal c is positive with respect to d, all the diodes conduct, terminal a & b are effectively shortened.

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• ModulatorsDiode Bridge Modulator


Diode Bridge ModulatorTherefore the the circuit act as a desired electronic switch, where

the terminal a & b open and close periodically with the carrierfrequency fc. When is applied across the terminal ab

To obtain m(t)w(t) we may place terminal ab in series or in parallelas:

twA ccos

Switching on and off m(t) for each cycle of the carrier, resulting inthe switched signal m(t)w(t) and passing through band pass filtergives the desired signal:

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Series-bridge diode modulator Shunt-bridge diode modulator


• ModulatorsRing Modulator


Ring Modulator

Consider the following circuit

During the positive half cycle of the carrier D1 & D3 conduct and D2

& D4 are open, hence terminal a is connected to c & b to d

During the negative half cycle of the carrier D1 & D3 are open andD2 & D4 conduct, hence terminal a is connected to d & b to c

Output is proportional to m(t) during positive cycle & -m(t) duringnegative cycle

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• ModulatorsRing Modulator


Ring ModulatorThe Fourier series of bipolar square wave is given by:

....7cos

7

15cos

5

13cos

3

1cos

4)(0 twtwtwtwtw cccc

....7cos)(

7

15cos)(

5

13cos)(

3

1cos)(

4)()( 0 twtmtwtmtwtmtwtmtwtm ccccFiltering this signal to bandpass filter tuned to wc gives the required

modulated signal:

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In this circuit there are two inputs m(t) and coswct, the input of thefinal band pass filter does not contain either of the inputs……

This circuit is an example of double balanced modulator


• Demodulation of DSB-SC SignalsThe demodulation involve multiplication of DSB SC


The demodulation involve multiplication of DSB-SCwith carrier signalAt receiver incoming signal multiply with local carrierLocal carrier must have frequency and phase

synchronization with incoming signalProduct is passed to low pass filterSuch demodulators are called synchronous or coherent

or homodyne demodulators

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Problem 4.2‐4


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Problem 4.2‐4Dr. Sarmad Ullah Khan

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Problem 4.2‐4Dr. Sarmad Ullah Khan

At point b

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At point c

Problem 4.2‐4

The minimum value of wc is to avoid overlapping


pp g

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Problem 4.2‐4

This may be verified that the identity for contains


This may be verified that the identity for contains a term when n is odd. This is not true when n is even. Hence, the system works for a carrier only when n is odd.

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Example 4.2

Frequency mixer or converter:

Frequency mixer or converter is used to change the carrier frequency of the


modulated signal m(t)coswct to some other frequency wl

Can be achieved by multiplying m(t)coswct by

where or

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Example 4.2

In both cases the filter tuned to Wl will pass the term m(t)coswlt and suppress the other term and giving the required output


m(t)coswct (the carrier frequency is translated to wl from wc)

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Frequency mixing or frequency conversion is also known as heterodyning.

All the modulators discussed previously can be used for frequency mixing.

Frequency selected as operation called up-conversion Frequency selected as operation called down-conversion

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Amplitude Modulation

• The demodulation requires the receiver to possess acarrier signal that is synchronized with incoming signal


• It is difficult to achieve in practice• Unknown frequency shifts

• Require sophisticated receiver and costly• Transmit a carrier Acoswct along with the modulated

signal m(t)coswct so no need to generate a carrier at thereceiver

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• This type of modulation is called AM modulation anddenoted by and given by


)(ty g y

• Its Fourier spectrum is

)(tAM

• The spectrum of is the same as m(t)coswct plus twoadditional impulses at ±ω

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)(tAM

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• DSB-SC signal m(t)coswct and AM signal are identical with A+m(t) as modulating signal instead of


are identical with A+m(t) as modulating signal instead of m(t)

• To sketch ,we sketch A+m(t) & -(A+m(t) ) and fill in between the carrier frequency.

)(tAM

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• For signal e(t)coswct, if e(t) varies slowly, its envelopwould be |e(t)|


would be |e(t)|

• It means if A+m(t)≥0 for all t, the envelop of is

|A + m(t)| = A + m(t)

• For envelop detection to properly detect m(t)

• fc >> bandwidth of m(t)

)(tAM

• fc >> bandwidth of m(t)

• A + m(t) ≥ 0

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• Message signals m(t) with zero offset Let ±m be the maximum and minimum value of m(t)


Let ±mp be the maximum and minimum value of m(t) m(t) ≥ -mp

Condition of envelop detection isA ≥ - mmin = mp

Modulation index μ isμ = mp/A

F l d t ti t b di t ti lFor envelop detection to be distortion less0 ≤ μ ≤ 1

This is required condition for distortion lessdemodulation of AM by envelop detector

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• Message signals m(t) with nonzero offset It is rare that m(t) will have nonzero offset


It is rare that m(t) will have nonzero offsetMaximum mmax and minimum mmin are not symmetric

mmin ≠ mmax

Change in offset does not change the envelop detectoroutput and

0 ≤ μ ≤ 1μBut

μ = (mmax - mmin) / (2A + mmax + mmin)

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• Sideband and Carrier Power Th i di d t f l d t ti i t f


There is a disadvantage of envelope detection in terms ofpower waste, as the carrier term does not contain anyinformation

The carrier power Pc and sideband power Ps is given by

Power efficiency is given by

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• Sideband and Carrier PowerFor the special case of tone modulation:


For the special case of tone modulation:

Hence

With the condition 0 ≤ μ ≤ 1,Thus under best condition only one third of the transmitted

power is used for carrying message, for practical signalsthe efficiency is even worst

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• Generation of AM signalAM signals can be generated by any DSB SC modulators


AM signals can be generated by any DSB-SC modulators. The input should be A + m(t) instead of just m(t). The modulating circuit do not have to be balanced because

there is no need to suppress the carrier

Switching action is provided by a single diode and controlled by with twc ccos

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c


• Generation of AM signal


The diode opens and short periodically with infect multiplying the input signal by w(t).

The voltage across is:

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• Demodulation of AM signalThe AM signal can be demodulated coherently by a locally


The AM signal can be demodulated coherently by a locallygenerated carrier. E.g.

There are two well known methods of demodulation of AMsignals:

1) Rectifier detection 2) Envelope detection

twtwtmA cc coscos)( No benefit of sending carrier on the channel

1) Rectifier detection 2) Envelope detectionRectifier detector:

AM signal is applied to a diode and resistor circuit, the negativepart of the AM wave will be suppressed.

The output across the resistor is the half wave rectified version ofthe AM signal means multiplying AM with w(t).

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• Demodulation of AM signalRectifier detector:


Rectifier detector:

The rectified output VR

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)(cos)( twtc

wtmAvR

...5cos

5

13cos

3

1cos

2

2

1cos)( t

cwt

cwt

cwt

cwtmA

otherTermstmA )(1

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• Demodulation of AM signalRectifier detector:


Rectifier detector:

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• Demodulation of AM signalEnvelop detector:


Envelop detector:In an envelope detector, the output follows the envelope

of the modulated signalThe following circuit act as an envelope detector

During the positive cycle of the input signal, the diodeconducts and the capacitor C charges up to the peakvoltage of the input signal

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Envelop detector:

When input signal falls below this peak value, the diodei t ff (b th di d lt hi h i l this cut off. (because the diode voltage which is nearly thepeak voltage is greater than the input signal voltagecausing the diode to open )At this stage the capacitor discharge at the slew rate

(with a time constant RC)During the next positive cycle the process repeats 59




p

During each positive cycle the capacitor charges up to theDuring each positive cycle the capacitor charges up to thepeak voltage of the input signal and then decays slowly untilthe next positive cycleThis behavior of the capacitor makes output voltage Vc(t)

follow the envelope of the input signalCapacitor discharges during each positive peaks causes a

ripple signal of frequency wc at the output60

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Envelop detector:

The ripple can be reduced by increasing the timeconstant RC so the capacitor discharges very littlebetween positive peaks of the input signalsMaking RC too large, makes capacitor voltage

impossible to follow the envelope

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Envelop detector:

RC should be large compared to 1/wc, but should be small compared to

Where B is the highest frequency in m(t)

B21

Also requires a condition which is necessary for well defined envelope.

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The envelope detector output is with a ripple of frequency wc

The DC term A can be blocked by a capacitor or a simple RC high pass filter, and the ripple may be reduced further by another low-pass RC filter.

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Outlines








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Bandwidth Efficient Amplitude Modulation

• DSB spectrum has two sidebands (USB, LSB)• Both carry complete information


• Both carry complete information• Bandwidth requirement is 2B• How to improve spectral efficiency?

– Utilize spectral redundancy– remove spectral redundancy

• Single Sideband (SSB) removes either LSB or USBSingle Sideband (SSB) removes either LSB or USB• Quadrature amplitude modulation (QAM) utilize

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• Single Sideband (SSB) ModulationLSB USB b d b b d filt


– LSB or USB can be suppressed by band pass filter– A scheme in which only one sideband is

transmitted is known as single-sideband ( SSB)transmission

– In SSB transmission the required bandwidth is halfcompared to DSB signalp g

– An SSB signal can be coherently (synchronously)demodulated. E.g

– For example multiplying USB signal by coswctshifts its spectrum to the left and right by wc

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• Single Sideband (SSB) ModulationL filt i ill i th i d b b d


– Low pass filtering will give the required basebandsignal at the receiver

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• Single Sideband (SSB) ModulationHilb t T f


– Hilbert Transform– xh(t) and H{x(t)} to denote Hilbert transform of

x(t)

Hilbert Transform of m(t)

and delays the phase of each component by

)(tmh

2

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• Single Sideband (SSB) ModulationHilb t T f


– Hilbert Transform– xh(t) and H{x(t)} to denote Hilbert transform of

x(t)

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• Single Sideband (SSB) ModulationTi d i t ti f SSB i


– Time domain representation of SSB is

– Where minus sign applies to USB and the plussign applies to LSB

twtmtwtmt chcSSB sin)(cos)()(

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• Single Sideband (SSB) Modulation


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• Single Sideband (SSB) Modulation


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Example 4.7 p‐174

Tone Modulation:

Find for a simple case of tone modulation that is when the)(tSSB


Find for a simple case of tone modulation, that is, when the modulating signal is a sinusoid

)(SSBtwtm mcos)(

Solution:


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Example 4.7 p‐174

Hence


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Example 4.7 p‐174


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• Single Sideband (SSB) Modulation– Two methods are generally used to generate SSB


Two methods are generally used to generate SSBsignals

1) Sharp cutoff filters

2) Phase shifting networks– In Sharp cutoff method, the DSB-SC signal is passed

through a sharp cutoff filter to eliminate the undesiredsidebandsideband

– To obtain USB, the filter should pass all componentsabove wc, attenuated and completely suppress allcomponents below wc

– Such an operation requires an ideal filter that ispractically not possible

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• Single Sideband (SSB) ModulationThi th d f ti SSB i l b d


– This method of generating SSB signal can be usedwhen there is some separation between the passbandand stopband

– In some application this can be achieved e.g. voicesignals

– Voice signals spectrum shows little power content atth i i Th filt i th t d id b d ithe origin. Thus filtering the unwanted sideband isrelatively easy

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Tests have shown that frequency components below 300Hz are not important.

600Hz transition region around the cutoff frequency wc , makes filtering easy and minimize the channel interference

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• Single Sideband (SSB) ModulationThe basis of Phase shifting network method is the


– The basis of Phase shifting network method is thefollowing equation


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• Single Sideband (SSB) ModulationThe basis of Phase shifting network method is the


– The basis of Phase shifting network method is thefollowing equation

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• Quadrature Amplitude ModulationThe DSB signals of AM require twice the bandwidth


– The DSB signals of AM require twice the bandwidthrequired for the baseband signal

– Try to send two signals m1(t) and m2(t) simultaneously bymodulating them with two carrier signals of samefrequency but shifted in phase by –/2

– The combined signal is

twtmtwtmtmtm sin)(cos)()()(

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twtmtwtmtmtm cc sin)(cos)()()( 2121


• Quadrature Amplitude ModulationBoth modulated signals occupy the same band


– Both modulated signals occupy the same band– At the receiver the two baseband signals can be separated

by using a second carrier that is shifted in phase by –/2– The first signal m1(t) can be detected by a multiplication

with 2cos(ct) followed by a low-pass filter– The second signal m2(t) can be detected accordingly by a

multiplication with sin( t) followed by a low-pass filtermultiplication with sin(ct) followed by a low pass filter

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• Quadrature Amplitude ModulationThus two baseband signals each of bandwidth B can be


– Thus, two baseband signals, each of bandwidth B, can besimultaneously transmitted over a channel with bandwidth2B

– This principle is called quadrature amplitudemodulation (QAM), because the carrier frequencies are inphase quadrature

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Outlines








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Amplitude Modulation: Vestigial Sideband (VSB)

• VSB is a compromise between DSB and SSB• It combines the advantages of DSB and SSB while avoid


It combines the advantages of DSB and SSB while avoiddisadvantages at small cost

• Its generation is relatively easy and bandwidth requirement is25% greater than SSB

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• If vestigial shaping filter produce VBS from DSB is Hi(f), Itsspectrum will bespectrum will be

• VBS filter allows transmission of one sideband but suppressother side band gradually, NOT completely

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• For demodulation,

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Chapter 4

Engineering

angle modulation dr

linearamplitude modulation

frequency dr

carrier dsbsc modulation

spectrum dr

baseband communication

angle modulation b vs

sarmadullahkhan frequency