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Modulation

• Introduction• The transmission of an information-bearing signal over

communication channel (telephone or satellite channel) requires a shift of the range of frequencies contained in the signal to another frequency range suitable for transmission.

• The shift in the signal frequency range is accomplished by modulation.

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• Modulation is defined as the process by which some characteristic of a carrier signal is varied in accordance with a modulating signal– The message is referred to as the modulating signal– The result of modulation is referred to as the

modulated signal

• The basic types of analog modulations are– Continuous wave (CW) modulation– Pulse modulation

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• In CW modulation, a sinusoidal signal is used as a carrier signal

• A general modulated signal can be represented as

– Where is the carrier frequency– and are called the instantaneous amplitude and

phase angle of the carrier.

twAtg cc cos)(

ttwtAtxc cos

c tA t

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• When is linearly related to the message , the result is amplitude modulation.

• If or its derivative is linearly related to , then we have phase or frequency modulation. The phase and frequency modulation are referred to as angle modulation.

• In pulse modulation, a periodic train of short pulses act as the carrier signal.

tA tm

tm t

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• Amplitude Modulation • In amplitude modulation, the modulated carrier is

represented by

• Depending on the nature of the spectral relationship between and , we have the following types of amplitude modulation scheme– Double-sideband (DSB) modulation– Amplitude modulation (AM) also known as DSBFC– Single-sideband (SSB) modulation– Vestigial-sideband (VSB) modulation

)cos( ttAtx cc

tA tm

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• Double-Sideband Modulation• DSB modulation results when is proportional to the

message signal . i.e

• DSB is the multiplication of a carrier , by the message signal .

• The spectrum of a DSB signal is given by

tA tm ttmtx cDSB cos

tmtccos

ccDSB MMX 2

1

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• Generation of DSB signals

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• The spectral range occupied by the message signal is called the baseband, and thus the message signal is referred to as the baseband signal.

• From the spectrum, has no identifiable carrier and this type of modulation is known as double-sideband suppressed-carrier (DSB-SC) modulation.

• Demodulation of DSB signal• Recovery of the message from the modulated signal

is called demodulation or detection.

txDSB

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• The message signal is recovered from the modulated signal by multiplying by a local carrier and using a lowpass filter (LPF) on the product as shown below.

• The local carrier must be in phase and frequency synchronism with the incoming carrier

txDSB

tm txDSB

X

Carrier replica

DSB-SC signal

Demodulation of a DSB-SC signal

Lowpass filter

Recovered message

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• Ordinary Amplitude Modulation• An ordinary amplitude modulated signal is generated by

adding a large carrier signal to the DSB signal. The ordinary AM signal has the form

• The spectrum of is given by

ttmAtAttmx cccAM coscoscos

AMx

cc

ccAM

A

MMX

2

1

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• Amplitude modulation

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• Demodulation of AM signals• The advantage of AM over DSB modulation is that

the envelope detection scheme can be used for demodulation if sufficient carrier power is transmitted.

• If is large enough, the envelope of the modulated waveform given by is proportional to .

• Demodulation reduces the detection of the envelope of the modulated carrier with no dependence on the exact phase or frequency of the carrier.

tm tmAA

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• If is not large enough, then the envelope of is not always proportional to .

• The condition for demodulation of AM by an envelope detector is

• or

• Modulation Index• The modulation index for AM is defined as

•

A

tm txAM

0 tmA

tmA min

A

tmmin

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• The condition for demodulation of AM by an envelope detector can be expressed as

• When , the carrier is said to be overmodulated, resulting in envelope distortion.

• Envelope Detector• An envelope detector consisting of a diode and a

resistor-capacitor combination is shown below

1

1

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Envelope Detector for AM

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• During the positive half-cycle of the input signal, the diode is forward-biased, and the capacitor C, charges up rapidly to the peak value of the input signal. As the input signal falls below its maximum, the diode turns off. This is followed by a slow discharge of the capacitor through resistor R until the next positive half-cycle, when the input signal becomes greater than the capacitor voltage and the diode turns on again.

• For proper operation of the envelope detector, the discharge time constant RC must be chosen properly such that

mcMc fRC

fff1111

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• Single-Sideband Modulation• Ordinary AM modulation and DSB modulation

waste bandwidth because they both require a transmission bandwidth equal to twice the message bandwidth.

• Since either the upper sideband or the lower sideband contains the complete information of the message signal, only one sideband is necessary for information transmission.

• When only one sideband is transmitted, the modulation is referred to as single-sideband (SSB) modulation.

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• Generation of SSB signals

• Frequency Discrimination Method• The easy way to generate an SSB signal is to generate a

DSB signal first and then suppress one of the sidebands by filtering. This method is called the frequency discrimination method.

• Phase-Shift Method• Read and make notes for yourself.• Assignment: Describe the phase-shift method in details.

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• Demodulation of SSB signals

• Demodulation of SSB signals can be achieved by using the coherent detector as used in the DSB demodulation and passing the resulting signal through a low-pass filter.

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• SSB signal

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• Power in AM wave

• The total power transmitted in the modulated wave will be

• **

• The first term is the unmodulated carrier power and is given by

rmsR

A

R

A

R

AP USBLSBcrt

222

R

A

R

A

R

AP c

c

crc 2

2 2

2

2

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• similarly

• Substituting the above equations in ** , we have

R

A

R

A

R

A

R

APP cc

c

SBUSBLSB 248

22

2222

2

2

)2

1()44

1(

4424242222

2222222

cct

cccccc

t

PPP

PPPR

A

R

A

R

AP

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• The ration of useful power to total power

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2

c

t

P

P

21:

2

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Vestigial-Sideband Modulation (VSB)

• In VSB, all of the one sideband is transmitted and a small amount (vestige) of the other sideband is transmitted as well.

• VSB overcomes two of the difficulties present in SSB modulation. By allowing a small amount or vestige, of the unwanted sideband to appear at the output of an SSB modulator, the design of the sideband filter is simplified since the need for a sharp cutoff at the frequency is eliminated.

• In addition, a VSB system has improved LF response compared to SSB & can even have DC response 29

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• Exercise:• For each of the following baseband signals• (i)

• (ii)

• (a) Sketch the spectrum• (b) Sketch the spectrum of DSB-SC signal with a

carrier frequency of

• (c) Identify the upper sideband (USB) and lower sideband (LSB) spectra.

ttxm 2000cos

tttxm 2000cos1000cos2

ttxc 20000cos12

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• Ex. • (a) A modulating signal represented by

modulates a carrier represented by

and resulting modulated signal is developed across a resistance of

(i) State the mathematical expression for the modulated wave

(ii) Using an appropriate mathematical identity, expand the expression in (i) to show the frequency composition for the wave

mVt1000sin2

mVt6102sin10

k2

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(iii) Sketch the resultant wave in frequency domain

(iv) Sketch the resultant wave in time domain

(v) Calculate the power in the wave

(vi) Calculate the power in the Carrier

(vii) The ratio of the useful power to the carrier power

(viii) What is the cutoff frequency of the lowpass filter that may be used to recover the

message at the receiver.

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QUIZ #1 • 1. Given the modulating signal: • a. Sketch the spectrum of m(t) (10)• b. Find and sketch the spectrum of the DSB-SC signal• (10)• c. From the spectrum in (b.) suppress the LSB to obtain the

USB spectrum [Draw and show how you do this] (10)• d. Write down an expression for the USB (10)• e. If the modulated wave was developed across a • resistor, find the power in the USB (10)

tttm 300cos2100cos)(

ttm 1000cos)(2

k2

)(tUSB

Quiz 2

• A standard AM broadcast station is allowed to transmit modulating frequencies up to 3.5 kHz. If the AM station is transmitting on a frequency 89.9 kHz,

• (a) compute the maximum and minimum upper and lower sidebands

• (b) and the total bandwidth • (c) plot the spectrum of the modulated signal• (d) find the total power of the modulated signal

given that the modulation index is 80%. 35

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