Analog Communication Unit4 Vtu

ANALOG COMMUNICATION (VTU) - 10EC53

UNIT 4

VESTIGIAL SIDE-BAND MODULATION (VSB): Frequency Domain description, Time

Domain description, Generation of VSB modulated wave, Envelop detection of VSB wave plus

carrier, Comparison of amplitude modulation techniques, Frequency translation, Frequency

division multiplexing, Application: Radio broadcasting, AM radio.

TEXT BOOKS:

1. Communication Systems, Simon Haykins, 5thEdition, John Willey, India Pvt. Ltd, 2009.

2. An Introduction to Analog and Digital Communication, Simon Haykins, John Wiley India

Pvt. Ltd., 2008

Special Thanks To:

Faculty(Chronological): Arunkumar G (STJIT), Ravitej B (GMIT), Somesh HB (REVA

ITM).

BY:

RAGHUDATHESH G P

Asst Prof

ECE Dept, GMIT

Davangere 577004

Cell: +917411459249

Mail: [email protected]

Quotes:

A real entrepreneur is somebody who has no safety net underneath them.

For every minute you are angry you lose sixty seconds of happiness.

Success is never final. Failure is never fatal. Its courage that counts.

You can do anything, but not everything.

The only true wisdom is knowing that you know nothing.

The old believe everything: the middle-aged suspect everything: the young know

everything

Vestigial Sideband Modulation Raghudathesh G P Asst Professor

ECE Dept, GMIT [email protected] Page No - 1

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VESTIGIAL SIDE-BAND MODULATION (VSB)

Definition: Vestigial sideband is a type of Amplitude modulation in which one side band is completely passed along with trace or tail or vestige of the other side band.

VSB is a compromise between SSB and DSBSC modulation. Why VSB:

Single side band modulation cannot be applied to all types of message signals, because of the strict adherence to the filter design.

The above reason makes SSB impractical to use for radio signals and wide band low pass signals. But the bandwidth efficiency of SSB is very high when

compared with DSB-SC and standard AM.

This necessitates the requirements of a modulation technique like VSB which has bandwidth efficiency almost equal to SSB and has the low pass frequency

characteristics of DSB-SC and standard AM.

Thus, if we relax the filter design constrains such that a very small part of unwanted sideband is also transmitted along with the desired sideband then this

type of modulation technique is called the Vestigial Side-Band Modulation

(VSB).

The unwanted sideband part is called Vestige. To generate a VSB signal, we have to first generate a DSB-SC signal and then pass it

through a sideband filter as shown in Figure below. This filter will pass the wanted

sideband as it is along with a part of unwanted sideband.

Advantages of VSB:

1. Reduction in bandwidth. It is almost as efficient as the SSB. 2. Due to allowance of transmitting a part of lower sideband, the constraint on the filters has

been relaxed. So practically, easy to design filters can be used.



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3. It possesses good phase characteristics and makes the transmission of low frequency components possible.

Applications of VSB:

VSB modulation has become standard for the transmission of Television signals. Because the video signals need a large transmission bandwidth if transmitted using DSB-FC or

DSF-SC techniques.

Frequency Domain Description:

The spectrum of VSB is as shown in Figure above. The spectrum of message signal m (t) has also been shown.

Here m(t) is the message signal which is band limited to W Hz < fc Hz. In the frequency spectrum it is assumed that the upper sideband is transmitted as it is and

the lower sideband is modified into vestigial sideband. It is also possible such that LSB is

transmitted as it is and vestige of USB.

From figure (c) The transmission bandwidth of the VSB modulated wave is given by,

Here, W = Message bandwidth and

fv = Width of the vestigial sideband



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Time domain Description:

Let s(t) denote a VSB modulated wave and assuming that s(t) containing upper sideband along with the Vestige of the Lower sideband.

VSB modulated wave s(t) is the output from Sideband shaping filter, whose input is DSBSC wave. The DSBSC Modulated wave is,

---------------- (1)

Using bandpass to low-pass transformation method we may replace the sideband shaping filter by an equivalent complex low-pass filter of transfer function H(f) as shown in

figure (a) above

We may express as in figure (b) as the difference between two components (f) and (f) as



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------------- (2)

These two components are considered individually as follows: The transfer function shown in figure (c) pertains to a complex low pass filter

equivalent to a band pass filter design to reject the lower side band completely.

is defined as,

----------- (3)

The transfer function as shown in figure (d) accounts for the generation of vestige of the lower sideband and removal of a corresponding portion from the

upper side band.

Putting Equation (3) in (2), we get

-------------- (4)

The signum function sgn(f) and transfer function are both odd functions of frequency f, Hence, both they have purely imaginary Inverse Fourier Transform.

Accordingly, we may introduce a new transfer function as

-------------- (5)

Figure (e) shows a plot of as a function of frequency in accordance with equation (5) and figure (d check). Rewrite equation (4) interms of HQ(f) as

-------------- (6)

We are now ready to determine the VSB modulated wave s(t).

----------- (7)

Here is the complex envelope of s(t).



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As is the output of the complex low-pass filter of transfer function , which is produced in response to the complex envelope of the DSBSC modulated wave, thus we

may express the spectrum of as,

----------- (8)

Substituting equations (1) and (4) in (8) we get,

----------- (9)

Taking the inverse Fourier transform of , we thus obtain

------------ (10)

Where mQ(t) is the response produced by passing the message signal m(t) through a low-pass filter of impulse response hQ(t). Finally, substituting Equation (10) in (7), we get

-------------- (11)

This is the desired representation for a VSB modulated wave containing a vestige of the lower sideband.

The component constitutes the in-phase component of this VSB modulated wave,

and

The component constitutes the quadrature component.

On the similar lines VSB modulated wave s(t), containing a vestige of the upper sideband, is

defined by

---------------- (12)



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Note:

1. The DSBSC and SSB waves may be regarded as special cases of the VSB modulated wave defined by Equation (11).

2. If the vestigial sideband is increased to the width of a full sideband, the resulting wave becomes a DSBSC wave with the result that mQ(t) vanishes.

3. If, the width of the vestigial sideband is reduced to zero, the resulting wave becomes an SSB wave containing the upper sideband, with the result that mQ(t) = , where

is the Hilbert transform of m(t).

Generation of VSB Modulated Wave:

The block diagram of a VSB modulator is shown in Figure above. The modulating signal m (t) is applied to a product modulator. The output of the carrier

oscillator is also applied to the other input of the product modulator.

The output of product modulator is DSB-SC modulated wave and is given by,

Applying Fourier transform on both sides we get,

This DSB-SC signal is then applied to a sideband shaping filter. The design of this filter depends on the desired spectrum of the VSB modulated signal.

The filter characteristics of sideband shaping filter is h(t) thus the transfer function of filter be H(f) then output of the sideband shaping filter is given by,



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Detection of VSB Modulated Wave:

1. Synchronous Coherent detector for VSB Demodulation:

The synchronous detector for the detection of VSB modulated wave is shown in Figure above

The VSB modulated wave is passed through a product modulator where it is multiplied with the locally generated carrier, which is frequency and phase synchronized with

transmitter.

The output of the product modulator is given by,

Applying Fourier transform on both sides we get,

------- (a)

We know that,

------- (1)

Replacing f by in (1),

------- (2)

Replacing f by in (1),

-------- (3)



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Substituting equations (2) and (3) in (a) we get,

----------- (4)

Equation (4) is passed through a LPF, which eliminates unwanted term and passes only the wanted term thus output of LPF is,

----------- (5)

If we want to obtain the undistorted message signal m (t) at the output of the demodulator, then V0 (f) should be a scaled version of M (f). For this the transfer function

H (f) should satisfy the condition as follows:

-------- (6)

The condition stated in Equation (6) will be satisfied if the filter frequency response is as shown in Figure below. Note that the magnitudes are normalized. The frequency response

of Figure has been drawn only for the positive frequencies.



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2. Envelope Detection of a VSB Wave Plus Carrier:

VSB modulation is used in the commercial TV broadcasting in which along with VSB transmission a carrier signal of substantial size is transmitted. Therefore it is possible to

use the envelope detection.

For picture transmission the VSB signal is amplitude scaled to ka (here ka is amplitude sensitivity) and a carrier wave Accos (2fct) is added, thus signal can be mathematically

represented as,

------------- (1)

Now we pass this VSB signal through an envelope detector, the output is given by,

-------- (2)

Using this expression we can estimate the distortions introduced by the envelope detector. The distortion in the output of the detector is due to the quadrature component

xQ (t).

Distortion in the detected signal can be reduced by taking the following correcting measures.

1. By reducing the percentage modulation to reduce "ka".



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2. By increasing the width of the vestigial sideband to reduce the quadrature component xQ (t).

Comparison of AM techniques:

Sl No Parameter DSBFC

(standard

AM)

DSBSC SSB VSB

1 Type of

modulation

Non-linear

Modulation

Linear

Modulation

Linear

Modulation

Linear

Modulation

2 Power in

Transmitted

Signal

Maximum Moderate Minimum Moderate

3 Carrier

Suppression

Not

Applicable

(NA)

Fully Fully NA

4 Sideband

(SB)

suppression

NA NA One SB

Completely

One SB

Suppressed

Partially

5 Number of

SBs 2 2 1 1+Vestige of

other

6 Bandwidth 2W 2W W W < BW < 2W

7 Transmission

Efficiency

Minimum Moderate Maximum Moderate

8 Number of

modulating

Inputs

1 1 1 1

Receiver

Complexity

Simple Complex Complex Complex

9 Application Radio

broadcasting

Radio

broadcasting

Point to point

communication

Television



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Frequency Translation:

Definition: It is a procedure where the frequency of the signal is translated to a higher or lower frequency such that it occupies a new frequency band.

It is a linear operation. In the processing of signals in communication systems, it is often convenient or necessary

to translate the modulated wave upward or downward in frequency, so that it occupies a

new frequency band. This frequency translation is accomplished by multiplication of the

signal by a locally generated carrier wave and subsequent filtering as shown below

As an example consider the DSBSC wave expressed as, --------- (1)

Here, m(t) = bandlimited message signal in the range W f W

The spectrum of s (t) occupies the frequency slot (fc - W) to (fc + W) and (- fc - W) to (- fc + W) as shown in below figure.

Now suppose that we want to translate this modulated waveform downwards in frequency to a new carrier fo such that fo < fc. This can be achieved using following

steps:

Step 1:Multiply the DSBSC wave s (t) by a locally generated carrier cos (2flt) as shown in Figure above

---------- (2)

This expression consists of two DSBSC waves The first term represents the first DSBSC wave with a carrier frequency of

( )



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The second term represents the second DSBSC wave with a carrier frequency of ( ).

The spectrum of v1 (t) is V1 (f) and it is shown in Figure below.

Step 2: Pass the multiplier output through a bandpass filter: Let the frequency of the local oscillator (fl) be adjusted such that,

------ (3)

The output of the multiplier vl (t) is Pass through a bandpass filter with a bandwidth 2W and center frequency of .

Then the output of the bandpass filter v2 (t) is given by,

----------- (4)

The spectrum of v2 (t) i.e. V2 (f) is shown in Figure below. Thus the frequency translation from fc to fo is achieved.



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Translation of the Spectrum to Higher Frequency:

We know that the output of multiplier is given by

Select a bandpass filter with centre frequency and bandwidth of 2W so that the

second term in the expression for vl (t) will appear in the filter output

Filter output,

Thus the new carrier = ( ) which is higher than fc and the up conversion is achieved.

Note:

1. Mixer is a device which performs the frequency translation of modulated wave. 2. The process of frequency translation itself is called as mixing or heterodyning. 3. The mixing is a linear operation in which it preserves the relation between the

sidebands of the incoming signal with the carrier.



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Problem: The incoming signal has a midband frequency that may lie in the range of 530

kHz to 1650 kHz. The associated a bandwidth is 10 kHz. This signal is to be translated to a

fixed frequency band centered at 470 kHz. Determine the tuning range that must be

provided by the local oscillator.

Solution:

Given

530 kHz < fc < 1650 kHz.

New center frequency fo = (fc - f1) = 470 kHz. fl = fc - fo = fc -470 kHz.

So when fc = 530 kHz, f1 = 530 kHz - 470 kHz = 60 kHz and

when fc = 1650 kHz, f1 = 1650 kHz - 470 kHz = 1180 kHz.

Hence the tuning range of oscillator is 60 kHz to 1180 kHz.

Multiplexing:

Definition: It is the process of simultaneously transmitting two or more individual signals over a single communication channel.

Due to multiplexing it is possible to increase the number of communication channels so that more information can be transmitted.

The typical applications of multiplexing are in telemetry and telephony or in the satellite communication.

Types of Multiplexing: There are two basic types of multiplexing. They are 1. Frequency division multiplexing (FDM): Used to deal with the analog information. Many signals are transmitted simultaneously where each signal occupies a

different frequency slot within a common bandwidth.

2. Time division multiplexing (TDM): Used to handle the digital information. The signals are not transmitted at a time; instead they are transmitted in different

time slots.

Frequency Division Multiplexing (FDM):

The operation of FDM is based on sharing the available bandwidth of a communication channel among the signals to be transmitted.

Many signals are transmitted simultaneously with each signal occupying a different frequency slot within a common bandwidth.

Each signal to be transmitted modulates a different carrier. The modulation can be AM, SSB, FM or PM. The modulated signals are then added together to form a composite

signal which is transmitted over a single channel.



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Generally the FDM systems are used for multiplexing the analog signals. He block diagram of FDM system is as shown below

The input message signals assumed to be of the low pass types are pass through the input LPFs.

These LPFs are designed to remove high frequency components that do not contribute significantly to signal representation but are capable of disturbing other message signals

that share the common channel.

The filtered message signals are then modulated with the carrier frequencies. The most widely used method of modulation in FDM is single side band modulation which requires

a bandwidth that is approximately equal to that of original message signal.

The BPFs following the modulators are used to restrict the band of each modulator wave to its prescribed range.

The resulting BPF outputs are next combines in parallel to form the input to the common channel.

At the receiver end, BPFs connected to the common channel in parallel to separate the message signals on the frequency occupancy basis.

Finally, the original message signals are recovered by individual demodulators.



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Transmission bandwidth:

Consider an FDM system using SSB modulation to transmit 24 independent voice inputs. Assume a bandwidth of 4 kHz for each voice input thus in order to accommodate an

FDM system using SSB modulation to transmit the 24 voice inputs, the communication

channel must provide the transmission bandwidth.

Here n = number of voice signal. Thus, 24 voice inputs having a bandwidth of 4 kHz for each voice inputs the transmission

bandwidth is given by,

Advantages of FDM:

3. A large number of signals (channels) can be transmitted simultaneously. 4. FDM does not need synchronization between its transmitter and receiver for proper

operation.

5. Demodulation of FDM is easy. 6. Due to slow narrow band fading only a single channel gets affected.

Disadvantages of FDM:

1. The communication channel must have a very large bandwidth. 2. Intermodulation distortion takes place. 3. Large number of modulators and filters are required. 4. FDM suffers from the problem of crosstalk. 5. All the FDM channels get affected due to wideband fading.

Radio Broadcasting:

In radio broadcasting one central transmitter radiates the message signal in all the possible directions. Such message signals can contain informative signals, entertainment

signals etc.

There are three general types of radio broadcasting: A.M. broadcasting F. M. broadcasting T. V. broadcasting

AM broadcasting uses the standard AM.



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FM broadcasting uses frequency modulation TV broadcasting makes use of AM for picture transmission and FM for sound

transmission.

AM radio:

Usual AM radio receiver is of the superheterodyne type, which is resented schematically in Figure above.

The receiver consists of : 1. Radio frequency (RF) section, 2. A mixer and local oscillator, 3. An intermediate frequency (IF) section, and 4. A demodulator.

Typical frequency parameters of commercial AM radio are: 1. Carrier range = 0.535-1.605 MHz 2. Midband frequency of IF section = 455 kHz 3. IF bandwidth = 10 kHz

The incoming amplitude modulated wave is picked up by the receiving antenna and amplified in the RF section. The combination of mixer and local oscillator provides a

frequency conversion or heterodyning function, whereby the incoming signal is

converted to a pre-determined fixed intermediate frequency,

Here, fLO = frequency of the local oscillator and

fRF = the carrier frequency of the incoming RF signal.



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fIF = called as the intermediate frequency because the signal is neither at the

original input frequency at the final baseband frequency.

The IF section consists of one or more stages of tuned amplification provides most of the amplification and selectivity in the receiver.

The output of the IF section is applied to an envelope detector, which recovers the baseband signal.

The final operation in the receiver is the power amplification of the recovered message. The loudspeaker constitutes the load of the power amplifier.

The superheterodyne operation refers to the frequency conversion from the variable carrier frequency of the incoming RF signal to the fixed IF signal.

Advantages:

1. No variation in bandwidth. The bandwidth remains constant over the entire operating range.

2. High sensitivity and selectivity. 3. High adjacent channel rejection.

Characteristics of Radio Receiver:

The performance of the radio receivers can be measured interms of following reciver

characteristics:

1. Selectivity 2. Sensitivity 3. Fidelity 4. Image frequency and its rejection 5. Double spotting.

Problems:

1. The single-tone modulating wave is used to generate the VSB

modulated wave

Where a is a constant, less than unity. Determine

a. The in-phase and quadrature components of the VSB modulated wave s(t). b. What is the value of constant a for which s(t) reduces to a DSBSC modulated wave? c. What are the values of constant a for which it reduces to an SSB modulated wave? d. The VSB wave s(t), plus the carrier is passed through an envelope

detector. Determine the distortion produced by the quadrature component.



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e. What is the value of constant a for which this distortion reaches its worst possible value? Solution:

VSB modulated wave is given as,

---- (1)

Expanding the above equation using cosine formula we get,

------ (2)

a. The in-phase components of the VSB modulated wave s(t)

Quadrature components of the VSB modulated wave s(t) is,

b. If a=1/2, the VSB wave s(t) in equation (2) reduces to DSB-SC modulated wave. Thus,



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c. If a=0, the VSB wave s(t) in equation (2) reduces to SSB modulated wave having LSB Only.

Thus,

If a=0, the VSB wave s(t) in equation (2) reduces to SSB modulated wave having USB Only.

Thus,

d. The VSB wave s(t), plus the carrier is given as,

The above signal is passed through an envelope detector thus output of it is given by,



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The distortion produced by the quadrature component is,

e. The distortion d(t) reaches its worst possible value when a = 0.



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Analog Communication Unit4 Vtu

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