Single Sideband and Vestigial Sideband Modulation

Lesson 08EEE 352 Analog Communication Systems

Mansoor KhanEE Dept.

CIIT Islamabad Campus

Single-Sideband Modulation

• 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.

Single-Sideband Modulation

• SSB Signals SSB signals offer three major benefits:

Spectrum space is conserved and allows more signals to be

transmitted in the same frequency range.

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.

Occupied bandwidth space is narrower and noise in the signal is

reduced.

Amplitude Modulation: Single Sideband (SSB)

• The idea is to transmit either the USB or LSB

SSB (cont)

• Let m+(t) and m-(t) be the complex conjugates of m(t)

• Where mh(t) is unknown

)()(2

1)( tjmtmtm h

)()(2

1)( tjmtmtm h

SSB (cont)

• To determine mh(t) we know that

• Comparing above equation with the one on the previous slide

)()()( wuwMwM

)sgn(1)(2

1wwM

)sgn()(2

1)(

2

1wwMwM

)sgn()()( wwMtjmh

• Hence

• Applying duality prop. to pair 12 of table 3.1 yields

• Which gives

• This is the Hilbert transform of m(t)

)sgn()()( wwjMwMh

ttmtmwM

wjt

hh

1)()()(

)sgn(1

d

t

mtmh

)(1)(

Hilbert Transform

• We can Hilbert transform m(t) if we pass it through a filter with

• It follows that |H(w)|=1 and that

0 1

0 12

2

wej

wejj

j

)sgn()( jH

0for 2 and 0for 2)( wwh

Hilbert Transform (cont)

Mathematics

• From previous figure USB spectrum can be expressed as

• The inverse transform yields

• Substituting m+(t) and m-(t) from previous eqs

)()()( ccUSB wwMwwMw

tjwtjw

USBcc etmetmt

)()()(

twtmtwtmt chcUSB sin)(cos)()(

Mathematics (cont)

• Similarly we can show

• General SSB signal can expressed as

twtmtwtmt chcLSB sin)(cos)()(

twtmtwtmt chcSSB sin)(cos)()(

EXAMPLE

Generation of SSB Signals

• Two methods are used for the generation of SSB signals

– Selective Filtering Method

– Phase Shift Method

Selective Filtering Method

• Selective Filtering using filters with sharp cutoff characteristics. Sharp cutoff filters are difficult to design

• The audio signal spectrum has no dc component, therefore , the spectrum of the modulated audio signal has a null around the carrier frequency

• This means a less than perfect filter can do a reasonably good job of filtering the DSB to produce SSB signals

Filtering (cont)

Filtering (cont)

Phase Shift Method

Demodulation

• SSB signals can be coherently modulated in the same way as DSB-SC

Demodulation (cont)

• Since

Amplitude Modulation: Vestigial Sideband (VSB)

• The generation of SSB signals is rather difficult in practice

• To produce SSB signal from DSB signal ideal filters should be used to split the spectrum in the middle so that the bandwidth of bandpass signal is reduced by one half

• The selective filtering method demands dc null in the modulating signal

• The generation of DSB signals is simple, but DSB signals require twice the signal bandwidth of SSB

Vestigial Sideband (cont)

• Vestigial sideband (VSB) modulation was designed to provide a compromise between DSB and SSB

• In VSB instead of rejecting one sideband completely, we do a gradual cutoff of one sideband

• It can be detected with a synchronous detector in conjunction with an appropriate filter at the receiver output

• If a carrier is sent along the transmission, the VSB can be recovered by an envelope or a rectifier detector

Vestigial Sideband (cont)

• Generation of VSB is done by multiplying m(t) by 2cos(wct)and applying this signal to a filter Hi(w)

Vestigial Sideband (cont)

• Because the VSB is not a SSB, the bandwidth is 25 to 33% larger only, but it also makes the band-pass filter easier to realize

Vestigial Sideband (cont)

• The VSB signal spectrum is given by

• Where Hi(w) is VSB shaping filter, which allows the transmission of one sideband and suppresses the other sideband gradually

wHwwMwwMw iccVSB

Vestigial Sideband (cont)

• We can recover the message by using synchronous demodulation

• Multiply the incoming VSB signal by 2cos(wct)

Vestigial Sideband (cont)

• The product e(t) is given by

• The Fourier Transform of e(t)

• After Passing the signal from low pass filter

twtte cVSB cos2

cVSBcVSB wwwwwE

wHwwwwwM ocVSBcVSB

• Hence

BwwwHwwH

wHcici

o 2 ,1

wHwwHwwHwMwM ocici

Vestigial Sideband (cont)

Spectrum of Hi(w) and Ho(w)

Linearity of Amplitude Modulation

• In all types of AM discussed before, linearity is satisfied

• produces the modulated signal

• The modulation system following the superposition theorem of spectra is known as linear modulation system

– The theorem states that the sideband spectrum of a multiple tone AM signal is equal to the sum of the sideband spectrum of the individual tone modulation.

)()( 2211 tmktmk )()( 2211 tktk

AM Broadcasting

• Allocated the band 530 kHz – 1600 kHz (with minor variations)

• 10 kHz per channel. (9 kHz in some countries)

• More that 100 stations can be licensed in the same geographical area.

• Uses AM modulation (DSB + C)

AM Broadcasting

• In radio communication systems, the transmitted signal is very weak when it reaches the receiver, particularly when it has traveled over a long distance.

• The signal has also picked up noise of various kinds.

• Receivers must provide the sensitivity and selectivitythat permit full recovery of the original signal.

• The radio receiver best suited to this task is known as the superheterodyne receiver.

Ability of a receiver to pick up weak signal

Ability of a receiver to select a signal of a desired frequency while rejecting those on

closely adjacent frequencies

Sensitivity

– A communication receiver’s sensitivity, or ability to pick up weak signals, is a function of overall gain, the factor by which an input signal is multiplied to produce the output signal.

– The higher the gain of a receiver, the better its sensitivity.

– The more gain that a receiver has, the smaller the input signal necessary to produce a desired level of output.

– High gain in receivers is obtained by using multiple amplification stages.

Selectivity

– A receiver with good selectivity will isolate the desired signal and greatly attenuate/eliminates other signals.

– To improve selectivity is to add stages of amplification, both before and after demodulator

– Eg : Tuned Radio Frequency

Tuned Radio Frequency (TRF) Receiver

Figure: Tuned radio-frequency (TRF) receiver.

Tuned Radio Frequency (TRF) Receiver

– In the tuned radio frequency (TRF) receiver sensitivity is improved by adding a number of stages of RF amplification between the antenna and detector, followed by stages of audio amplification.

– The RF amplifier stages increase the amplitude /gain before it is applied to the detector.

– The recovered signal is amplified further by audio amplifiers, which provide sufficient gain to operate a loudspeaker.

Tuned Radio Frequency (TRF) Receiver

– The main problem with TRF receivers is tracking the tuned circuits.

– In a receiver, the tuned circuits must be made variable so that they can be set to the frequency of the desired signal.

– Another problem with TRF receivers is that selectivity varies with frequency.

Superheterodyne Receivers

• Superheterodyne receivers convert all incoming signals to a lower frequency, known as the intermediate frequency (IF), at which a single set of amplifiers is used to provide a fixed level of sensitivity and selectivity.

• Gain and selectivity are obtained in the IF amplifiers.

• The key circuit is the mixer, which acts like a simple amplitude modulator to produce sum and difference frequencies.

• The incoming signal is mixed with a local oscillator signal.

Superheterodyne Receiver Block Diagram

Antenna

IF Stage(intermediate frequency)

IF Amplifier

& IF BPF

X

Converter

(Multiplier)

a(t) b(t) d(t)

c(t)

Envelope Detector

Diode, Capacitor,

Resistor, & DC blocker

Audio Stage

Power amplifier

d(t) e(t) f(t) g(t)

Ganged RF

BPF and

Oscillator

RF Stage(radio frequency)

RF Amplifier

& RF BPF

Local

Oscillator

cos[(c+

IF)t]

Notes:

• With one knob, we are tuning the RF Filter

and the local oscillator.

•The filter are designed with high gain

to provide amplification as well.

Superheterodyne Receivers

RF Amplifier

– The antenna picks up the weak radio signal and feeds it to the RF amplifier

– provide some initial gain and selectivity and are sometimes called preselectors.

– Pick up desired station by tuning filter to right frequency band

Superheterodyne Receivers

Figure: Concept of a mixer.

Mixer

FromRF

output

Superheterodyne Receivers

Mixing Principles– Mixers accept two inputs: The signal to be translated to

another frequency is applied to one input, and the sine wave from a local oscillator is applied to the other input.

– Like an amplitude modulator, a mixer essentially performs a mathematical multiplication of its two input signals.

– The oscillator is the carrier, and the signal to be translated is the modulating signal.

– The output contains not only the carrier signal but also sidebands formed when the local oscillator and input signal are mixed.

Local Oscillator

• What should be the frequency of the local oscillator used for translation from RF to IF?

fLO = fc + fIF (up-conversion)

or fLO = fc fIF (down-conversion)

• Tuning ratio = fLO, max / fLO, min

• Up-Conversion: (1600 + 455) / (530+455) ≈ 2

• Down-Conversion: (1600–455) / (530–455) ≈ 12

• Easier to design oscillator with small tuning ratio.

Superheterodyne Receivers

IF Amplifiers

• The primary objective in the design of an IF stage is to obtain good selectivity.

• Narrow-band selectivity is best obtained at lower frequencies.

• At low frequencies, circuits are more stable with high gain.

Superheterodyne Receivers

IF Amplifiers– The output of the mixer is an IF signal containing

the same modulation that appeared on the input RF signal.

– The signal is amplified by one or more IF amplifier stages, and most of the gain is obtained in these stages.

– Selective tuned circuits provide fixed selectivity.– Since the intermediate frequency is usually lower

than the input frequency, IF amplifiers are easier to design and good selectivity is easier to obtain.

Superheterodyne Receivers

Demodulators

– The highly amplified IF signal is finally applied to the demodulator, which recovers the original modulating information.

– The demodulator may be a diode detector (for AM), a quadrature detector (for FM), or a product detector (for SSB).

– The output of the demodulator is then usually fed to an audio amplifier.

Superhetrodyne AM Receiver

Why IF

• At very high frequencies, signal processing circuitry performs poorly

• It is difficult to build amplifiers, filters, and detectors that can be tuned to different frequencies

• It is also used to improve frequency selectivity

Advantage Superhetrodyne

• Overcome equipment : cannot operate at high frequency

• Component operate at fixed frequency

– Optimize utilization

– Reduce cost

Radio AM Radio FM

Carrier range RF 0.535 – 1.605 MHz 88 – 108 MHz

IF 0.455 kHz 10.7 MHz

Bandwidth IF 10 kHz 200 kHz

AM Vs FM