linear modulation: lecture-3 amplitude modulation: · pdf filedr. m. venu gopala rao,...

Dr. M. Venu Gopala Rao, Professor, Dept. of ECE, KL University.

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Linear Modulation: Lecture-3

Amplitude Modulation: Single Side Band (SSB) Modulation

3.0 Introduction.

3.1 Baseband Signal SSB Modulation.

3.1.1 Frequency Domain Description.

3.1.2 Time Domain Description.

3.2 Single Tone SSB Modulation

3.3 SSB Generation (Modulators)

3.3.1 Frequency Discrimination / Filter Method

3.3.2 Phase Discrimination Method

3.4 Demodulation or Detection of SSB Signals

3.4.1 Coherent Detection

3.5 Advantages and Disadvantages

3.6 Applications

3.7 References

Objectives:

Understanding the Hilbert Transform and inverse Hilbert Transform

Define and describe AM Single Sideband Suppressed Carrier (SSB-SC)

Develop the mathematical expression for SSB using Hilbert Transform

Understanding the SSB in frequency domain

Compare SSB transmission to conventional AM and DSB-SC

Explain advantages and disadvantages of SSB transmission

Describe the operation of Filter and Phase Discrimination Method

Describe the coherent SSB detection


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Single Side Band (SSB) Modulation

3.0 Introduction: As discussed earlier conventional AM and DSB-SC is wasteful from the band

width point of view and requires a bandwidth equal to twice the message signal bandwidth. In

transmitted signal one half is occupied by USB, while the other half is occupied by LSB. How-

ever the USB and LSB are unequally related to each other by virtue of their symmetry about the

carrier. More over the message signal information is available in both sidebands. As per the

transmission is concerned only one sideband is necessary to reproduce the baseband signal

unequally at the receiver end. Thus in a conventional AM, if the carrier and one of the sidebands

is suppressed, no information is lost. The advantage of such suppression is that the transmission

bandwidth required for this case is equal to the message signal bandwidth only. A modulation

scheme in which one sideband is transmitted is known as SSB-SC or simply SSB modulation.

Ex1: Calculate the percentage power saving when the carrier and one of the sidebands are

suppressed in AM wave modulated to a depth of (a) 100 %, and (b) 50 %.

Solution: (a) We Know that 2

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ctP P

.

For 1 , 1.5 ctP P Watts,

Then the total sideband power 1.5 0.5c c c ctSBP P P P P P Watts

0.5 / 2 0.25c cLSB USBP P P P Watts

Power saving = Carrier power + one sideband = cP + orLSB USB

P P = 1.25 cP Watts

Percentage power saving = Power saving 1.25

100 100 100 83.33%1.25

1.5 1.5c

ct

P

P P X X X

(b) For 0.5 , 2 20.5

1 1 1.1252 2

c c ctP P P P

Total sideband power 1.125 0.125c c c ctSBP P P P P P Watts

0.125 / 2 0.0625c cLSB USBP P P P Watts

Power saving = Carrier power + one sideband =

or 0.0625 1.0625c c c cLSB USBP P P P P P Watts


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Percentage power saving = Power saving

100tP

X

1.0625 1.0625

100 100 94.44%1.125 1.125

c

c

P

P X X

3.1 Baseband Signal SSB Modulation: We will study first the SSB baseband modulation and

then single tone modulation.

3.1.1 Frequency Domain Description:

Let the message signal ( )m t is band limited to ’W’ Hz and its Hilbert Transform is ( )hm t .

Fig 1(a) shows the spectrum of ( )M f . Fig 1(c) shows its right half ( )+M f , and Fig 1(e) shows

its left half ( )-M f . From Fig 1(c) and (e), we observe that

1 1

( ) ( ) ( ) ( ) 1 sgn( ) ( ) ( )+2 2

hM f M f f M f f M f j M fu and

1 1

( ) ( ) ( ) ( ) 1 sgn( ) ( ) ( )2 2

hM f M f f M f f M f j M fu

where ( )hM f is F.T. of ( )hm t (which is Hilbert transform of ( )m t ), ( )fu and ( )fu are unit

step functions in the directions of f and f . Now we can express the SSB signal in terms of

( )m t and ( )hm t .

( ) ( ) ( )+

1 1( ) ( ) ( ) ( )

2 2

USB

h h

f M f f M f fc c

M f f M f f M f f M f fc c c cj

Similarly ,

( ) ( ) ( )+

1 1( ) ( ) ( ) ( )

2 2

LSB

h h

f M f f M f fc c

M f f M f f M f f M f fc c c cj

3.1.2 Time Domain Description:

From the frequency shifting property, the inverse Fourier transform of the equations

( )USB f and ( )LSB f are as follows

( ) ( )cos ( )sinUSB ht m t ω t m t ω tc c .

Similarly, ( ) ( )cos ( )sinLSB ht m t ω t m t ω tc c


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Hence in general SSB signal can be expressed as

( ) ( )cos ( )sinSSB ht m t ω t m t ω tc c ,

where minus sign applies to USB and the plus sign applied to LSB. If the Ac is the magnitude of

the carrier, then ( ) ( )cos ( )sinSSB ht A m t ω t m t ω tc c c .

Fig. 1 SSB spectra in terms of ( )+M f and ( )-M f .


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3.2 Single Tone SSB Modulation:

We know that the

( ) ( )cos ( )sinSSB ht A m t ω t m t ω tc c c .

Let a single tone message single be

( ) cosm t A ω tm m . Recall that the Hilbert

Transform delays the phase of each spectral

components by / 2 . Then the H.T of the

message signal is given by

( ) Hilbert Transform ( )

cos sin2

hm t m t

ω t ω tm m

Hence Fig.2 Frequency spectrum of single Tone SSB Modulation

( ) cos cos sin sin cos( )SSB t A A ω t ω t ω t ω t A A ω ω tc m m c m c c m c m

Thus ( ) cos( )USB t A A ω ω tc m c m and ( ) cos( )LSB t A A ω ω tc m c m . The spectrum of

Single Tone SSB Modulation is illustrated in Fig 2.

3.3 SSB Generation (Modulators): From the foregoing discussion it is seen that SSB-SC wave

can be described in frequency domain as well as time-domain for arbitrary baseband signal. A

closer examination of the two descriptions reveals that an SSB can be generated by taking help

of either representation. Thus SSB waves can be generated by frequency discrimination method

and by the phase discrimination method based on frequency domain and time domain

descriptions of SSB respectively.

3.3.1 Frequency Discrimination / Filter Method : An SSB modulator based on frequency

discrimination consists of a balanced modulator and a filter which is designed to pass the desired

sideband and suppress the undesired one. This method is also known as filter method of

generation of SSB signal. The most severe requirement of this method of SSB generation arises

from the desired sideband by twice the lowest frequency component of the modulating signal. A

typical arrangement for generating SSB signal by frequency discrimination method is shown in

Fig 3. For a satisfactory performance of the system the following two requirements have to be

satisfied.


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1. The pass band of the filter should be same as that of the desired sideband.

2. The transition band of the filter should not exceed twice the minimum frequency

component present in the baseband signal.

This kind of frequency discrimination is possible by using highly selective filter, which can

be realized using high Q (on the range of 1000 to 2000) crystal resonator.

There is another problem associated with the generation of SSB by frequency discrimination

method when the SSB wave occupies a frequency band which is much larger than the baseband

signal. For example, consider the translation of voice signals (approximately 300 to 3400 Hz) to

high frequency range of radio spectrum. In such cases it is difficult to design a filter to pass the

desired band and reject the other using the simple arrangement.

To overcome this difficulty, multistage modulation and filtering scheme may be used to ease

the filtering requirements. This is shown in Fig.3, where two stage modulation has been used. In

this arrangement the SSB wave at the first filter output is used as the modulating wave for the

second balanced modulator, which produces DSB-SC wave with a spectrum that is

symmetrically spaced around the second carrier. The frequency separation between the two

sidebands of the DSB-SC wave is effectively twice the first carrier frequency. This enables the

easy removal of the unwanted sidebands. The following example will make this more clear.

Fig.3 Block diagram of Frequency discrimination SSB Modulation

Consider that we desire to generate an SSB signal with a carrier of 10 MHz and the baseband

signal consists of voice signal occupying frequency band 300 Hz to 3kHz. Suppose we use a two

stage modulation scheme in which we select first carrier frequency f1=100 kHz and the second

one as f2 = 10 MHz.


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Stage 1: In the first stage, a balanced modulator with carrier frequency f1=100 kHz is

used for generation of DSB-SC wave. The spectrum of the DSB-SC wave s1(t) appearing at the

output of first balanced modulator has a lower sideband occupying the frequency band 97 to 99.7

kHz and the upper sideband occupying 100.3 to 103 kHz. By assuming that only USB

occupying 100.3 to 103 kHz is selected resulting in the SSB wave. In order to achieve this, the

first band pass filter (transfer function H1) must have a lower transition band from 99.7 to 100.3

kHz, so as to suppress the LSB. The transition band is 600 Hz as shown in Fig 4. This

requirement which is 6% of the center frequency can met easily.

Fig.4 SSB generation using two stage filtering method.


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Stage 2: In the second stage, a balanced modulator with carrier frequency f2=10 MHz

is used for generation of DSB-SC wave. The spectrum of the DSB-SC wave s2(t) appearing at

the output of second balanced modulator has a lower sideband occupying the frequency band

9.897 to 9.8997 MHz and the upper sideband occupying 10.1003 to10.1030 MHz. Here again

assuming that only USB occupying 10.1003 to10.1030 MHz is selected by filtering using

second BPF (transfer function H2) resulting in the desired SSB wave.

The separation between the lowest frequency USB and highest frequency LSB is 200.6 kHz in

this case. Thus the transition band of second filter is to be adjusted is 200.6 kHz which is

approximately 2% of center frequency can be easily designed. Thus by multistage modulation

and filtering scheme, a SSB wave with desired carrier wave cane easily designed. This would not

have been possible in the single stage scheme. For example in single stage modulation scheme,

one requires the transition band of the filter to be adjusted within 600 Hz at a center frequency of

10 MHz, a percentage frequency change of 0.006% of the carrier frequency. Filters such sharp

selectivity are extremely difficult to design. Hence multistage modulation and filtering scheme is

much useful to generate SSB wave.

3.3.2 Phase Discrimination Method: This method is based on the time domain description of

SSB signal. It can easily seen that SSB signal can be generated by using two separate

simultaneous DSB modulation and combining them suitably depending on the desired sideband.

A typical arrangement is shown in Fig. It consists of two balanced modulators with carrier wave

in-phase quadrature to each other. The incoming baseband signal m(t) is applied to the Balanced

Modulator ‘A’, producing a DSB-SC wave that

translates the spectrum of m(t) symmetrically

spaced about the carrier frequency fc . The phase

shifted version (Hilbert Transform) of m(t),

( )hm t is applied to the Balanced Modulator-B

producing a DSB-SC wave that contains

sidebands having identical amplitude spectrum

as those of modulator A, but of different relative

phase Fig.4 Block diagram of Phase Discrimination method


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Vector addition or subtraction of the two modulators outputs in the summing device results

in cancellation on one set of sidebands and reinforcement of the other set. The use of Modulator-

B output with a plus sign at the summing junction yields an SSB wave with only one lower

sideband. In this way either form of SSB wave can be generated. This arrangement is also known

as Hartley modulator.

Mathematical Discription:

The output of Balanced Modulator-A is given by ( )cosA m t ω tc c . Similarly the output of

Balanced Modulator-B is ( )sinhA m t ω tc c , where ( )hm t and sinω tc are Hilbert Transforms of

( )m t and cosω tc respectively.

Then the output of the summing junction is given by

( ) ( )cos ( )sinSSB ht A m t ω t A m t ω tc c c c .

The upper side band SSB signal is ( ) ( )cos ( )sinUSB ht A m t ω t A m t ω tc c c c , and

The lower side band SSB signal is ( ) ( )cos ( )sinLSB ht A m t ω t A m t ω tc c c c .

The generation of SSB wave by Phase Shifting method seems to be simpler compared to

frequency discrimination method. In practice however, this is not so. The most difficult part is

perhaps the design of wideband 900 phase shifter generate the Hilbert transform ( )hm t of the

baseband signal m(t). For this purpose, we require a network that shifts the phase angle of every

frequency component of m(t) by 900, but leaves the amplitude un-changed. In practice it is

difficult to design such a network over a wide frequency range of the modulating wave. However

it is possible to have required constant phase difference with any desired tolerance over any

prescribed frequency range by using a phase shifting network in each modulation path.

3.4 Demodulation or Detection of SSB Signals: Like DSB-SC modulation signal can be

demodulated by synchronous detection. The incoming signal is multiplied with locally generated

sinusoidal signal and then filtered by low pass filter. The filter is chosen to have the same

bandwidth as the message signal bandwidth ‘W’ or somewhat larger. It is necessary that local

oscillator is exactly synchronized with the carrier in phase and frequency.


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3.4.1 Coherent Detection: The arrangement is

similar to one used in detecting DSB-SC signal

and is shown in Fig. For the purpose of analysis,

let us consider the input to be SSB with upper

sideband given by Fig. Block diagram of Coherent Detection

( ) ( )cos ( )sin2

USB hAc

t m t ω t m t ω tc c

Let the local oscillator generates synchronous carrier cosω tc . Then the output of the product

modulator is given by

( ) ( ) cos ( )sin cos2

( )( )1 cos 2 sin 2

2 2 2

( )( )cos 2 ( )sin 2

4 4

h

h

h

cAc

s t m t ω t m t ω t ω tc c c

m tA m tcω t ω tc c

A m t Ac cm t ω t m t ω tc c

The first term in the equation is the desired message signal with magnitude / 4Ac , while the

second term represents another SSB wave corresponding to a carrier frequency 2ωc (or 2 fc ).

The desired signal can be obtained by removing the high frequency component using a low pass

filter. Therefore the output of LPF is the baseband signal.

It is to be noted that the local oscillator at the receiver must be synchronized in both frequency

and phase with the transmitted carrier signal. Any discrepancy in the frequency and phase of

local carrier give rise to a distortion in the detector output. It is thus instructive to examine the

detected output when the local carrier frequency and phase are different from the carrier of the

incoming DSB-SC signal. We consider the following two situations.

1. The local oscillator has an ideal frequency, but arbitrary phase difference measured with

respect to the carrier is referred to as ‘Phase Error’ ( 0; 0f ).

2. The local oscillator has identical phase but a difference frequency with respect to carrier

is referred to as ‘Frequency error’ ( 0; 0f ).


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(a) Phase Discrepancy ( 0; 0f ): The effect of phase discrepancy can be

understood by assuming the local oscillator signal to be cos( )ω tc . Then the output of the

product modulator is

( ) ( ) cos ( )sin cos( )2

( )cos cos( ) ( )sin cos( )2

( )( )cos cos 2 sin 2 sin

2 2 2

( )cos ( )sin ( )cos 2 ( )sin 24 4

h

h

h

h h

cAc

s t m t ω t m t ω t ω tc c c

Acm t ω t ω t m t ω t ω tc c c c

m tA m tcω t ω tc c

A Ac cm t m t m t ω t m t ω tc c

The LPF removes the second term which is high frequency component and the output of LPF

becomes ( ) ( )cos ( )sin4

hoAc

s t m t m t . Thus the demodulated signal contains an

unwanted component ( )sinhm t which cannot be removed by filtering. Thus this term in turn

gives rise to a phase distortion. This distortion is not usually very serious for voice

communication because human ear is relatively very insensitive to phase changes. However in

transmission of music or video signals, this distortion may not always acceptable.

(b) Frequency Discrepancy ( 0; 0f ): Let the local oscillator is cos2 ( )f f tc , where

f is frequency error.

( ) ( )cos ( )sin cos 2 ( )2

( )cos cos 2 ( ) ( )sin cos 2 ( )2

( )( )cos 2 cos 2 (2 ) sin 2 (2 ) sin 2

2 2 2

( )cos 2 ( )sin 24

h

h

h

h

cAc

s t m t ω t m t ω t f f tc c c

Acm t ω t f f t m t ω t f f tc c c c

m tA m tcft f f t f f t fc c

Acm t ft m t f

( )cos 2 (2 ) ( )sin 2 (2 )4

hAc

t m t f f t m t f f tc c

The LPF removes the high frequency term (second term). Then the output of the LPF is given by

( ) ( )cos 2 ( )sin 24

hoAc

s t m t ft m t ft


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It can be observed that the demodulated signal is no longer corresponds to the baseband

signal. Although f is very small compared to the carrier frequency, the value of f is not

negligible in comparison with the frequency of the base band signal. For example, a small

fraction of the carrier frequency may become comparable with the frequencies present in the

baseband signal.

3.5 Advantages and Disadvantages: The advantages and disadvantages of SSB modulation are

briefly outlined as below.

3.5.1: Advantages:

(a) More bandwidth efficient than DSB-SC. SSB requires bandwidth equivalent to message

signal bandwidth.

(b) Carrier power and one sideband power saving. Power saving 83.33% for 100% modulation.

(c) Reduced interference of noise, because of low bandwidth.

3.5.2: Disadvantages:

(a) Generation and reception is complicated.

(b) The SSB transmitter and receiver need to have excellent frequency stability. A slight

change in frequency will distort both the transmitted and received signals. Therefore it is

needed ideal filters in implementations.

(c) Cannot be used signal with DC.

3.6 Applications:

(a) SSB used in applications where the power saving and low bandwidth requirements are

important.

(b) Widely used in point to point communications. Land or Air Mobile Communications,

Telemetry, Military, Navigation and Amateur Radio.

3.7 References:

1. B.P. Lathi and Zhi Ding, “Modern Digital and Analog Communication Systems”, International

4th Edition, Oxford University Press, 2010.

2. Wayne Tomasi, ‘Electronic Communications Systems fundamentals through advanced’,

Pearson Education, fifth edition, 2011.

3. H Taub & D. Schilling, Gautam Saha, ”Principles of Communication Systems, TMH, 2007, 3rd

Edition.


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KL University, Vaddeswaram, Dept. of ECE

Analog Communications 11 EC-207

SSB-SC- Question Bank

SSB Basic Theory:

1. How a Hilbert transform is useful for development of SSB signal? Illustrate with necessary

mathematical equations and waveforms. Determine its spectrum and sketch.

2. Explain the frequency domain description of the SSB-SC wave.

3. Develop a SSB signal for a single tone modulating signal. Determine and sketch the

spectrum.

4. Explain with diagram of single sideband system. Compare the relative power distribution

and frequency spectra of conventional AM and single sideband (SSB) systems.

5. Draw waveform of SSBFC and SSBSC signal. Compare single sideband transmission with

conventional AM.

6. Compare with waveforms following AM transmission systems

(i) DSB-FC (ii) DSB-SC (iii) SSB-SC

7. Discuss the virtues and limitations of single sideband transmission.

SSB Modulation:

1. Discuss the SSB modulation techniques in brief.

SSB Demodulation:

1. Discuss the effect of frequency and phase error in demodulator of SSB-SC wave using

synchronous detector.

2. Explain how coherent detection accomplishes the demodulation of SSB signal.

3. Draw the block diagram of phase cancellation SSB generator and explain how the carrier

and unwanted side band are suppressed.

SSB Problems:

1. A 400 W carrier is modulated on a depth of 75%. Calculate the total power in the modulated

wave in the following forms of AM.

(i) A.M. (ii) DSB-SC (ii) SSB-SC

Ans: 512W, 112W and 56W


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2. For two tone test signal of 1.5 KHz and 3 KHz and a carrier frequency of 100 KHz,

determine and draw the output spectrum if only the upper sideband is transmitted. Also find

the transmission power and bandwidth, if the load resistance is 50 Ω.

Ans: The output spectrum consists of 101.5 KHz and 103 KHz.

The transmission power = 0.5 Watts

The transmission bandwidth = 6 KHz.

3. An SSB AM signal is generated by modulating an 800 kHz carrier by the message signal

( ) cos2000 2sin 2000m t t t . Assume that the amplitude of the carrier is Ac = 100.

(a) Determine the Hilbert transform of the message signal.

(b) Find the time-domain expression for the lower sideband SSB (LSSB) AM signal.

(c) Determine the spectrum of the LSSB AM signal.

Ans:

linear modulation: lecture-3 amplitude modulation: · pdf filedr. m. venu gopala rao,...

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