Lecture-3 Amplitude Modulation: Single Side Band (SSB) Modulation

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1 Lecture-3 Amplitude Modulation: Single Side Band (SSB) Modulation 3.0 Introduction. 3.1 Baseband Signal SSB Modulation Frequency Domain Description Time Domain Description. 3. Single Tone SSB Modulation 3.3 SSB Generation (Modulators) Frequency Discrimination / Filter Metod 3.3. Pase Discrimination Metod 3.4 Demodulation or Detection of SSB Signals Coerent Detection 3.5 Advantages and Disadvantages 3.6 Applications 3.7 References 1

2 Amplitude Modulation: Single Side Band (SSB) Modulation 3.0 Introduction: As discussed earlier conventional AM and DSB-SC is wasteful from te band widt point of view and requires a bandwidt equal to twice te message signal bandwidt. In transmitted signal one alf is occupied by USB, wile te oter alf is occupied by LSB. How- ever te USB and LSB are unequally related to eac oter by virtue of teir symmetry about te carrier. More over te message signal information is available in bot sidebands. As per te transmission is concerned only one sideband is necessary to reproduce te baseband signal unequally at te receiver end. Tus in a conventional AM, if te carrier and one of te sidebands is suppressed, no information is lost. Te advantage of suc suppression is tat te transmission bandwidt required for tis case is equal to te message signal bandwidt only. A modulation sceme in wic one sideband is transmitted is known as SSB-SC or simply SSB modulation. 3.1 Baseband Signal SSB Modulation: Frequency Domain Description: Let te message signal mt () is band limited to W Hz and its Hilbert Transform is m () t. Fig 1(a) sows te spectrum of M( f ). Fig 1(c) sows its rigt alf M+ ( f ), and Fig 1(e) sows its left alf M-( f ). From Fig 1(c) and (e), we observe tat M+ ( f ) M ( f ) u ( f ) M ( f ) 1 1 sgn( f ) 1 M ( f ) j M ( f ) and M ( ) ( ) ( ) ( ) 1 1 sgn( ) 1 f M f u f M f f M ( f ) j M( f ) were M( f ) is F.T. of m() t (wic is Hilbert transform of mt ()), u( f ) and u( f ) are unit step functions in te directions of f and f. Now we can express te SSB signal in terms of mt () and m () t. USB ( f ) M+ ( f fc) M ( f fc) 1 1 M ( f fc) M ( f fc) M ( f fc) M ( f fc) j Similarly, LSB( f ) M+ ( f fc) M ( f fc) 1 1 M ( f fc) M ( f fc) M ( f fc) M ( f fc) j

3 3.1. Time Domain Description: Fig. 1 SSB spectra in terms of M+ ( f) and M-( f ). From te frequency sifting property, te inverse Fourier transform of te equations USB ( f ) and LSB ( f ) are as follows USB ( t) m( t)cos m( t)sin. Similarly, LSB ( t) m( t)cos m( t)sin Hence in general SSB signal can be expressed as SSB( t) m( t)cos m( t)sin, were minus sign applies to USB and te plus sign applied to LSB. If te is te magnitude of te carrier, ten SSB( t) m ( t)cos m( t)sin. 3

4 3. Single Tone SSB Modulation: We know tat te SSB( t) m ( t)cos m( t)sin. Let a single tone message single be m( t) Amcos ωmt. Recall tat te Hilbert Transform delays te pase of eac spectral components by /. Ten te H.T of te message signal is given by m ( t) Hilbert Transform m( t) cosωmt sin ωmt Hence Fig. Frequency spectrum of single Tone SSB Modulation SSB( t ) A c A m cos ω m t cos ω c t sin ω m t sin ω c t A c A m cos( ω c ω m) t Tus USB ( t ) A c A m cos( ω c ω m) t and LSB ( t ) A c A m cos( ω c ω m) t. Te spectrum of Single Tone SSB Modulation is illustrated in Fig. 3.3 SSB Generation (Modulators): From te foregoing discussion it is seen tat SSB-SC wave can be described in frequency domain as well as time-domain for arbitrary baseband signal. A closer examination of te two descriptions reveals tat an SSB can be generated by taking elp of eiter representation. Tus SSB waves can be generated by frequency discrimination metod and by te pase discrimination metod based on frequency domain and time domain descriptions of SSB respectively Frequency Discrimination / Filter Metod : An SSB modulator based on frequency discrimination consists of a balanced modulator and a filter wic is designed to pass te desired sideband and suppress te undesired one. Tis metod is also known as filter metod of generation of SSB signal. Te most severe requirement of tis metod of SSB generation arises from te desired sideband by twice te lowest frequency component of te modulating signal. A typical arrangement for generating SSB signal by frequency discrimination metod is sown in Fig 3. For a satisfactory performance of te system te following two requirements ave to be satisfied. 4

5 1. Te pass band of te filter sould be same as tat of te desired sideband.. Te transition band of te filter sould not exceed twice te minimum frequency component present in te baseband signal. Tis kind of frequency discrimination is possible by using igly selective filter, wic can be realized using ig Q (on te range of 1000 to 000) crystal resonator. Tere is anoter problem associated wit te generation of SSB by frequency discrimination metod wen te SSB wave occupies a frequency band wic is muc larger tan te baseband signal. For example, consider te translation of voice signals (approximately 300 to 3400 Hz) to ig frequency range of radio spectrum. In suc cases it is difficult to design a filter to pass te desired band and reject te oter using te simple arrangement. To overcome tis difficulty, multistage modulation and filtering sceme may be used to ease te filtering requirements. Tis is sown in Fig.3, were two stage modulation as been used. In tis arrangement te SSB wave at te first filter output is used as te modulating wave for te second balanced modulator, wic produces DSB-SC wave wit a spectrum tat is symmetrically spaced around te second carrier. Te frequency separation between te two sidebands of te DSB-SC wave is effectively twice te first carrier frequency. Tis enables te easy removal of te unwanted sidebands. Te following example will make tis more clear. Fig.3 Block diagram of Frequency discrimination SSB Modulation Consider tat we desire to generate an SSB signal wit a carrier of 10 MHz and te baseband signal consists of voice signal occupying frequency band 300 Hz to 3kHz. Suppose we use a two stage modulation sceme in wic we select first carrier frequency f 1 =100 khz and te second one as f = 10 MHz. Stage 1: In te first stage, a balanced modulator wit carrier frequency f 1 =100 khz is used for generation of DSB-SC wave. Te spectrum of te DSB-SC wave s 1 (t) appearing at te output of 5

6 first balanced modulator as a lower sideband occupying te frequency band 97 to 99.7 khz and te upper sideband occupying to 103 khz. By assuming tat only USB occupying to 103 khz is selected resulting in te SSB wave. In order to acieve tis, te first band pass filter (transfer function H 1 ) must ave a lower transition band from 99.7 to khz, so as to suppress te LSB. Te transition band is 600 Hz as sown in Fig 4. Tis requirement wic is 6% of te center frequency can met easily. Fig.4 SSB generation using two stage filtering metod. Stage : In te second stage, a balanced modulator wit carrier frequency f =10 MHz is used for generation of DSB-SC wave. Te spectrum of te DSB-SC wave s (t) appearing at te output of 6

7 second balanced modulator as a lower sideband occupying te frequency band to MHz and te upper sideband occupying to MHz. Here again assuming tat only USB occupying to MHz is selected by filtering using second BPF (transfer function H ) resulting in te desired SSB wave. Te separation between te lowest frequency USB and igest frequency LSB is 00.6 khz in tis case. Tus te transition band of second filter is to be adjusted is 00.6 khz wic is approximately % of center frequency can be easily designed. Tus by multistage modulation and filtering sceme, a SSB wave wit desired carrier wave cane easily designed. Tis would not ave been possible in te single stage sceme. For example in single stage modulation sceme, one requires te transition band of te filter to be adjusted witin 600 Hz at a center frequency of 10 MHz, a percentage frequency cange of 0.006% of te carrier frequency. Filters suc sarp selectivity are extremely difficult to design. Hence multistage modulation and filtering sceme is muc useful to generate SSB wave Pase Discrimination Metod: Tis metod is based on te time domain description of SSB signal. It can easily seen tat SSB signal can be generated by using two separate simultaneous DSB modulation and combining tem suitably depending on te desired sideband. A typical arrangement is sown in Fig. It consists of two balanced modulators wit carrier wave in-pase quadrature to eac oter. Te incoming baseband signal m(t) is applied to te Balanced Modulator A, producing a DSB-SC wave tat translates te spectrum of m(t) symmetrically spaced about te carrier frequency fc. Te pase sifted version (Hilbert Transform) of m(t), m () t is applied to te Balanced Modulator-B producing a DSB-SC wave tat contains sidebands aving identical amplitude spectrum as tose of modulator A, but of different relative pase Vector addition or subtraction of te Fig.4 Block diagram of Pase Discrimination metod two. modulators outputs in te summing device results in cancellation on one set of sidebands and reinforcement of te oter set. Te use of Modulator-B output wit a plus sign at te 7

summing junction yields an SSB wave wit only one lower sideband. In tis way eiter form of SSB wave can be generated. Tis arrangement is also known as Hartley modulator.

8 summing junction yields an SSB wave wit only one lower sideband. In tis way eiter form of SSB wave can be generated. Tis arrangement is also known as Hartley modulator. Matematical Discription: Te output of Balanced Modulator-A is given by m( t)cos ωt c. Similarly te output of Balanced Modulator-B is m ( t)sin ωt c, were m () t and sin ωt c are Hilbert Transforms of mt () and cosωc trespectively. Ten te output of te summing junction is given by SSB( t) m( t)cos m( t)sin. Te upper side band SSB signal is USB ( t) m( t)cos m( t)sin, and Te lower side band SSB signal is LSB ( t) m( t)cos m( t)sin. Te generation of SSB wave by Pase Sifting metod seems to be simpler compared to frequency discrimination metod. In practice owever, tis is not so. Te most difficult part is peraps te design of wideband 90 0 pase sifter generate te Hilbert transform m () t of te baseband signal m(t). For tis purpose, we require a network tat sifts te pase angle of every frequency component of m(t) by 90 0, but leaves te amplitude un-canged. In practice it is difficult to design suc a network over a wide frequency range of te modulating wave. However it is possible to ave required constant pase difference wit any desired tolerance over any prescribed frequency range by using a pase sifting network in eac modulation pat. 3.4 Demodulation or Detection of SSB Signals: Like DSB-SC modulation signal can be demodulated by syncronous detection. Te incoming signal is multiplied wit locally generated sinusoidal signal and ten filtered by low pass filter. Te filter is cosen to ave te same bandwidt as te message signal bandwidt W or somewat larger. It is necessary tat local oscillator is exactly syncronized wit te carrier in pase and frequency Coerent Detection: Te arrangement is similar to one used in detecting DSB-SC signal and is sown in Fig. For te purpose of analysis, let us consider te input to be SSB wit upper sideband given by Fig. Block diagram of Coerent Detection USB ( t) m( t)cos m ( t)sin 8

9 Let te local oscillator generates syncronous carrier cos ωt c. Ten te output of te product modulator is given by sc( t) ( )cos ( )sin cos m t m t m() t m () 1 cos t sin m() t A c mt ( )cos ω c t m ( t )sin ω c t 4 4 Te first term in te equation is te desired message signal wit magnitude /4, wile te second term represents anoter SSB wave corresponding to a carrier frequency ωc (or fc ). Te desired signal can be obtained by removing te ig frequency component using a low pass filter. Terefore te output of LPF is te baseband signal. It is to be noted tat te local oscillator at te receiver must be syncronized in bot frequency and pase wit te transmitted carrier signal. Any discrepancy in te frequency and pase of local carrier give rise to a distortion in te detector output. It is tus instructive to examine te detected output wen te local carrier frequency and pase are different from te carrier of te incoming DSB-SC signal. We consider te following two situations. 1. Te local oscillator as an ideal frequency, but arbitrary pase difference measured wit respect to te carrier is referred to as Pase Error ( 0; f 0 ).. Te local oscillator as identical pase but a difference frequency wit respect to carrier is referred to as Frequency error ( 0; f 0 ). (a) Pase Discrepancy ( 0; f 0 ): Te effect of pase discrepancy can be understood by assuming te local oscillator signal to be cos( ωt c ). Ten te output of te product modulator is sc( t) ( )cos ( )sin cos( ) m t m t ( )cos cos( ) ( )sin cos( ) mt ω c t ω c t m t ω c t ω c t m() t m () cos cos t sin sin A m( t)cos m( t)sin c m( t)cos m( t)sin 4 4 9

10 Te LPF removes te second term wic is ig frequency component and te output of LPF. Tus te demodulated signal contains an 4 becomes so( t) m( t)cos m ( t)sin unwanted component m ( t)sin wic cannot be removed by filtering. Tus tis term in turn gives rise to a pase distortion. Tis distortion is not usually very serious for voice communication because uman ear is relatively very insensitive to pase canges. However in transmission of music or video signals, tis distortion may not always acceptable. (b) Frequency Discrepancy ( 0; f 0 ): Let te local oscillator is cos ( fc f ) t, were f is frequency error. sc( t) ( )cos ( )sin cos ( ) m t m t fc f t ( )cos cos ( ) ( )sin cos ( ) mt ω c t f c f t m t ω c t f c f t m() t m () cos cos ( ) t ft fc f t sin ( fc f ) t sin f m ( t )cos ft m ( t )sin f t m( t)cos ( fc f ) t m( t)sin ( fc f ) t 4 4 Te LPF removes te ig frequency term (second term). Ten te output of te LPF is given by so( t) m( t)cos ft m( t)sin ft 4 It can be observed tat te demodulated signal is no longer corresponds to te baseband signal. Altoug f is very small compared to te carrier frequency, te value of f is not negligible in comparison wit te frequency of te base band signal. For example, a small fraction of te carrier frequency may become comparable wit te frequencies present in te baseband signal. 3.5 Advantages and Disadvantages: Te advantages and disadvantages of SSB modulation are briefly outlined as below : Advantages: (a) More bandwidt efficient tan DSB-SC. SSB requires bandwidt equivalent to message signal bandwidt. (b) Carrier power and one sideband power saving. Power saving 83.33% for 100% modulation. (c) Reduced interference of noise, because of low bandwidt. 10

11 3.5.: Disadvantages: (a) Generation and reception is complicated. (b) Te SSB transmitter and receiver need to ave excellent frequency stability. A sligt cange in frequency will distort bot te transmitted and received signals. Terefore it is needed ideal filters in implementations. (c) Cannot be used signal wit DC. 3.6 Applications: (a) SSB used in applications were te power saving and low bandwidt 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. H Taub & D. Scilling, Gautam Sae, Principles of Communication Systems, TMH, 007, 3rd Edition.. Simon Haykin, Principles of Communication Systems,Jon Wiley, nd Ed. 3. B.P. Lati and Zi Ding, Modern Digital and Analog Communication Systems, International 4 t Edition, Oxford University Press, George Kennedy, Electronic Communication Systems, 3rd edition, Tata McGraw-Hill Edition. 5. Wayne Tomasi, Electronic Communication Systems- fundamentals troug advanced, 5 t edition, Pearson Education Inc, Jon G. Proakis, Masond, Salei, Fundamentals of Communication Systems, PEA,

Outline. Communications Engineering 1

Outline. Communications Engineering 1 Outline Introduction Signal, random variable, random process and spectra Analog modulation Analog to digital conversion Digital transmission through baseband channels Signal space representation Optimal