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Single Sideband Modulation (SSB) - Ryerson University

S(t)>Vc: diode conducts (forward biased) C charges quickly to the max value ofs(t) s(t)<Vc: diode does not conduct (reverse biased) C discharges overRLuntils(t)>Vc The output of the ED is then lowpass filtered to eliminate the ripple, followed byblocking out the DC Sideband Modulation (SSB)Standard AM and DSB-SC techniques are wasteful of bandwidth because they both requiretransmission bandwidth of2 BHz, whereBis the bandwidth of the baseband modulatingsignalm(t).In both cases the transmission bandwidth (BT) is occupied by the upper Sideband (USB) andlower Sideband (LSB).Observations USB and LSB are uniquely related to each other, as they are symmetric , to transmit information contained withinm(t)we used to transmit only oneside band.

Single Sideband Modulation (SSB) Standard AM and DSB-SC techniques are wasteful of bandwidth because they both require transmission bandwidth of 2B Hz, where B is the bandwidth of the baseband modulating signal m(t). In both cases the transmission bandwidth (B T) is occupied by the upper sideband (USB) and lower sideband (LSB). Observations

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Transcription of Single Sideband Modulation (SSB) - Ryerson University

1 S(t)>Vc: diode conducts (forward biased) C charges quickly to the max value ofs(t) s(t)<Vc: diode does not conduct (reverse biased) C discharges overRLuntils(t)>Vc The output of the ED is then lowpass filtered to eliminate the ripple, followed byblocking out the DC Sideband Modulation (SSB)Standard AM and DSB-SC techniques are wasteful of bandwidth because they both requiretransmission bandwidth of2 BHz, whereBis the bandwidth of the baseband modulatingsignalm(t).In both cases the transmission bandwidth (BT) is occupied by the upper Sideband (USB) andlower Sideband (LSB).Observations USB and LSB are uniquely related to each other, as they are symmetric , to transmit information contained withinm(t)we used to transmit only oneside band.

2 As far as demodulation is concerned, we can coherently demodulate SSB (as we did theDSB-SC signal) by multiplying SSB withcos( ct)followed by domain representation of SSB signalsGiven the baseband signalm(t)with spectrumM( ), the spectrum of DSB-SC and SSB areshown below (textbook, p174):30In either of the USB/LSB cases we can demodulate and extractm(t)fromSSB+orSSB ,by regular coherent demodulation, shown as (omega)DSB SCSSB+ (USB)SSB (LSB)Figure 6: SSB - frequency m(t)USB signalspectrum of carrierfc 2 fcspectrum @ C2 fc 2 fc2 fcspectrum @ inputfcFigure 7: SSB demodulation, frequency domain representation of SSB signals Hilbert TransformFirst, define some notations.

3 M(f),m(t)baseband modulating signal (real) M+(f),m+(t)upper Sideband (USB) signal (cannot be real) M (f),m (t)lower Sideband (LSB) signal (cannot be real)33 Time domain representation of SSB signals - Hilbert TransformFrom the spectrum relationship, we haveM+(f)=M(f)u(f)=M(f)12[1 +sgn(f)] =12[M(f)+jMh(f)](11)M (f)=M(f)u( f)=M(f)12[1 sgn(f)] =12[M(f) jMh(f)](12)where12jMh(f)=12M(f)sgn(f)(13 )which impliesMh(f)=M(f) [ jsgn(f)](14)Considering the Fourier transform pair1/( t) jsgn(f), taking inverse Fouriertransform then we havemh(t)=m(t) 1 t=1 m( )t d (15)34On the other hand, the transfer function can be written asH(f)= jsgn(f)= jf 0jf<0H(f): wideband phase shifter (Hilber Transform).

4 Thus, if we delay the phase of every component ofm(t)by /2(without changing itsamplitude), the resulting signal ismh(t), the Hilbert transform ofm(t). Therefore, a Hilberttransformer is an ideal phase shifter that shifts the phase of every spectral component by on the Hilbert transform, we havem+(t)=12[m(t)+jmh(t)](16)m (t)=12[m(t) jmh(t)](17)wheremh(t)is called Hilbert Transform ofm(t).36 Time domain representation of SSB signals using Hilbert TransformThe USB spectrum is USB(f)=M+(f fc)+M (f+fc)(18)=12[M(f fc)+M(f+fc)] 12j[Mh(f fc) Mh(f+fc)]The inverse Fourier transform is thensUSB(t)=m(t) cos( ct) mh(t)sin( ct)(19)Similarly, we can show thatsLSB(t)=m(t) cos( ct)+mh(t)sin( ct)(20)Hence, a general SSB signal can be expressed assSSB(t)=m(t) cos( ct) mh(t)sin( ct)(USB and LSB)(21)37 Generation of SSB SignalsA.

5 Selective Filtering MethodIt is the most common method of generation SSB. The basic idea is the following Usingm(t)to generate DSB-SC (m(t) cos ct) DSB-SC goes through a BPFcarrierBPFm(t)SSBFor successful implementation of this method, we must have B<<fc m(t)must have little or no low-frequency content, ,M( )has a hole atzero-frequency. For example, voice grade speech signal [ ] khz. Why do we need frequency hole ? If not, low frequency component cannot be filter (not realizable).B. Phase-shift Method SSB(t)=m(t) cos( ct) mh(t)sin( ct)39 Demodulation of SSB SignalsA. Coherent demodulationObserve thatsSSB(t) cos ct=m(t) cos2( ct) mh(t)sin( ct) cos( ct)=12m(t)+12m(t) cos 2 ct 12mh(t)sin2 ctIf we filter SSBcos ctwith a LPF, we can eliminate the components centered at2fcandthe filter output will be m(t)Hence, any of the coherent demodulation techniques applicable for DSB-SC signals can Envelope Detection with a Carrier (SSB+C)As a variation to the basic SSB case, we can add a carrier to the SSB signal and attempt to40use envelope detectorsSSB+C(t)=Acos( ct)+m(t) cos( ct) mh(t)sin( ct)=[A+m(t)] cos( ct) mh(t)sin( ct)=E(t) cos( ct+ (t))whereE(t)is envelope, given asE(t)

6 = [A+m(t)]2+[mh]2and the phase is given as (t)=tan 1(mhA+m(t))At the receiver, a properly designed envelope detector will extractE(t)fromsSSB+ thatE(t)=[A2+2m(t)A+m2(t)+m2h(t)]1/2(22) =A[1+2m(t)A+m2(t)A2+m2h(t)A2]1/241 IfA>>|m(t)|or|mh(t)|,E(t)can be approximated asE(t) A[1+2m(t)A]1/2 Using a series expansion and discarding higher order terms due tom/A<<1, we haveE(t) A[1+m(t)A+ ]=A+m(t)It is evident that for a large carrier, the SSB+C can be demodulated by an envelope AM, we needA>mp=|m(t)|, while SSB+C, we needA>>|m(t)|. Therefore,SSB+C is very Sideband Modulation (VSB)Some observations SSB Modulation is well suited for transmission of voice signals (or for all signals whichexhibit a lower component atf 0).

7 DSB generation is much simpler, but requires twice the signal bandwidth. VSB Modulation represents a compromise between SSB and DSB Modulation systems. Simply stated VSB: one Sideband is passed almost completely whereas just a trace (orvestige) of the other Sideband is (f)DSBfcSSB (USB)fcHi(f): HPFVSBfc f1fcfc+Bfcm(t)carrierHPFVSBVSB generationFigure 8: Illustration (f)is vestigial shaping filter that produces VSB from DSB. It allows thetransmission of one Sideband , but suppresses the other Sideband , not completely, butgradually. How do we designHi(f)to generate VSB signal?A(w)O(w) VSB(f)= DSB SC Hi(f)=[M(f+fc)+M(f fc)] Hi(f)(23)It can be demodulated by multiplying the carrier:A(f)=[ VSB(f+fc)+ VSB(f fc)] [M(f 2fc)+M(f)]Hi(f fc)+[M(f+2fc)+M(f)] Hi(f+fc)=[Hi(f fc)+Hi(f+fc)]M(f)+other termsO(f) H0(f)[Hi(f fc)+Hi(f+fc)]M(f)=M(f)45 Thus, we requireH0(f)=1Hi(f+fc)+Hi(f fc)|f| B(24)Furthermore, if we chooseHi(f fc)+Hi(f+fc)=1|f| Bthe output filter is just a simple low-pass observations limfv 0[VSB]=SSB,limfv B[VSB]=DSB VSB is demodulated using coherent detector.

8 As an alternative, we can use VSB+C (envelope detector) BT(VSB) (SSB) 1/3 (AM)> (VSB+C)> (SSB+C)46 Superheterodyne Receiver Consider the FDM signal, to receive this signal and to tune in to a particular channel ,we may require a receiver with the following structurefc1fc2fc3 AudioamplifierTunableRF stageDemodulator The above system will function as required. However, the design and implementation ofa tunable front-end, the RF stage, with sharp cut-off frequencies and high gain over awide-range of frequencies, is a difficult task. Consider the following scenarios47fc1fc2fc3fc1fc2fc3 Signal mixedTunable RF, move over the entire spectrum[540 1600]kHzSignal move over the spectrum by mixingRF stage FIXED!

9 We know how to mix the input signal, , how to move the spectrum up and down(multiplying the input signal with the output of a local oscillator). We can also design a fixed frequency RF stage which has all the desired filtering andamplication properties. Heterodyning: translating or shifting in frequency. The concept which we described invery general terms above is called heterodyning. This technique consists of eitherdown-converting or up-converting the input signal to some convenient frequency. We use a fixedIntermediate Frequency (IF)band. IF is fixed and is independent of thefc(the carrier frequency) of the signal we Commercial AM broadcastfIF= 455kHz.

10 Carrier frequency assignmentfc [540,1600]kHz. Let us consider an AM radio station broadcasting at the carrier frequency offc= 1000kHz, thenfLO=fc+fIF= 1000 + 455 = 1455kHz Image station:2fIFabovefc,fimage=fc+2fIF= 1000 + 2 455 = 1910kHzwould also appear simultaneously at the IF output if it were not filtered out by the RFfilter. The RF filter is hard to provide selectivity against adjacent stations separated by 10 kHz,but it can provide reasonable selectivity against a station separated by 910 amplifier with bandpassfilters tunableFrequencyconverter(mixter)amplifi erIFDetectorAudioamplifierRF amplifier with bandpassfilters tunableFrequencyconverter(mixter)[Ac+m(t )]cos ct[Ac+m(t)]cos IFtLocal oscillator c+ IFKm(t)to desired cFigure 9: FM stereo


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