AC - 3 Unit SSB Modulation

UNIT-111 SSB MODULATION. SSB. modulation:- -Standard Amplitude modulation 4 DSB-SC modulation are wasteful of Bow because they both require a transmission Bw equal to twice the mig Bandwidth ie B.w=2fm. -In both case (AM & DSB-SC) half of transmision Bw Is occupied by USB of modulated wave, whereas the other half of transmission Bw is occupied by wowe. LSB of modulated -uniquely related to each other Carrier frequency 'to' Upper & Lower sidebands are by virtue of their symmetry about the Thus only one Sideband id information, it both the necessaray for transmision of Carrier and other sideband Suppressed at Tx, no information is lost. are .. Channel required the same Bow of mig signal. Sideband is transmited, modulation -When only one SSB referred to as A Frequency Domain Description of SSB- -It depends on which sideband is transmitted S(t)= m (+) Ac Coszafet. = = A_{m}*A_{c} Cos 27tmt. Cod27fct. AcAm cofcttm)+ AcAm cos2x (f_{c} - f_{m}) * t . 2 2 $(t) = AcAm cos 2x (fc+fm)t 2 USB IS TX. cod 271 (fc-fm)t LSB IS TX. = (A_{c}*A_{m})/2 = (A_{C}*A_{m})/2 cos 2x (f_{c} plus/minus f_{m}) * t . = AcAm cos 2xfct. Cos 2.5fmt = sin 2xfet-sin2xfmt] 2 (t) A c 2 [m(t)cos 2 pi f c t: mp hat m(0sin 2pi*f_{c}*t] Time Domain Description! - We will describe SSB ware in time domain, this is Canonical form. s(t)= sc (t) cos (2ntct) - Ss (t) sinartct. where Sc(t) in Anphase Component of SSB is Quadrature Component. for USB-and sslt) -Sc (t) except for a from s(t) by first multiplying s(t) by Cos(27fct) and Scaling factor may be derived then Posing throug Similarly the product modulator through IPF. s(t) by Ss(t) except for scaling factor, may be from s(t) by first multiplying sin(2nfct) and then passing through product modulator derived through an identical LPF. - We thus Stt) as follows: find F.T of sclt) and Ss(t) to SSB ware Sc (t) = s(f-fc)+s(f+tc), for - wefew. {" 0 elsewhere (2) Ss(t)= &j [s(f-fc-s(t+fc), for-wstew elsewhere where -wsf≤w defines freq band occupied by m(t). ∴∴ S_{c}(t) = 1/2 * A_{c}*M(t) ①. F* tau fm(t) Accordingly sc(+) is where M(t) is as (5) defined S_{c}(t) = 1/2 * A_{c}*m(t) -⑤ Next on basis of tig (b) we may write S_{s}(f) = -1/2 A_{c}*M(t) , f > 0 . 40 3/2 A_{c}*M(t) 2o. S_{S}(f) = A_{c} sgn(t)m(4) -. where sgn(t) is to, equal to +1 for tive treg, and zero for f = 0 and k = - 1 for-ive frequencies- There is one relation i,e where hat M(f) is F.T of (t), Hillbert transform of m(t). Hence Sub in we get Which Shows that Quadrature Component S_{s}(t) is defined by ... By substituting of eap& in we get So it we Cosenfet m(t) - ½ Acsinanfct ^(+) Consider in above Case USB LSB. then, S S (f)= 1/2 A c hat A (f)- oplus S(t) LSB = 1/2 * A_{C} * cot 2pi*f_{C}*tmH )+ 1 2 A C sin 2 pi f C t hat m (t) - j * sqn(t) * m(t) = A(t) - (t) S S (t)= 1 2 A c hat m(t) - (9) s(t) USB = 1/2 * A_{c} Single tore modulation of SSB-SC:- - 4t m(t) is having one freq, Component single tone. m(t) = Am cos 2ntmt - Hilbert Transform of signal abore is m(t)= A_{m} fmt. S(t) for SSB-SC for USB is S(t) = sclt) Colantct - Acm(+) sinartet -3. Sub 04 in S(t) USB = 1 2 A C A m int cos(2pi*f_{m}*t) * Cos(2pi*f_{c}*t) - sin(2pi*f_{m}*t) ]. S(t) usB= i/2 * A_{c}*A_{m}*cd [2 pi(t c +f m ) dot t ]-Q COSA Card-Sinasing by Superdupdates.org This is same as result obtained lower side treg f_{c} - f_{m} of Corresponding DSB-SC ware -The SSB ware of and its spectrum is S(f) USB = 1 4 A c A m [ delta(f - (f_{c} + f_{m}) + delta(f + (f_{c} + f_{m}))] . ↑M(+) -fm 이 f_{m} → f ↑ ↑ S(f) USB YACAMO -fc-fm fctfm f Illy tor LSB we get S(t) LSB = 1/2 * A_{c}*m(t) * cos 2pi*f_{C}*t + 1 2 A C hat m (t)sin 2 pi f c t . = 1/2 * A_{c}*A_{m} * integrate C d(2pi*f_{m}*t) * cos(2pi*f_{C}*t) +sin 2 pi f C t** sin 2 pi f m t S l (t) LSg = - 1/2 * A_{c}*A_{m} * integrate c d(2pi*f_{m}*t) * cos(2pi*f_{c}*t) S[t) LSB = 1/2 * A_{C}*s_{m} * cos[2pi(f_{C} - f_{m}) * t] - It we draw Spectrum then it is S(f)= 1 4 A c A m [ delta( f - (f_{c} - f_{m}) + delta(f + (f_{c} - f_{m})] ↑ M(f) -fm b fm Generation of SSB waves!- Frequency Discrimination method. 2. Phase Discrimination or Hartley modulator. Phave Discrimination method! - Inphove path m(t). PM 소 Set) Ac Cas (28tct). SSB wide band -90 Phoue shift OSC -90° Ac Sin (2ntet) بلد PM Hilbert tranform A(t). Quadratne path S(t) → It uses two product modulators I &&, Supplied with Carrier wave in phose quadrature to each other. m(t), c(t) is directly applied to DSB-SC woul. PM I, producing Hilbert transform (t) (-90 phase shift of m(t)), c(t) shifted by 90 applied to P.M Q, producing DSB-SC. Sp (t) = m(+) Accos(2xfct). Sop (t) = m (t) Acsin (2xfct). S₁(t) & Sq(t) are fed to a Summer www.jntuworldupdates.org 이 of Summer is s(t) = s(t) ± Sq (t). $(t) = Acm(t) Cosanfct ± Acm(t)sinzafet. SL(t)= Acm (t) coszintet + Acm(t) sinzitet LSB Su(t) = Acm (t) cos 2afct - Acm (+) Sinzħfet USB. Frequency Discrimination ог Filtering methods- frequency SS B Discrimination method Can be used for generating ware if m(t) satisfies following Condition: (i) m(t) should not have any low freq, Content. (11) Highest freq, Component 'W' of met) is much lers thorn Carrier freq, fo' m(t) mt P.MBPF SSB ↑ c(t) BSB-SC. -It Consist of P.M, carrier osc, BPF designed to pous desired Sideband. At olp of P.M, we get get DSB-SC. which Contains two Sidebands -BPF will pous only one sideband and produce SSB. Demirts!- 4 →Freq, diff blw highest freq, in LSB & lowest freq, in USB is too small, which makes difficult, because its freq response design of BPF extremly need to have very sharp Change over from attenuation to paus band & vice-vers. Demodulation of SSB waves:- SSB S(+) → \mathcal{P} / M v(t) LPF v_{0}(t) . ↑ cos(2pi*f_{c}*t) Fig: coherent detection of SSB. P.M is having is cos(2pi*f_{c}*t) two Alps, one is s(t) and other v(t) = s(t) * cos(2pi*f_{c}*t) + 0 WKT S(t)= A C az^ 2 int m(t) * cos(2pi*f_{C}*t) pm hat m (t)sin(2 pi f C t)] --②. . Subin V(t)= Lambda c dt [m(t)cos 2 pi f c t. pm hat m(t) * sin 2pi*f_{c}*t ] = A C 2Q m(t)cos 2 pi f C t^ prime pm A_{C}/(2Q) * mn(t) * sin 2pi*f_{C}*tcd * 2pi*f_{C}*t . 4 sqrt CodACo * dB = dot C od(A+ beta)+ dot C cos(A-B) 2 cos A * SinB = (sin(A + B) - Sin(A - B))/2 Psi(t)= A c Q m(t) int c cd(2 pi f c +2 pi f c ) t + c*phi(2pi*f_{c} - 2pi*f_{c}) * t ] pm A c Q hat m(t) * [sin(2pi*f_{c} + 2pi*f_{c}) * t + sin(2pi*f_{c} - 2pi*f_{c}) * t] . A_{c}/Q * m(t)[csu*pi*f_{c}*t + cos(o)] pm A c Q hat m (t)[sin u pi f c t+sin is)] cos(0) = 1 sin (0)=0 = A_{c}/2 * m(t) + A_{c}/2 * m(t) * cd(4pi*f_{c}*t) pm A c 4 hat m t)* sin(4 pi f c t) V(t)= A c q m(t)+ A c q int m(t) * cos(u*pi*f_{c}*t) pm hat m (t)sin(u pi f c t)] Scaled my sh unwanted terms. → when v(t) is passed through LPF o/p v_{o}(t) = (Ac)/q * m(t) -The detection of there is SSB is based on assumption that a perfect synchronization blw Lo e Tx both. in freq & phase. But in practise a phase error $ may arise in L.O. Thus detector olp is modified due to phare engr as V o (t)= A_{c}/2 * m(t) * los*phi pm A c 2 hat m (t)sin phi Note- distortion is not serious with voice Communicatin 1. Phase because human ear The is relative insensitivity to phase distortion. presence of phase distortion gives rise to Donald Duck voice effect 2. phase distortion Cannot be tolerable in transmission music & video signal. Advantages of SSB:- 1. It requires half the Biw of AM 4 DSB-SC. 2. Power is Saved due to suppression of Carrier, one sideband 3. Reduced interference of noise. This is due to reduced B.w ↑, amount of noise added to sigral will increase. Disadvantage:- 1. Generation & reception of SSB is Complex. 2. Since Carrier is absent, SSB TX & Rx need to have an excellent frequency stability. 3. Highly expensive & Complen to implement. Applications:- t. Used where power sowing is required in mobile system 2. Used where B.w requirements are low. Eg:- Telemetry, radio navigation **Powers in AM, DSB-SC, SSB-SC and temperie g- = P_{c} + (P_{c} * mu ^ 2)/4 + (P_{c} * mu ^ 2)/4 Power in AM P pm = P_{c}[1 + (mu ^ 2)/2] Power in DSB-SC:- dot P_{t} = (A_{c} ^ 2 * A_{m} ^ 2)/8 + (A_{c} ^ 2 * A_{m} ^ 2)/8 = (A_{c} ^ 2 * A_{m} ^ 2)/4 Power in SSB!- P t = A_{c} ^ 2 * A_{m} ^ 2 8 = (4 + mu ^ 2)/(2(2 + mu ^ 2)) -i dagger →% of power saving Power Saved Total power X100. (1)% of Power wing = P_{c}/(P_{c}(i + (mu ^ 2)/2)) * xioo . -it DSB is used in place of A = 2/(2 + mu ^ 2) (i) power Saved from AM to SSB!- = P c + P_{C} + (P_{C} * mu ^ 2)/4 P C (1+ mu^ 2 2 ) = (mu ^ 2)/mu * 2/(2 + mu ^ 2) P_{C} = (A_{c} ^ 2)/2 Single Tone SSB Modulation:- (1) for transmitting USB only!. Let m(t)= Am cos(27tmt) (1. Hillbert transform of m(t) is obtained by passing it through - 9 * b deg phase shifter. so hat m (t)=A m sin(2pi*f_{m}*t) oplus omega*xT SSB with USB A S u (t)= A c 2 int m(t) * cos(2pi*f_{c}*t) - hat m (t)sin(2 pi f c t)]- beta) . Sub 0, 6in (3 S_{mu}(t) = A_{c}/2 * [A_{m} * cos(2pi*f_{m}*t) * cos(2pi*f_{c}*t) - A_{m} * sin(2pi*f_{m}*t) * f * sin(2pi*f_{c}*t)] WET Cos(A + B) = CodA * cos B - sin A * sin B . S u (t)= A c A m 2 [ matrix cos(2pi*f_{c}*t) * cos(2pi*f_{m}*t) - sin(2pi*f_{c}*t) * sin(2pi*f_{m}*t) ] S_{u}(t) = (A_{c}*A_{m})/2 * [c(2pi*f_{c}*t + 2pi*f_{m}*t)] . Su(t)= AcAm 2 Ceb 21 (fc+ fm)t 14 Egn & shows that SSB wave Consists of cup SB(f_{c} + f_{m}) , * This is exactly same as the result obtained by suppressing the lower side frequency (f_{c} - f_{m}) of the corresponding DSB-SE "Spectrum of SSB with lover sideband suppressed stt t S_{1}(f) ↑ -fc-fm 0 f_{c} + f_{m} (ii) For teransmitting LSB only:- * Set the modulating signal met) is represented as, m(t) = A_{m} * cos(2pi*f_{m}*t) 1 * The hilbert transform of the modulating signd m(t) is obtained by passing it through a -90° phase shifter, so the test transfarm is given by: hat m(t) = A_{m} * sin(2pi*f_{m}*t) w.k.t. the SSB wave with only LSB is guen by, S L (t)= A c 2 [ m(t) * co(2pi*f_{c}*t) + hat m (t)* dot an (2 pi f c t)] Sulestituting equo & equin equ we get Su(t)= A (Am Cao (2Tfmt) coo (2171fct) + Amusin (211-fint): sin (atfects) 2 SL(E) = AcAm 2. [ cos (2Tlfct), cos (211fmt) + sin (271fct.sing COD (A) COO(B) sin (A) in (21fmt)] sin (B) w.k.t. Cos(A-B) = cos A. CosB+ sin A sin B SL(t) = AcAm [Coo(2fct-21fmt)] G 2 SL(t) = AcAm Coo 211 [fc-fmt 2. Equation shows that the SSB ware consists of only the lowern side frequency (fc-fm) * This is exactly same as as the result obtained by suppressing the er side frequency (fctfm) of the corresponding DSB-SCwave.