Question

Consider the message signal m(t)=2cos(2001Tt)+3sin(4001Tt). Work out by hand the expected frequency spectrum and output waveform when m(t) is input to the AM DSB FC modulator, and a modulation index of 0.8 is achieved. Assume that the carrier frequency of the modulator is set to 2 MHz.

Answer 1

9. Given that message signal carréer frequency of the modulator - 20MHZ Cos( 2007+) - Sin (907 20011) mit): 2005 (2007+) + 3SinChoont) It is ilo to the DSBFC modulator modulation index, 3 : 0.8 If m(t) = Am Coswmt C(1 : Ac Cas wat thein DSB-FC Signal will be S[+) = Ac [1+M(+)] Coswet here We 211fct By this we can conclude that overall modulated Signal. iS SLE) : 5.(t) + S, () Modulated let m. (t): 2005 (2007) 5,C4) Modulated - Az [1+ )] Cos wet Ac [ 17 2Cos(200774) ] Cos 271fct Ac We know that Sin (90+0) - Cose CS anned with CamScanner

Silt bredelated Ac + Ac 25 in (90+200nt] Cosafat 70) We know that modulation index B : Am Ac By ab serving the above Equation() Am = 2 arel given that B= 0.8 by this we can calculate Ac 2.5 :: Ac Am B. 2 0.8 : 2.5 : Ac Substitute Ac in Eq-1 5,10)). (2.5 tubes in [90+ 2007it] ] Cos 2i fet -> (2) It is Equation 2. mod let pa (t) : 3 sin 4000 t : 3QS (90-4001T+ .: IS2Ct) limeid Ac [17 mCk)] cos 2018ct Ac Amsin Hoe krem -). (Ac + 3 les 278m [ ] Ws2nfct here BE Aom Ac 0.8 - 3. olev ๒ ) Ac : 3.75 0.8 . Ac - 3.75 CSscanned with hemscanner

Sa(t) mod ; 11.25 (3.75 + winLouit) Cos 271fct -> (1293) now add Equation 2&3 to get modulated Signat 5lt) - S(t): 5,(1) mod + Salt! mod 3 (2.5 trepte 11.25 3 B5in (90+ 2007+])605271fct +(3.757 eggs in 400 it) 6s27ifct - Selena = 2.5(1+šas:n[90+200 776]] w5271 fck + 3.75 Clt er en sin 60017 + J Cosztifict Row fourier transform for los and Sin Signal 1611-in) + Ź SCP+Pro ) Cos211 fmt - 2 SC f + fm) Casarifet Sin 20ifret -> I.dlfo fm) + 2 Given Signal MCH 2 Cos (200 77t) + 35 in 400 T + Apply fourier transform ly th's Mater): 22 here 27 fo = 200 7 & 20tn 2007 ..fm = 100 fm=200 CSbcanned with camisa

2 .: MCS): (SC – 100) +8CF +100)] + *foff-708)48" 3 Co (f-200) + SC +200) + is now graph MCF) (3/2 100 100 -200 200 (2) SCE) 'mod 2.5[1+ 2sin (90 +20074 +2017+).]cos 271 x2x10++ + 3.75-1+ 38:n (40071+]) cos 277 x2x1067 CSchanned with CamScanner