Question

Let a modulated signal be: s(t)=100cos(2100st) +100cos(2000xt) + 100cos(1900xt) where unmodulated carrier is c(t)=100cos(2000xt) where the carrier amplitude is Ac=100V and the carrier frequency is fc=1000Hz (6=2000m). a. Find the complex envelope g(t) for the modulated signal. b. Whaktype of modulation is involved? What is the modulating signal m(t)? c. Evaluate and draw the Power Spectral Density P.) of the modulated signal. d. Find the average (normalized) power P for this modulated signal. e. Evaluate the actual Peak Envelope Power Prep for this modulated signal on a 1092 load.

Answer 1

given modulated signal 5(#) = 100 cosla100) + 100 Cos (200074) + 100 cos (1900 +) 100 65 (200004) + 100 x 6S (2000+) CS1OOT) 100 [1+9 WS (10018)] 65 200014 --Ú ( 605 A+ W5B = 2 605(446). COS(ALB) compare equation © with standard AM equation SH) - Ac [lt u cos adm] wartet de = 1000 H3 A = 100V, (a) complex envelope git) complex Ielope of 87 (+) = g(+ + i glu) (4) = Het [git) fm= 50HZ e=8 enu Act) = 8+6+) evantet here [J143=5(4)] j Hilbeet tranfoom Hot [ W5WH) = 65(WT-90) = dem Wt 87(4) = 100 Los (200011) + 100 ws G1000) +100 ws(igcoñt) +j[ re sin B00078) + 100 sin barvon t) + 100 singeo ) (² cos wat j sinut ejut ) 1900 17 j2ooont 100 e Y21001 8+() = "I love + Too -jandet ev 200 2018 complexe envelope gc (t) = 8+(t) e felt) = 100bezovt j. 100 7.47 3190072) 100L Ite CS Scartney Secondo je tt) = 100114& 60510074) j lookt - j loont t e

By equation (0 modulated signal Sl&)= 100 cita Wsloone) as 2ooont signal is Am modulated signal with m(t) = cos loont following and U modulation index = 2. 5C - 100 60512100 +) + lov 656200074) + 100 OS(1900RA) 100[ S[++1050) + (F-1050)/+160 [ SIF +1000) +8(F-1000] +16 [ 8(6+950) + 6(F-950).] a Ps(f) Apreutatude 50 SO ty 50 50 Pot et -957 950 -1000 de=1000 1050 HZ -1050 power p for modulated signal average (normalized) Pt = Pc (1+2) 2 5000 100X100 Pc = Ac² CS Scanned with CamScanner

Pt = 5000 (1+2) 15000 W Pt => 5000X3 @ by ean (1) 100 (Ita WS (100 M 4)] Cos 2000TA SA- envelope of the given signal is (1001x)] 100 (Italos AC poucest ac power Peak envelope power 10000 (+7) R R=102 PPEP - 10,000 X3 10 un -> 3000 w Ppep Scanned with CamScanner