Bandpass ouniaion and he Coplex Envelope EELE445-4 Leure 5 Coplex Envelope Review seions 4- o 4-4 in he ex look a he oplex envelope represenaions in able 4- be able o alulae or ind: oplex envelope o a waveor expression alulae he sinal power alulae he PEP deine Modulaion
Soe Deiniions baseband waveor has a speral aniude ha in nonzero or requenies in he viiniy o he oriin i.e. 0 and neliible elsewhere. bandpass waveor has a speral aniude ha is nonzero or requenies in soe band onenraed abou a requeny /- where is uh reaer han zero. Modulaion is he proess i iparin he soure inoraion ono a bandpass sinal wih a arrier requeny by he inroduion o apliude or phase perurbaions or boh. The resulin bandpass sinal is alled he odulaed sinal s, and he baseband soure sinal is alled he odulain sinal Fiure 4 Bandpass Couniaion syse. Couh, Diial and nalo Couniaion Syses, Sevenh Ediion 007 Pearson Eduaion, In. ll rihs reserved. 0-3-449-0
3 Coplex Envelope Theore: ny physial bandpass waveor an be represened by: { } { }, Re Re j j e R e jy x w requeny arrier s envelope o oplex par real denoes e s θ ω π Coplex Envelope { } { } { } j j e y x s x y y x R R y R x e R e jy x ω θ ω ω θ θ θ Re sin os an sin I os Re
Coplex Envelope x jy x is he I or In phase odulaion y is he Q or Quadraure odulaion R is >0 and deerines he sinal power [ ] [] is he appin operaor or [ ] union deerines he bandpass odulaion ype Coplex Envelope- Veor Modulaor { j ω e } s x os ω y sin ω Re os π π ll odulaion ypes ay be eneraed usin a veor odulaor 4
5 Coplex Envelope: ie and requeny doain { } [ ] [ ] * 0 4 Re R d P v P P P P G G V e v v v v v j : Power PSD : Speru : : waveor Bandpass ω Coplex Envelope, o various odulaions
Coplex Envelope, R θ, o various odulaions DSB-SC and M EELE445-4 Leure 6 6
7 DSB-SC seion 5- in he ex This is M wihou he Carrier ll o he power in he PSD is dependen on he inoraion The odulaion eiieny is 00% Synhronous deodulaion is required os π envelope pre - os s π DSB-SC Speru [ ], os M M S M G s d noralize envelope pre - π
DSB-SC Sinals Waveors Vols 0 0 5. 0 4 0.00 0.005 0.00 0.99 0 3 Carrier Volae Modulaion Volae ie DSB-SC Sinal DSB-SC and Envelopes Vols s.dsb n n n n 0 0 5. 0 4 0.00 0.005 0.00 0 n.99 0 3 s posiive envelope neaive envelope Tie 8
DSB-SC Sinal DSB-SC Volae Speru Vols peak DSB k 0.5 0 0 0 5000. 0 4.5. 0 4. 0 4 0 k.ax Frequeny Hz 0KHz M seion 5- s [ ] [ ]os π % odulaion pre - envelope ax in 00 ax[ ] in[ 00 9
0 M seion 5- in he ex [ ] 0 : s s power sideband power Carrier 0 ean, or Sideband shi Carrier Carrier Couh, Diial and nalo Couniaion Syses, Sevenh Ediion 007 Pearson Eduaion, In. ll rihs reserved. 0-3-449-0 Fiure 5 M sinal waveor. [ ] [ ] power he deerines envelope wavor physial os s ω
Mahad M sinal waveor, u50% Couh, Diial and nalo Couniaion Syses, Sevenh Ediion 007 Pearson Eduaion, In. ll rihs reserved. 0-3-449-0 Mahad M sinal waveor μ0.5.5 M Modulaion Volae Speru.5 Vols peak 0.75 0.5 0.5 0 6 8 0 4 Frequeny KHz 0.5 M Power 0.45 0.4 0.35 0.3 Was 0.5 0. 0.5 0. 0.05 0 6 8 0 4.03 Frequeny KHz Couh, Diial and nalo Couniaion Syses, Sevenh Ediion 007 Pearson Eduaion, In. ll rihs reserved. 0-3-449-0
Mahad M sinal waveor μ M and Envelopes.5 M Modulaion Volae Speru.5 Vols 0 Vols peak 0.75 0.5 0.5 0 5. 0 4 0.00 0.005 0.00 s Posiive Envelope Neaive Envelope Tie 0 0.5 0.45 0.4 0.35 0.3 6 8 0 4 Frequeny KHz M Power Was 0.5 0. 0.5 0..5 0.05 0 6 8 0 4 Frequeny KHz Couh, Diial and nalo Couniaion Syses, Sevenh Ediion 007 Pearson Eduaion, In. ll rihs reserved. 0-3-449-0 M Power and odulaion eiieny s [ ] Carrier power power shi in arrier sideband power
3 M seion 5- [ ] 00 in[ ] ax[ 00 % ]os [ in ax R s odulaion, : envelope real π Couh, Diial and nalo Couniaion Syses, Sevenh Ediion 007 Pearson Eduaion, In. ll rihs reserved. 0-3-449-0 Fiure 4 Speru o M sinal.
M seion 5- in he ex use your lass noes and review seion 5- in he ex. also review haper 4 or M deeion and he superheerodyne reeiver. M is used or oerial broadasin in order ha low os envelope deeion ay be used. Bandpass Diial Sinal Exaples on board EELE445-4 4
syeri Sideband Sinals USSB, LSSB, VSB EELE445-3 Leure 7 Fiure 5 4 Speru or a USSB sinal. Couh, Diial and nalo Couniaion Syses, Sevenh Ediion 007 Pearson Eduaion, In. ll rihs reserved. 0-3-449-0 5
Fiure 5 5 Generaion o SSB. Couh, Diial and nalo Couniaion Syses, Sevenh Ediion 007 Pearson Eduaion, In. ll rihs reserved. 0-3-449-0 Fiure P5 Weaver s ehod or enerain SSB. Couh, Diial and nalo Couniaion Syses, Sevenh Ediion 007 Pearson Eduaion, In. ll rihs reserved. 0-3-449-0 6
Sinle Side Band- Phasin Mehod ˆ ˆ Sinle Side Band- Phasin Mehod M Mˆ H h M 0-0 G M Mˆ 7
Sinle Side Band U- Sinle Side Band 8
Sinle Side Band Sinle Side Band 9
Sinle Side Band Sinle Side Band 0
Sinle Side Band Sinle Side Band
Fiure 5 5 Generaion o SSB. Couh, Diial and nalo Couniaion Syses, Sevenh Ediion 007 Pearson Eduaion, In. ll rihs reserved. 0-3-449-0 Sinle Side Band
Sinle Side Band Sinle Side Band 3
Fiure 5 6 VSB ransier and spera. Couh, Diial and nalo Couniaion Syses, Sevenh Ediion 007 Pearson Eduaion, In. ll rihs reserved. 0-3-449-0 4