ELG3175 Introduction to Communication Systems. Angle Modulation Continued

Transcription

1 ELG3175 Iroduio o Couiaio Sye gle Modulaio Coiued

2 Le araériique de igaux odulé e agle PM Sigal M Sigal Iaaeou phae i Iaaeou requey Maxiu phae deviaio D ax Maxiu requey deviaio D ax Power p p p x où 0 d p d d ax ax x x ax d d x ax d où

3 Modulaio idex ue ha = o. The reulig M ad PM igal are : or he PM igal, we deie or he M igal i o o o M p PM D ax p p ax D

4 Modulaio idie or ay whih ha badwidh B, we deie he odulaio idie a : p p D ax ax p ax D B B ax

5 Exaple The igal = 5i 10. id he odulaio idex or 1. PM odulaio wih p = 0.3 rad/v.. M odulaio wih = 0 Hz/V. SOLUTION ax = 5, hereore p = = 1.5 rad. B = 10Hz, hereore = 0 5/10 = 10.

6 Narrowbad M Coider a M igal : We ay ha M i a arrowbad M igal. or exaple, oider whe = o. M d o 1 d where i o i o M M

7 Narrowbad M Whe << 1, he M igal i NBM. o+b = oob-iib. Thereore d d d d M i o i i o o o i << 1, o 1 ad i.

8 NBM Modulaor o + + NBM d 0 0 d i Tra. Hilber -

9 NBM Speru The peru o a NBM igal i give by: uig M0 = 0, he M- = 0 a = ad M+ = 0 a =-. The badwidh o NBM i hereore B where B i he badwidh o. NBM M M S

10 Widebad M - WBM or a M igal o be NBM, << 1. y igal ha i o arrowbad i hereore widebad. However, ypially > 1 or a M igal o be oidered widebad. The badwidh o WBM igal i larger ha NBM ie D ax i ireaed.

11 WBM igal or = o ad i oplex evelope. Le u oider = o. The reulig M igal i : M i o i o j M e i Re } ~ Re{ j M M e i ~ j M e

12 The ourier erie o he WBM igal whe = o. The preeedig oplex evelope i periodi wih udaeal requey. ~ S ~ M where 1/ 1/ 1/ 1/ ~ S e e e j j i j i e j d d

13 The ourier erie o he WBM igal whe = o. S ~ Replaig by x, beoe ~ S e j i xx dx The h order Beel uio o he ir id, J i give by: J Thereore ~ S 1 e J j i xx dx

14 The ourier erie o he WBM igal whe = o. Thereore we a expre he oplex evelope o he WBM igal a d he WBM igal iel beoe: j M e J ~ j j M M J e J e o Re } Re{ ~

15 Speru o he WBM igal whe = o. The peru o hi igal i: S M J Thi expreio how ha he M igal peru i ade up o a iiie uber o ipule a requeie = +. Thereore, heoreially, hi WBM igal ha iiie badwidh. However, he properie o he Beel uio how ha o o hee ipule oribue lile o he overall power o he igal ad are egilgible. We deie he praial badwidh a he rage o requeie whih oai a lea 99% o he oal power o he WBM igal.

16 The uio J =0 =1 = =3 J

17 Properie o J 1 3 I i a ieger : J = J - or eve ad J =-J - or odd whe << 1 J 0 1 J 1 / ad J 0, > 1 J 1 4 I{J }=0

18 Power o he M igal The power o a M igal i: P M M J o The power o he above expreio i: P J

19 ilerig a WBM igal o lii i badwidh. M J o B - x We wa o hooe B o ha he power o x I a lea 0.99 he power o M. X x J o X where X i he greae ieger ha aiie : X B ad X B

20 The power o x i: X P x J X Thereore we u hooe X o ha: X X J 0.99 We ow ha J = J -. Thereore J 0 J X

21 Value o J. =0.1 =0. =0.5 =1 = =3 =5 =

22 Exaple The igal = o i o be raied uig M ehique. id he praial badwidh i a = 5V, = 0 Hz ad = 4 Hz/V b = 10V, = 400 Hz ad = 00 Hz/V. SOLUTION a IN hi exaple, = 54/0 X = 1. We eed o id X o ha S = J 0 J ro he able, i X = 1, S = = I X =, S = = Thereore X = ad B = 4. b Here, = 1000/400 = 5. We a how ha X = 6 yield S = Thereore B = 1.

23 Caro Rule or = o, Whe i a ieger, we alway id ha X = +1. Thereore we a eiae ha he praial badwidh o a M igal i B = +1. or ay rado wih axiu value ad badwidh B, he rue badwidh i diiul o id. ordig o Caro, he wor ae i whe he peru o i oeraed aroud = B uh a a iuoid. Baed o experie by Caro, he badwidh o a WBM igal, B M, a be eiaed by B 1 B ***** M