Ch5 Appendix Q-factor and Smith Chart Matching

Transcription

1 Ch5 Appedx -factr ad mth Chart Matchg 5B-1 We-Cha a udwg, F Crcut Deg hery ad Applcat, Chapter 8 -type matchg etwrk w-cmpet Matchg Netwrk hee etwrk ue tw reactve cmpet t trafrm the lad mpedace t the dered put mpedace. 5B- Fgure 8-1 Eght pble cfgurat f dcrete tw-cmpet matchg etwrk.

2 Impedace rafrmat mth Chart C mpedace trafrmat repe mth chart Iductr reult mvemet tward the upper half. Capactace reult mvemet tward the lwer half. 5B-3 ere hut ere C hut C Fgure 8-3 Impedace effect f ere ad hut cect f ad C t a cmplex lad the mth Chart. Frbdde eg Frbdde eg ca develped fr all -type matchg etwrk. haded area ca t matchg t 50 5B-4 Fgure 8-7 Frbdde reg fr -type matchg etwrk wth = 0 = 50

3 Frequecy epe f -type Matchg Netwrk Ex. he frequecy repe f thee tw etwrk, where C =.65pF, =80Ω, / ad aume that the peratg frequecy fr th crcut f = 1 GHz 5B-5 Fg.8-8 w deg realzat f a -type matchg etwrk Fg.8-9 Frequecy repe f the tw matchg etwrk realzat. Badpa Flter Equvalet (1) fd the badwdth f the matchg etwrk, Fg.8-8 (c) ca be redraw a a badpa flter wth a laded qualty factr. f BW 5B-6 Fg.8-10 (a) Equvalet badpa flter Fg.8-10 (b) Frequecy repe f the matchg etwrk cmpared t the equvalet crcut

4 5B-7 Badpa Flter Equvalet () Frt, the ad C replaced by a equvalet parallel cect f P ad C P, ad addg the capactace C = C + C P. get ad N, replacg the ere cect V,, ad wth the Nrt equvalet curret urce I N. 1 1 ) /( N N N G Y V I 5B-8 Badpa Flter Equvalet (3) Next, the curret urce I N ad cductace G N are cverted back t a heve equvalet vltage urce 6.54 ; / ) ( 1.) (1 / 1 C N N N C C G V V G I V

5 Badpa Flter Equvalet (4) 5B-9 Frm the kw, BW=f / =1.63 GHz Frm the Fg.8-9 (b) 3dB pt fr f <f 0 at f m = 0.4 GHz fr f >f 0 at f max =.19 GHz, BW= f max -f m =1.79 GHz he equvalet badpa flter aaly allw u t expla the repe f the matchg etwrk ear f 0 Fg.8-8(c) Fg.8-9(b) Ndal ualty Factr he equvalet badpa flter aaly cmplexty ad a mpler methd f etmatg the qualty factr called dal qualty factr. At each de f the matchg etwrk the mpedace ca be expreed a a equvalet mpedace r admttace YP GP BP B G P P he relat f the laded qualty factr ad dal qualty factr. h reult true fr ay -type matchg etwrk he laded qualty factr f the matchg etwrk uually etmated a the maxmum dal qualty factr 5B-10

6 Ctat- Ctur mth Chart bta the equat fr Ctat- ctur, the rmalzed mpedace: 1 r r x (1 ) (1 he dal qualty factr ca be wrtte a: x r 1 r r, r) 1 r 1 1 5B-11 Fg.8-11 Ctat Ctur dplayed the mth Chart -matchg wth Ctur mth Chart(1) Example 8-4 Deg -type matchg etwrk f 1GHz 0 z (5 0), ( ), z B-1 <l> Bth f tw -type matchg etwrk have equal dal qualty factr =1 BW f / f / GHz 0 Fg.8-11(b)(C) Impedace rafrmat the mth Chart

7 -matchg wth Ctur mth Chart() 5B-13 Fg.8-11(a) Impedace rafrmat the mth Chart Nte: -type matchg cat determe the ad badwdth. -matchg wth Ctur mth Chart(1) 5B-14 Becaue -type matchg etwrk prvde ctrl ver the value f, We ca trduce the thrd elemet the matchg etwrk ad matchg etwrk Example 8-5 Deg the -mathcg etwrk wth determed f0 1GHz ( 60 0), (10 0) Aume that dal qualty factr = 3 <l> Fg type matchg etwrk tplgy Fg type matchg etwrk crcut

8 -matchg wth Ctur mth Chart() 5B-15 he extra f freedm t adut the qualty factr (badwdth) f matchg etwrk cme at the expee f a addtal crcut elemet. f0 1GHz ; ( 60 0), (10 0) Fg.8-15 Deg f a -type matchg etwrk fr a pecfed =3 -matchg wth Ctur mth Chart(1) 5B-16 ce the lad ad put mpedace are fxed, we cat prduce a matchg etwrk that ha a qualty factr lwer tha the hghet. Example 8-5 Deg the -mathcg etwrk wth lwet f0. 4GHz (10 (0 10), 40), / / 1 <l> ce the lad ad put mpedace are fxed > we cat prduce a matchg etwrk that ha a qualty factr lwer tha the hghet =. Fg type matchg etwrk Cfgurat

9 -matchg wth Ctur mth Chart() 5B-17 he badwdth cat be creaed arbtrarly by reducg the dal factr. he lmt are et by the dered cmplex put ad utput mpedace. f0. 4GHz (10 (0 10), 40), / / 1 Fg.8-17 Deg f a -type matchg etwrk ug mmal Cclu 5B-18 ce -type matchg etwrk prvde ctrl ver the value f, => We ca trduce the 3rd elemet the matchg etwrk & matchg etwrk he extra f freedm t adut the qualty factr (badwdth) f matchg etwrk cme at the expee f a addtal crcut elemet. he badwdth cat be creaed arbtrarly by reducg the dal factr. => he lmt are et by the dered cmplex put ad utput mpedace.