Ch5 Appendix Q-factor and Smith Chart Matching
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1 h5 Appedx -factr ad mth hart Matchg 5B-1 We-ha a udwg, F rcut Desg Thery ad Applcat, hapter 8 Frequecy espse f -type Matchg Netwrks 5B- Fg.8-8 Tw desg realzats f a -type matchg etwrk.65pf, 80 f 1 GHz Fg.8-9 Frequecy respse f the tw matchg etwrk realzats.
2 5B-3 Badpass Flter Equvalet (1) T fd the badwdth f the matchg etwrk, Fg.8-8 (c) ca be redraw as a badpass flter wth a laded qualty factr BW f (Detal the fllwg pages) Fg.8-10 (a) Equvalet badpass flter Fg.8-10 (b) Frequecy respse f the matchg etwrk 5B-4 Badpass Flter Equvalet () Frst, the & s replaced by a equvalet parallel cect f P & P, ad addg the capactaces T P. T get T & N, replacg the seres cect V s, s, & wth the Nrt equvalet curret surce I N. ( ) ( ) ( ) ( ) ( ) 1 1 ) /( N N s s N j G j j j Y j V I
3 Badpass Flter Equvalet (3) Next, the curret surce I N & cductace G N are cverted back t a Theve equvalet vltage surce 5B-5 V T T I N / G N T V s 6.54Ω j 1 ( ) T GN Frm resatr thery : V (1 T j1.) T 1/( ) T 0.61 Badpass Flter Equvalet (4) 5B-6 Frm the kw (0.61), BWf / 1GHz/ 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 The equvalet badpass flter aalyss allw us t expla the respse f the matchg etwrk ear f 0 Fg.8-8(c) Fg.8-9(b)
4 Ndal ualty Factr (1) The equvalet badpass flter aalyss s cmplcated > a smpler methd f estmatg the qualty factr s called dal qualty factr. At each de f the matchg etwrk the mpedace ca be expressed as a equvalet mpedace Z j r admttace Y P GP jbp > B G P P 5B-7 Z Z B Z Z Fg.8-8(c).65pF, 80 f 1 GHz Z B Z B Ndal ualty Factr () The maxmum dal qualty factr s btaed frm the pt B. B 1.3 The relat f the laded qualty factr ad dal qualty factr. 5B-8.61, 1. 3 / 0 Ths result s true fr ay -type matchg etwrk Fg.8-10 (a) Equvalet badpass flter (frm a example, t prf) The laded qualty factr f the matchg etwrk s usually estmated as the maxmum dal qualty factr
5 mth V3.10 & AD chematc Accrdg t the AD crcut respse, BW GHz f BW Frm the mth chart maxmum dal, , 1., 1.3 Ndal ualty Factr (3) m4 m4 1.3 freq 1.005GHz db((4,3))-3.344e-5 Peak 5B-9 db((4,3)) m freq 405.0MHz db((4,3)) m freq.10ghz db((4,3)) Num3 Z50 Ohm H 0.6 pf 3.6 pf 4 Num4 Z80 Ohm freq, GHz stat- turs mth hart T bta the equats fr stat- cturs, the rmalzed mpedace: Z r 1 Γ jx (1 Γ r r ) Γ Γ Γ j (1 Γ Γ r) The dal qualty factr ca be wrtte as: x Γ 1 1, Γr 1 r Γ ± 1 Γ Γ r 5B-10 1 Γr ( Γ ± 1) 1 1 ceter (0, ± 1) a crclewth radus Fg.8-11 stat turs dsplayed the mth hart
6 -matchg wth turs mth hart(1) Example 8-4 Desg -type matchg etwrks f0 1GHz Z ( 5 j0) Zs 50Ω z (0.5 j0.4) zs 1Ω 5B-11 Bth f tw -type matchg etwrks have the same maxmum dal qualty factr 1 BW f / f / GHz 0 Fg.8-11(b)() Impedace Trasfrmat the mth hart -matchg wth turs mth hart() 5B-1 Fg.8-11(a) Impedace Trasfrmat the mth hart Nte: -type matchg cat determe the ad badwdth.
7 mth V3.10 -matchg wth turs mth hart(3) 5B-13 Z Z Z Z AD chematc -matchg wth turs mth hart(4) ( BW f / f / GHz /1 GHz) 0.0 Frm AD BW 1.995GHz GHz 5B Nu Z50 Ohm pf 0.8 H 3.18 H Num Z5 Ohm db((,1)) freq 1.000GHz db((,1))-1.116e-6 Max m freq 1.955GHz db((,1)) freq, GHz m BW.4GHz GHz( f / ) 3 Num3 Z50 Ohm H 3.54 pf H 4 Num4 Z5 Ohm
8 T-matchg wth turs mth hart (1) 5B-15 Because -type matchg etwrks prvde ctrl ver the value f > Itrduce the 3rd elemet the matchg etwrk T ad π matchg etwrk >The extra f freedm t adjust the qualty factr (badwdth) Example 8-5 Desg the T-mathcg etwrk wth determed f0 1GHz Z ( 60 j0) Ω 0 / 60 1/ 3 ; Z ( 10 j0) Ω 0 /10 If the dal qualty factr s set t be 3 Fg.8-15 Desg f a T-type matchg etwrk fr a specfed 3 T-matchg wth turs mth hart () 5B-16 mth V3.10 & AD chematc Accrdg t the dal qualty factr 3, f 1.5, BW 0.67 GHz Accrdg t the AD crcut respse, BW GHz db((,1)) - freq 685.0MHz db((,1)) m freq 1.75GHz db((,1)) m Nu 7.85 H Z(10-j*0) Ohm pf 3.53 pf Num Z(60-j*30) Ohm freq, GHz
9 π -matchg wth turs mth hart(1) 5B-17 ce the lad ad put mpedaces are fxed, we cat prduce a matchg etwrk that has a qualty factr lwer tha the hghest. Example 8-5 Desg the π -mathcg etwrk wth lwest f0. 4GHz Z Z <l> (10 (0 j10) j40) / / 1 ce the lad ad put mpedaces are fxed > we cat prduce a matchg etwrk that has a qualty factr lwer tha the hghest. Fg.8-17 π-type matchg etwrk fgurat π -matchg wth turs mth hart() 5B-18 The badwdth cat be creased arbtrarly by reducg the dal factr. The lmts are set by the desred cmplex put ad utput mpedaces. f0. 4GHz Z Z (10 (0 j10) j40) / / 1 Fg.8-17 Desg f a π-type matchg etwrk usg mmal
10 π-matchg wth turs mth hart () 5B-19 mth V3.10 & AD chematc Accrdg t the dal qualty factr,.4 f 1, BW.4GHz 1 Accrdg t the AD crcut respse, BW GHz 0-1 freq.395ghz db((,1))-7.60e-6 Peak db((,1)) m freq 1.760GHz db((,1)) m m4 freq 4.355GHz db((,1)) m Nu Z(0-j*40) Ohm pf 1.66 H 1.31 H Num Z(10-j*10) O freq, GHz clus ce -type matchg etwrks prvde ctrl ver the value f, > We ca trduce the 3rd elemet the matchg etwrk T &π matchg etwrk The extra f freedm t adjust the qualty factr (badwdth) f matchg etwrk cmes at the expese f a addtal crcut elemet. The badwdth cat be creased arbtrarly by reducg the dal factr. > The lmts are set by the desred cmplex put ad utput mpedaces. 5B-0
Ch5 Appendix Q-factor and Smith Chart Matching
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
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