Analysis and Dsign f Basic Intcnncts (Pat ) Outlin Tw-wi lins and caxial lins Stiplin Stiplin gmty and fild distibutin Chaactizing stiplins Micstip lin Micstip gmty and fild distibutin Chaactizing micstip lins Embddd micstips Lsss in stiplins and micstip lins 2
Tw-Wi Lins Unsuitabl f high-fquncy applicatins Thy hav high adiatin lsss (lag EMI) (R. Ludwig and P. Btchk, RF Cicuit Dsign, Pntic Hall, 2000) 3 2-Wi Lin Tansmissin Lin Paamts μ csh D L π 2a πε' C csh ( D / 2a) Rs R (Ω/m) aπ πωε'' G csh ( D / 2a) (H/m) (F/m) (S/m) wh R s ε ε ' jε '' ε '( ε ' ε ε ε μ σδ s j tanδ ) μ μ 8.854 0 4π 0 sufac sistivity δ s skin dpth πfσμ 7 2 (F/m) (H/m) (D. M. Pza, Micwav Engining, Wily, 2005) μ 4 2
Tw-Wi Lin (Nglcting Lsss) μ csh D L π 2a (H/m) πε' C csh ( D / 2a) (F/m) csh π D 2a μ ε ' (Ω) 376.73 csh D π ε 2a (Ω) 5 Tw-Wi Lin Pactical Issus Th mst cmmn 2-wi TL is th twin-lad lin Typical f twin-lad lins: 75Ω, 300Ω, and 400Ω Thy us cpp f th wis, spaatd by a plastic (typically plythyln) ibbn 300-Ω twin-lin 400-Ω ladd twin-lin 300Ω t 75Ω balun (K. L. Kais, Tansmissin Lin Matching and Csstalk, CRC, 2005) 6 3
Caxial Cabls Typical caxial cabls a usd up t 0 GHz (high-nd caxial lins can b usd up t 80 GHz) Thy hav almst n adiatin lsss (ut cnduct is gundd) Typical dilctics: Plystyn (ε 2.5, tanγ 0.0003 * ) Plythyln (ε 2.3, tanγ 0.0004 * ) Tfln (ε 2., tanγ 0.0004 * ) * at 0 GHz (R. Ludwig and P. Btchk, RF Cicuit Dsign, Pntic Hall, 2000) 7 Caxial Cabls Tansmissin Lin Paamts μ b L ln 2π a (H/m) 2πε' C ln( b / a) (F/m) R s R + 2π a b (Ω/m) 2πωε '' G ln( b / a) (S/m) wh R s ε ε ' jε '' ε '( ε ' ε ε ε μ σδ s j tanδ ) μ μ 8.854 0 4π 0 sufac sistivity δ s skin dpth πfσμ 7 2 (F/m) (H/m) (D. M. Pza, Micwav Engining, Wily, 2005) μ 8 4
Caxial Cabls (Nglcting Lsss) μ b L ln 2π a 2πε' C ln( b / a) (H/m) (F/m) ln b 2π a μ ε ' (Ω) 376.73 ln b 2 π ε a (Ω) 9 Caxial Lin Pactical Issus Typical f caxial lins: 50Ω, 75Ω and 93Ω Th mst cmmn typ is th RG-6 cabl (TV, 75Ω) Dtaild tchnical data-shts a availabl f ach typ RG-59 Cnncts (http://n.wikipdia.g/wiki/caxial_cabl#rfncs, 2009) 0 5
Stiplins A stiplin tac is immsd in a dilctic and sandwichd btwn tw mtallic plans Th lctic and magntic filds a cnfind t th dilctic (TEM ppagatin if lsss a small) TEM Ppagatin Th lctic and magntic filds in th dictin f ppagatin a z (R. Ludwig and P. Btchk, RF Cicuit Dsign, Pntic Hall, 2000) 2 6
Stiplin Gmty and Fild Distibutin v p c ε ε ε c 300Mm/s (D. M. Pza, Micwav Engining, Wily, 2005) 3 Chaactizing Stiplins ( Thicknss) 30π ε ( W b + 0.44b) wh W is th ffctiv width givn by W b W b 0 W (0.35 ) b 2 W f 0.35 b W f 0.35 b (D. M. Pza, Micwav Engining, Wily, 2005) 4 7
Chaactizing Stiplins (Nn Thicknss) (S. C. Thiauf, High-Spd Cicuit Bad Signal Intgity, Atch, 2004) 5 Chaactizing Stiplins (Nn Thicknss) 94.5 w f 0.35 w C f b t ε k + b 8.854ε wh k t b and C f is th finging capacitanc givn by C f 8.854ε k 2 π [ 2k ln( k + ) ( k )ln( ) ] (pf/m) (S. C. Thiauf, High-Spd Cicuit Bad Signal Intgity, Atch, 2004) 6 8
Chaactizing Stiplins (Nn Thicknss) wh 60 4 ln b ε πd f w < 0.35 b t d w t 4πw t + + ln + 0.5π 2 πw t w 2 (S. C. Thiauf, High-Spd Cicuit Bad Signal Intgity, Atch, 2004) 7 Chaactizing Stiplins (Nn Thicknss) (S. C. Thiauf, High-Spd Cicuit Bad Signal Intgity, Atch, 2004) 8 9
Micstips A micstip tac is sandwichd btwn tw vy diffnt dilctics Du t this nn-hmgnus mdia, micstips ppagat in nn TEM md Using th ffctiv dilctic cnstant appach, micstips can b mdld as if thy had an hmgnus mdia (quasi TEM ppagatin if th lsss a small) 9 Micstip Gmty and Fild Distibutin Substats with high ε duc fild lakag and css cupling Substats with small ε duc dilctic lsss (R. Ludwig and P. Btchk, RF Cicuit Dsign, Pntic Hall, 2000) 20 0
Micstip Gmty (cnt) Expsd micstip: Embddd micstip: sld mask (S. C. Thiauf, High-Spd Cicuit Bad Signal Intgity, Atch, 2004) 2 Chaactizing Expsd Micstip Lins v p c c 300Mm/s ε ε + ε + 2 2 ε + (0h / w) (R. Ludwig and P. Btchk, RF Cicuit Dsign, Pntic Hall, 2000) 22
Chaactizing Expsd Micstip Lins (cnt) nglcting thicknss (t 0) Mdl : Walk s fmula if w, h 60 8 ln h w + ε w 4h w 20π if >, 6 h ε w 2.42 0.44 h + h + h w w Ω Ω (C.S. Walk, Capacitanc, Inductanc and Csstalk Analysis; Atch, 990) 23 Chaactizing Expsd Micstip Lins (cnt) Mdl 2: Gupta s fmula if w, h 60 8 ln h w + ε w 4h Ω if w >, h 20π ε w.393 0.667ln w +.444 + + h h Ω (K.C. Gupta t. al, Cmput-Aidd Dsign f Micwav Cicuits; Atch, 98) 24 2
Chaactizing Expsd Micstip Lins (cnt) 400 350 Chaactistic Impdanc f a Micstip Lin Gupta Walk 300 250 (hms) 200 ε 50 00 ε 2.2 ε 4.5 ε 9 50 0 0 0.5.5 2 2.5 3 3.5 4 w/h 25 Chaactizing Expsd Micstip Lins (cnt) Effcts f t 0 n (R. Ludwig and P. Btchk, RF Cicuit Dsign, Pntic Hall, 2000) 26 3
Chaactizing Expsd Micstip Lins (cnt) cnsiding thicknss (t 0) if w > 2, h if w 2, h 60 5.98 ln h ε 0.8w + t 20π ε w.393 0.667ln w +.444 + + h h Ω Ω (S. C. Thiauf, High-Spd Cicuit Bad Signal Intgity, Atch, 2004) 27 50-Ω Stiplin and 50-Ω Embddd Micstip w 5mil t 0.65mil h 6.mil w 5mil t 0.65mil (S. C. Thiauf, High-Spd Cicuit Bad Signal Intgity, Atch, 2004) 28 4
Lsss in Tansmissin Lins Th ttal lss α t is th sum f th cnduct and dilctic lsss α α α + α t Cnduct lsss α c a du t th sistiv lsss in th signal tac and th tun path (pducd by a cnductiv cunt) Dilctic lsss α d a du t th ngy lst in th dilctic lays (pducd by a displacmnt cunt) c d 29 50-Ω Stiplin and 50-Ω Embddd Micstip (S. C. Thiauf, High-Spd Cicuit Bad Signal Intgity, Atch, 2004) 30 5