3.1 General solutions for TEM, TE and TM waves Procedure to analyze a TEM (Ez, Hz=0) line

Transcription

1 Chpt 3 Tnsmissin Lins n Wvguis 3.1 Gnl slutins f TEM, TE n TM wvs pus, 3.5 Cxil lin (TEM lin) TEM m, high m t 3.7 Stiplin (TEM lin) nfml mpping slutin, ltstti slutin 3.8 Mistip (qusi-tem lin) npt, nfml mpping slutin, ltstti slutin 3.11 Summy f tnsmissin lins n wvguis 3-1

2 3.1 Gnl slutins f TEM, TE n TM wvs Pu t nlyz TEM (Ez, Hz=0) lin 1) slv (x, y) fm Lpl' s qutin t (x, y) 0 ) pply B.C. ( x,y ) 3) (x, y) (x, y) E (x, y, z) (x, y) t 1 Ex h(x, y) zˆ (x, y), ZTEM H (x, y, z) h(x, y) Z H TEM 1 1 4) V E l, I H l jz V L LC 1 5) vp,, Z ε v I C C v C p Pu t nlyz TE (Ez=0) TM (Hz=0) lin y 1) slv hz ( x, y) fm Hlmhltz qutin ( k ) ( ) 0: TE s C hz x, y p jz x y slv z( x,y) fm Hlmhltz qutin ( k ) z( x,y) 0 : TM s x y 3-

3 ) pply B.C. t fin k 3) H ( x, y,z) h ( x, y) z jβ H jβ H j H j H H, H, E, H : TE s z z z z x y x y k x k y k y k x E ( x, y,z) ( x, y) z z z j E j Ez H x, H, E k y k x z y jz jz x x 4) k k,ztm ( ), ZTE ( ) H y k H y x j E j E k x k y z,h y E E k Dilti lss j k tn ( NP / m ) : TEM s k tn ( NP / m ) : TE TM s z : TM s 3-3

4 (ivtin f th ilti lss xpssin) wv q E k E E k E E k E. 0 ( xy z ) 0 xy ( ) 0 E k E 0, k k xy j k k k ( ' j") '(1 j tn ) k 1 j tn " tn, k ' ' k k (1 j tn ) k k jk tn k k k 1 jk tn k k j 1 k tn tn ( NP / m ) : TE TM s k tn ( NP / m ) : TEM s k j

5 y 3.5 Cxil lin TEM m (, ) ln b V ln b jkz V E (,, z) t(, ) ln b 1 V H (,, z) zˆ E (,, z) Z ln b jkz V ( z) E (,, z) l V V V jkz I ( z) H (,, z) l I ln b Z V ( z) ln b I ( z) jkz jkz TEM b jkz jkz ˆ ˆ 60 b L ln, k C b L ln, C (Tbl.1, p.54) ln b / 3-5 b V x

6 High m t TE11 m (p.133 Fig.3.17) f mx f 1 ( b ) Pw mt utput pw 3-6 f

7 Disussin 1. Cnfml mpping slutin (Cllin, Fil thy f gui wvs, p.6) y Z-pln Z x jy b V x W ln Z ln ln j u ln b u V ln b ln 3-7 jv j ln b V ( ) ( ) u v b 0 ln 1 1 W uv CV ln 1 b C, Z ln, ln b v C C p v W-pln V 0 ln ln b u

8 nmliz vlus. Rsns f slting Z=50 Cxil lin hs minimum ttnutin s Z=77 (Pb. -7), n mximum pw pity s Z=30 (Pb. 3-8) ttnutin is lwst t 77 hms hm stn pw hnling pity pks t 30 hms htisti impn f xil ilins (hms) 3. Typs f xil nnts typ-n, SMA, APC3.5, APC.4,.. (p.134, pint f intst) 3-8

9 3.7 Stiplin Cnfml mpping slutin (Cllin s bk, p.65) = 0 =V W b = 0 = 0 b/ W-pln = 0 =V =V = 0 x -1 Z W A B Z( Z 1) Z-pln C W' A w sh b 3-9 Z 1 B Z( Z x v )( Z 1) =V 1 v C W -pln 4, v Z C

10 Eltstti slutin ( x, y ) 0 x, 0 y b t B.C. ( x, y ) 0 x, y 0,b nπ nπ An s x sinh y 0 y b -/ ( x, y) nπ nπ An s x sinh ( b y ) b y b nπ nπ nπ An ( )s x sh y 0 y b Ey y nπ nπ nπ An ( )s x sh ( b y ) b y b 1 x W ρs ( x) Dy ( x, y b ) Dy ( x, y b ) An...(3.189) 0 x W b nπ V Ey( x 0, y) y Ansinh b, Q 4 0 Q L 1 ε C...(3.19), Z V C v C C p 3-10 W W ρ ( x) x W s y b W / x

11 Disussin 1. nlysis q.(3.179) synthsis q.(3.180). Z k tn, W,b, Z,b, q.(3.181) W / b 3-11 Z W Z

12 3.8 Mistip W Chtistis fbitin by pint iuit vis n b bn t stip mpnnt ssibl in-iuit htiztin f vis is stightfw t implmnt s wll s signls n b tnsmitt lg vitin in Z > mnlithi pplitins stutu is ugg n n withstn high vltgs n pw lvls pw hnling is bst with BO substt us up t 300GHz m qusi-tem m f <<λ 3-1

13 npt L TEM lin Z, v p, β k ε, C ε i fill mistip (TEM lin) Z L 1 1 mistip (qusi-tem lin) Z, v, k, p C vpc LC Z C 1 C g, ( ) ff Z C C vp L C 1 C 3-13

14 1 ( 1) 1 ( 1) 1 filling ft q q (1 q)1 1 q ( 1), q 1 1 ( 1) 3-14 W /

15 y Cnfml mpping slutin (Gupt, Gg n Bhl, Mistip lins n sltlins, p.9) y s -s s W/ Z-pln y Z s j tnh x Z' Z -pln Z' y s g x s s" s' s" g' ' s q g' g x g x 3-15

16 t Eltstti slutin y ( x, y ) 0 x, 0 y B.C. ( x, y ) 0 x, y 0, nπ nπ An s x sinh y 0 y -/ / x ( x, y) nπ nπ n( y ) An s x sinh y nπ nπ nπ An ( ) s x sh y 0 y Ey y nπ nπ nπ n( y ) An ( )s x sinh y 1 x W ρ ( x) D ( x, y ) D ( x, y ) E ( x, y ) E ( x, y ) A 0 x W V s y y y y n 0 E y nπ ( x 0, y) y Ansinh, Q ρs( x) x W Q C L 1 ε C, ε, Z V C C v C C p W W 3-16 W

17 Disussin 1. nlysis q.(3.196, 195) synthsis q.(3.197, 195) k ( W,, Z 1)tn (3.198), ( 1),, α Z, W, Rs Z W (3.199) W/

18 (ivtin f q.(3.198)) TEM lin mistip lin: 1 (1) q (1 q) q( 1) 1 q 1 () k tn k tn " (3)tn tn, " q" 0(1 q) q" k tn k q" kq" kq " k 1 tn 1 k tn

19 4. substt mtil ε Al O 3(99.5%) tnδ@10ghz GAs qutz RT/ui RT/ui BO FR4 (G-10) Si * * SiO 4 Si N 3 4 *: MIM pit 7.6 (vp phs) 6.5 (sputting) nut mtil R s ( /sq 10-7 f ) (um)@ghz Ag Cu Au Al C T z Cu 1.4 mil (35 um) thiknss skin pth δ s ωμσ s 3-19

20 3.11 Summy f tnsmissin lins n wvguis mpisn f xil lin, stiplin n mistip, (p.158, Tbl 3.6) W CPW (pln wvgui) s s fbitin sy qusi-tem ptin itin pblm whn gp with pphs / mnlithi pplitins lss itin thn mistip if wll-bln high ms (upl slt m) f mput ssist tnsmissin lin nlysis 3-0

21 Slv Pblms Pb. 3.8 Fin Z f xil lin t hv mximum pw pity 6 V b bkwn fil stngth f i E 310 V / m V mx E ln b ln 1 V mx b E b mximum pw pity Pmx, Z ln Pmx ln Z Pmx b b ln Z ln 30 ADS xmpls: Ch3_pj 3-1