微波電路講義. eff concept, conformal mapping solution, electrostatic solution 3.11 Summary of transmission lines and waveguides 3-1

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1 Chpte 3 Tnsmissin Lines n Wveguies 3. Genel slutins f TEM, TE n TM wves peues, 3.5 Cxil line (TEM line) TEM me, highe e me et 3.7 Stipline (TEM line) nfml mpping slutin, eletstti slutin 3.8 Mistip (qusi-tem line) nept, nfml mpping slutin, eletstti slutin 3. Summy f tnsmissin lines n wveguies 3-

2 3. Genel slutins f TEM, TE n TM wves Peue t nlyze TEM (Ez, Hz=0) line ) slve (x, y) fm Lple' s equtin t (x, y) 0 ) pply B.C. ( x,y ) 3) e(x, y) (x, y) E (x, y, z) e(x, y)e t E x h(x, y) zˆ e(x, y), TEM H (x, y, z) h(x, y)e H TEM 4) V E l, I H l jz V L LC 5) vp,, ε v I C C v C p Peue t nlyze TE (Ez=0) TM (Hz=0) line x y slve ez( x,y) fm Helmhltz equtin ( k ) ez( x,y) 0 : TM se x y 3- ) slve hz( x,y) fm Helmhltz equtin ( k ) ( ) 0 : TE se C hz x,y y p jz

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

4 (eivtin f the ieleti lss expessin) wve eq 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") '( jtn ) k jtn " tn, k ' ' k k ( jtn ) k k jk tn k k k tn jk k k k tn j j tn ( NP / m ):TE TM se k tn ( NP / m ):TEM se k 0 3-4

5 y 3.5 Cxil line TEM me (, ) ln V ln jkz V E (,, z) t (, ) e e ln V H (,, z) zˆ E (,, z) e ln TEM jkz V ( z) E (,, z) l V e V e V jkz I ( z) H (,, z) l e I e ln L V ( z) ln I ( z) jkz jkz ˆ jkz ˆ 60 L ln, k C ln, C (Tle., p.54) ln / 3-5 jkz V x

6 Highe e me et TE me (p.33 Fig.3.7) f mx f ( ) Pwe mete utput pwe 3-6 f

7 Disussin. Cnfml mpping slutin (Cllin, Fiel they f guie wves, p.6) y -plne x jy j W ln ln e v W-plne V ln j V 0 u jv x ln ln u ln u V ln ln ln V ( ) ( ) u v 0 ln We uv CV ln C, ln, ln v C C 3-7 p

8 . Resns f seleting =50 Cxil line hs minimum ttenutin s =77 (P. -7), n mximum pwe pity s =30 (P. 3-8) ttenutin is lwest t 77 hms nmlize vlues hm stn pwe hnling pity peks t 30 hms hteisti impene f xil ilines (hms) 3. Types f xil nnets type-n, SMA, APC3.5, APC.4,.. (p.34, pint f inteest) 3-8

9 3.7 Stipline Cnfml mpping slutin (Cllin s k, p.65) = 0 =V W = 0 = 0 / W-plne = 0 =V -plne =V = 0 x - W A B ( ) w sh 3-9 W' A B ( x )( ) v =V C v 4 C, v W -plne C

10 Eletstti slutin t ( x, y ) 0 x, 0 y W B.C. ( x, y ) 0 x, y 0, nπ nπ An s x sinh y 0 y ( x, y) nπ nπ An s x sinh ( y ) y nπ nπ nπ An ( )s x sh y 0 y E y y nπ nπ nπ An ( )s x sh ( y ) y x W ρs( x) Dy( x,y ) Dy( x,y ) An...(3.89) 0 x W W nπ V Ey( x 0,y) y An sinh, Q ρs ( xx ) W 4 0 Q L ε C...(3.9), V C v C C p 3-0 W y -/ / x

11 Disussin. nlysis eq.(3.79) synthesis eq.(3.80)., k tn W,,,, eq.(3.8) W / 3- W

12 3.8 Mistip W Chteistis fitin y pinte iuit evies n e ne t stip mpnent e essile in-iuit hteiztin f evies is stightfw t implement s well s signls n e tnsmitte lge vitin in > mnlithi pplitins stutue is ugge n n withstn high vltges n pwe levels pwe hnling is est with BeO sustte use up t 300GHz me qusi-tem me f <<λ 3-

13 nept L TEM line, v p,β k ε, C ε i fille mistip (TEM line) L mistip (qusi-tem line), v, k, p C vpc LC C C, ( ) g e ff C C vp L C C 3-3

14 ( ) ( ) filling ft q q ( q) q ( ), q ( ) 3-4 W /

15 y Cnfml mpping slutin (see Gupt, Gg n Bhl, Mistip lines n sltlines, p.9) y s -s s W/ -plne y s j x ' tnh -plne ' y s g x s s" s' s" g' ' s q g' g x g x 3-5

16 Eletstti slutin t ( x, y ) 0 x, 0y 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 e y nπ nπ nπ An ( ) s x sh y 0 y Ey y nπ nπ nπ n( y) An ( )s x sinh e y 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( xx ) W Q C L ε C (3.), ε, V C C v C C W W p 3-6 W y

17 Disussin. nlysis eq.(3.96, 95) synthesis eq.(3.97, 95) k ( )tn ( ) W,, (3.98),,, α, W, R s W (3.99) W/

18 (eivtin f eq.(3.98)) k tn k TEM line mistip line: tn () q ( q) q( ) q () " (3)tntn, " q" 0( q) q" k tn k q" kq " kq " k tn k tn 3-8

19 4. sustte mteil nut mteil GAs Al qutz RT/ui 5880 RT/ui 6006 BeO FR4 (G -0) Si * * SiO Si 3 O N 3 4 (99.5%) *: MIM pit ε (vp phse) 6.5 (sputtein g) Ag Cu Au Al C T z skin R s ( /sq 0-7 f ) (um)@ghz Cu.4 mil (35 um) thikness epth δ s ωμσ s 3-9

20 3. Summy f tnsmissin lines n wveguies mpisn f xil line, stipline n mistip, (p.58, Tle 3.6) W CPW (pln wveguie) s s fitin esy qusi-tem petin itin plem when gp with pphes / mnlithi pplitins less itin thn mistip if well-lne highe e mes (uple slt me) f mpute ssiste tnsmissin line nlysis 3-0

21 Slve Plems P. 3.8 Fin f xil line t hve mximum pwe pity ekwn fiel stength f mximum pwe pity P mx 0 ln P i mx E ln 30 V mx, 6 V 377 ln V / m ln 30 P V mx mx E E ln ln ADS exmples: Ch3_pj 3-