Microwave Engineering

Transcription

1 Micrwave Engineering Cheng-Hsing Hsu Deparmen f Elecrical Engineering Nainal Unied Universiy

2 Ouline. Transmissin ine Thery. Transmissin ines and Waveguides eneral Sluins fr TEM, TE, and TM waves ; Parallel Plae waveguide ; ecangular Waveguide ; Caxial ine ; Sripline ; Micrsrip 3. Micrwave Newrk Analysis Impedance and Equivalen Vlages and Currens ; Impedance and Admiance Marices ; The Scaering Marix ; ABCD Marix ; Signal Flw raphs ; Discninuies and Mdel Analysis 4. Impedance Maching and Tuning Maching wih umped Elemens ; Single-Sub Tuning ; Duble-Sub Tuning ; The Quarer-Wave Transfrmer ; The Thery f Small eflecins 5. Micrwave esnars Series and Parallel esnan Circuis ; Transmissin ine esnars ; ecangular Waveguide Caviies Dielecric esnars 6. Pwer Dividers and Direcinal Cuplers Basic Prperies f Dividers and Cuplers ; The T-Juncin Pwer Divider ; The Wilkinsn Pwer Divider ; Cupled ine Direcinal Cuplers ; 8 hybrid 7. Micrwave Filers Peridic Srucure ; Filer Design by he Inserin ss Mehd ; Filer Transfrmains ; Filer Implemenain ; Elecrnic Maerials and Devices Applicains ab

3 4. Impedance Maching and Tuning Maching wih umped Elemens Single-Sub Tuning Duble-Sub Tuning The Quarer-Wave Transfrmer The Thery f Small eflecins Tapered ines Elecrnic Maerials and Devices Applicains ab

4 Impedance maching is fen a par f he larger design prcess fr a micrwave cmpnen r sysem, and he maching circui is ideally lssless, avid unnecessary lss f pwer and is usually designed s ha he impedance seen lking in he maching newrk is. Then reflecins are eliminaed n he ransmissin line he lef f he maching newrk. Impedance maching r uning is impran fr he fllwing reasns: (I) Maximum pwer is delivered when he lad is mached he line (assuming he generar is mached), and pwer lss in he feed line is minimized. (II) Impedance maching sensiive receiver cmpnens (anenna, lw-nise amplifier, ec) imprves he signal--nise rai f he sysem. (III) Impedance maching in a pwer disribuin newrk (such as an anenna array feed newrk) will reduce ampliude and phase errrs. As lng as he lad impedance,, has sme nnzer real par. Facrs ha may be impran in he secin f a paricular maching newrk include he fllwing: Cmplexiy - he simples design ha saisfies he required specificains is generally he ms preferable Bandwidh Implemenain - depending n he ype f ransmissin line r waveguide being used ; uning subs are much easier implemen in waveguide Adjusabiliy adjusmen mach a variable lad impedance A lssless newrk maching an arbirary lad impedance a ransmissin line. Elecrnic Maerials and Devices Applicains ab

5 Maching wih umped Elemens ( Newrks) Simples ype f maching newrk is he -secin, which uses w reacive elemens mach an arbirary lad impedance a ransmissin line. => If he nrmalized lad impedance, z = /, is inside he + j x circle n he Smih Char, hen he circui as he fig. (a). If he nrmalized lad impedance is uside he + j x circle n he Smih Char, hen he circui as he fig. (b). The + j x circle is he resisance circle n he impedance Smih Char fr which r =. In addiin, he reacive elemens may be eiher inducrs r capacirs., depending n he lad impedance. (eigh disinc pssibiliies fr he maching circui fr varius lad impedance) -secin maching newrks. (a) Newrk fr z inside he + jx circle. (b) Newrk fr z uside he + jx circle. Elecrnic Maerials and Devices Applicains ab

6 Elecrnic Maerials and Devices Applicains ab

7 Analyic Sluins Cnsider he circui f Fig. (a), le = + j X => We saed ha his circui wuld be used when z = / is inside he + j x circle n he Smih char => implies ha > The impedance seen lking in he maching newrk fllwed by he lad impedance mus be equal, fr a mach jx jb / jx B X X ; X BX Since X B earranging and separaing in real and imaginary pars gives w equains fr he w unknwns, X and B The sluin is / X Then he series reacance can be fund as X B Slving abve equain fr X and subsiuing in abve equain gives a quadraic equain fr B. X X B X, he argumen f he secnd square r is always psiive. Tw sluins are pssible fr B and X. Bh f hese sluins are physically realizable, since bh psiive and negaive values f B and X are pssible. (psiive X implies an inducr, negaive X implies a capacir, while psiive B implies a capacir and negaive B implies an inducr) B -secin maching newrks. (a) Newrk fr z inside he + jx circle. (b) Newrk fr z uside he + jx circle. Elecrnic Maerials and Devices Applicains ab

8 Elecrnic Maerials and Devices Applicains ab

9 Cnsider he circui f Fig. (b), le = + j X => We saed ha his circui wuld be used when z = / is uside he + j x circle n he Smih char => implies ha < The admiance seen lking in he maching newrk fllwed by he lad impedance mus be equal /, fr a mach jb j X jx earranging and separaing in real and imaginary pars gives w equains fr he w unknwns, X B X X ; X X Slving abve equain fr The sluin is X B / X X B X and subsiuing in abve equain gives a quadraic equain fr B. Since, he argumen f he square rs are always psiive. In rder mach an arbirary cmplex lad a line f characerisic impedance, he real par f he inpu impedance he maching newrk mus be, while he imaginary par mus be zer. This implies ha a general maching newrk mus have a leas w degrees f freedm => in he -secin maching circui hese w degrees f freedm are prvided by he values f w reacive cmpnens. ; B / and B -secin maching newrks. (a) Newrk fr z inside he + jx circle. (b) Newrk fr z uside he + jx circle. Elecrnic Maerials and Devices Applicains ab

10 Elecrnic Maerials and Devices Applicains ab

11 EX: Design an -secin maching newrk mach a series C lad wih an impedance = j, a line, a a frequency f 5MHz. Elecrnic Maerials and Devices Applicains ab

12 Elecrnic Maerials and Devices Applicains ab

13 Single-Sub Tuning I is anher cnsider a maching echnique ha uses a single pen-circuied r shrcircuied lengh f a ransmissin line (a sub ), cnneced eiher in parallel r in series wih he ransmissin feed line a a cerain disance frm he lad. The w adjusable parameers are he disance, d, frm he lad he sub psiin, and he value f suscepance r reacance prvided by he shun r series sub. [ Fr shun : selec d s ha he admiance,, seen lking in he line a disance d frm he lad is f he frm +jb -> hen he sub suscepance is chsen as jb ] ; [ Fr series : he disance d is seleced s ha he impedance,, seen lking in he line a a disance d frm he lad, is f he frm +jx -> hen he sub reacance is chsen as jx ] The prper lengh f pen r shred T can be prvide any desired value f reacance and impedance Can mach varius impedance (real par ) Elecrnic Maerials and Devices Applicains ab

14 Elecrnic Maerials and Devices Applicains ab

15 Shun subs Elecrnic Maerials and Devices Applicains ab

16 EX. Fr a lad impedance =6-j8, design w single-sub (shr circui) shun uning newrks mach his lad a 5 line. Assuming ha he lad is mached a Hz, and he lad cnsiss f a resiser and capacir in series, pl he reflecin cefficien magniude frm Hz 3 Hz fr each sluin. <Sl> nrmalized lad impedance: z =.-j.6 -> cnsruc he apprpriae SW circle, and cnver he lad admiance, y. -> Nw nice ha SW circle inersecs he +jb circle a w pins (y and y ). Thus he disance d, frm he lad he sub, is given by eiher f hese w inersecins. eading he WT scale => d = =.; d = =.6 There is an infinie number f disances, d, n he SW circle ha inersec he +jb circle. Usually, i is desired keep he maching sub as clse as pssible he lad, imprve he bandwidh f he mach and reduce lsses caused by a pssibly large sanding wave rai n he line beween he sub and he lad. y =. + j.47 ; y =. j.47 => suscepance f j.47 and j.47 l =.95; l =.45 lad impedance => = 6and C =.995 pf Elecrnic Maerials and Devices Applicains ab

17 Sluin Example 5.. (a) Smih char fr he shun-sub uners. Elecrnic Maerials and Devices Applicains ab

18 Elecrnic Maerials and Devices Applicains ab -B B B B l B B l, fr π π fr, π d / -X X X X X / d X X X B X jb d jx j j jx j X / l d s s s s where an an : - circuied sub a shr fr an an an pen - circuied sub : fr an an hen, If fr, / chsen s ha ) is (which implies Nw ; where, is pin The admiance a his an where line frm he lad is f d, lengh, dwn a he impedance le he lad impedance be wrien as, and T derive frmulas fr

19 Series Subs Elecrnic Maerials and Devices Applicains ab

20 EX. Mach a lad impedance f =+j8 a 5 line using a single series pen-circui sub. Assuming ha he lad is mached a Hz, and he lad cnsiss f a resiser and inducr in series, pl he reflecin cefficien magniude frm Hz 3 Hz fr each sluin. <Sl> nrmalized lad impedance: z =-j.6 -> draw he SW circle. Fr he series-sub design, he char is an impedance char. -> Nw nice ha SW circle inersecs he +jx circle a w pins (z and z ). The shres disance, d, frm he lad he sub is, frm he WT scale, => d =.38.8 =.; while he secnd disance is d = (.5.8)+.7 =.463 z =. - j.33 ; z =. + j.33 => reacance f j.33 and -j.33 l =.397; l =.3 lad impedance => = and = 6.37 ph Elecrnic Maerials and Devices Applicains ab

21 Sluin Example 5.3. (a) Smih char fr he series-sub uners. Elecrnic Maerials and Devices Applicains ab

22 Elecrnic Maerials and Devices Applicains ab -X X X X l X X l, fr π π fr, π d / -B B B B B / d B B B X B jx d jb j j jb d j B / l d s s s s where an an : an pen - circuied sub fr an an : - circuied sub a shr fr an an hen, If fr, / chsen s ha ) is (which implies Nw ; where, is pin The admiance a his /,and an where line frm he lad is f, lengh, dwn a he admiance le he lad admiance be wrien as fr he series - sub uner,, and T derive frmulas fr

23 Duble-Sub Tuning The duble sub uner, which uses w uning subs in fixed psiins, can be used. Such uners are fen fabricaed in caxial line, wih adjusable subs cnneced in parallel he main caxial line. -> he duble sub uner cann mach all lad impedances. The duble sub uner circui, where he lad may be an arbirary disance frm he firs sub. Alhugh his is mre represenaive f pracical siuain, where he lad has been ransfrmed back he psiin f he firs sub, is easier deal wih and des n lse any generaliy. => he subs are shun subs, which are usually easier implemen in pracice han are series subs. (pen-circuied r shr-circuied) => d /8 r 3/ 8 Elecrnic Maerials and Devices Applicains ab

24 Smih Char Sluin. The suscepance f he firs sub, b (b ), mves he lad admiance y (y ) => These pins lie n he raed + jb circle; he amun f rain is d wavelengh ward he lad, where d is he elecrical disance beween he w sub.. Transfrming y (y ) ward he generar hrugh a lengh, d, f line leaves us a he pin y (y ) which mus be n he +jb circle. => he secnd sub hen adds a suscepance b (b ), which brings us he cener f he char, and cmplee mach. Elecrnic Maerials and Devices Applicains ab

25 EX. Design a duble sub shun uner mach a lad impedance =6-j8 a 5 line. The subs are be pen-circuied subs, and are spaced / 8 apar. Assuming ha his lad cnsiss f a series resisr and capacir, and ha he mach frequency is Hz, pl he reflecin cefficien magniude verus frequency frm Hz 3 Hz. <Sl> nrmalized lad admiance: y =.3+j.4. -> cnsruc he raed +jb cnducance circle, by mving every pin n he g = circle / 8 ward he lad => he firs sub : b =.34 ; b = -.4 => Transfrm he / 8 secin f line by raing alng a cnsan radius (SW) circle / 8 ward he generar => y = - j3.38 ; y = + j.38 The suscepance f he secnd sub shuld be b = 3.38 ; b = -.38 The lenghs f he pen-circuied subs are hen fund as l =.46, l =.48; l =.4, l =.35 lad impedance => = 6and C =.995 pf Elecrnic Maerials and Devices Applicains ab

26 Sluin Example 5.4. (a) Smih char fr he duble-sub uners. Elecrnic Maerials and Devices Applicains ab

27 The lef f he firs sub, he admiance is and B Since 4 is he suscepance f he firs sub. jb A his pin, he real par f B B B 4 B B is real, he quaniy wihin he square r which gives he range n he secnd sub suscepance B l fr pen - circuied sub : an ls fr shr - circuied sub : an Afer d has been fixed, he firs sub suscepance can be deermined Afer ransfrming hrugh a lengh d f ransmissin line, he admiance jus he righ f he secnd sub is B j -B B B B jb jb where an d,and mus equal Slving fr, which leads he equain ha can bemached fr a given sub spacing, d. B B j / : mus be nnnegaive B sin where, d where B B r B jb is he lad admiance Elecrnic Maerials and Devices Applicains ab

28 The quarer-wave ransfrmer The quarer-wave ransfrmer is a simple and useful circui fr maching a real lad impedance a ransmissin line. An addiinal feaure f he quarer-wave ransfrmer is ha i can be exended mulisecin designs in a mehdical manner, fr brader bandwidh. => If nly a narrw band impedance mach is required, a single-secin ransfrmer may suffice. One drawback f he quarer-wave ransfrmer is ha i can nly mach a real lad impedance. => A cmplex lad impedance can always be ransfrmed a real impedance by using an apprpriae lengh f ransmissin line beween he lad and he ransfrmer, r an apprpriae series r shun reacive subs. Elecrnic Maerials and Devices Applicains ab

29 The single secin quarer wave maching ransfrmer circui is shwn in Figure. The characerisic impedance f Γ Since Γ A he design frequency, f where an d an,and j j, his reduces Γ he reflecin cefficien magniude is / 4 4 / in in Γ bu a her frequencies he lengh is differen s a prefec mach is n lnger bained The inpu impedance seen lking in he maching secin is and he fracinal band widh is csθ, If we assume TEM lines, hen he maching secin is fr θnear π/ πf v p θ βl v 4 f Δf f p, he elecrical lengh f he maching secin is λ/ 4, f j apprximae expressin fr he mismach versus frequency f f πf, f m f f / θ m in 4θm π j j l / a he design frequency, f., since an 4 cs π θ sec Nw if we assume ha he frequency is near he design frequency, f, hen l λ/ 4 and θ π/.then sec sec Γm Γ m θ herefre he frequency f he lwer band edge a θ θ Elecrnic Maerials and Devices Applicains ab θ m

30 The hery f small reflecin Single-secin Transfrmer = ( - )/( + ) ; = - ; 3 = ( - )/( + ) ; T = + = /( + ) ; T = + = /( + ) ; Elecrnic Maerials and Devices Applicains ab

31 Mulisecin Transfrmer Parial reflecin cefficiens can be defined a each juncins = ( - )/( + ) ; n = ( n+! - n )/( n+ + n ) ; N =( - N )/( + N ) ; Elecrnic Maerials and Devices Applicains ab

32 Taped ines Discuss hw an arbirary real lad impedance culd be mached a line ver a desired bandwidh by using mulisecin maching ransfrmers => As he number, N, f discree secins increases, he sep changes in characerisic impedance beween he secins becme smaller.=> Thus, in he limi f an infinie number f secins, we apprach a cninuusly apered line. A apered ransmissin line maching secin and he mdel fr an incremenal lengh f apered line. (a) The apered ransmissin line maching secin. (b) Mdel fr an incremenal sep change in impedance f he apered line. Elecrnic Maerials and Devices Applicains ab

33 A maching secin wih an expnenial impedance aper. (a) Variain f impedance. (b) esuling reflecin cefficien magniude respnse. A maching secin wih a riangular aper fr d(in //dz. (a) Variain f impedance. (b) esuling reflecin cefficien magniude respnse. Elecrnic Maerials and Devices Applicains ab

34 Elecrnic Maerials and Devices Applicains ab