Theory and Applications of Transmission Lines

Transcription

1 Thory and Applications of Transmission ins 1

2 Introduction Typs Topics Gnral Transmission-in Equations Wav Charactristics on Finit Transmission ins Wavguids Optical Fibr 2

3 Transmission ins Usd for guiding lctromagntic (EM) wavs Point-to-point guidd transmission of powr and information from sourc to rcivr,.g., data signal. (unguidd=antnna) Transvrs EM (TEM) wavs applid to most transmission lins xcpt wavguids. TEM wavs -> uniform plan wavs 3

4 Typs classifid by matrials Mtallic Transmission ins (Conductor) Hollow or Dilctric-filld Wavguids (Conductor and dilctric) Optical Fibr (dilctric) 4

5 Transmission ins Two fundamntal typs ow Frquncy usd for powr transmission High Frquncy usd for RF transmission wavlngths ar shortr than or comparabl to th lngth of cabl 5 Not - transmission lin = conductor - but only us surfac

6 Typs of Mtallic Transmission Paralll in ins Twistd Pair (Shildd & Unshildd) Coaxial Microstrips Strip in 6

7 Paralll Pair Spacrs ow loss dilctric 7

8 Paralll in (aka Ribbon Cabl) Simpl Construction Usd primarily for powr lins, rural tlphon lins or TV antnna cabl Frq up to 2MHz ovr short distancs High Radiation oss moving currnt = A nd to b awar of othr mtallic conductors 8

9 Twin ad Cabl Balancd 3 Ω Balun = 276log( D / r) Balancd to unbalanc transformr 9

10 Twistd Pair mtal cladding Shildd protctiv dilctric Unshildd 1 coating is papr, rubbr, PVC can also hav singl pair, ach wrappd individually

11 Twistd Pair Twists tnd to cancl radiation loss Hlps rduc crosstalk Still fairly inxpnsiv Frquncy < 1MHz Gnrally short distancs analog ~5-6 km digital ~2-3 km Not - powr lin intrfrnc 11

12 CAT5 Cabl UTP 4 pair trminating in RJ45 1MHz max frquncy 1 Mbps transmit rat Asid: Wir Gaug (smallr is biggr) 12

13 13 Coaxial Cabl

14 Coaxial Cabl Gomtry crats a shildd systm no EM nrgy outsid th cabl Can support frquncis > 1MHz Can support data rats > 1GHz ow slf-inductanc allows gratr BW Usd for long-distanc tlphon trunks, urban ntworks, TV cabls Expnsiv must kp dilctric dry 14

15 Striplins Micro Striplin Embddd Striplin Coplanar Striplin oss Mtallic Skin dpth ocalizd currnt flow Dilctric oss tangnt ε'' ε = ε' jε'' Tanδ = ε Surfac roughnss ' 15

16 Microstrips Usd for vry high frquncis in smiconductors 16

17 E & H Filds Microstrip Cas How dos th signal mov Signal path from sourc to load? Rmmbr filds ar stup givn an applid forcing function. (Sourc) Th signal is rally th wav propagating btwn th conductors Y (into th pag) X Elctric fild Magntic fild Ground rturn path 17

18 Transmission Thory Currnt and Voltag chang with tim along th lin (th signal) suprposition of wavs in both dirctions but ovr short distancs (<λ) ar constant Enrgy is lost (hat - rsistanc) or stord (magntic - inductanc) / (capacitiv - capacitanc) v = Ri v = di dt = Attnuation osss i = C dv dt 18

19 Transmission in Concpt Powr Frquncy (f) 6 Hz Wavlngth (λ) is m ( Ovr 3,1 Mils) Powr Plant Consumr Hom 19

20 PC Transmission ins Signal Frquncy (f) is approaching 1 GHz Wavlngth (λ) is 1.5 cm (.6 inchs) Microstrip Intgratd Circuit Striplin T Striplin Coppr Trac PCB substrat W Cross Sction of Abov PCB Cross sction viw takn hr Via FR4 Dilctric Micro- Strip Signal (microstrip) T Coppr Plan Ground/Powr Signal (striplin) Signal (striplin) Ground/Powr Signal (microstrip) 2 W

21 Ky point about transmission lin opration Voltag and currnt on a transmission lin is a function of both tim and position. 21 V I = = f f ( z, t) ( z, t) I 1 V 1 V 2 dz Th major dviation from circuit thory with transmission lin, distributd ntworks is this positional dpndnc of voltag and currnt! Must think in trms of position and tim to undrstand transmission lin bhavior This positional dpndnc is addd whn th assumption of th siz of th circuit bing small compard to th signaling wavlngth I 2

22 Transmission in Modl Distributd circuit concpt 22 R is th rsistanc in both conductors pr unit lngth in W /m is th inductanc in both conductors pr unit lngth in H/m G is th conductanc of th dilctric mdia pr unit lngth in S/m C is th capacitanc btwn th conductors pr unit lngth in F/m

23 Transmission in Modl (cont d) Using Kirchhoff s voltag law on th circuit in th figur ltting z w gt (1) 23

24 Transmission in Modl (cont d) To gt anothr quation rlating G and C w apply Kirchhoff s currnt law on th circuit and gt: ltting z in this quation also w gt: (2) (1),(2) : Gnral Transmission-lin Equations 24

25 Transmission in Modl (cont d) Ths quations can b simplifid if th voltag v(z,t) and th currnt i(z,t) ar tim-harmonic cosin functions th gnral transmission lin quations bcom: (3) (4) 25

26 Wav quations & solutions By combining (3) and (4): whr γ is th propagation constant: (5) (6) Th gnral solution of (5), (6) (7) (8) Charactristic Impdanc 26

27 Spcial Cass osslss in (R=,G=) γ = α jβ = jω C ; u p = ω / β = 1/ C ; = / Distortionlss in (R/,G/C) C γ = α jβ = ( R jω)( RC / = C / ( R jω); α = R C / ; β = ω C u = ω / β = 1/ C; C p = / jωc) 27

28 Finit Transmission ins In an infinitly long lin thr ar only forward travlling wavs and no rflctd wavs. Th scond trm in (7) and (8) will b zro. This is howvr also tru for a lin trminatd with its charactristic impdanc. A lin is calld a matchd lin whn th load impdanc is qual to th charactristic impdanc. If w considr a lin with th charactristic impdanc, a propagation constant γ and with th lngth l trminatd with a load impdanc connctd to a sinusoidal voltag sourc, and thn th voltag and currnt distribution on th lin can b calculatd as: 28 V ( z) = V γz V γz ; I( z) = I γz I = V I V = I γz

29 29 Finit Transmission ins (2) Finit Transmission ins (2) / / V V V V I I V V I V I V l l l l l l l l l z γ γ γ γ γ γ γ γ = = = = =

30 3 Finit Transmission ins (3) Finit Transmission ins (3) ( ) ( ) ( ) ( ) l l l l I I V V I I V V γ γ γ γ = = = = ; ( ) ( ) [ ] ( ) ( ) [ ] ) ( ) ( ) ( ) ( 2 ) ( ; 2 ) ( z l z l z l z l I z I I z V = = γ γ γ γ

31 31 Finit Transmission ins (4) Finit Transmission ins (4) ( ) ( ) [ ] ( ) ( ) [ ] z l z I z I I z V z z z z = = = ' ; 2 ') ( ; 2 ') ( ' ' ' ' γ γ γ γ

32 32 Finit Transmission ins (5) Finit Transmission ins (5) ' tanh ' tanh ') ( z z z γ γ = l l l z i γ γ tanh tanh ) ' ( = = = Input Impdanc: Matchd load if =

33 33 Rflction Cofficint Rflction Cofficint ( ) ( ) [ ] ( ) ( ) [ ] ' 2 ' ' 2 ' ' ' ') ( z z z z z z I I I z V γ γ γ γ γ γ Γ = = = Γ Γ = Γ= jθ 1 1 min max Γ Γ = = V V S Rflction Cofficint Standing Wav Ratio (SWR)

34 Rflction and Transmission Incidnt 1Γ Transmittd Γ Rflctd 34

35 Spcial Cass to Rmmbr A: Trminatd in o Vs s o o ρ= oo o o = B: Short Circuit Vs s o ρ= o o =1 C: Opn Circuit Vs s o ρ = o o =1 35

36 Wavguids aka plumbing width is ~ wavlngth 36

37 Wavguids Uss a diffrnt transmission mthod Ducting not conducting >1GHz Expnsiv May nd to b filld Cannot turn sharp cornrs Any dfcts will caus significant attnuation (sparking) 37

38 Optical Fibr Can b considrd circular wavguids 38

39 History of Fibr Optics John Tyndall dmonstration in 187 Total Intrnal rflction is th basic ida of fibr optic 39

40 History of Fibr optics During 193, othr idas wr dvlopd with this fibr optic such as transmitting imags through a fibr. During th 196s, asrs wr introducd as fficint light sourcs In 197s All glass fibrs xprincd xcssiv optical loss, th loss of th light signal as it travld th fibr limiting transmission distanc. This motivatd th scintists to dvlop glass fibrs that includ a sparating glass coating. Th innrmost rgion was usd to transmit th light, whil th glass coating prvntd th light from laking out of th cor by rflcting th light within th boundaris of th cor. Today, you can find fibr optics usd in varity of applications such as mdical nvironmnt to th broadcasting industry. It is usd to transmit voic, tlvision, imags and data signals through small flxibl thrads of glass or plastic. 4

41 Optical fibr transmits light. But, what prvnts th light from scaping from th fibr? 41

42 How Dos fibr optic transmit light? 42

43 Sourc and transmittrs A basic fibr optic communications systm consists of thr basic lmnts: Fibr mdia ight sourcs ight dtctor 43

44 A ight Sourcs ED (ight mitting diod) ID (injction lasr diod) 44

45 Dtctors Dtctor is th rciving nd of a fibr optic link. Thr ar two kinds of Dtctors 1. PIN (Positiv Intrinsic Ngativ) 2. APD (Avalanch photo diods) PIN 45 APD

46 Th advantags of fibr optic ovr wir cabl Thinnr Highr carrying capacity ss signal dgradation ight signal ow powr Flxibl Non-flammabl ightwight 46

47 Disadvantag of fibr optic ovr coppr wir cabl Optical fibr is mor xpnsiv pr mtr than coppr Optical fibr can not b join togthr as asily as coppr cabl. It rquirs training and xpnsiv splicing and masurmnt quipmnt. 47

48 48 Fibr Tchnology

49 49 Fibr Tchnology

50 5 Total intrnal Rflction

51 Fibr mdia Optical fibrs ar th actual mdia that guids th light Thr ar thr typs of fibr optic cabl commonly usd Stp-indx Multimod fibr Singl Mod Plastic optic fibr 51

52 52 Fibr Typs

53 53 Fibr Typs

54 Th loss of fibr optic Matrial absorption Matrial Scattring Wavguid scattring Fibr bnding Fibr coupling loss 54

55 55 Fibr Attnuation

56 56 Fibr Bandwidth

57 57 Fibr Bandwidth

58 Puls Propagation through Fibrs Rspons of a multi-mod fibr to a singl short puls Broadning of a short puls aftr transmission through diffrnt typs of fibrs 58 Fundamntals of Photonics - Salh and Tich

59 Fibr Attnuation and Chromatic Disprsion Attnuation (db/km) Attnuation (all Fibr typs) TruWav Fibr Disprsionunshiftd Fibr Wavlngth (nm) Input Puls EDFA band Disprsionshiftd Fibr Output Puls Disprsion (ps/nm km) Disprsion 59 Slid Courtsy of Stan umish

60 Four Wav Mixing (FWM) TruWav Fibr (5 km) D 2.5 ps/nm-km 2 nm 1 nm 1.5 nm 1 db/division Disprsion-Shiftd Fibr (25 km) D ps/nm-km 2 nm 1 nm 1.5 nm λ Wavlngth (1 nm/division) Wavlngth (1 nm/division) Optical aunch Powr = 3 dbm/channl Slid Courtsy of Stan umish 6