Lesson 2 Transmission Lines Fundamentals

Transcription

1 Lesson Transmsson Lnes Funamenals 楊尚達 Shang-Da Yang Insue of Phooncs Technologes Deparmen of Elecrcal Engneerng Naonal Tsng Hua Unersy Tawan

2 Sec. -1 Inroucon 1. Why o scuss TX lnes srbue crcus?. Crera of usng srbue crcus 3. Backgroun knowlege

3 Why o scuss ransmsson lnes-1 Curren elecronc echnology s base on lumpe crcu heory smple powerful: 1. Lumpe elemens R C L epenen sources are connece n seres or shun. Conucng wres play no role

4 Why o scuss ransmsson lnes- In fac elemens an wres proe a framework oer whch elecrc charges can moe an se up he oal EM ecor fels. The behaor of crcu s hus eermne.

5 Why o scuss ransmsson lnes-3 Dsrbue crcu ransmsson lnes heory s somewhere n beween: 1. Can escrbe some wae properes waelengh phase elocy reflecon whch are crucal n power ransmsson hgh-spee IC.. Only eal wh scalar quanes requre no complcae ecor analyss

6 Crera of usng srbue crcus Fne spee of propagaon c n << sg sg sg sg

7 Example -1: Power lnes V AA V0 cos π 60 V BB [ 60 ] V0 cos π l T 1 60 sec Lumpe crcu s naequae when rule of humb l > 50 km > 0. 01T

8 Example -: Inerconnecon of ICs 1-cm slca nerconnecon l 67 ps Logc 1 Logc 0 rse me Lumpe crcu s naequae when r ps < rule of humb. Fas CMOS can hae r 100 ps!

9 Backgroun knowlege-1 Moels of lnear crcu elemens: R C L

10 Backgroun knowlege- Krchhoff s laws : k k 0 k k 0

11 Backgroun knowlege-3 Phasors of snusoal funcons: V { j ω ω φ V e } V cos Re 0 V cosφ snφ jφ 0e V0 j V Re j ω Re e { j ω jωv e } n n jω n Deraes Algebrac mulplcaon

12 Sec. - Equalen Crcu an Equaons of Transmsson Lnes 1. Geomery of ypcal TX lnes. Equalen crcu 3. TX lne equaons 4. Soluons

13 Geomery of ypcal ransmsson lnes Two long conucors separae by some nsulang maeral 0 across ± 0 along he conucors

14 Equalen crcu-1 Snce he olage curren can ary wh use of srbue crcu moel.e. a TX lne consss of nfnely many couple lnes of nfnesmal lengh Δ

15 Equalen crcu- Currens on a shor lne se up magnec fel Ampere s law magnec flux Tme-aryng curren flux olage changes along he lne Faraay s law o couner he change of curren Len s law seres nucor Δ L

16 Equalen crcu-3 The upper an lower conucors of he ajacen shor lnes are connece respecely shun capacor Δ C

17 Equalen crcu-4 Imperfec conucng maerals olage rop along he conucng lne seres ressor Imperfec nsulang maerals leakage curren beween conucors shun conucor

18 Equalen crcu-5 Complee moel: {R L G C} as {ressance nucance conucance capacance} per un lengh

19 Equalen crcu-6 By he equalen crcu he behaor of ecor EM fels can be escrbe by scalar olage an curren. Values of R L G C epen on he geomery an maerals of he ransmsson lne.

20 Transmsson lne equaons-1 Assume R0 G0: by KVL L Δ Δ L L L Δ

21 Transmsson lne equaons- L Δ Δ Le 0 Δ L.1 L Δ Δ L Δ Δ 1s-orer PDE wh unknown funcons an

22 Transmsson lne equaons-3 By KCL: C C C Δ C Δ Δ Δ

23 Transmsson lne equaons-4 Le 0 Δ C Δ Δ Δ C. C Δ Δ Δ C Δ Δ Δ 1s-orer PDE wh unknown funcons an

24 Takng for boh ses of eq.. Transmsson lne equaons-5 Takng for boh ses of eq..1 L L C C

25 Transmsson lne equaons-6 Combne he wo equaons: LC LC LC n-orer PDE wh 1 unknown funcon.3.4

26 Soluons o he ransmsson lne equaons-1 LC Compare x u x c x u wh TX lne eq. 1-D wae eq. LC p 1 ~ a wae propagang wh elocy

27 Soluons o he ransmsson lne equaons- D Alembar s soluon o wae equaon: any funcon f of arable p τ ± f ~ soron-free wae raelng n he p recon wh elocy p

28 Soluons o he ransmsson lne equaons-3 f p ~ soron-free wae raelng n he - recon wh elocy p General soluon o he olage superposon: f f p p.6 Can be oally fferen funcons eermne by BCs an ICs. Ther superposon may hae soron.

29 Commens 1 p LC Phase elocy only epens on he nsulang maerals hough L C also epen on he geomery of he lnes

30 Soluons o he ransmsson lne equaons-4 p p f f Subsue olage soluon no he 1s-orer PDE: L L f f p p τ τ τ τ 1 1 f f L L p τ τ τ τ τ Q τ τ τ τ τ f f L C

31 Soluons o he ransmsson lne equaons-5 [ ] 1 0 f f Z p p C L Z 0 f f p p Characersc mpeance no he ressance of he conucor or nsulaor Z 0 Physcal meanng

32 Example -3: Infnely long lne no reflece wae TX lne ~ a loa of ressance Z 0 L C Z 0 s 0 Vs V0 Z0 Rs