Lesson 03 Transient Response of Transmission Lines

Transcription

1 Eecromagneics P- esson Transien esponse of Transmission ines Inroucion Paria refecion an ransmission occur wheneer a wae mees wih a isconinuiy ie an inerface beween feren maerias Muipe isconinuiies cause successie counerpropagaing waes an he superposiion of a componen waes wi eermine he exac signa aong he ine In his esson we wi quaniaiey anayze ransien response of a erminae ransmission ine or cascae ines excie by a sep-ike oage source which is imporan in igia inegrae eecronics an compuer communicaions efecion a isconinuiy Exampe -: sep oage source of ampiue an inerna resisance ries a ossess ransmission ine of characerisic impeance Z engh phase eociy p one-way signa raeing ime an is erminae by a oa resisance Fig p - Fig - Finie ossess ransmission ine rien by a sep oage source s in Exampe - a oage signa sars o propagaes in he z irecion wih eociy a z p z p oherwise ai for a > bu is ony inerese uring Eie by: hang-da Yang

2 Eecromagneics P- Z z [ ] where When he isurbance z arries a he oa z Z a a refece oage wae z z > oherwise p ai for a > wi be generae an propagae in he z irecion The oa oage a he oa a is equa o heir superposiion: y eq 9 he oa curren a z is: i Z Z ubsiuing eq s ino he bounary coniion i impose by he oa resisance gies: Diiing he aboe equaion by [ ] Z for boh sies of equaiy an efining he oa oage refecion coefficien oage z we arrie a: Γ as he raio of he refece oage z Γ Z Γ Γ Z Z o he incien The refece oage wae z wi arrie a he source z a generaing a refece oage z z p oherwise ai for a > propagaing in he z irecion This process can be iewe as a oage isurbance propagaing on a ine of characerisic impeance Z an being incien on a resisance of y eq he source oage refecion coefficien Γ is: Eie by: hang-da Yang

3 Eecromagneics P- Γ Z Z 4 Noe ha z is creae a an wi coninue o exis foreer The oa oage an curren a he source a are formuae as: Γ Γ Γ i Z Z Z Z Γ Γ Γ This process wi coninue inefiniey The oa oage a he source wi conerge o: im Γ Γ Γ Γ Γ Γ Γ Γ Γ [ ] Γ Γ Γ Γ Γ Γ Γ Z y an eq s 4 we hae: Z im Γ Γ Γ 5 Commen> You wi fin ha he oa oage a arbirary posiion z [ ] wi aso conerge o eq 5 In oher wors he seay sae appears as he ransmission ine were absen! ounce iagram ounce iagram is a isance s ime po iusraing successie refecions aong a ransmission ine rien by a sep oage source Fig -a I can be use conenieny o eermine: The spaia oage isribuion a some insan z : Mark a poin P z on he po Fig -b The souion becomes: Eie by: hang-da Yang

4 Eecromagneics P-4 ef for z z; z righ for z z where ef righ resu from he superposiion of proper numbers of bouncing oage waes k z k z k respeciey For exampe he case of Fig -b eas o a souion of Fig -c where ef Γ Γ Γ z z z righ Γ z z Fig - a ransmission ine excie by a sep oage source an erminae by a resisie oa b The corresponing bounce iagram c The spaia oage isribuion a he ime The empora oage isribuion a some posiion z a : Draw a erica ine z za inersecing wih he ines of he po a successie imes k k which k are he insans when he oage wae k z k z arries a he poin of ineres z z a The souion becomes: Eie by: hang-da Yang

5 Eecromagneics P-5 za Γ 6 Γ ΓΓ Fig - a The bounce iagram b The empora oage isribuion a he posiion z za inge ransmission ine wih resisie erminaion Exampe -: Consier a sysem shown in Fig - where s 5Z open circuie oa Fin he ermina oages Fig -4 a The bounce iagram b-c The normaize ermina oages of Exampe - Eie by: hang-da Yang

6 Eecromagneics P-6 Z ns: 8 Z y eq s 4 Γ 6 Γ Draw he corresponing bounce iagram Fig -4a For z z a egenerae 4 y eq 6 8 Γ ΓΓ 4 ee Fig -4b For z za k k k egenerae y eq 6 Γ 6 ee Fig -4c Commen> oh an conerge o as preice by eq 5 Oershooing an ringing effecs uring he ransien sae cou be harmfu for circuis Exampe -: Consier a sysem shown in Fig - where s 4Z Z mache oa Fin he ermina oages Fig -5 a The bounce iagram b-c The normaize ermina oages of Exampe - Eie by: hang-da Yang

7 Eecromagneics P-7 Z ns: Z y eq s 4 Γ 6 Γ Draw he corresponing bounce iagram Fig -5a For z z a egenerae 4 y eq 6 8 > ee Fig -5b For z za k k k egenerae y eq 6 Γ > ee Fig -5c Commen> oh an conerge o as preice by eq 5 No oershooing an ringing for he mache oa preens successie refecions Eie by: hang-da Yang

8 Eecromagneics P-8 Cascae ransmission ines Exampe -4: Consier a sysem shown in Fig -6a Fin he ermina oages Fig -6 a ysem configuraion b The bounce iagram c- The normaize ermina oages of Exampe -4 ns: When a oage isurbance z arries a he uncion z beween ines an a ime a refece wae z an a ransmie wae z are generae simuaneousy ounary coniion requires ha he oa oages on boh sies of he uncion mus be equa: Eie by: hang-da Yang

9 Eecromagneics P-9 Eie by: hang-da Yang Diiing for boh sies of he equaiy eas o: y eq we hae: T Γ 7 where T is he ransmission coefficien Z Z 75 5 y eq s 4 Γ Γ T Γ 4 T 6 Γ Draw he corresponing bounce iagram Fig -6b 8 ns; 4 4 ns 9 4 ns; ns 5 ns; 75 Fig -6c 5 ns; 5 ns 96 ns; 7 ns 8 7 ns; Fig -6