1 / 32

TELECOMMUNICATIONS

TELECOMMUNICATIONS. Dr. Hugh Blanton ENTC 4307/ENTC 5307. Transmission Lines. Transmission lines. Transmission line parameters, equations Wave propagations Lossless line, standing wave and reflection coefficient Input impedence Special cases of lossless line Power flow Smith chart

alida
Télécharger la présentation

TELECOMMUNICATIONS

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. TELECOMMUNICATIONS Dr. Hugh Blanton ENTC 4307/ENTC 5307

  2. Transmission Lines

  3. Transmission lines • Transmission line parameters, equations • Wave propagations • Lossless line, standing wave and reflection coefficient • Input impedence • Special cases of lossless line • Power flow • Smith chart • Impedence matching • Transients on transmission lines Dr. Blanton - ENTC 4307 - Transmission Lines 3

  4. Transmission line parameters, equations B A VBB’(t) Vg(t) VAA’(t) L A’ B’ VAA’(t) = Vg(t) = V0cos(t), Low frequency circuits: VBB’(t) = VAA’(t) Approximate result VBB’(t) = VAA’(t-td) = VAA’(t-L/c) = V0cos((t-L/c)), Dr. Blanton - ENTC 4307 - Transmission Lines 4

  5. B A VBB’(t) Vg(t) VAA’(t) L A’ B’ • Transmission line parameters, equations Recall: =c, and  = 2 VBB’(t) = VAA’(t-td) = VAA’(t-L/c) = V0cos((t-L/c)) = V0cos(t- 2L/), If >>L, VBB’(t)  V0cos(t) = VAA’(t), If <= L, VBB’(t) VAA’(t), the circuit theory has to be replaced. Dr. Blanton - ENTC 4307 - Transmission Lines 5

  6. B A VBB’(t) Vg(t) VAA’(t) L A’ B’ • Transmission line parameters • time delay VBB’(t) = VAA’(t-td) = VAA’(t-L/vp), • Reflection: the voltage has to be treated as wave, some bounce back • power loss: due to reflection and some other loss mechanism, • Dispersion: in material, Vp could be different for different wavelength Dr. Blanton - ENTC 4307 - Transmission Lines 6

  7. B E • Types of transmission lines • Transverse electromagnetic (TEM) transmission lines B E a) Coaxial line b) Two-wire line c) Parallel-plate line d) Strip line e) Microstrip line Dr. Blanton - ENTC 4307 - Transmission Lines 7

  8. Types of transmission lines • Higher-order transmission lines a) Optical fiber b) Rectangular waveguide c) Coplanar waveguide Dr. Blanton - ENTC 4307 - Transmission Lines 8

  9. Lumped-element Model • Represent transmission lines as parallel-wire configuration A B Vg(t) VBB’(t) VAA’(t) B’ A’ z z z R’z L’z L’z R’z L’z R’z Vg(t) G’z C’z C’z C’z G’z G’z Dr. Blanton - ENTC 4307 - Transmission Lines 9

  10. Transmission line equations • Represent transmission lines as parallel-wire configuration i(z,t) i(z+z,t) L’z R’z V(z,t) V(z+ z,t) G’z C’z V(z,t) = R’z i(z,t) + L’z  i(z,t)/ t + V(z+ z,t), (1) i(z,t) = G’z V(z+ z,t) + C’z V(z+ z,t)/t + i(z+z,t), (2) Dr. Blanton - ENTC 4307 - Transmission Lines 10

  11. i(z,t) i(z+z,t) L’z R’z V(z,t) V(z+ z,t) G’z C’z jt jt V(z,t) = Re( V(z) e i (z,t) = Re( i (z) e ), ), • Transmission line equations V(z,t) = R’z i(z,t) + L’z  i(z,t)/ t + V(z+ z,t), (1) -V(z+ z,t) + V(z,t) = R’z i(z,t) + L’z  i(z,t)/ t - V(z,t)/z = R’ i(z,t) + L’  i(z,t)/ t, (3) Rewrite V(z,t) and i(z,t) as phasors, for sinusoidal V(z,t) and i(z,t): Dr. Blanton - ENTC 4307 - Transmission Lines 11

  12. i(z,t) i(z+z,t) L’z R’z V(z,t) V(z+ z,t) G’z C’z jt e j = Re(i ), - dV(z)/dz = R’ i(z) + jL’ i(z), (4) • Transmission line equations Recall: jt di(t)/dt= Re(d i e )/dt - V(z,t)/z = R’ i(z,t) + L’  i(z,t)/ t, (3) Dr. Blanton - ENTC 4307 - Transmission Lines 12

  13. Transmission line equations • Represent transmission lines as parallel-wire configuration i(z,t) i(z+z,t) L’z R’z V(z,t) V(z+ z,t) G’z C’z V(z,t) = R’z i(z,t) + L’z  i(z,t)/ t + V(z+ z,t), (1) i(z,t) = G’z V(z+ z,t) + C’z V(z+ z,t)/t + i(z+z,t), (2) Dr. Blanton - ENTC 4307 - Transmission Lines 13

  14. i(z,t) i(z+z,t) L’z R’z V(z,t) V(z+ z,t) G’z C’z jt jt V(z,t) = Re( V(z) e i (z,t) = Re( i (z) e ), ), • Transmission line equations i(z,t) = G’z V(z+ z,t) + C’z V(z+ z,t)/t + i(z+z,t), (2) - i (z+ z,t) + i (z,t) = G’z V(z + z ,t) + C’z  V(z + z,t)/ t -  i(z,t)/z = G’ V(z,t) + C’  V(z,t)/ t, (5) Rewrite V(z,t) and i(z,t) as phasors, for sinusoidal V(z,t) and i(z,t): Dr. Blanton - ENTC 4307 - Transmission Lines 14

  15. i(z,t) i(z+z,t) L’z R’z V(z,t) V(z+ z,t) G’z C’z jt e j = Re(V ), - d i(z)/dz = G’ V(z) + jC’ V(z), (7) • Transmission line equations Recall: jt dV(t)/dt= Re(d V e )/dt - i(z,t)/z = G’ V(z,t) + C’  V(z,t)/ t, (6) Dr. Blanton - ENTC 4307 - Transmission Lines 15

  16. i(z,t) i(z+z,t) L’z R’z V(z,t) V(z+ z,t) G’z C’z - d i(z)/dz = G’ V(z) + jC’ V(z), (7) - dV(z)/dz = R’ i(z) + jL’ i(z), (4) - d²V(z)/dz² = R’ di(z)/dz + jL’ di(z)/dz, (8) • Telegrapher’s equation in phasor domain Take d /dz on both sides of eq. (4) Dr. Blanton - ENTC 4307 - Transmission Lines 16

  17. - dV(z)/dz = R’ i(z) + jL’ i(z), (4) - d²V(z)/dz² = R’ di(z)/dz + jL’ di(z)/dz, (8) • Telegrapher’s equation in phasor domain - d i(z)/dz = G’ V(z) + jC’ V(z), (7) substitute (7) to (8) d²V(z)/dz² = (R’ + jL’) (G’+ jC’)V(z), or d²V(z)/dz² - (R’ + jL’) (G’+ jC’)V(z) = 0, (9) d²V(z)/dz² - ²V(z) = 0, (10) ² = (R’ + jL’) (G’+ jC’), (11) Dr. Blanton - ENTC 4307 - Transmission Lines 17

  18. i(z,t) i(z+z,t) L’z R’z V(z,t) V(z+ z,t) G’z C’z - d i(z)/dz = G’ V(z) + jC’ V(z), (7) - dV(z)/dz = R’ i(z) + jL’ i(z), (4) • Telegrapher’s equation in phasor domain Take d /dz on both sides of eq. (7) - d² i(z)/dz² = G’ dV(z)/dz + jC’ dV(z)/dz, (12) Dr. Blanton - ENTC 4307 - Transmission Lines 18

  19. - dV(z)/dz = R’ i(z) + jL’ i(z), (4) • Telegrapher’s equation in phasor domain - d i(z)/dz = G’ V(z) + jC’ V(z), (7) - d² i(z)/dz² = G’ dV(z)/dz + jC’ dV(z)/dz, (12) substitute (4) to (12) d² i(z)/dz² = (R’ + jL’) (G’+ jC’)i(z), or d² i(z)/dz² - (R’ + jL’) (G’+ jC’) i(z) = 0, (9) d² i(z)/dz² - ²i(z) = 0, (13) ² = (R’ + jL’) (G’+ jC’), (11) Dr. Blanton - ENTC 4307 - Transmission Lines 19

  20.  = Re (R’ + jL’) (G’+ jC’) ,  = Im (R’ + jL’) (G’+ jC’) , • Wave equations d²V(z)/dz² - ²V(z) = 0, (10) d² i(z)/dz² - ²i(z) = 0, (13)  =  + j, Dr. Blanton - ENTC 4307 - Transmission Lines 20

  21.  = Re (R’ + jL’) (G’+ jC’) ,  = Im (R’ + jL’) (G’+ jC’) , z -z -z z e e e e • Wave equations d²V(z)/dz² - ²V(z) = 0, (10) d² i(z)/dz² - ²i(z) = 0, (13)  =  + j, Solving the second order differential equation + - V(z) = V0 (14) + V0 + - + i(z) = I0 (15) I0 Dr. Blanton - ENTC 4307 - Transmission Lines 21

  22. + - - + - + and are related to V0 V0 I0 V0 V0 I0 and by characteristic impedance Z0. -z -z z z e e e e • Wave equations + - V(z) = V0 (14) + V0 + - + i(z) = I0 (15) I0 where: and are determined by boundary conditions. Dr. Blanton - ENTC 4307 - Transmission Lines 22

  23. + - V(z) = V0 (14) + V0 + - + i(z) = I0 (15) I0 + - - V0 V0  + - - dV(z)/dz = R’ i(z) + jL’ i(z), (4) i(z) = ) - (V0 V0 = (R’ + jL’) i(z), (16) (R’ + jL’) -z -z z z -z z z -z e e e e e e e e  - - + + - I0 I0 = = V0 V0 (R’ + jL’) (R’ + jL’) • Characteristic impedance Z0 recall: (17) (18) Dr. Blanton - ENTC 4307 - Transmission Lines 23

  24. (R’ + jL’) V0  = (R’ + jL’) (G’+ jC’) +  I0 (R’ + jL’) (G’+j C’)  - + - - + I0 I0 = = V0 V0 (R’ + jL’) (R’ + jL’) • Characteristic impedance Z0 (17) (18) Define characteristic impedance Z0 recall: + Z0  = = Dr. Blanton - ENTC 4307 - Transmission Lines 24

  25. + - V(z) = V0 (14) + V0 + - + i(z) = I0 (15) I0 + V0  = (R’ + jL’) (G’+ jC’) Z0  + I0 (R’ + jL’) (G’+j C’) = z -z -z z e e e e • Summary: (19) (20) Dr. Blanton - ENTC 4307 - Transmission Lines 25

  26. jL’ = Z0 j C’  = (R’ + jL’) (G’+ jC’) j = L’C’ L’C’ (R’ + jL’) (G’+j C’) = • Example, an air line : R’ = 0 , G’ = 0 /, Z0 = 50,  = 20 rad/m, f = 700 MHz L’ = ? and C’ = ? solution: = 50  =  + j,  =  = 20 rad/m Dr. Blanton - ENTC 4307 - Transmission Lines 26

  27. = (R’ + j L’ ) (G’+ jC’) j  = = L’C’ L’C’ • lossless transmission line :  =  + j, = (R’ + jL’) (G’+ jC’) If R’<< j L’ and G’ << jC’,   = 0 lossless line  Dr. Blanton - ENTC 4307 - Transmission Lines 27

  28. jL’ = Z0 j C’  = L’C’ L’C’ L’C’ (R’ + jL’) Z0 1 (G’+j C’)  = 2/ = =  1 L’ = = Vp = / C’ • lossless transmission line : lossless line  = 0   = 2/ Dr. Blanton - ENTC 4307 - Transmission Lines 28

  29. + - V(z) = V0 + V0 c 1 c 1 1 + = = = = = - + i(z) = I0 I0 Z0     = = = = L’C’ L’C’ rr  rr L’C’  L’C’  L’ -jz jz -jz jz e e e e = C’ • For TEM transmission line : L’C’ =  Vp  • summary : Vp  Dr. Blanton - ENTC 4307 - Transmission Lines 29

  30. B A Z0 VL Vg(t) Vi ZL l z = - l z = 0 + + + - - - V0 V0 V0 V0 V0 V0 + - V(z) = V0 + V0 + - + + - - VL iL - i(z) = V0 V0 V0 V0 V0 V0 Z0 Z0 Z0 Z0 Z0 Z0 i(z) V(z) z = 0 z = 0 - ZL Z0 -jz jz jz -jz e e e e = + ZL Z0 • Voltage reflection coefficient : VL = = + - iL = = + ZL = = - Dr. Blanton - ENTC 4307 - Transmission Lines 30

  31. + + + i0 V0 V0 i  = - = -  - - - i0 V0 V0 • Voltage reflection coefficient : - ZL Z0   = + ZL Z0 • Current reflection coefficient : • Notes : • || 1, how to prove it? • If ZL = Z0, = 0. Impedance match, no reflection from the load ZL. Dr. Blanton - ENTC 4307 - Transmission Lines 31

  32. An example : A RL = 50 f = 100MHz Z0 = 100 A’ CL = 10pF z = 0 ZL = RL + j/CL = 50 –j159 - ZL Z0  = + ZL Z0 Dr. Blanton - ENTC 4307 - Transmission Lines 32

More Related