# Transmission Lines. Transmission Lines :: Topics. Introduction Wave Propagation Termination Reflections Summary. Introduction.

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1 Transmission Lines Digial Design and Compuer Archiecure David Money Harris and Sarah L. Harris Transmission Lines :: Topics Inroducion Wave Propagaion Terminaion Reflecions Summary TL-<1> TL-<2> Inroducion Reurn Pahs We have assumed wires are equipoenial nodes Same volage along he enire lengh of wire Signals acually propagae a he speed of ligh Volage and curren will vary along he line Imporan for long wires or high speeds Transmission lines capure his behavior Curren always flows in loops We usually hink abou he curren flowing ou along a wire Bu here mus be a pah for he curren o reurn Ofen reurns hrough he GND nework If his is no well conrolled, ineresing hings may happen TL-<3> TL-<4> 1

2 Transmission Lines Many ways o provide a signal and a reurn pah Prined Circui Board Typically use 4 or more muliple layers Signal races Power/GND planes Coaxial Cable Signal flows in he inner conducor Reurns in ouer ground conducor Ad-Hoc Curren may reurn hrough unknown pahs May increase delay and cause unpredicable noise TL-<> Speed of Ligh in a Medium Speed of ligh in free space: 1 v c με 8 3 m/s Speed of ligh in a medium 1 1 v με LC For a PCB wih ε 4 ε,v c/2 1 cm/ns TL-<6> Transmission Time Characerisic Impedance Fligh ime along a wire of lengh l d l / v Example: a 12 race across a large board has a 2 ns fligh ime The characerisic impedance of a ransmission line, Z, is he raio of volage o curren in a wave raveling along he wire No he resisance of he wire (ypically close o ) Depends on inducance and capaciance Typically o 7 Ω Z L C I V - + Z L C TL-<7> TL-<8> 2

3 Transmission Line Behavior Mached Terminaion Visualize wave of volage propagaing along he line a he speed of ligh When he wave his he end, i may be absorbed or refleced, depending on he erminaion Reflecions ravel back along he line, adding o he volage already on he line Afer all reflecions die ou, he volage will be he same as if he line were a simple wire Terminaions Mached Open Shor Mismached Z L Z Wave of V V s Wave ravels a velociy v Wave is absorbed by Z L Equivalen seady-sae circui Final value V s d/3 d d d TL-<9> TL-<> Mached Source and Load Terminaion Z S Z L Z Open Terminaion Z S Z Z L Volage divider a source Equivalen seady-sae circui Final value V s /2 Curren flowing down he line has nowhere o go a he end and mus reflec TL-<11> TL-<12> 3

4 Shor Terminaion Z S Z Z L Volage a he end mus be, so a negaive wave mus be refleced Reflecance Coefficien When a wave of volage V i reaches eiher end of a ransmission line, par (V r ) will be refleced if he erminaion i impedance Z T does no mach he line impedance Vr kv r i ZT Z kr Z + Z T Special cases Z T Z : k r (mached load, wave absorbed) Z T : k r 1 (open load, wave refleced) Z T : k r -1 (shor load, negaive wave refleced) TL-<13> TL-<14> Mismached Terminaion (Example 1) Mismached Terminaion (Example 2) Load erminaion mismached Boh erminaions mismached 7 2d 4d 6d k r (7-)/(7+) 1/ Wave of (1/)V s /2 V s / reflecs off end, bringing oal o 3V s / Wave of V V s / k r 1 a end, 4/ a sar Waves reflec off each end unil line sars o approach is final value of V s 7 d d 7 d 11 d 13 d 17 d d 3 d d TL-<1> TL-<16> 4

5 Bounce Diagram When o use Transmission Line Models Bounce diagram shows reflecions 7 2d 4d 6d 7 d d 7 d 11 d 13 d 17 d d 3 d d TL-<17> Wires should be modeled as ransmission lines when d > 2% of he rise/fall ime of he signal i.e. when reflecions don dissipae while signal is ransiioning Recall ha signals on a PCB ravel a 1 cm/ns For a TTL signal wih a ns edge rae, rea a wire as a ransmission line if i exceeds 3 cm For a fas signal wih a 2 ns edge rae, rea a wire as a ransmission line if i exceeds 6 cm (2. inches) Don make signals faser han necessary Copyrigh 2 Elsevier TL-<18> Proper Terminaion Comparison Transmission lines should be properly erminaed a he load (parallel) or source (series) Parallel Terminaion + All poins on he line see valid logic levels + Good for busses wih muliple receivers - Consumes los of power (V 2 /Z ) Series Terminaion + Consumes lile power - Midpoin sees indeerminae logic level for a ime - Only suiable for poin-o-poin links Copyrigh 2 Elsevier TL-<19> Copyrigh 2 Elsevier TL-<2>

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