lecture3_ee689_tlines

lecture3_ee689_tlines - Sam Palermo Analog &...

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Unformatted text preview: Sam Palermo Analog & Mixed-Signal Center Texas A&M University ECEN689: Special Topics in High-Speed Links Circuits and Systems Spring 2011 Lecture 3: Transmission Lines Announcements HW1 due 1/28 One page summary of recent link design paper Lecture Reference Material Dally, Chapter 3.1 3.4 2 Agenda Transmission Lines Propagation constant Characteristic impedance Loss Reflections Termination examples Differential transmission lines 3 Wire Models Model Types Ideal Lumped C, R, L RC transmission line LC transmission line RLGC transmission line Condition for LC or RLGC model ( vs RC ) 4 L R f 2 Wire R L C >f (LC wire) AWG24 Twisted Pair 0.08/m 400nH/m 40pF/m 32kHz PCB Trace 5/m 300nH/m 100pF/m 2.7MHz On-Chip Min. Width M6 (0.18m CMOS node) 40k/m 4H/m 300pF/m 1.6GHz RLGC Transmission Line Model 5 ( ) ( ) ( ) t t x I L t x RI x t x V = , , , ( ) ( ) ( ) t t x V C t x GV x t x I = , , , dx As (1) (2) General Transmission Line Equations Time-Harmonic Transmission Line Eqs. Assuming a traveling sinusoidal wave with angular frequency, 6 ( ) ( ) ( ) x I L j R dx x dV + = ( ) ( ) ( ) x V C j G dx x dI + = Differentiating (3) and plugging in (4) (and vice versa) ( ) ( ) x V dx x V d 2 2 2 = ( ) ( ) x I dx x I d 2 2 2 = where is the propagation constant ( )( ) ( )-1 m C j G L j R j + + = + = (5) (6) Time-Harmonic Transmission Line Equations (3) (4) Transmission Line Propagation Constant Solutions to the Time-Harmonic Line Equations: 7 ( ) ( ) ( ) x r x f r f e V e V x V x V x V + = + = What does the propagation constant tell us? Real part ( ) determines attenuation/distance (Np/m) Imaginary part ( ) determines phase shift/distance (rad/m) Signal phase velocity ( ) ( ) ( ) x r x f r f e I e I x I x I x I + = + = where ( )( ) ( )-1 m C j G L j R j + + = + = (m/s) = Transmission Line Impedance, Z...
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This note was uploaded on 01/01/2012 for the course ECEN 689 taught by Professor Enjeti during the Spring '07 term at Texas A&M.

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lecture3_ee689_tlines - Sam Palermo Analog &...

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