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ESE370: Circuit-Level This Week Modeling, Design, and Optimization for Digital Systems Day 34: December 1, 2010 Transmission Lines 1 Penn ESE370 Fall2010 -- DeHon • • • • • • • • General wire formulation Lossless Transmission Line End of Transmission Line? Termination Where arise? Implications Discuss Lossy See in action in lab Penn ESE370 Fall2010 -- DeHon 2 Intuitive: Lossless Transmission Line • Pulses travel as waves without distortion • When resistance is negligible – Have LC wire = Lossless Transmission Line – More typical of Printed Circuit Board wires 3 Penn ESE370 Fall2010 -- DeHon Impedance Propagation • • w=1/sqrt(LC) – Rate of propagation – Delay linear in length • V(x,t) = A+Be-(wt+x) Be-(wt+x)=LCw2Be-(wt+x) w= • Ici=CdVi/dt • Ici=wCBe-(wt+x) • Z0 = Vi/Ii ~Vi/Ici = 1/wC = 1/(C/sqrt(LC)) 1 LC w= • CL = εµ c0 ε r µr € rµr) – w=1/sqrt(εµ)=c0/sqrt(ε – Where c0=speed of light in vacuum=30cm/ns Penn ESE370 Fall2010 -- DeHon € 4 Penn ESE370 Fall2010 -- DeHon 5 – (really Ii --- differs in phase) Vi-1 Ii Vi Ii+1 Vi+1 Ici Penn ESE370 Fall2010 -- DeHon 6 1 End of Line Reflection Infinite Lossless Transmission Line • Transmission line looks like resistive load Z0 = L C Z0 € ⎛ R − Z 0 ⎞ Vi ⎜ ⎟ = Vr ⎝ R + Z 0 ⎠ • Input waveform travels down line at velocity 1 – Without distortion w= LC 7 Penn ESE370 Fall2010 -- DeHon 8 Penn ESE370 Fall2010 -- DeHon € € ⎛ 2R ⎞ Vi ⎜ ⎟ = Vt ⎝ R + Z 0 ⎠ € Back at Source? R≠Z0 • What happens at source? • What happens? – Depends on how terminated – Looks like at sink end – 75 Ω termination on 50 Ω line – 50 Ω termination on 75 Ω line 9 Penn ESE370 Fall2010 -- DeHon Penn ESE370 Fall2010 -- DeHon 10 50Ω line, 75Ω termination Simulation • For these, with direct drive from voltage source – Source looks like short circuit • Source cannot be changed Penn ESE370 Fall2010 -- DeHon 11 ⎛ R − Z 0 ⎞ ⎛ 75 − 50 ⎞ Vr = Vi ⎜ ⎟ = 0.2Vi ⎟ = Vi ⎜ ⎝ 75 + 50 ⎠ Penn ESE370 Fall2010 -- DeHon ⎝ R + Z 0 ⎠ 12 € 2 75Ω line, 50Ω termination Series Termination • What happens here? ⎛ R − Z 0 ⎞ ⎛ 50 − 75 ⎞ Vr = Vi ⎜ ⎟ = −0.2Vi ⎟ = Vi ⎜ ⎝ 50 + 75 ⎠ R + Z Penn ESE370 Fall2010 -- DeHon⎝ 0 ⎠ 13 14 Penn ESE370 Fall2010 -- DeHon € Simulation Series Termination • Rseries = Z0 • Initial voltage divider – Half voltage pulse down line • End of line open circuit – sees single transition to full voltage • Reflection returns to source and sees termination Rseries = Z0 • No further reflections Penn ESE370 Fall2010 -- DeHon 15 16 Penn ESE370 Fall2010 -- DeHon Termination Cases Admin • Parallel at Sink • Lab on Friday – Pix – Lecture Wednesday • Series at Source – pix Penn ESE370 Fall2010 -- DeHon 17 Penn ESE370 Fall2010 -- DeHon 18 3 Idea (still working on) • Transmission lines – high-speed – high throughput – long-distance signaling • Termination • Signal quality Penn ESE370 Fall2010 -- DeHon 1 c0 = LC ε r µr L Z0 = C w= € ⎛ R − Z 0 ⎞ Vr = Vi ⎜ ⎟ € ⎝ R + Z 0 ⎠ 19 € 4