Day 34: December 1, 2010 Transmission Lines ESE370: Circuit-Level Modeling, Design, and Optimization for Digital Systems Day 34: December 1, 2010 Transmission Lines Penn ESE370 Fall2010 -- DeHon

This Week 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

Transmission Line When resistance is negligible Have LC wire = Lossless Transmission Line More typical of Printed Circuit Board wires Penn ESE370 Fall2010 -- DeHon

Intuitive: Lossless Pulses travel as waves without distortion Penn ESE370 Fall2010 -- DeHon

Propagation CL = em Be-(wt+x)=LCw2Be-(wt+x) w=1/sqrt(LC) Rate of propagation Delay linear in length CL = em w=1/sqrt(em)=c0/sqrt(ermr) Where c0=speed of light in vacuum=30cm/ns Penn ESE370 Fall2010 -- DeHon

Impedance Ici=CdVi/dt Ici=wCBe-(wt+x) V(x,t) = A+Be-(wt+x) Ici=CdVi/dt Ici=wCBe-(wt+x) Z0 = Vi/Ii ~Vi/Ici = 1/wC = 1/(C/sqrt(LC)) (really Ii --- differs in phase) Ii+1 Ii Vi-1 Vi Vi+1 Ici Penn ESE370 Fall2010 -- DeHon

Infinite Lossless Transmission Line Transmission line looks like resistive load Input waveform travels down line at velocity Without distortion Z0 Penn ESE370 Fall2010 -- DeHon

End of Line Reflection Penn ESE370 Fall2010 -- DeHon

Back at Source? What happens at source? Depends on how terminated Looks like at sink end Penn ESE370 Fall2010 -- DeHon

R≠Z0 What happens? 75 W termination on 50 W line Penn ESE370 Fall2010 -- DeHon

Simulation For these, with direct drive from voltage source Source looks like short circuit Source cannot be changed Penn ESE370 Fall2010 -- DeHon

50W line, 75W termination Penn ESE370 Fall2010 -- DeHon

75W line, 50W termination Penn ESE370 Fall2010 -- DeHon

Series Termination What happens here? Penn ESE370 Fall2010 -- DeHon

Simulation Penn ESE370 Fall2010 -- DeHon

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

Termination Cases Parallel at Sink Series at Source Pix pix Penn ESE370 Fall2010 -- DeHon

Admin Lab on Friday Lecture Wednesday Penn ESE370 Fall2010 -- DeHon

Idea (still working on) Transmission lines high-speed high throughput long-distance signaling Termination Signal quality Penn ESE370 Fall2010 -- DeHon