Penn ESE370 Fall DeHon 1 ESE370: Circuit-Level Modeling, Design, and Optimization for Digital Systems Day 35: December 5, 2012 Transmission Lines Modeling and Termination

Transmission Line Agenda Where arise? General wire formulation Lossless Transmission Line See in action in lab Impedance End of Transmission Line? Termination Discuss Lossy Implications Penn ESE370 Fall DeHon 2

From Day 33 Signal propagate as wave down transmission line V(x,t) = A+Be (x-wt) –Delay linear in wire length –Speed Penn ESE370 Fall DeHon 3

Wire “Resistance” What is the resistance at V i ? Q to charge V i ? I i given velocity w? R = V i /I i ? Penn ESE370 Fall DeHon 4 ViVi V i+1 V i-1 IiIi I i+1 I ci

Wire “Resistance” Q=CV I = dQ/dt Moving at rate w I=wCV R=V/I=1/(wC) Penn ESE370 Fall DeHon 5 ViVi V i+1 V i-1 IiIi I i+1 I ci

Impedance Z 0 =R= 1/wC = 1/(C/sqrt(LC)) Penn ESE370 Fall DeHon 6 ViVi V i+1 V i-1 IiIi I i+1 I ci

Impedance Assuming infinitely long wire, how look different at V i, V i+1, V i+2 ? Penn ESE370 Fall DeHon 7 ViVi V i+1 V i-1 IiIi I i+1 I ci

Impedance Transmission line has a characteristic impedance –Looks to driving circuit like a resistance Penn ESE370 Fall DeHon 8

Infinite Lossless Transmission Line Transmission line looks like resistive load Input waveform travels down line at velocity –Without distortion Penn ESE370 Fall DeHon 9 Z0Z0

End of Line What happens at the end of the transmission line? –Short Circuit Hint: what must happen in steady state? –Terminate with R=Z 0 –Open Circuit Penn ESE370 Fall DeHon 10

Short Penn ESE370 Fall DeHon 11

Terminate R=Z 0 Penn ESE370 Fall DeHon 12

Open Penn ESE370 Fall DeHon 13

Longer LC (open) 40 Stages L=100nH C=1pF Stage delay? Drive with 2ns Pulse No termination (open circuit) Penn ESE370 Fall DeHon 14

Pulse Travel RC Penn ESE370 Fall DeHon 15 V1,V3,V4,V5,V6 about 10 stages apart

Analyze End of Line Penn ESE370 Fall DeHon 16

Analyze End of Line Incident wave V i =I i ×Z 0 end end V=IR relationships? Relate all three V’s using R, Z 0 Penn ESE370 Fall DeHon 17

Analyze End of Line Incident wave V i =I i ×Z 0 KCL: I i =I r +I t KVL: V i +V r =V t V r =I r ×Z 0 I r =V r /Z 0 V t =I t ×R I t =V t /R I i =V i /Z 0 Penn ESE370 Fall DeHon 18

Analyze End of Line V i +V r =V t Penn ESE370 Fall DeHon 19 Eliminate V t

Analyze End of Line V i +V r =V t Penn ESE370 Fall DeHon 20

Analyze End of Line V i +V r =V t Penn ESE370 Fall DeHon 21

Reflection Sanity check with previous –Short –Matched –Open Penn ESE370 Fall DeHon 22

Pulse Travel RC Penn ESE370 Fall DeHon 23

Visualization Penn ESE370 Fall DeHon 24

Back to Source Penn ESE370 Fall DeHon 25

Back at Source? What happens at source? –Depends on how terminated –Looks like at sink end Penn ESE370 Fall DeHon 26

R≠Z 0 What happens? –75  termination on 50  line –“Short-Circuit” source? Penn ESE370 Fall DeHon 27

Simulation For these, with direct drive from voltage source –Source looks like short circuit ( not typical of CMOS ) Source cannot be changed Penn ESE370 Fall DeHon 28

50  line, 75  termination Penn ESE370 Fall DeHon 29

Step Response Penn ESE370 Fall DeHon 30

Series Termination What happens here? Penn ESE370 Fall DeHon 31

Simulation Penn ESE370 Fall DeHon 32

Series Termination R series = Z 0 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 R series = Z 0 No further reflections Penn ESE370 Fall DeHon 33

Termination Cases Parallel at Sink –Pix Series at Source –pix Penn ESE370 Fall DeHon 34

CMOS Driver / Receiver What does a CMOS driver look like at the source? –I d,sat =1200  A/  45nm What does a CMOS inverter look like at the sink? Penn ESE370 Fall DeHon 35

Admin Project 3 –Due Friday –Make sure you’ve looked at min-size inverter baseline case –Suggest think through recommendations and hints before Paul’s office hours Wednesday Penn ESE370 Fall DeHon 36

Idea Signal propagate as wave down transmission line –Delay linear in wire length –Speed –Impedance Behavior at end of line depends on termination Both src and sink are “ends” Penn ESE370 Fall DeHon 37