1. 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 Fall DeHon

2. 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 Fall DeHon

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

4. Intuitive: Lossless Pulses travel as waves without distortion
Penn ESE370 Fall DeHon

5. 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 Fall DeHon

6. 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 Fall DeHon

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

8. End of Line Reflection
Penn ESE370 Fall DeHon

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

10. R≠Z0 What happens? 75 W termination on 50 W line
Penn ESE370 Fall DeHon

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

12. 50W line, 75W termination
Penn ESE370 Fall DeHon

13. 75W line, 50W termination
Penn ESE370 Fall DeHon

14. Series Termination
What happens here?
Penn ESE370 Fall DeHon

15. Simulation
Penn ESE370 Fall DeHon

16. 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 Fall DeHon

17. Termination Cases Parallel at Sink Series at Source Pix pix
Penn ESE370 Fall DeHon

18. Admin
Lab on Friday
Lecture Wednesday
Penn ESE370 Fall DeHon

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