Download presentation

Presentation is loading. Please wait.

Published byJoey Hudgeons Modified over 2 years ago

1
Penn ESE370 Fall2011 -- DeHon 1 ESE370: Circuit-Level Modeling, Design, and Optimization for Digital Systems Day 33: November 30, 2011 Transmission Line Introduction and Analysis

2
Next few Lectures/Lab Where arise? General wire formulation Lossless Transmission Line See in action in lab (Friday) End of Transmission Line? Termination Discuss Lossy Implications Penn ESE370 Fall2011 -- DeHon 2

3
Where Transmission Lines Arise Penn ESE370 Fall2011 -- DeHon 3

4
Transmission Lines Cable: coaxial PCB –Strip line –Microstrip line Twisted Pair (Cat5) Penn ESE370 Fall2010 -- DeHon 4

5
Transmission Lines How do these wires behave? –25m of category-5 cable? –VGA cable? (Analog?) How differ from –Ideal equipotential? –RC-wire on chip? Penn ESE370 Fall2011 -- DeHon 5

6
Transmission Lines This is what wires/cables look like –Aren’t an ideal equipotential –Signals do take time to propagate –Maintain shape of input signal Within limits –Shape and topology of wiring effects how signals propagate …and the noise effects they see Penn ESE370 Fall2010 -- DeHon 6

7
Transmission Lines Need to understand –How to model how to reason about –What can cause noise –How to engineer high performance communication Penn ESE370 Fall2010 -- DeHon 7

8
Wire Formulation Penn ESE370 Fall2011 -- DeHon 8

9
Wires In general, our “wires” have distributed R, L, C components Penn ESE370 Fall2011 -- DeHon 9

10
RC Wire When R dominates L –We have the distributed RC Wires we saw on Day 21 –Typical of on-chip wires in ICs Penn ESE370 Fall2011 -- DeHon 10

11
Transmission Line When resistance is negligible –Have LC wire = Lossless Transmission Line –More typical of Printed Circuit Board wires Penn ESE370 Fall2011 -- DeHon 11

12
Build Intuition from LC What did one LC do? What will chain do? Penn ESE370 Fall2011 -- DeHon 12

13
Intuitive: Lossless Pulses travel as waves without distortion –(up to a characteristic frequency) Penn ESE370 Fall2011 -- DeHon 13

14
SPICE Simulation Penn ESE370 Fall2011 -- DeHon 14

15
SPICE Simulation Penn ESE370 Fall2011 -- DeHon 15

16
Penn ESE370 Fall2011 -- DeHon 16 Contrast RC Wire

17
Visualization See: http://www.research.ibm.com/people/r/r estle/Animations/DAC01top.html http://www.research.ibm.com/people/r/r estle/Animations/DAC01top.html Penn ESE370 Fall2011 -- DeHon 17

18
Setup Relations Penn ESE370 Fall2011 -- DeHon 18 ViVi V i+1 V i-1 IiIi I i+1 I ci

19
Setup Relations V i -V i-1 = I ci = I i -I i+1 = Penn ESE370 Fall2011 -- DeHon 19 ViVi V i+1 V i-1 IiIi I i+1 I ci

20
Setup Relations V i -V i-1 = Ldi i /dt I ci =CdV i /dt I i -I i+1 =I ci Penn ESE370 Fall2011 -- DeHon 20 ViVi V i+1 V i-1 IiIi I i+1 I ci i is spatial dimension V i at different positions

21
Setup Relations V i -V i-1 = Ldi i /dt I ci =CdV i /dt I i -I i+1 =I ci Penn ESE370 Fall2011 -- DeHon 21 ViVi V i+1 V i-1 IiIi I i+1 I ci Maybe sign wrong on LdI/dt

22
Reduce to Single Equation Eliminate I ci ? I i -I i+1 =I ci dI i /dt-dI i+1 /dt=dI ci /dt I ci =CdV i /dt dI ci /dt i =Cd 2 V i /dt di i /dt - di i+1 /dt=Cd 2 V i /dt Penn ESE370 Fall2011 -- DeHon 22

23
Reduce to Single Equation di i /dt - di i+1 /dt=Cd 2 V i /dt V i -V i-1 = Ldi i /dt V i+1 -V i = Ldi i+1 /dt Eliminate Is ? V i -V i-1 -(V i+1 -V i )= Ldi i /dt - Ldi i+1 /dt d 2 V/dx =-LCd 2 V/dt V i+1 -V i-1 =-LCd 2 V i /dt Penn ESE370 Fall2011 -- DeHon 23 Multiple sign problems

24
Implication V i+1 -V i-1 =LCd 2 V i /dt Once V i settles, settle to same value d 2 V/dx = LCd 2 V/dt Wave equation V(x,t) = A+Be (x-wt) Be (x-wt) =LCw 2 Be (x-wt) w=1/sqrt(LC) –Rate of propagation Penn ESE370 Fall2011 -- DeHon 24

25
Propagation V(x,t) = A+Be (x-wt) If V(1cm,1ns)=Va and w = 10cm/ns for what t does V(2cm,t)=Va ? Penn ESE370 Fall2011 -- DeHon 25

26
Propagation V(x,t) = A+Be (x-wt) If V(x0,t0)=Va And V(x0+ x,t0+ t)=Va What is w? Penn ESE370 Fall2011 -- DeHon 26

27
Propagation Rate in Example L=1uH C=1pF What is w ? Penn ESE370 Fall2011 -- DeHon 27

28
Signal Propagation Penn ESE370 Fall2011 -- DeHon 28

29
Propagation Be (x-wt+x) =LCw 2 Be (x-wt) w=1/sqrt(LC) –Rate of propagation –Delay linear in length Compare RC wire delay quadratic in length Penn ESE370 Fall2011 -- DeHon 29

30
Contrast RC Wire Penn ESE370 Fall2011 -- DeHon 30

31
Propagation Be (wt+x) =LCw 2 Be (wt+x) w=1/sqrt(LC) –Rate of propagation –Delay linear in length Compare RC wire delay quadratic in length From Day 32 we know for wire: CL = –w=1/sqrt c 0 /sqrt r r –Where c 0 =speed of light in vacuum=30cm/ns Penn ESE370 Fall2011 -- DeHon 31

32
Class Ended Here Penn ESE370 Fall2011 -- DeHon 32

33
Wire “Resistance” What is the resistance at V i ? Penn ESE370 Fall2011 -- DeHon 33 ViVi V i+1 V i-1 IiIi I i+1 I ci

34
Wire “Resistance” Q=CV I = dQ/dt Moving at rate w I=wCV R=V/I=1/(wC) Penn ESE370 Fall2011 -- DeHon 34 ViVi V i+1 V i-1 IiIi I i+1 I ci

35
Impedance Z 0 =R= 1/wC = 1/(C/sqrt(LC)) Penn ESE370 Fall2011 -- DeHon 35 ViVi V i+1 V i-1 IiIi I i+1 I ci

36
Impedance Assuming infinitely long wire, how look different at V i, V i+1, V i+2 ? Penn ESE370 Fall2011 -- DeHon 36 ViVi V i+1 V i-1 IiIi I i+1 I ci

37
Impedance Transmission line has a characteristic impedance –Looks to driving circuit like a resistance Penn ESE370 Fall2011 -- DeHon 37

38
Infinite Lossless Transmission Line Transmission line looks like resistive load Input waveform travels down line at velocity –Without distortion Penn ESE370 Fall2011 -- DeHon 38 Z0Z0

39
End of Line What happens at the end of the transmission line? –Short Circuit –Terminate with R=Z 0 –Open Circuit Experimentally in Lab Friday Mathematically in Class Monday Penn ESE370 Fall2011 -- DeHon 39

40
Admin In Lab on Friday –Lab instructions online HW6 –Includes writeup for previous and this lab –Also two questions –Due Monday Project 3 –Should have tools to attack Penn ESE370 Fall2011 -- DeHon 40

41
Idea Signal propagate as wave down transmission line –Delay linear in wire length –Speed –Impedance Penn ESE370 Fall2011 -- DeHon 41

Similar presentations

Presentation is loading. Please wait....

OK

Time for a BREAK! You have 45 Minutes.

Time for a BREAK! You have 45 Minutes.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on combination of resistances training Ppt on self awareness worksheets Ppt on juvenile rheumatoid arthritis Ppt on law against child marriage pictures Ppt on conservation of wildlife and natural vegetation of india Ppt on railway track security system Decoding in reading ppt on ipad Download ppt on ghosts and spirits Download ppt on strings in c language Ppt on earth damage