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CSE 464 Transmission Line Equations (Dally/Poulton Notation) January 2009

CSE 464 Transmission Line Equations (Dally/Poulton Notation) January 2009. Based on Notes by Fred U. Rosenberger David M. Zar Washington University in St. Louis dzar@wustl.edu. Transmission Line Equations. Superposition (if linear). General Equations. For Parallel Plates:.

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CSE 464 Transmission Line Equations (Dally/Poulton Notation) January 2009

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  1. CSE 464 Transmission Line Equations(Dally/Poulton Notation) January 2009 Based on Notes by Fred U. Rosenberger David M. Zar Washington University in St. Louis dzar@wustl.edu

  2. Transmission Line Equations Superposition (if linear)

  3. General Equations For Parallel Plates:

  4. Transmission Line Equations Zs +- Z0 Vs + - +- V0 ZT Vl 0 L (ZS-Z0)/(ZS + Z0)= KrS (ZT-Z0)/(ZT + Z0)= KrT

  5. General Equations (VT = 0)Use Superposition for Multiple Sources 1) 2l since we have to go “there and back” to see it at the start of the line 2) 2) into 1), 3) At arbitrary x, 4) From 2) & 3), 5)

  6. Equations Continued Repeat 3) into 4), 3) into 5), • At x = 0, • At x = l, • Now can find V0, Vl at any time.

  7. Example Driving T-Line Apply to problem, Zs Z0 ZT This is the time to go from l0 l for the last (N) time.

  8. Steady State Value and Error Term, Example With algebra, Attenuation in steady state Error 0 as N • For We get

  9. Example Continued • For 2 foot line, this could be on the order of 85ns (or even 3.55 ns for a 1 inch line!) • What to do? • Wait a long time • Real wire will have some resistance (Zs≠0) • CS solution: use 1900 Ohm transmission Line • Reduce resistance of receiver to match t-line • Increased power • May be a problem with driver resistance (e.g. 10 to 50 Ohms) • Increase resistance of driver to match t-line • 100 Ohms in series with driver gives 2.5% error after only l/v,or after 2ns for one foot line (this is the minimum possible)

  10. Transmission Line Equations for Wire r1 r2 Wire over ground plane (warning, not accurate for r close to s) r s Between 2 Wires: 1/2 capacitance of wire over ground plane

  11. PC Board Equations Parallel Plates (ignoring fringing) s w

  12. w t air h dielectric PC Board Equations (Careful here, approximations grossly wrong for some values: large w/h) Microstrip Stripline w h1 b t h2=h1

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