Electromagnetics - Telegraphers EQs - 3 parallel lines

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SUMMARY

The discussion focuses on a multisection transmission line comprising three lossless lines connecting a 5V step source with a 6Ω output impedance to two 66Ω load resistances. The line parameters are L = 364.5 nH/m and C = 125 pF/m, with a length of 40 cm. The user successfully calculated the necessary variables using the equations for reflection coefficients and characteristic impedance but encountered confusion regarding a 0.2V bounce in the voltage diagram. The user is seeking clarification on the origin of this voltage in the bounce diagram.

PREREQUISITES
  • Understanding of transmission line theory
  • Familiarity with reflection coefficients (Γ_S and Γ_L)
  • Knowledge of characteristic impedance (Z_0) calculations
  • Ability to sketch and interpret bounce diagrams
NEXT STEPS
  • Study the derivation of reflection coefficients in transmission lines
  • Learn about voltage standing wave ratios (VSWR) in transmission lines
  • Explore the impact of load mismatches on voltage reflections
  • Investigate advanced transmission line modeling techniques
USEFUL FOR

Electrical engineering students, transmission line designers, and professionals involved in signal integrity analysis will benefit from this discussion.

VinnyCee
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Homework Statement



A multisection transmission line consists of three lossless transmission lines used to connect an ideal step source of 5V amplitude and 6\Omega output impedance to two separate load resistances of 66\Omega each. All three lines are characterized by the line parameters L = 364.5 nH/m and C = 125 pF/m and length of 40cm. Sketch voltages Vs and V_L versus t for 0 < t < 20 ns.

http://img23.imageshack.us/img23/5678/problem218lq7.jpg


Homework Equations



\Gamma_S\,=\,\frac{R_S\,-\,Z_0}{R_S\,+\,Z_0}

\Gamma_L\,=\,\frac{R_L\,-\,Z_0}{R_L\,+\,Z_0}

Z_0\,=\,\sqrt{\frac{L}{C}}

v_p\,=\,\frac{1}{\sqrt{L\,C}}

t_d\,=\,\frac{l}{v_p}


The Attempt at a Solution



http://img168.imageshack.us/img168/8978/problem218solnpu5.jpg

I found all the variables quite easily using the formulas above. I started making the bounce diagram and got a few t_d into it. But when I get to 3t_d=8.1 ns, I am confused by one of the bounced voltages. I have the answer, but I have no idea where the writers are getting a 0.2V bounce in the diagram.

On the right side, between 8.1ns < t < 10.8ns, there are three voltages. 0.8V, -0.1V and the mysterious 0.2V. I understand that the 0.8V line comes from the 1.2V on the left, and the -0.1V line comes from the reflection of the 0.3V line above. Actually there should be two of the 0.1V lines considering the reflection from both of the right hand lines. But where is that third 0.2V line coming from?

Please help!
 
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The bounce diagram is wrong? I really can't think of any other explanation. I will ask TA tomorrow I guess!
 

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