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Finding input impedance with smith chart

  1. Dec 4, 2013 #1
    1. The problem statement, all variables and given/known data
    Find an input impedance of a 50 Ω transmission line of length transmission line of length 3λ/8
    terminated with a load of 10 Ω.


    2. Relevant equations
    Zl'=(Zl/Zc)
    Zin(L)=(Zl-jtan(kL))/(1+jZltan(kL))


    3. The attempt at a solution
    I have uploaded my attempt how far off am I?
     

    Attached Files:

  2. jcsd
  3. Dec 4, 2013 #2
    Ok so 0 on the smith chart is the line which goes down the middle and R=0 is at the final outer 0 but where is the imaginary part 0.02?
     
  4. Dec 4, 2013 #3
    Look at the values on the outer ring. The imaginary lines will extend from there. Why are you looking for the input impedance on the smith chart after computing it? Normally if you are asked to find the input impedance using the smith chart you do not actually compute the input impedance numerically, you actually do the entire analysis on the smith chart.
     
    Last edited: Dec 4, 2013
  5. Dec 4, 2013 #4
    Ok so how should I proceed? I am confused do you have any more hints
     
  6. Dec 4, 2013 #5
    To find the input impedance using the smith chart you want to enter the smith chart at the normalized load impedance. You then rotate about the point where the reflection coefficient is zero clockwise until your starting length is increased by 3λ/8. The starting length will be the outer point that is associated with a straight line segment extending from the centre of the smith chart (zero reflection) and passing through your normalized load impedance.

    It is rather tedious to try and explain this process via words. Graphical demonstrations are much easier to get the point across.
     
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