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Two port network model

  1. Sep 25, 2013 #1
    1. The problem statement, all variables and given/known data
    Calculate the characteristic impedance ( Z0) of the two port network shown below:

    Could you help me with this question please.


    2. Relevant equations



    3. The attempt at a solution
     

    Attached Files:

  2. jcsd
  3. Sep 25, 2013 #2

    gneill

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    Staff: Mentor

    agata78, the Relevant Equations and Attempt at a Solution sections are not optional. If you want help, you'll have to show your attempt first so we'll know how to help you. We can't do your homework for you!
     
  4. Sep 26, 2013 #3
    Calculate the characteristic impedance (Z0) of the two port network shown below:

    In this example :
    R1 = 40 ohm
    R2 = 40 ohm
    R3 = 20 ohm

    V1 = I1 (R1+R2)

    Then, Z11 = V1/I1 = R1+R3 = 40+20 = 60 ohm

    V2 = V1 (R3 / R1+R3) = I1 (R3+ R1) (R3 / (R1+R3)) = I1 R3

    Then, Z21 = V2 / I1 = R3 = 20 ohm

    Am I correct so far?
     
    Last edited: Sep 26, 2013
  5. Sep 26, 2013 #4

    gneill

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    Staff: Mentor

    Sure. Note that you can drive a port with a current source rather than a voltage source. This might make some of your work easier, not having to fiddle about with voltage dividers and determining the input current separately.

    For example, for Z21 if you drive I1 into the first port then the output voltage on the second port is clearly V2 = I1*20Ω, yielding V2/I1 = 20Ω.
     
  6. Sep 27, 2013 #5
    I found the way to calculate T network, where Zor is a characteristic impedance

    Zoc= R1 + R2 = 40 + 20 = 60Ω

    Zso = (R1 * R2 ) /( R1 + R2 ) + R1

    Zso= (40 + 20) / (40+ 20 ) + 40

    Zso= 800/ 60 + 40 = 13.333+ 40 = 53.333Ω


    Zor= √ Zoc Zsc = √60 + 53.333= √ 113.333 = 10.645 Ω

    I hope im on right path this time
     
  7. Sep 27, 2013 #6
    This may or may not help you or not...
    But the key moment when I was learning 2 port neworks is that Z and Y (I think dont have access to my notes atm) are bassically you just doing Mesh and Nodal Analysis
     
  8. Sep 28, 2013 #7
    I am still confused. Is the workings out in my previous posting correct or incorrect?

    I don't want to start going down the wrong track.
     
  9. Sep 28, 2013 #8

    The Electrician

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    Gold Member

    The part in red is incorrect. You have Zor = sqrt(Zoc) + Zsc

    It should be Zor = sqrt(Zoc * Zsc) = sqrt(60 * 53.333) = sqrt(3200) = 56.57
     
  10. Sep 29, 2013 #9
    Zoc = R1 + R2 = 40 + 20 = 60Ω

    Zso = (R1 * R2 ) /( R1 + R2 ) + R1

    Zso = (40 + 20) / (40+ 20 ) + 40

    Zso = 800/ 60 + 40 = 13.333+ 40 = 53.333Ω


    Zor = √ Zoc Zsc = √60 x 53.333 = √ 3200 = 56.568

    Characteristic Impedance = 56.57 Ω

    Thanks for your help! Can you please let me know that this is the correct answer for the Characteristic Impedance or is there further calculations?
     
  11. Sep 30, 2013 #10

    The Electrician

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    Gold Member

    This is correct.
     
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