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Transmission line and measuring Zo

  1. Aug 21, 2016 #1
    1. The problem statement, all variables and given/known data
    upload_2016-8-21_21-29-5.png
    Figure 2:
    upload_2016-8-21_21-30-4.png

    2. Relevant equations


    3. The attempt at a solution

    3.2) I made an equation for the input voltage and input current
    Vi = Vs*(Zi)/(Zi+Rs+Rm)

    Ii = Vs/(Zi+Rs+Rm)

    I am a bit confused about what voltages V1 and V2 are measuring, and what do they mean by using the phase ?, I don't know the phase

    3.3) After some research I found this equation for a twisted pair cable

    TwistedImpedanceFig1.gif

    Though i'm not sure what to use for Er. On the site it says
    εR=(c/v)^2

    but I don't know the velocity of the signal

    http://www.sigcon.com/Pubs/edn/TwistedImpedance.htm
     
  2. jcsd
  3. Aug 21, 2016 #2

    tech99

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    No none else answering yet, this is my best shot:-
    1) One of the methods of finding Zo is from Zo = SQRT (Zoc * Zsc)
    To find Zsc and Zoc, the test circuit is used to find an unknown impedance.
    I am a simple person, so I think you can solve the test circuit using a phasor diagram, but it is a bit complicated. Take Ii as the reference, as it is a series circuit, and then V50, Vrm and V2 will add up vectorially to Vs. V50 and Vrm are in phase with Ii and are found from Ii using Ohm's Law. Then the complex ratio of V2/Ii give the cable input impedance.
    2) The question is very weak on the matter of dielectric, because the conductors have only a thin covering and are not embedded in the dielectric. So we presume Er may lie somewhere between air=1 and polyethylene=2.3.
    You have my total sympathy with this laborious question.
     
  4. Aug 21, 2016 #3
    Thanks for the reply, I have a few questions,

    By V50, You mean the the signal generator impedance voltage ?
    V2 is measuring the input voltage to the transmission line or the input impedance voltage ?
    And what voltage is V1 measuring ?
     
  5. Aug 22, 2016 #4

    tech99

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    V50 is the voltage across Rs.
    V2 is the voltage across the line at its input point.
    V1 is the voltage across the output terminals of the signal generator.
     
  6. Aug 22, 2016 #5

    rude man

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    Assume air as the dielectric. What is εr for air?
    Also assume lossless line.
    There is a formula stating that V2 = V2(V3, θ, Z2, Z0).
    θ = βx, γ = jβ and x = physical line length. So θ is unknown.
    But you know V2, V3 and Z2 for 2 cases so you have 2 equations and 2 unknowns so you can solve for γ and Z0.

    These of course are all phasors, i.e. voltages with attendant phase shifts.
     
  7. Aug 22, 2016 #6

    tech99

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    I don't think we are given the line length and velocity factor.
     
  8. Aug 22, 2016 #7
    Can't I just use a voltage divider ?

    V2 = Vs*(Zin)/(Zin+Rs+Rm)

    Since we know V2, Vs, Rs and Rm we can calculate Zin
     
  9. Aug 22, 2016 #8

    tech99

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    This not accurate because Zin is possibly reactive.
     
  10. Aug 22, 2016 #9

    rude man

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    As I said, line length x is an unknown. But you will solve for θ so forget x. x and θ are related per what I gave you.
     
  11. Aug 22, 2016 #10

    rude man

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    How do you propose to solve for Z0 and γ?
     
  12. Aug 22, 2016 #11

    rude man

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    It's "accurate" but it's no help.
     
  13. Aug 22, 2016 #12
    I forgot to note that the length of the transmission line is known, 56m. Their is a formula for calculating Zo
    upload_2016-8-22_20-25-56.png

    So Zsc would be the input impedance I measure when the load is short circuited. And Zoc would be the input impedance I measure when their is no load

    upload_2016-8-22_20-18-26.png

    upload_2016-8-22_20-20-59.png

    And for a open circuit line,
    upload_2016-8-22_20-22-47.png

    And for short circuit,
    upload_2016-8-22_20-23-31.png

    So once I have found Zoc and Zsc and hence Zo, I can use one of the above equations to calculate Beta = Gamma
     
  14. Aug 22, 2016 #13

    rude man

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    How do you propose to get β?
     
  15. Aug 22, 2016 #14
    By finding the input impedance, for example Zsc using the voltage divider equation
    V2 = Vs*(Zin)/(Zin+Rs+Rm)

    Then finding Zoc, using the same equation but for open circuit

    Then Zo, using this equation
    upload_2016-8-22_20-25-56-png.104974.png

    And since I have Zsc and Zoc, I can use either of the equations I listed above to solve for Beta
    upload_2016-8-22_20-23-31-png.104973.png

    I have the length of the line = 56m
     
  16. Aug 22, 2016 #15

    rude man

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    Looks good now RedDevil!
     
  17. Aug 23, 2016 #16
    Thanks guys
     
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