Zin of 3 Lossless Transmission Transmission Lines

Discussion in 'Homework Help' started by Jess_88, May 25, 2011.

  1. Jess_88

    Thread Starter Member

    Apr 29, 2011
    174
    1
    Hi guys :)

    I'm having a little difficulty determining the input impedances for the circuit

    I need to determine, when the lines are disconnected
    1)Zin looking into line 1 towards the 200Ω load.
    2)Zin looking into Line 2 towards the short circuit
    With lines RECONNECTED
    3) Zin looking into line 3.

    [​IMG]

    For question 1 I have
    Zin = Zo[(ZL + jZotanβl)/(Zo + jtanβl)]

    and l = λ/4 and β = 2π/λ
    βl = π/2

    or (Zo^2)/ZL
    but I don't know what Zo is???

    For question 2 I have.
    Zin = Zo[(ZL + jZotan(π/2))/(Zo + jtan(π/2))]
    ZL = 0
    Zi = Zo[(jZotan(π/2))/Zo]
    =jZotan(π/2) = ∞
    so it appears as an open circuit

    I have no idea how to approach question thee :(.
    would it be λ/2 wave length for both line one and line two?
    how on earth do I fined Zo for my calculations???

    thanks guys:)
     
    Last edited: May 25, 2011
  2. Jess_88

    Thread Starter Member

    Apr 29, 2011
    174
    1
    I just noticed I have a typo in the thread title... sorry :S

    So doing a little more looking around and this is what I have.
    It appears to be a dipole antenna feed configuration. right??
    And for part three of my question (impedance input at line 3) it looks like some similar questions I found online, which used line one and line two in parallel.
    Would I also do this for my circuit configuration?

    I'm still lost when it comes to the line impedances Zo.
     
    Last edited: May 26, 2011
  3. Jess_88

    Thread Starter Member

    Apr 29, 2011
    174
    1
    Is this question even possible without the transmission line impedance or a operating frequency???
     
  4. t_n_k

    AAC Fanatic!

    Mar 6, 2009
    5,448
    782
    Yes it is possible.

    The quarter wave line (or quarter wave transformer) has the well known property you noted - Zin=(Zo^2)/ZL.

    The shorted quarter wave line has infinite impedance. This part of the circuit will therefore have no effect on the rest of the circuit.

    Zin for the quarter wave line 1 terminated in 200Ω will be (Zo^2)/200.

    This impedance will be the load referred to the input quarter wave line 3.

    So what impedance will you see with a quarter wave line [with characteristic impedance Zo] terminated in [(Zo^2)/200]?
     
    Jess_88 likes this.
  5. Jess_88

    Thread Starter Member

    Apr 29, 2011
    174
    1
    nice!

    so Zin on line 3 = ((Zo^2)/ZL) where ZL = (Zo^2)/200
    so Zin(line 3) = 200 ohms right?

    but how can you determine the input impedance of line 1 without Zo
     
  6. t_n_k

    AAC Fanatic!

    Mar 6, 2009
    5,448
    782
    Yes 200Ω is correct.

    You can't find the actual numerical value of impedance for line 1 - you can only state the impedance in terms of Zo.
     
  7. Jess_88

    Thread Starter Member

    Apr 29, 2011
    174
    1
    ah ok, thanks :)
     
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