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Homework Help: Two port network model and analysis

  1. Oct 8, 2011 #1
    1. The problem statement, all variables and given/known data
    Greetings. I am having difficulty with a couple of parts to a homework problem. Mainly coming up with the transfer functions to plot V_o. See the picture for the problem statement:
    [PLAIN]http://img827.imageshack.us/img827/5481/problempa.jpg [Broken]

    2. Relevant equations

    [tex]l \leqq v_{ph}*T_{rise} / 10[/tex]

    [tex] Z_o = Z_c = 75\Omega [/tex]

    I've also included the model parameters for the two-port network:
    [PLAIN]http://img8.imageshack.us/img8/1712/modelsz.jpg [Broken]

    3. The attempt at a solution

    I found T_rise to be 6.66ns. I am able to calculate L and C for the line using the characteristic impedance equation from Z so L = 0.5*10^-6 H/m and C = 88.88*10^-12 F/m. I'm having difficulty with the transfer functions. I can find it for the 7 model:

    [tex]\frac{1/LC}{s^2+s\frac{R}{L}+\frac{1}{LC}} = H(s) [/tex]

    But not for the other two. Also. In order to plot Vo correctly, we have to incorporate a delay operator with the ramp function as such:

    [tex]\frac{1-e^{sT_{rise}/0.8}}{T_{rise}/0.8} = D(s) [/tex]

    So our final plot would be the step response (or ramp, as my colleagues and I think the professor wants) of D(s)*H(s).

    Any and all help would be greatly appreciated! Other examples for this type of problem is very difficult to find on the internet.
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Oct 8, 2011 #2

    rude man

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    I don't know about your various models, but it should be helpful to know the following: if an ideal transmission line is source-terminated in its characteristic impedance and the other end is open-circuited, there is no distortion of Vi at Vo. There is only a time-delay.

    You can show this easily by using ABCD parameters for the resistor and for the line, then concatenating.
  4. Oct 8, 2011 #3
    I think that's what the problem is. We have to show that measured delay in the line with the given parameters.
  5. Oct 8, 2011 #4

    rude man

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    I am addressing only your parts 4 and 5. The 2nd and 3rd are standard lumped-parameter exercises. Not sure about the first. I would have said there is no finite rise time that will repoduce exactly at the output with a lumped-parameter circuit.

    The delay time is simply physical line length divided by phase velocity = 0.1/1.5e8 s.
    Last edited: Oct 8, 2011
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