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Find V(L) for Lumped vs distributive circuits

  1. Sep 11, 2013 #1
    1. The problem statement, all variables and given/known data
    Find V(L) voltage across load
    29384ki.png


    2. Relevant equations
    Vg=2cos(wt)
    Zg=Zl=200
    Zo=50
    [itex]\Gamma[/itex]=[itex]\frac{Zl-Zo}{Zl+Zo}[/itex]
    L'R'=με (all TEM lines)
    μ0=4∏E-7
    ε0=8.854E-12
    11aycee.png

    3. The attempt at a solution
    Basically I think that with the 1st one, i don't have to deal with reflection or whatever. i could be wrong, since Zo does not equal Zl in both problems, which means there has to be reflection. but the equation I used for the 1st problem was in my book, and its similar to the voltage source equation. 2cos(wt-θ) where θ=wl/c. Since we have to graph V(L) for both as a function of length which is in terms of wavelength, this is also listed in book as θ=2∏*(l/λ). The only other thing that confuses me is that frequency is not given, so i can't find w. How can I vary both length (in terms of wavelength) and frequency, which is nowhere mentioned in the problem?? maybe i am doing this wrong.

    for the 2nd problem. i think this is basically the same as the 1st one, except now we deal with reflection. since we also deal with R' L' G' C' (with R'=G'=0). the main breakthrough ive had with this problem is finding [itex]\Gamma[/itex]=0.6 which was easy. But i have no idea what to do from here. if I ASSUME that the relative permittivity is the same as in in air (that is εr=1) THEN i calculate R' L' using the equations Zo=50=sqrt(L'/C') and β=w*sqrt(L'C')=w*sqrt(με), and if i do that I get C'=6.671E-11 and L'=1.668E-7 but, i dont want to assume anything. can someone help me? i have the equations but theres no problem like this in my book, plus im lacking values like frequency and εr, so im not sure what exactly to do.
     
    Last edited: Sep 11, 2013
  2. jcsd
  3. Sep 11, 2013 #2

    rude man

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    Gold Member

    1st problem: there is definitely reflection, not that that's important here.
    What equation relates load voltage to source voltage with the given parameters w, L', C', l, RL, RG, Z0?

    2nd problem: this is a lumped circuit. There are by definition no reflections with lumped circuits.
     
  4. Sep 12, 2013 #3
    the only equation i see in my book is V(z)=V0+(e-jβz)+V0-(ejβz)
    at the load voltage VL is at z=0 and given by V0+ + V0-
    V0+/V0- are related to reflection coefficient by: V0- = [itex]\Gamma[/itex]V0+

    to find V0+ i would have to find Zin. where Zin=Z0[(zL+jtanβl)/(1+j(zLtanβl)] where zL=ZL/Z0=4 and β=w*sqrt(L'C')=w*sqrt(με). So I have Zin=50[(4+jtanβl)/(1+j(4tanβl)] but i have trouble finding β without L' and C'. my book also has another equation β=2∏/λ but im not sure if i should use that.
     
    Last edited: Sep 12, 2013
  5. Sep 12, 2013 #4

    rude man

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    Your answer will include ω, L' and C', also l plus the given parameters Zg, ZL. You can't get numerical answers without those but you can compare V(0) for a transmission line vs. the lumped circuit.

    You also have the relations in that post, plus β = ω√(L'C') and Z0 = √(L'/C').

    Start with your equation from post 3 for V(z), solve for V(0) as function of V(l).

    You then have to compute Zin since that forms a voltage divider with Zg. You have the formula for that too I see.

    So V(l) = Vs[Zin/(Zin + Zg).

    Then relate V(l) to V(0).
     
    Last edited: Sep 12, 2013
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