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Transmission line secondary coefficients

  1. Aug 26, 2015 #1
    1. The problem statement, all variables and given/known data
    A transmission line has the primary coefficients R= 2 ohm/m, L=8 nH/m, G= 0.5 mS/m and C= 0.23 pF/m. Determine the lines secondary coefficients Zo, α and β at a frequency of 1 GHz.

    2. Relevant equations
    ω= 2 π f

    See uploaded formulas document

    3. The attempt at a solution
    I'm not sure if i've approached this right but this is what i've done:

    I started by calculating the angular frequency from the given 1GHz frequency

    ω= 2 π f = 2π*1exp^9 = ω= 6283185307 rad/s

    Using this I went on to calculate Zo

    Sqrt ((2+j6283185307*8exp^-9)/(0.5exp^-3+j6283185307*0.23exp^-12))

    Zo= 26.4316 + j0.0000327906 or Zo= 26.4316 θ 0.0000711° Ω

    then using the above formulas I calculated the following

    β=sqrt(1/2*(6283185307^2*8exp^-9*0.23exp^-12-2*0.5exp^-3+sqrt(2^2+6283185307^2*(8exp^-9)^2)*((0.5exp^-3)^2+6283185307^2*(0.23exp^-12)^2))

    =1.65952exp^5

    β=246.2946 rad m^-1


    α=sqrt (1/2*(2*0.5exp^-3-6283185307^2*8exp^-9*0.23exp^-12+sqrt(2^2+6283185307^2*(8exp-9)^2)*((0.5exp-3)^2+6283185307^2*(0.23exp^-12)^2))

    = 3.24771exp^5

    α=482.0029Np m^-1

    Am i along the right lines with this? (hope you can understand the above workings...It got complicated with all the brackets etc)
     

    Attached Files:

  2. jcsd
  3. Aug 26, 2015 #2

    Svein

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    Science Advisor

    Just checking Z0 using the simplified formula: [itex]
    Z_{0}\approx \sqrt{\frac{L}{C}}=\sqrt{\frac{8\cdot 10^{-9}}{0.23\cdot 10^{-12}}}=\sqrt{34782.6087
    }=186.5[/itex].
     
  4. Aug 26, 2015 #3

    rude man

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    Homework Helper
    Gold Member

    You need to use symbols instead of numbers until the very end. Keeping track of all those numbers gives me and a lot of other helpers a splitting headache!

    I went as far as checking your formula for Z0 (but not your math) which looks OK.
     
  5. Aug 26, 2015 #4

    rude man

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    Homework Helper
    Gold Member

    This is not a small-attenuation line. In particular, the requirement G/ωC << 1 is not met. (= 0.35). But I agree, the OP's number looks off.
     
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