1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Transmission line Secondary Coefficients

  1. Jan 31, 2017 #1
    1. The problem statement, all variables and given/known data
    A transmission line has the primary coefficients as given below.

    ##R=2\Omega/m##
    ##L=8 nH/m##
    ##G=0.5 mS/m##
    ##C=0.23 pF/m##

    Determine the lines secondary coefficients ##Z0##. ##\alpha## and ##\beta## at a frequency of ##1 GHz##

    2. Relevant equations

    In my notes I am given

    ##\alpha=\frac{R}{2}\sqrt\frac{C}{L} +\frac{G}{2}\sqrt\frac{L}{C}## and ##\beta=\omega\sqrt{LC}##

    3. The attempt at a solution

    ##\alpha=\frac{2}{2}\sqrt\frac{0.23 X 10^-12}{8 X 10^-9} +\frac{0.5 X 10^-3}{2}\sqrt\frac{8 X 10^-9}{0.23 X10^-12}##

    ##\alpha=1 X \sqrt{2.875 X 10^-5} + (2.4 X 10^-4)\sqrt{34,782.6}##

    ##\alpha=\sqrt{2.875 X 10^-5} + (2.4 X 10^-4)\sqrt{34,782.6}##

    ##\alpha=(5.362 X 10^-3) +0.044760 = 0.050121902## nepers per meter

    I think this is correct. I am unsure how to input the single multiplication sign `X` in LaTeX form. I think my " to the power of`s" are correct for ##R, L, G## and ##C## but I am unsure about the final result in nepers per meter

    For the second part I got the following:-

    ##\beta=\omega\sqrt{LC}##

    ##(2\pi)(1 X 10^9) \sqrt{(8 X 10^-9)(0.23 X 10^-21)}##

    So I have ##6,283,185,307\sqrt{1.84 X 10^-21}##

    So ##6,283,185,307(4.289522 X 10^-11)=0.269518623## radians

    So ##\beta= 0.269518623## radians

    This second answer I am not so sure as I have some very large numbers but I have followed the examples in my notes.

    Any comments on the two attempts above would be appreciated.

    Thanks




     
  2. jcsd
  3. Jan 31, 2017 #2

    gneill

    User Avatar

    Staff: Mentor

    The values look okay. ##\beta## should be radians per meter. You'll want to round to the appropriate number of significant figures to match your "givens".

    For multiplication in LaTeX you can use \times or \cdot : ##a \cdot b = a \times b##.
     
  4. Jan 31, 2017 #3
    Thanks a lot for your help with this
     
  5. Apr 6, 2018 #4
    l Following onto this question i got all the same workings however we needed to find Zo aswell. Using [​IMG] with the values above I got Zo=179.427+j26.5060 Ω or in polar Zo=181.375 /_+8.403° Ω (sorry don't currently have software to do the polar expression so used /_ to signify the angle).Does this sound correct for this answer?
     
  6. Apr 6, 2018 #5
    https://www.wolframalpha.com/input/?i=√((2+(16π)i)/(0.0005+i(0.00046π))) Here's my workings using wolframalpha
     
  7. Apr 6, 2018 #6

    gneill

    User Avatar

    Staff: Mentor

    Looks good.
     
  8. Apr 6, 2018 #7
    Thanks @gneill! Only bit i was struggling on! But I hoped it'll be as simple as use the equation and plug in values. Helpful as always :)
     
  9. Apr 11, 2018 #8
    In my opinion, the correct formula it is as follows:
    α+jβ=sqrt[(R+jꞷL)x(G+jꞷC)]
    The formula α=1/2xRxSQRT(C/L)+1/2xGxSQRT(L/C) it is good in the case in which
    we can neglect R with respect to ꞷ*L and G with respect to ꞷ*C.
    The difference is not more than 1-2%, indeed.
    a=0.051409 and b=0.272549
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Loading...