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Help please to solve equation

  1. Mar 9, 2010 #1
    Hi Guys,

    Its been a while since I studied math and I would appreciate if someone could be of assistance in solving an equation for me.

    I need to solve for K in the following:

    W/B=1/Pi*[ln〖(1+R)/(1-R )〗-D/B*ln〖(K+R)/(K-R) 〗 ]

    where

    R=√(K*(K*B-D)/(B-K*D ))

    I have attached a jpeg of the equations in scientific format.

    Thanks for your help.

    Cheers,

    Bazza2
     

    Attached Files:

    • eqn.JPG
      eqn.JPG
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      Views:
      151
  2. jcsd
  3. Mar 10, 2010 #2
    hi your eq. is confusing...could use latex ..?
     
  4. Mar 10, 2010 #3
    Hi Rajini,

    Unfortunately I am not familiar with latex. However, I have redone the equations in Word's Equation Editor so it should be clear now. Please find it attached.

    W/B=1/Pi*{ln[(1+R)/(1-R )]-D/B*ln[(K+R)/(K-R )] }

    R=√((K*(K*B-D ))/(B-K*D ))

    Thanks,

    Bazza2
     

    Attached Files:

    • eqn.JPG
      eqn.JPG
      File size:
      7.6 KB
      Views:
      148
  5. Mar 10, 2010 #4

    berkeman

    User Avatar

    Staff: Mentor

    Wow, what is that equation from? Do you know that there is a closed form solution? Do you have Mathematica? You might also try Wolfram|Alpha to see if it's able to solve it for you.
     
  6. Mar 10, 2010 #5
    Hi Berkeman,

    It is transmission line analysis. And I'm afraid it's been too long since I was last at Uni to remember how to solve such equations. I tried Wolfram Alpha - quite interesting but just kept changing things around.

    I would appreciate if anyone could help me out here.

    Thanks,

    Bazza2
     
  7. Mar 11, 2010 #6
    hi bazza,
    i have access to matlab (but i am new to it!)...just give some time..i will check and let you know..
     
  8. Mar 11, 2010 #7
    Thanks Rajini. Much appreciated.

    Cheers,

    Bazza
     
  9. Mar 14, 2010 #8
    Hi Rajini,

    Have you been able to solve this equation using Matlab?

    I appreciate you help.

    Cheers,

    Bazza
     
  10. Mar 14, 2010 #9
    No explicit solution could be found for the equation:

    [tex]\frac {w} {b} = \frac{1} {\pi} \ln\!\left(-\frac{\sqrt{-\frac{k\, \left(d - b\, k\right)}{b - d\, k}} + 1}{\sqrt{-\frac{k\, \left(d - b\, k\right)}{b - d\, k}} - 1}\right)\, \ln\!\left(\frac{k + \sqrt{-\frac{k\, \left(d - b\, k\right)}{b - d\, k}}}{k - \sqrt{-\frac{k\, \left(d - b\, k\right)}{b - d\, k}}}\right)}[/tex]

    Here is the equation in string form I used in the "solve()" function:

    eqn = 'w/b = (1 / pi) * ( log( (1 + (-(k*(d - b*k))/(b - d*k))^(1/2)) / (1 - (-(k*(d - b*k))/(b - d*k))^(1/2)) ) * log( (k + (-(k*(d - b*k))/(b - d*k))^(1/2))/(k -(-(k*(d - b*k))/(b - d*k))^(1/2))))'

    Here is the solve() output:

    >> solve(eqn,'k')

    Warning: Explicit solution could not be found.
    > In solve at 170

    ans =

    [ empty sym ]

    MATLAB is a fickle mistress :(
     
  11. Mar 14, 2010 #10

    hotvette

    User Avatar
    Homework Helper

    You may need to resort to numerical methods to solve for K.
     
  12. Mar 14, 2010 #11
    Thanks Glustro and hotvette for your time.

    Excuse my ignorance but what do you mean by numerical methods?

    Cheers,

    Bazza
     
  13. Mar 14, 2010 #12
    Root-finding algorithms.

    Assume values for all variables except K, and then use something like Newton-Raphson, Wegstein, or substitution method to iterate on a value of K until it converges.

    (This is not done by hand - you use a computer.)
     
  14. Mar 14, 2010 #13

    hotvette

    User Avatar
    Homework Helper

    Since you are dealing with a single unknown (i.e. K), you could even use something as simple as bisection if you knew a range that brackets the value you want. Converges slowly but very simple to implement.
     
  15. Mar 14, 2010 #14
    Unfortunaely, the K is a variable in an even more complex equation so i have no idea of what sort of value it should be.

    Cheers,

    Bazza
     
  16. Mar 15, 2010 #15

    hotvette

    User Avatar
    Homework Helper

    Sorry, don't understand. I thought K was the solution to the equation in your first post, meaning you know the values of all other quantities (i.e. W, B, D) and K is the only unknown. Not true?
     
  17. Mar 15, 2010 #16
    Hi hotvette,

    Yes I am looking for the solution of K.

    Then K goes in this equation:

    Zdbs=293.9/Math.Sqrt(Er)*D/B*0.5* Math.Log[((1+K))/((1-K) )]

    and it is actually Zdbs that I want at the end of the day.

    Cheers,

    Bazza
     
  18. Mar 15, 2010 #17
    Hi i am sorry i cant help..
    i copy and past the eqn from clustro..i always get undefined variable as error!
     
  19. Mar 15, 2010 #18

    hotvette

    User Avatar
    Homework Helper

    Thanks for clarifying. If finding the value of K by numerical methods is acceptable, then you should be able to obtain a solution. Here is a suggestion. Tell me the values of W, B, and D and I'll play around with it and let you know what may be a reasonable approach.

    Question: is this a one time only solution, or do you need to repeatedly find the value of K based on multiple values of W, B, D?
     
  20. Mar 15, 2010 #19
    Thanks Rajini for trying.

    It will be calculated using different values. Typical values are:
    W= 5, D=5 & B=10

    Thanks hotvette.

    Cheers,

    Bazza
     
  21. Mar 15, 2010 #20
    I tried it again and it worked.

    Rajni, are you sure you have the Symbolic Math Toolbox? solve() is contained in that toolbox.

    Bazza: If you know all of those values you can easily extract a root for K.
     
  22. Mar 15, 2010 #21
    Hi clustro,
    i have to say you..that i really a amateur in matlab..never used..but i notice many people use and strongly recommend it..But at least i would like to sue it to solve this problem..
    At present only one thing i can do for baza..if he could tell me hot to execute and send me the codes i can execute and let you know..
    PS: i login to linux pc..then go to mat lab from command by typing matlab then a window comes...there f(x):...here i typed your codes..after entering no error but when i type solve(..)..like k not define invalid char...
     
  23. Mar 15, 2010 #22

    Jmf

    User Avatar

    Can I ask what aspect of the analysis of a transmission line you're doing? Maybe there's an easier way.
     
  24. Mar 15, 2010 #23
    I thought this may be easy to solve but it seems not. I have another way to solve this which is less accurate but it will have to do.

    Thanks guys for your time.

    Cheers,

    Bazza
     
  25. Mar 16, 2010 #24

    hotvette

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    Homework Helper

    For the above values of W, D, B, K = 0.978619036085362. Newton-Raphson worked well but because of the logs, there is a relatively narrow range of starting points that can be used (~0.95 to ~0.99).

    I'm curious about something. Does K represent some sort of efficiency?

    Just for fun I varied the values for W, D, and B. The result follows:

    Code (Text):
    W      D       B       K
    1      5       10      0.756276579421452
    2      5       10      0.865849758609811
    3      5       10      0.926653501309252
    4      5       10      0.960270604440607
    5      5       10      0.978619036085362
    6      5       10      0.988538243178375
    7      5       10      0.993869188156523
    8      5       10      0.996724645149870
    9      5       10      0.998251307920962
    5      4       10      0.953551108282295
    5      3       10      0.915051241605172
    5      2       10      0.860069503637580
    5      1       10      0.782715023759189
    5      5       11      0.959554866316289
    5      5       12      0.935843903716909
    5      5       13      0.909035721120116
    5      5       14      0.880465274020010
    5      5       15      0.851159374048799
     
    Last edited: Mar 16, 2010
  26. Mar 17, 2010 #25
    Well, after a couple of hours of work, I figured out how to get K explicit in the first equation. I came up with the following:

    K = (-R[1-e^([W*pi]/[D*ln([1+R]/[1-R])])])/(1+3^[(W*pi)/(D*ln[(1+R)/(1-R)])])

    It should be fairly easy to subsititute the second equation in for R, and then substitute that entire thing into the third equation.

    Sorry for the sloppy text, LaTeX really doesn't like me. I'll attach a picture to make it easier to read.
     

    Attached Files:

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