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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:
      107
  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:
      109
  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.
     
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