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I have a function call S11 enter image description here

and I want the formula simplified with variables: Q, k, wn.

enter image description here

enter image description here

But I new with Mathematica, don't know how to do it. And I can't find the function doing this. Please help me out! Maybe show me some easy example or useful function. Thank you!

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    $\begingroup$ it will be easier to help you if you enter the Mathematica code in plain text that one can copy and not images. But to do replacements, so do S11/. { Q-> Rs*w0, wn-> etc.....} lookup the /. command which is short cut for ReplaceAll $\endgroup$
    – Nasser
    Commented Jul 15 at 9:27
  • $\begingroup$ Thanks for ur response. I'll try to enter the Mathematica code in plain text next time. But I think u misunderstood me. I want the formula became like the last figure, represent with the variables {Q, k, wn}. $\endgroup$
    – CTChang
    Commented Jul 15 at 11:15
  • $\begingroup$ I guess is the same question over here, but I copy the code and run, it didn't work. mathematica.stackexchange.com/questions/276464/… $\endgroup$
    – CTChang
    Commented Jul 15 at 11:30
  • $\begingroup$ I do not see Rs anywhere in your images. You could try Simplify with side relation. But if you are not able to post plain text code showing clearly the input you have, it will be hard to help. The link you pointed to has nothing that looks like the image you posted at the top. $\endgroup$
    – Nasser
    Commented Jul 15 at 12:28

1 Answer 1

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You have to provide rules for substitution, e.g. Solve for relevant parameters and try to give them the form as they apear, as here in the last line going to $M^2$

  rep = Solve[{M^2 == k L1 L2 , 
               C1 == 1/(\[Omega]0^2 L1 (1 - k^2)), 
               \[Omega]0 == \[Omega]/ Subscript[\[Omega], n], 
                Q == RS C1 \[Omega]0}, 
               {C1, M, L1, , \[Omega]0}][[1]] /. 
        {(M -> a_) :> (M^2 ->  PowerExpand[a^2])}



  p1=    (-(M^2/((L1*L2 - M^2)^2*\[Omega]^2)) + 
  (1/150 + I/(L1*(1 - M^2/(L1*L2))*\[Omega]) - 
    I*C1*\[Omega])*
   (1/150 - I/(L2*(1 - M^2/(L1*L2))*\[Omega]) + 
    I*C2*\[Omega]))/(M^2/((L1*L2 - M^2)^2*\[Omega]^2) + 
  (1/150 - I/(L1*(1 - M^2/(L1*L2))*\[Omega]) +
  I*C1*\[Omega])*(1/150 - 
   I/(L2*(1 - M^2/(L1*L2))*\[Omega]) - I*C2*\[Omega]))


 p1

 p1 /. rep // Together // FullSimplify

$$ {}_{\frac{ \left(-(M^2/((L1*L2 - M^2)^2*\omega^2)) + (1/150 + I/(L1*(1 - M^2/(L1*L2))*\omega) - I*C1*\omega)*(1/150 - I/(L2*(1 - M^2/(L1*L2))*\omega) + I*C2*\omega)\right)} { \left(M^2/((L1*L2 - M^2)^2*\omega^2) + (1/150 - I/(L1*(1 - M^2/(L1*L2))*\omega) + I*C1*\omega)* (1/150 - I/(L2*(1 - M^2/(L1*L2))*\omega) - I*C2*\omega)\right) }}$$

$${}_{\frac{150 (-1 + k^2) Q (-150 + L2 \omega (-I + 150 C2 \omega)) - I (150 + (-1 + k) L2 \omega (-I + 150 C2 \omega)) \omega_n (RS - 150 I Q \omega_n)} {150 (-1 + k^2) Q (150 + L2 \omega (I + 150 C2 \omega)) + (-150 I + I (-1 + k) L2 \omega (I + 150 C2 \omega)) \omega_n (RS + 150 I Q \omega_n)}}$$

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