I have a function call S11
and I want the formula simplified with variables: Q, k, wn.
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!
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
$$ {}_{\frac{ \left(-(M^2/((L1*L2 - M^2)^2*\omega^2)) + (1/150 + I/(L1*(1 - M^2/(L1*L2))*\omega) - I*C1*\omega)*(1/150 - I/(L2*(1 - M^2/(L1*L2))*\omega) + I*C2*\omega)\right)} { \left(M^2/((L1*L2 - M^2)^2*\omega^2) + (1/150 - I/(L1*(1 - M^2/(L1*L2))*\omega) + I*C1*\omega)* (1/150 - I/(L2*(1 - M^2/(L1*L2))*\omega) - I*C2*\omega)\right) }}$$
$${}_{\frac{150 (-1 + k^2) Q (-150 + L2 \omega (-I + 150 C2 \omega)) - I (150 + (-1 + k) L2 \omega (-I + 150 C2 \omega)) \omega_n (RS - 150 I Q \omega_n)} {150 (-1 + k^2) Q (150 + L2 \omega (I + 150 C2 \omega)) + (-150 I + I (-1 + k) L2 \omega (I + 150 C2 \omega)) \omega_n (RS + 150 I Q \omega_n)}}$$
S11/. { Q-> Rs*w0, wn-> etc.....}lookup the/.command which is short cut forReplaceAll$\endgroup$Rsanywhere in your images. You could trySimplifywith 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. $\endgroup$