band passfilterpassive-filtertransfer function
i was doing some homework and one thing I had to do was to derivate the transfer function of a given bandPass. I have done it myself but i dont know if it is correct nor if i followed the right path / right assumptions. I'd be happy if someone of you could look at it and give me some feedback. Important: In my notes Ua = V(out) and Ue = V(in) the rest should be (I Hope) self explanatory.This is how I've done it: 
And this is the bandpass:
Thank you in advance!
No. Whilst a standard second-order bandpass section can be defined in this way ...
\$H(s) = \dfrac{\dfrac{\omega_m}{Q}s}{s^2+\dfrac{\omega_m}{Q}s+\omega_m^2}\$
... it is also possible to have a second-order bandpass filter with the same characteristic frequency and Q but with a different transfer function. This previous question which addresses a filter with a stop-band attenuation of 1 is a case-in-point.
Furthermore, higher-order filters will require more than just these two parameters to define them since there are more coefficients.
You did not include R3 into your equations. Below you can find a solution using Mathematica.
Best Answer
Yes, it appears to be correct and you have followed the right path. Apart from the number "1" missing on the first line - you put \$j\omega C\$ rather than \$j\omega C_1\$. You also omitted brackets around the top line numerator but corrected that in the denominator.
I derived it my way (to avoid me being influenced) and got the same answer.
Feel Happy!
Here's my scrappy mess: -
This is why you should take the time and use Latex!! The very bottom line is me just checking the j terms match yours.