# Transfer function high order filter

Hi I have tried to extract the transfer function of the filter above, as you see it a high order filter.

I have combined the c1 in parallel with R & C2 then make a voltage divider in order to add the inductor. I always miss the capacitor or i dont get the same result. please anyone can tell me where is my mistake.

• What do you mean by "always miss the capacitor"? – TisteAndii Apr 8 '16 at 21:50
• The given transfer function is correct - you can derive it using the voltage divider rule. However, the form is a bit "uncommon" (factor D identical to a capacitor). Recommendet form: D=1 and factor C=time constant. – LvW Apr 9 '16 at 8:20
• above you can see the derivated transfer function, I have got completely different answers!! – Fadi Apr 9 '16 at 9:51
• Shouldn't the voltage gain actually be Z/sL+Z? – A. Darwin Apr 9 '16 at 9:53
• it is a voltage divider, isnt it ? – Fadi Apr 9 '16 at 9:58

The transfer function should be $$T(s) = \frac{1 + C2 R s}{1 + C2 R s + (C1 L + C2 L) s^2 + C1 C2 L R s^3}$$ Your calculation of Z is correct, however you made some mistake during the calculation of $$T(s) = \frac{Z}{sL + Z}$$