[SOLVED] 2nd Order Passive Low Pass RC Filter Design Equation

[orionsbelt]

Hello everybody

I don't know whether this is the right forum for this particular mathematical problem. It is about the transfer function of 2nd Order Passive Low Pass RC Filter. Please find attached the calculation.
At the end of the calculation, I have circled the term which seems to be the error. But I cannot figure out where I actually made the mistake! It would be helpful if someone could help me with the derivation.

Thanks!

//OB

 

[Dominik Przyborowski]

You have an error. The transfer function has two poles but without any zeros. The correct form is:
\[K_v = \frac{1}{1+s [(C_1+C_2)R_1+C_2 R_2] + s^2 C_1 C_2 R_1 R_2}\]

Notice that your output voltage is measure at C_2 not C_1 as You are calculated above.

 

[ravindragudi]

Agree with Dominik. The Vo calculations have to be done at C2 and not at C1 by forming Z1.

My suggestion would be to use KCL for deriving the TF. Apply first KCL at the node R1, C1, R2 - call it as V1. With this you can get equation having Vi, Vo and V1.
Now apply KCL at Vo. You will get equation having Vo and V1. Rearrange it to get equation for V1 and replace this in earlier equation having Vo and Vi.

With that you would be able to get the proper TF for this filter.

 

[orionsbelt]

Thanks for your help. It's solved now.