How do I find the transfer function of an STC circuit?

For example, suppose I am given the circuit (attached), and want to find the transfer function of OUT relative to input V1.

My answer would be to use a voltage divider of (R1||C1) in parallel with C2, this gets me: s/[s+1/[(C1+C2)R]]

But this answer is off by a factor of C2/(C1+C2) - what am I doing wrong?

Thanks a ton!

-V

 

Valce,

Use the potientiometer method.

R1||C1 ===> (R1/sC1)/(R1+1/sC1) = R1/(sR1C1+1)

R1||C1/(R1||C1+C2) ===> sR1C2/(sR1C2+sR1C1+1)

Ratch

 

How do I find the transfer function of an STC circuit?

For example, suppose I am given the circuit (attached), and want to find the transfer function of OUT relative to input V1.

My answer would be to use a voltage divider of (R1||C1) in parallel with C2, this gets me: s/[s+1/[(C1+C2)R]]

But this answer is off by a factor of C2/(C1+C2) - what am I doing wrong?

Thanks a ton!

-V

You have the denominator of your answer correct.

Can you post your effort so that we can take a look to see if we can determine where you got off track?

hgmjr

 

I get the right answer for R1||C1... but it seems I'm not getting the right total impedance for the circuit...?

I'm doing...

(R1||C1)+C2 --> R1/(sR1C1+1) + 1/sC2

... which doesn't seem to get me the right answer at all

-V

 

All you are computing using your technique is the impedance across the input voltage.

You need to be calculating the attenuation.

hgmjr

 

The attenuation is R1||C1/(Total impedance) right?

With the value of total impedance that I get, I don't seem to get the right attenuation

Sorry for my continued ignorance

 

What I mean by attenuation is outlined below.

\(\frac{Z_{o}(s)}{Z_{i}(s)}=\frac{Z_2}{Z_1+Z_2}\)

Where:

\(Z_{1}=X_{C2}=\frac{1}{sC_{2}}\)

\(Z_{2}=R_{1}||X_{C1}\)


hgmjr

 

Thank you!!

My algebra is absolutely horrible... Thanks for putting up with it

Much love,
-V