# Transfer-function form of OPAMP-circuit

#### kasperrepsak

I am given an opamp circuit (noninverting opamp with 1st order lowpassfilter).
Please view the attachment for the circuit.
I have to show that the transfer function H(f)=Uo/Us is of the form:

H(f)=α( 1 + j(f/f1)) / ( 1 + j(f/f2))

Using basic circuit analysis I came to the following (already checked that its correct) transfer function:

H(f)=Uo/Us= (R4/(R3+R4) ) x (R1 + Z2)/R1

Where Z2 is the equivalent impedance of the capacitor C2 in parallel with the resistor R2.

So: Z2 = R2/(jωCR2+1)

After substituting this into my transfer-function equation i cant get it into form they want me to. Again:
How can I get H(f)=Uo/Us= (R4/(R3+R4) ) x (R1 + Z2)/R1 with Z2 = R2/(jωCR2+1) in the following form:

H(f)=α( 1 + j(f/f1)) / ( 1 + j(f/f2))

I tried many times. I am pretty good at algebra but i just cant seem to grasp this one. Could someone please help me out? This is very important to me. If someone feels like something isnt clear then please write it,ill do anything to make it more clear.

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#### rude man

Homework Helper
Gold Member
Combine Z2 and R1. Everything you did otherwise is A-OK. So just finish the algebra.

(I will give you the answer but you realize that if you're going to learn anything from this you have to finish the problerm yourself.)

Ans: a = R1R4/[(R3+R4)(R1+R2)],
f1 = w1/2pi where w1 = R1R2C/(R1+R2)
f2 = w2/2pi where w2 = R2C.

That assumes I did the math right myself!! :tongue:

#### kasperrepsak

I've tried many times. I'll try again with your answers. Thank you :)

#### kasperrepsak

I can't .. :/ I have spent so much time on this problem already it's too much..

#### kasperrepsak

A teacher at my uni helped me out.. Your math is incorrect. For anyone trying to figure out this problem, when you end up with an extra term R2/R1, then just divide the whole nominator by (1+ R2/R1) and incorporate the (1 +R2/R1) into the alpha constant to get the desired form. : ) Thanks for the help rude man. :)

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