# Op Amp transfer function

Discussion in 'General Electronics Chat' started by RFeng, Jul 5, 2012.

1. ### RFeng Thread Starter New Member

May 30, 2012
27
0
Hi,

I'm trying to figure out the transfer function of the following Op Amp Intergrator:

Thank you!

2. ### Wendy Moderator

Mar 24, 2008
20,879
2,659
It is a integrator. Not sure what the biasing network on the + input is about, it could be replaced with either power supply or a resistor network and a single power supply.

3. ### WBahn Moderator

Mar 31, 2012
19,154
5,177
Replace the feedback network with a single impedance that is the parallel combination of the R and C. Then analyze it like any other opamp circuit, noting that the voltage on the inverting input is not at virtual ground, but rather at Vplus.

4. ### RFeng Thread Starter New Member

May 30, 2012
27
0
Hi guys.
Thanks!

I analyzed it and reach its transfer function:
* R1 - Resistor at (-) Input
* Zf - Impedance of Feedback

How can you tell what is the pole of this transfer function?

Thanks again!

5. ### RFeng Thread Starter New Member

May 30, 2012
27
0
Back to page 1 if I may

6. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
784
$Z_f=\frac{R_ f\frac{ 1}{ C_f s}} {R_f+\frac{ 1}{C_f s } }$

etc.

No negative sign.

Apr 27, 2009
97
1
Well, I do not see R1 in your schematic so the transfer function must be:

Vo = -Zf/R2 * Vi + V(+)*(1+Zf/R2)

Since V(+) is DC, it has no dynamic influence. It just moves the output DC level up or down depending on the combination of VSET and Vdc DC voltage level. The signal rides on top of this DC level. So, the transfer function can be rewritten as:

Vo = -Zf/R2 * Vi + V(+)*(1+Rf/R2)

The signal amplitude is given by

Vo_signal = -Zf/R2 * Vi, and can be written as

Vo_signal = -1/(1+ s Cf Rf)* Rf/R2 * Vi

So the pole is at

1/(2 pi Cf Rf) = 159.15 kHz. It is only determined by Cf Rf time constant. Since both resistors Rf and R2 are 1kohm, the signal amplitude is identical with the input amplitude (inverted), but rides on top of the DC level we discussed. The unity gain starts dropping after 159.15kHz.

Last edited: Jul 7, 2012