Finding Feedback Resistance of Op Amp

simulate this circuit – Schematic created using CircuitLab

How would the feedback resistance be found in this setup? I am used to seeing the negative-feedback resistance as a single resistor between the inverting input of the op amp and the output of the op amp. I am not sure how to calculate this resistance with the resistor going to ground in the mix.

• I considered that but I didn't see a way for it to work. I figure to do Thevenin we would put the entire circuit in a box, and put our terminals at the node connecting R1, R2, and the inverting terminal of the op amp and the node connecting R4, R5, and the output of the op amp. The issue I see is that the feedback resistance seems to be the resistance between these two nodes specifically in the feedback loop as opposed to the resistance between these two nodes in the whole circuit. Sorry if that is hard to understand, it is difficult to explain without drawing it out again. – Señor Sandia Mar 21 '16 at 1:39
• Try finding the Thevenin equivalent looking to the right into R2, based on the output voltage of OA1. Only R2/R3/R4 in the box. – Spehro Pefhany Mar 21 '16 at 1:44
• Does the ground that R3 is connected to get included in the box also? Otherwise I am unsure how to solve for the Thevenin resistance as there are three terminals. – Señor Sandia Mar 21 '16 at 1:57
• Yes, the ground is part of the circuit included. – Spehro Pefhany Mar 21 '16 at 1:58
• Above you say "based on the output voltage of OA1". How is this found? I am looking for this feedback resistance in order to calculate the output voltage of the op amp. Also, if this is found I am unsure how I would proceed. It is not clear to me how to find the Thevenin resistance with the ground included in the circuit. – Señor Sandia Mar 21 '16 at 2:23

I'll give you a hint here. You can calculate the Thevenin equivalent of the what is seen looking into R2.

By inspection its source resistance is:

$R_T = R_2+(R_3||R_4)$, and the open-circuit source voltage is:

$V_{OUT}\cdot \frac {R_3}{R_3+R_4}$

So the gain from the (virtual) Thevenin source is just -Rt/R1, but the output voltage must be higher by a factor of $\frac {R_3+R_4}{R_3}$.

You can then calculate the gain and the output voltage. Chances are if this is actually built the op-amp will saturate at the negative rail.

There are other, more general, ways to solve a problem like this (write the equations out) but with this way the answer drops out pretty easily.

• How do you take R3 and R4 in parallel? R4 has R5 between itself and ground. – Señor Sandia Mar 21 '16 at 4:36