I have the following op amp circuit:

I was wondering what the input resistance seen by Vs is? How exactly do you calculate input resistance. I feel like it's just ∞ because the second unity gain buffer will force it to see ∞ resistance. If not, how do I go about calculating the input resistance? Thank you.

 

No, the second amplifier has little effect on the input resistance of the previous stage.

The way to approach this problem is to consider the following:

1. The input impedance is Vs divided by the sum of the currents through R1 and R3.

2. The voltage on the inverting (-) and the non-inverting (+) input is the same.

3. The voltage of the non-inverting input (+) is Vs times R4/(R3+R4). It's a simple voltage divider.

That should get you started.

 

No, the second amplifier has little effect on the input resistance of the previous stage.

The way to approach this problem is to consider the following:

1. The input impedance is Vs divided by the sum of the currents through R1 and R3.

2. The voltage on the inverting (-) and the non-inverting (+) input is the same.

3. The voltage of the non-inverting input (+) is Vs times R4/(R3+R4). It's a simple voltage divider.

That should get you started.

I think I might have gotten it. I replaced the input Vs with a Vtest, and calculated Vtest/Itest (Itest is immediately leaving the voltage source). If we assume that i1 is going through R1, then i1 = (R3/(R1+R3))*Itest. We also know that i1 = (Vtest-Vtest(R4/(R3+R4))/R1, so putting them together:
(Vtest-Vtest(R4/(R3+R4))/R1 = (R3/(R1+R3))*Itest
and then manipulating to find Vtest/Itest got me Rin = (R1(R3+R4))/(R1+R3).
Seems good?

 

The final step would be

Rin=Vs/(i1+i3)

Which because the Vs terms all cancel, leaves you with Rin in terms of R1, R3 & R4. That's it.

 

I'll go ahead and give my answer. My Zin agrees with de1337ed.

Zin = Na/Da

Na=R1(R3+R4)
Da=R1+R3

Also interesting is the gain, Vo/Vs.

Vo/Vs=Nb/Db

Nb=R1*R4-R2*R3
Db=R1(R3+R4)

By the way, Nx and Dx are the numerators and denominators, respectively.