# Calculating input resistance of an Op Amp?

Discussion in 'Homework Help' started by de1337ed, Feb 27, 2012.

1. ### de1337ed Thread Starter New Member

Mar 6, 2011
23
0
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.

2. ### mlog Member

Feb 11, 2012
276
36
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.

3. ### de1337ed Thread Starter New Member

Mar 6, 2011
23
0
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?

Last edited: Feb 28, 2012
4. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
782
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.

5. ### mlog Member

Feb 11, 2012
276
36
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.