Hi,

I'm currently doing a course on OP amps and I am trying to figure out this question. For the life of me I am not able to figure out the differential gain (Av diff) and the Common mode gain (Av cm). I feel like I have a good understanding of the 2 yet when i apply what I think I know the answer isn't even in the ball park. I was hoping you someone here could spend a bit of time and give me some feedback.

I've attached a picture of the problem in question. Av diff is 95.9 and Avcm is -8.18. I can't get those numbers.

What I thought:

Well I can find the current in that circuit by taking Vb1 / R1 + R3. I can then find all the drops across the 4 resistors and i found Vout to be -.1818V. This is correct as it is the right answer. The part that eludes me is...av diff is Vout/v1 - v2. V1 is Vy and V2 is Vx and I found values of -0.0999V and -.08999V respectively. Yet my numbers dont seem to work so either i made a ciruit analysys mistake or I dont quite grasp the idea of Av diff and Av cm yet....

*apologies for the sideways image :S

 

Hey man,

funny because I am in the same course as you and i am also studying like a mad man for this final. What you need to do since you have the operating equation(eg. Vout = Av(V1-V2) for the op-amp is look at his notes that he states V1 = Vcm + Vdiff/2 and V2 = Vcm - Vdiff/2. Just need to plug and play and solve for those values and you should get what you're looking for. I hope this helps. Good luck on finals.

 

Forgot to mention there's a question like this in the work book.

 

Thanks for the tip man. Yeah I noticed your question on the transconductance amp and was like "That looks reallllly familiar". Again thanks very much for the tip good luck on your studies as well.

 

In order to determine the common mode and differential mode gains, you have to be clear on what you inputs are. Those do not appear to be identified in the schematic. The signals at the op-amp input pins are generally NOT the input signals but, instead, you want the functional input and output signals (in other words, if this circuit were placed in a black box with two inputs and one output, what circuit nodes would those I/O ports connect to? My best guess here is that the two input nodes would be Vx and Vy.

So set Vx = Vcm + Vdm/2 and Vy = Vcm - Vdm/2 and find Vout. It should be a linear combination of Vcm and Vdm of the form Vout = Acm*Vcm + Adm*Vdm.

I get Acm = -8.18 but I get Adm = -95.9 (the negative of what you are saying the answer should be). Examination of the circuit shows that the differential gain must be negative. To see this, imagine that the circuit is in equalibrium with some input voltage and output voltage. Not increase the input voltage such that Vx goes up a little bit. What direction does Vout have to go in order to reestablish equilibrium?