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Why am I so bad with op amp calculations?

Hello all.. I have this circuit:

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It's just a basic summer circuit in single supply mode. I don't understand why I cannot resolve the equation similar to the one they have in Texas Instrument's Single Supply Op Amp Collection document.

Please help me understand.

I derived my calculations using superposition. First I derived V_out1 by shorting V2 and V3. Then, I found V_out2 by shoring V2 and V1. Last, I shorted V1 and V3 to find V_out3. I got the following:

V_out1 = - (R2 / R1) * V1 V_out2 = - (R2 / R3) * V3

V_out3 = V2 * [ (R3 || R1) + R2] / R2 = V2 * [ ( (R3 || R1) / R2) + 1] (I treated V_out3 like a basic non-inverting configuration)

Now I have V_out = V_out1 + V_out2 + V_out3, which does not match with TI's document and with my simulation results.

Any insights? Thank you very much!

Reply to
MRW
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It seems to me that you're making your equations too complicated.

Graham

Reply to
Eeyore

Hi Graham, how would your approach this?

I threw away the original paper with my doodle and redid my work. I actually figured out my mistake this time. I made a mistake in the voltage divider portion in deriving V_out3. I switched the order of resistors. Tsk. Now it matches up to things.

Reply to
MRW

My insight would be to ignore the printed sums, come in cold and just understand that when the opamp is working OK, both pins 2 and 3 - must- be the same voltage, the pins are are just voltage sensors and take no current. This means you can straight away work out the currents in R2 and R3 and the direction the currents are travelling. The gives a resulting current that may be heading towards, or moving from pin 2. This current is the exact current that R2 must supply.to balance the input at 2.5V. Hence the output voltage can be worked out from R2 and that current.

Reply to
john

Agreed.

Graham

Reply to
Eeyore

I am not quite sure why R1 is not represented in your text. To the best of my understanding, I have something like this.

Something like this?

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Using KCL, I got the following:

V_o = - (R2 / R1)*(V1-V2) - (R2 / R3)*(V3-V2) + V2

It took less than three steps and coincides with the simulation results. Very nice.

Thanks!

Reply to
MRW

You must read News For Nerds as well. 8-)

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Reply to
JeffM

Yes. My "R2" should be R1. (for pictorial clarity I'd have the I2 I3 arrows going the other way)

Reply to
john

Hmm.. now I have a problem. Here are my two equations so far:

Using KCL: V_o = - (R2 / R1) * V1 - (R2 / R3) * V3 + (R2 / (R3 || R1))

  • V2
+ V2

Using Superposition: V_o = - (R2 / R1) * V1 - (R2 / R3) * V3 + ((R2 / R1) + (R2 / R3) + 1)

  • V2

But somehow when I compare the V2 coefficients:

(R2 / (R3 || R1))

  • V2
= ((R2 / R1) + (R2 / R3)
  • V2
(R2 * (R2 + R3)) / (R3 * R1) = ((R2 / R1) + (R2 / R3)

I don't get the same relationship:

(R2 * (R3 +R1)) / (R1 * R3) =! (R2 * (R2 + R3)) / (R3 * R1) , this only works when R1 = R2

:/

Reply to
MRW

Never mind. The reason why I am bad with op amp calculations is because I always make a mistake somewhere. In this case, (R2 / (R3 || R1)) was turned into R2*(R2 + R3) / (R3 * R1) on my paper instead of R2 * (R1 + R3) / (R3 *R1). I am stupid.

Reply to
MRW

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