Why am I so bad with op amp calculations?

[MRW]

Hello all.. I have this circuit:
http://bayimg.com/aAclCaabB

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!

 

[Eeyore]

Hello all.. I have this circuit:
http://bayimg.com/aAclCaabB

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!

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

Graham

 

[MRW]

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

Graham

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.

 

[[email protected]]

Hello all.. I have this circuit:http://bayimg.com/aAclCaabB

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!

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.

 

[Eeyore]

Hello all.. I have this circuit:http://bayimg.com/aAclCaabB

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!

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.

Agreed.

Graham

 

[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.

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? http://bayimg.com/EACLNAAbD

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!

 

[JeffM]

To the best of my understanding, I have something like this.
[...]http://bayimg.com/EACLNAAbD

You must read News For Nerds as well.
http://www.google.com/search?q=site:slashdot.org+bayimg+Uncensored.Image.Hosting

 

[[email protected]]

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? http://bayimg.com/EACLNAAbD

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!

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

 

[MRW]

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

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

:/

 

[MRW]

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

:/

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.