How Do You Calculate A at Vo1 and Vo2 in OP-AMP Circuits?

[darwinharianto]

Homework Statement

http://puu.sh/8mUJ5.png
here is the image
the question is to find the A at Vo1 and Vo2

The attempt at a solution
I don't know how to calculate A at Vo1
but at Vo2, what I need to do is just
A= 1 + R/R
is that right?

At Vo1, what I think is only A= 4R/R
but is that right?

 

[gneill]

Homework Statement

http://puu.sh/8mUJ5.png
here is the image
the question is to find the A at Vo1 and Vo2

The attempt at a solution
I don't know how to calculate A at Vo1
but at Vo2, what I need to do is just
A= 1 + R/R
is that right?

At Vo1, what I think is only A= 4R/R
but is that right?

Note that you've got feedback from the output of the final stage to the input of the first stage, so it's going to affect the gain of the overall circuit, including the first stage. So your guess about the gain of the first stage (Vo1/Vin) is not correct.

Your expression for the gain of the second stage looks good. Note that R/R is 1 no matter the value of R. So what then is the equation relating Vo2 to Vo1?

Can you write a node equation at the input terminal of the first stage?

 

[darwinharianto]

Note that you've got feedback from the output of the final stage to the input of the first stage, so it's going to affect the gain of the overall circuit, including the first stage. So your guess about the gain of the first stage (Vo1/Vin) is not correct.

Your expression for the gain of the second stage looks good. Note that R/R is 1 no matter the value of R. So what then is the equation relating Vo2 to Vo1?

Can you write a node equation at the input terminal of the first stage?

thx for reply

ok, so the Vo2 = 2Vo1 right?
then, for the Vo1, Vo2 affects the Vo1
is it what you mean?

so i put the node before the first amp
then the equation go like this?
Vin/R = Vo1/4R + Vo2/4R
so Vo1 + Vo2 = 4Vin
because Vo2=2Vo1, then 3Vo1 = 4Vin
the results is Vo1 = 4/3 Vin
and Vo2 = 2Vo1

is this right?

 

[gneill]

thx for reply

ok, so the Vo2 = 2Vo1 right?
then, for the Vo1, Vo2 affects the Vo1
is it what you mean?

Yes.

so i put the node before the first amp
then the equation go like this?
Vin/R = Vo1/4R + Vo2/4R
so Vo1 + Vo2 = 4Vin
because Vo2=2Vo1, then 3Vo1 = 4Vin
the results is Vo1 = 4/3 Vin
and Vo2 = 2Vo1

is this right?

Be careful of the signs you assign to the currents when you write the node equation. If Vin/'R is the current flowing into the node then the other currents on the RHS of your equation should have signs that reflect that they are flowing out of the node.

Once you've written the node equation you can substitute for Vo2 with the relationship Vo2 = 2Vo1 that you found, and then solve for Vo1 (in terms of Vin).

 

[darwinharianto]

Yes.



Be careful of the signs you assign to the currents when you write the node equation. If Vin/'R is the current flowing into the node then the other currents on the RHS of your equation should have signs that reflect that they are flowing out of the node.

Once you've written the node equation you can substitute for Vo2 with the relationship Vo2 = 2Vo1 that you found, and then solve for Vo1 (in terms of Vin).

thx for replying again

so, the equation go like this?
Vin/R = -Vo1/4R + -Vo2/4R
because Vo1 and Vo2 going backward
then -(Vo1 + Vo2) = 4Vin
and Vo1 = -4/3 Vin?
is it right??

 

[gneill]

thx for replying again

so, the equation go like this?
Vin/R = -Vo1/4R + -Vo2/4R
because Vo1 and Vo2 going backward
then -(Vo1 + Vo2) = 4Vin
and Vo1 = -4/3 Vin?
is it right??

Looks good.

 

[darwinharianto]

Looks good.

oic
thanks
so Vo2 is -8/3 Vin
and Vo1 is -4/3 Vin
thanks for your assistance :D