Analyzing a Circuit with an Op-Amp

[Temp0]

Homework Statement

http://i.imgur.com/TBrFMIT.png

Homework Equations

The Attempt at a Solution

So I basically start with node voltages at the positive terminal of the op-amp, and I label that node E, so the node voltage goes:

VE/80 + (VE - VD)/20 = 0 (I labelled the node at the bottom of the diamond D)

Continuing from this equation, I then analyze the circuit at node D, and I know the left node in the diamond is 10V, because it is connected to a voltage source which is connected to the ground. I also know the right node is 0V, because it's directly connected to the ground, so then I get the equation:

(VD - 10)/40 + (VD - VE)/20 + VD/60

From the node voltage equation at node E, I learn that VE = 0.8 VD, which means I can then substitute that value into my equation to solve for VD. Skipping the calculations, I get that VD = 4.84V.

From there, I analyze the node on the right of the diamond, which I know to be 0V, this gives me the equation:
-VD/60 + (-VC)/30 = 0 (I name the top node C)
Simplifying this equation and substituting in the number for VD gives me a VC value of -2.42V
I can also solve for VE using the equation I had earlier, VE = 0.8VD, so I get that VE = 3.87V.

With these values, I use the summing point constraints, and I know that the voltage in the node connected to the negative terminal of the op-amp is the same as the voltage in the node connected to the positive terminal, giving me VE' = 3.87V (Naming the negative terminal E')

Doing node voltage analysis on the node E' gives me an equation to solve for Vo, but I get a ridiculously high number when I try this. Could someone identify where I am going wrong with my work? Thank you in advance.

 

[gneill]

Homework Statement

http://i.imgur.com/TBrFMIT.png

Homework Equations

The Attempt at a Solution

So I basically start with node voltages at the positive terminal of the op-amp, and I label that node E, so the node voltage goes:

VE/80 + (VE - VD)/20 = 0 (I labelled the node at the bottom of the diamond D)

Continuing from this equation, I then analyze the circuit at node D, and I know the left node in the diamond is 10V, because it is connected to a voltage source which is connected to the ground. I also know the right node is 0V, because it's directly connected to the ground, so then I get the equation:

(VD - 10)/40 + (VD - VE)/20 + VD/60

From the node voltage equation at node E, I learn that VE = 0.8 VD, which means I can then substitute that value into my equation to solve for VD. Skipping the calculations, I get that VD = 4.84V.

From there, I analyze the node on the right of the diamond, which I know to be 0V, this gives me the equation:
-VD/60 + (-VC)/30 = 0 (I name the top node C)
Simplifying this equation and substituting in the number for VD gives me a VC value of -2.42V
I can also solve for VE using the equation I had earlier, VE = 0.8VD, so I get that VE = 3.87V.

With these values, I use the summing point constraints, and I know that the voltage in the node connected to the negative terminal of the op-amp is the same as the voltage in the node connected to the positive terminal, giving me VE' = 3.87V (Naming the negative terminal E')

Doing node voltage analysis on the node E' gives me an equation to solve for Vo, but I get a ridiculously high number when I try this. Could someone identify where I am going wrong with my work? Thank you in advance.

Your value for the potential at the V+ input of the op-amp looks okay.

Can you show your work for the node voltage analysis to determine Vo?

 

[Temp0]

Nevermind, I figured out why I was wrong, it's because I can't use the 0V node for node analysis, because there's an unknown current coming out of the ground.