Determining the gain of an op-amp with feedback?

[richyw]

Homework Statement

Homework Equations

I have two "golden rules" I was given which are "no current into the op-amp" and $V_{-} = V_{+}$

and the open loop gain is infinite

Basically my notes and textbooks are leaving me with pretty much nothing though

The Attempt at a Solution

tried determining the currents like we did in other methods. tried figuring out the case when x=1 and x=0. I don't get how current can flow across the resistor if V_=V+. I'm basically completely lost. No Idea where to start.

 

[gneill]

Using your "golden rules", given a voltage V_in at the input, what will be the voltage at the + terminal of the op-amp? (Hint: you're looking at a simple voltage divider).

So, what then is the voltage at the "-" terminal?

 

[richyw]

well I would say $$V_{+}=\frac{xR}{(1-x)R+xR}V_{in}$$$$V_{+}=x$$

 

[richyw]

and my golden rule says that V_=V+

 

[gneill]

well I would say $$V_{+}=\frac{xR}{(1-x)R+xR}V_{in}$$$$V_{+}=x$$

Well, $x\,V_{in}$, right?

and my golden rule says that V_=V+

Good. So what's the current through the input resistor, R?

 

[richyw]

oops I meant V-=xV_in

 

[richyw]

the current through the input resistor would be $$\frac{V_{in}-xV_{in}}{R}=\frac{(1-x)V_{in}}{R}$$so$$(1-x)V_{in}=xV_{in}-V_{out}$$$$1-x=x-\frac{V_{out}}{V_{in}}$$$$\frac{V_{out}}{V_{in}}=2x-1$$?

 

[richyw]

if my work is hard to follow I just said that the current through the input resistor must equal the current through the feedback resistor after the "so".

 

[richyw]

this makes sense to me now so I hope it's correct haha.

 

[gneill]

Looks good. For someone who started out with "no idea", you've carried it off nicely

 

[richyw]

thanks a lot. I guess usually I just have "no idea where to start". sucks on exams!