Hello guys how are you.

I have been knocking my head to reach the final formula of a finite gain negative feedback op amp.

here is the circuit and final formula.

 

hi T,
Check this link for guidance.
http://www.electronics-tutorials.ws/opamp/opamp_2.html
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Hello guys how are you.

I have been knocking my head to reach the final formula of a finite gain negative feedback op amp.

here is the circuit and final formula.
View attachment 111563

View attachment 111564

Hi,

I can see why

The text reads, "collecting terms", yet there are not enough "terms" to collect yet.
They are missing the expression for i2 so there is no way you can "collect terms" and get the result they got.

The result they got does appear to be correct, but they dont show the complete solution so you'd have to write the expression for i2 yourself then see if you can "collect terms".

It's funny what you find sometimes in the literature. I find mistakes all the time.

 

All the information that is needed is there and their result is correct.

The only problem they have is that they have two definitions of 'v1' -- one is the voltage of the input signal and the other is the voltage of the inverting input to the opamp. As a result, their initial equation for i1 is (v1 - v1) / R1, which is identically zero (for nonzero R1). But they interpret both instances of 'v1' in the final equation on that line.

They don't provide an expression for i2 probably because they assume that, by this point, people are able to apply KCL at the inverting input and arrive at the reasonable conclusion that i2 = i1 since they explicitly note that the current into the inverting input of the opamp is zero.

The only thing that is "missing" -- and which they probably also assume that people that have reached this point are able to do without too much handholding -- is expression vo in terms of vs (I am renaming the signal voltage to vs instead of v1 for clarity), i1, R1 and R2. Or, since what we are seeing is a snippet of the solution, that may well have been provided above the two lines that were posted.

 

As a result, their initial equation for i1 is (v1 - v1) / R1, which is identically zero (for nonzero R1).

The initial equation is (vI - v1) / R1, not (v1 - v1) / R1

 

The initial equation is (vI - v1) / R1, not (v1 - v1) / R1

Ah. My eyes aren't what they were. I looked pretty hard and couldn't see a difference -- but with that heads up I can. I was wondering if the two v's were different, perhaps upper/lower case or one was italics. But I couldn't see any difference between the subscripts. Thanks.