# Op am unity gain buffer derivation

#### antiantianti

Joined Aug 4, 2016
45
Hello
Can someone help how did they find this formula this is for the case Ao is different from infinity

#### LesJones

Joined Jan 8, 2017
2,317
Here is a hint. (As I suspect this is homework.) Think of it like this. The input to an op amp is the difference between the + input and the - input. So the output will be this value times the open loop gain. So you should now be able to write down the equation between the input and the output.

Les.

#### MrAl

Joined Jun 17, 2014
6,485
Hello
Can someone help how did they find this formula this is for the case Ao is different from infinity
Hi,

In short, they treat the op amp as a voltage controlled voltage source (VCVS) which is a dependent voltage source. If you study the VCVS you will be able to solve this circuit as well as many other circuits involving dependent voltage sources.

The main types of dependent sources are:
VCVS (voltage controlled voltage source)
CCVS (current controlled voltage source)
VCCS (voltage controlled current source)
CCCS (current controlled current source)

Sometimes the VCCS is used to emulate an op amp then the frequency response has to be included in the model or when it makes the analysis easier then when using a VCVS.

• Hypatia's Protege

#### Hypatia's Protege

Joined Mar 1, 2015
3,197
Hello
Can someone help how did they find this formula this is for the case Ao is different from infinity
Thought this one would find its way to Homework #### RBR1317

Joined Nov 13, 2010
490
Neglecting the frequency response, the output of an op amp equals the voltage difference between the input terminals multiplied by the open-loop gain.

Vo = ({V+}-{V-})∙Ao

Examine the circuit to determine what {V+} and {V-} must be, then substitute into the above equation to derive the expected result. However, that may be difficult since the circuit and the result appear to be unrelated (Vin is not identified on the circuit).