The inverting amplifier has a configuration as shown below

It can also be represented as

Similarly The IC Configuration for it is

The non-inverting input is connected to ground and a pair of resistors, Rin and Rf is used to define the gain.

Characteristics

· The gain A is very high

· v+ = 0,

· No current flows into the inputs due to high in put impedance

Finding Vo

We know

Here Vi+ is zero as it is connected to ground

Now finding Vi- : If we notice in diagram , we will observe that v- has two voltage sources acting on it . 1 is VI and other is VO. So we need to find the voltage at the Op amp input Vi- due to the combined voltage contribution of this source

Super position theorem can be used to find the effect of two voltage sources in a circuit .

Step1 : Now the rule is simple to use , we will find the voltage at red junction due to source 1 VI while shorting V0 (Vo=0)

Step 2 : Then we will find the voltage at red junction due to source 2 V0while shorting VI (VI=0)

Step3 : Than we will add both answer to get the combined effect of both voltages for vi –

Solving with respect to Source 1 (VI)

Solving with respect to Source 2 (V0)

Finding (vi-) by adding equation 3 and 4

Plugging in the values of equation 5 in Equation B

Ignoring 1

Here we can take one more assumption knowing that A is very very large . so we can ignore Rf and Rin from denominator