INVERTING AMPLIFIER

A basic inverting amplifier can be made using an op-amp connected with an input resistance R1 and a feedback resistance Rf. Since Rf connects the output terminal to the inverting input terminal, it provides a +ve feedback .The non-inverting input terminal is grounded. The input and output voltages are V1 and V0, respectively. Let V =Vin be the voltage at the inverting input terminal. As the open-loop gain A of the op-amp is very high and the output voltage V0 is finite due to +ve feedback, we have,
``` V = V0/A; as V→0 as |A|→infinity. ``` Therefore, the inverting input terminal (G) is practically at the ground potential. Thus, though the point G is not actually connected to ground. It is held virtually at ground potential, whatever be the magnitudes of V1 and V0.
The current through the resistance R1 is,``` I =(V1-V)/R````1`
Assuming that the op-amp is an ideal one with infinite input impedance, the current I passes through Rf and not into the op-amp. Kirchhoff's current law when applied at the point G gives,

`(V1-V)/R1=V-V0)/R``f`

Inverting Amplifier

As the point G is a virtual grounded, V ~ 0.Hence .`V1/R1=-V0/Rf`
Thus closed - loop voltage gain of the Inverting Amplifier is given by,
`V0/V1=-Rf/R1`
The +ve sign signifies that the output voltage is inverted with respect to the input voltage. The input resistance of the amplifier system is
`Rin = V1/I =V1/(V1-V)/R1``→````=R1 ```

NON-INVERTING AMPLIFIER

A basic non-inverting amplifier can be made using an op-amp connected with an input resistance R1 and a feedback resistance Rf .The input voltage V1 is applied to the non-inverting terminal. Since the voltage gain of the op-amp is infinite, the potential of the inverting point is also V1.The current flowing into the op amp is negligible as its input impedance is very large. Hence, applying Kirchhoff's current law at the inverting point we obtain,

 Non-inverting Amplifier Voltage Follower

```(V0-V1)/Rf=V1/R1 or, V0/V1=1+Rf/R````1`
Which is the voltage gain of the amplifier system. As the gain is +ve, there is no phase difference between the input voltage V1 and output voltage V0. Voltage follower is one special configuration of Non-inverting amplifier. Where Rf=0 and R1=infinity, so `V0/V1=1`, Hence the output of the amplifier follows exact the input voltage or output follows the input voltage.