INVERTING AMPLIFIER
A basic inverting amplifier can be made using an opamp connected with an input resistance R_{1} and a feedback resistance R_{f}. Since R_{f} connects the output terminal to the inverting input terminal, it provides a +ve feedback .The noninverting input terminal is grounded. The input and output voltages are V_{1} and V_{0}, respectively. Let V =V_{in} be the voltage at the inverting input terminal. As the openloop gain A of the opamp is very high and the output voltage V0 is finite due to +ve feedback, we have,
V = V_{0}/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 V_{1} and V_{0}.The current through the resistance R_{1} is,
I
=(V_{1}V)/R
_{1}Assuming that the opamp is an ideal one with infinite input impedance, the current I passes through R_{f} and not into the opamp. Kirchhoff's current law when applied at the point G gives,
(V_{1}V)/R_{1}=VV_{0})/R
_{f}
Inverting Amplifier
As the point G is a virtual grounded, V ~ 0.Hence .V_{1}/R_{1}=V_{0}/R_{f}
Thus closed  loop voltage gain of the Inverting Amplifier is given by,
V_{0}/V_{1=}R_{f/}R_{1}
The +ve sign signifies that the output voltage is inverted with respect to the
input voltage. The input resistance of the amplifier system is
R_{in} = V_{1}/I =V_{1}/(V_{1}V)/R_{1}
→
=R_{1
}
NONINVERTING AMPLIFIER
A basic noninverting amplifier can be made using an opamp connected with an input resistance R1 and a feedback resistance Rf .The input voltage V1 is applied to the noninverting terminal. Since the voltage gain of the opamp 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,


Noninverting Amplifier 
Voltage Follower 
(V_{0}V_{1})/R_{f}=V_{1}/_{R1}
_{1}
or, V_{0}/V_{1}=1+R_{f}/R
Which is the voltage gain of the amplifier system. As the gain is +ve, there is
no phase difference between the input voltage V_{1} and output voltage V0.
Voltage
follower is one special configuration of Noninverting amplifier. Where
R_{f}=0 and
R_{1}=infinity, so
V_{0}/V_{1}=1
, Hence the output of the amplifier follows exact the input
voltage or output follows the input voltage.