In an inverting amplifier, the input voltage is connected through a resistor to the inverting terminal. Meanwhile, the non-inverting terminal is grounded and a feedback resistor is established between the inverting and output terminal, as depicted in Figure 1.

Figure 1: The inverting amplifier

The objective is to discern the relationship between the input voltage (v_i) and the output voltage (v_o). By applying Kirchhoff's Current Law (KCL) and presuming the operational amplifier to be ideal, the expression for gain is obtained. An inverting amplifier has the ability to reverse the polarity of the input signal while simultaneously amplifying it. It is worth noting that the gain depends solely on the external elements connected to the op-amp, with the gain being the feedback resistance divided by the input resistance.

Another critical application of the op-amp is seen in the noninverting amplifier, as illustrated in Figure 2.

Figure 2: The non-inverting amplifier

Here, the input voltage (v_i) is applied directly at the non-inverting input terminal, while resistor R is connected between the ground and the inverting terminal. The focus here is on the output voltage and the voltage gain. Applying KCL at the inverting terminal and substituting the voltage values gives an expression for voltage gain. If the feedback resistor gets short-circuited or if the input resistor is open-circuited, the gain transforms into unity, forming a voltage follower or unity gain amplifier. Such a circuit possesses a high input impedance, making it useful as an intermediate-stage (or buffer) amplifier to segregate one circuit from another.