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An inverting amplifier connects the input voltage through a resistor to the inverting terminal, grounds the non-inverting terminal, and uses a feedback resistor between the inverting and output terminals. By applying Kirchhoff's Current Law and assuming an ideal operational amplifier, the voltage gain expression is derived. The gain depends solely on the external resistors: feedback resistance divided by input resistance.

Inverting amplifiers reverse the input signal's polarity while simultaneously amplifying it. This capability makes them valuable for noise cancellation applications, where the inverted signal eliminates unwanted noise in audio processing. They are also used for signal amplification, conversion, and filtering in various audio systems.

A non-inverting amplifier applies input voltage directly to the non-inverting terminal, with a resistor connecting the inverting terminal to ground and a feedback resistor for negative feedback. Unlike inverting amplifiers, non-inverting amplifiers maintain signal polarity while amplifying. Applying KCL at the inverting terminal yields the voltage gain expression, which again depends on the feedback and input resistances.

A voltage follower, or unity gain amplifier, forms when the feedback resistor is short-circuited or the input resistor is open-circuited in a non-inverting amplifier, resulting in a gain of one. It possesses high input impedance and functions as a buffer amplifier to segregate one circuit from another. This configuration efficiently converts high-impedance inputs to low-impedance outputs for signal transfer to low-impedance loads.

Non-inverting amplifiers have high input impedance, making them ideal intermediate-stage buffer amplifiers. This high impedance allows efficient signal transfer to low-impedance loads while minimizing loading effects on source circuits. The voltage follower configuration particularly leverages this characteristic to isolate circuit stages and preserve signal integrity across cascaded systems.

Both inverting and non-inverting amplifiers calculate gain using external resistor values through KCL analysis. For inverting amplifiers, gain equals negative feedback resistance divided by input resistance. For non-inverting amplifiers, gain equals one plus feedback resistance divided by input resistance. In both cases, the operational amplifier's characteristics of practical op amps determine the circuit's overall performance and accuracy.

Negative feedback, established through the feedback resistor in both inverting and non-inverting configurations, stabilizes the amplifier gain and determines the amplification factor. The feedback path allows KCL analysis to derive predictable gain expressions independent of the op-amp's internal characteristics. This feedback mechanism ensures that gain depends solely on external resistor values, making amplifier performance reliable and controllable.