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A summing amplifier, or adder, uses an operational amplifier to merge multiple input signals into a single output. Input resistors generate currents that flow through feedback resistors, producing an output voltage proportional to the weighted sum of input signals. Applying Kirchhoff's current law and Ohm's Law at the op amp's input node determines this relationship, making summing amplifiers essential in audio mixer applications.

A difference amplifier, or subtractor, amplifies the disparity between two input signals while rejecting common signals. By applying Kirchhoff's current law at the inverting and non-inverting nodes, the circuit produces an output voltage that represents only the difference between inputs. When resistance ratios meet specific conditions, the difference amplifier nullifies noise common to both channels, improving audio track clarity.

A difference amplifier functions as a subtractor when the resistance R2 equals R1, and R3 equals R4. These equal resistance ratios ensure the circuit properly rejects common-mode signals while amplifying only the difference between the two inputs. This balanced configuration is critical for achieving true signal subtraction and common-mode rejection in practical applications.

Input resistors in a summing amplifier initiate currents that traverse feedback resistors, determining the output voltage magnitude and weighting of each input signal. The relationship between input and feedback resistor values controls the gain applied to each input channel. Using Ohm's Law, the output voltage becomes a weighted sum where each input's contribution depends on its corresponding resistor ratio.

Kirchhoff's current law (KCL) applied at the op amp's input nodes establishes the mathematical relationships governing output voltage in both summing and difference amplifiers. At the inverting and non-inverting nodes, KCL ensures current conservation, allowing engineers to derive output voltage expressions. Combined with Ohm's Law, KCL provides the theoretical foundation for predicting circuit behavior and designing precise signal-processing circuits.

Differential amplification amplifies the difference between two input signals, while common-mode rejection suppresses signals identical on both inputs. A difference amplifier achieves both by using matched resistance ratios: it amplifies the differential component while nullifying the common component. This dual capability makes difference amplifiers valuable for noise reduction in audio and instrumentation applications where unwanted signals appear equally on both channels.

Operational amplifiers extend beyond basic amplification through summing and difference configurations. Summing amplifiers combine multiple weighted inputs into a single output, enabling audio mixing and signal combination. Difference amplifiers amplify signal disparities while rejecting common signals, supporting noise reduction and instrumentation tasks. These configurations demonstrate how op-amps perform addition and subtraction operations essential to signal processing and circuit design.