3.1. The Adder (Summing Amplifier)

An adder, or summing amplifier, is a circuit whose output voltage is the sum of the input voltages applied to its inverting terminal.

The general formula for the output voltage of a two-input adder is: V₀ = -R_f * (V₁/R₁ + V₂/R₂)

The most insightful case is when all resistors (R_f, R_1, and R_2) are of equal value. In this scenario, the formula simplifies beautifully to: V₀ = -(V₁ + V₂)

Key Takeaway: The summing amplifier’s output is the inverted sum of its inputs. By using equal-value resistors, it becomes a pure, though inverted, voltage adder.

3.2. The Subtractor (Difference Amplifier)

A subtractor, or difference amplifier, is a circuit that produces an output voltage equal to the difference between two input voltages.

When all resistors in the circuit are of the same value, the output voltage is given by the simple formula: V₀ = V₁ – V₂

Key Takeaway: The difference amplifier directly subtracts the inverting terminal’s input from the non-inverting terminal’s input, making it a true voltage subtractor when all resistors are equal.

From basic arithmetic, we can move on to an even more advanced application: using op-amps to perform the fundamental operations of calculus.