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Imagine measuring a light sensor that outputs 5.0Β V5.0\text{ V}, but the instant you connect it to an analog-to-digital converter or a meter, the signal drops to 0.8Β V0.8\text{ V}.
This signal collapse is the loading effect, which happens when a high-resistance source cannot supply enough current to a low-resistance load without dropping its internal voltage.
How do we isolate a delicate sensor so it delivers its exact voltage without losing signal strength to the load?

The Unity-Gain Buffer

A voltage follower (also known as a unity-gain buffer) is an operational amplifier circuit that outputs the exact same voltage it receives at its input, producing a voltage gain of Av=1A_v = 1.
In 1927, Bell Labs engineer Harold Black discovered that feeding an amplifier's entire output back to its inverting input stabilizes the signal completely, creating 100% negative feedback.
How do we prove mathematically that connecting the output directly to the inverting input forces the gain to be exactly one?

Circuit Derivation

A standard non-inverting amplifier has a voltage gain equation of Av=1+RfR1A_v = 1 + \frac{R_f}{R_1}, where RfR_f is the feedback resistor and R1R_1 connects the inverting terminal to ground.
In a voltage follower, the feedback path is a direct wire with zero resistance (Rf=0 ΩR_f = 0\ \Omega), and the resistor to ground is completely removed (R1=∞ ΩR_1 = \infty\ \Omega).
Substituting these values into the gain formula yields Av=1+0∞=1A_v = 1 + \frac{0}{\infty} = 1, which proves that Vout=1Γ—Vin=VinV_{out} = 1 \times V_{in} = V_{in}.