Negative Feedback Amplifiers
Feed a little output back to the inverting input and infinite, sloppy gain becomes exact, resistor-programmed gain.
Builds on: 6.1 The Operational Amplifier2.2 Voltage Dividers
Taming infinity
Raw op-amp gain is huge but useless for amplifying music — everything clips. The 1927 insight of Harold Black (scribbled on a newspaper on the Hudson ferry): throw most of the gain away, deliberately. Feed a fraction of the output back to the inverting input. If the output drifts too high, the feedback nudges the difference negative and pulls it back; too low, the reverse. The amplifier constantly corrects itself toward equilibrium.
With negative feedback in place, two golden rules describe the equilibrium:
- The op-amp drives its output until V₊ = V₋ (else the huge gain would move it).
- The inputs draw no current — they only observe.
Gain by resistor ratio
In the non-inverting amplifier, the output feeds a voltage divider (Rf over Rg — Lesson 2.2 yet again) whose tap goes to V₋. The golden rules then force the divider tap to equal the input, which pins the output at:
Two resistors — parts with 1% tolerance costing a cent — now define the gain, and the op-amp’s messy internal 100 000× barely matters. That trade — surplus gain exchanged for precision — is the deepest idea in this course, and it runs your car’s cruise control, your body’s thermostat, and every audio amplifier ever sold.
The humble, mighty buffer
Wire the output straight to V₋ and the gain is exactly 1. Pointless? Remember the divider’s loading problem (Lesson 2.2): connect a heavy load and the divider sags. Put a buffer between them and the divider sees the op-amp’s do-nothing inputs while the load gets a copy of the voltage backed by the op-amp’s muscle. Gain of one; problem of many, solved.
Feedback or not, the output can never exceed its supply rails. Ask a gain-6 amplifier for 6 × 2 V from ±9 V rails and the peaks flat-top at the rail — clipping, the crunch of an overdriven guitar amp. Watch it happen in the lab.
⚡ Lab — Gain by Numbers
Three classic feedback circuits with live waveforms and rails that bite.
- Non-inverting, Rf = 47 k, Rg = 10 k: verify the gain is 5.7× on the scope.
- Push the input amplitude until the output flat-tops. That's clipping.
- Inverting mode: the output flips upside down. Buffer mode: two identical traces — and that's the point.