S4-1.4 Negative Feedback Amplifiers

What this is and why it exists

Negative feedback is the most consequential idea in analog design: give away raw gain, and in exchange the amplifier becomes stable, wideband, predictable and largely indifferent to which individual transistor you soldered in. Every op-amp circuit you will ever build runs on this trade. The unit's difficulty is the four topologies; the cure is knowing exactly two questions to ask of any circuit.

The vocabulary

• Open-loop gain (A) — the amplifier's gain before feedback.
• Feedback factor (β) — the fraction of the output fed back to the input.
• Loop gain (Aβ) — the product; how strongly the loop corrects errors, and the quantity every improvement is priced in.
• Closed-loop gain — A divided by one plus Aβ; for large loop gain it approaches one over β, set by resistors rather than by the transistor.
• Sampling — what the feedback network measures at the output: the voltage across the load, or the current through it.
• Mixing — how the fed-back signal re-enters the input: in series with the source voltage, or in shunt as a current.

The mental model

A thermostat for gain. The feedback network reports a fraction of the output; the input stage compares that report with what was asked for and amplifies only the difference. If the raw gain doubles because of temperature or a part swap, the error shrinks and the loop cancels most of the change: closed-loop gain moves barely at all, because it is set by the reporting network — two resistors — not by the device. The same correction acts on distortion born inside the loop and widens bandwidth by the same factor, one plus Aβ, that it divides gain by. One currency, loop gain, buys every improvement.

The four topologies stop being confusing when reduced to the two questions. What is sampled? Sampling the output voltage makes the output stiffer — output resistance falls. Sampling the output current makes it a better current source — output resistance rises. How is it mixed? Series mixing raises input resistance (the fed-back voltage opposes input current); shunt mixing lowers it (the fed-back current absorbs input current). Four combinations, and each impedance conclusion follows from its question alone: voltage-series (the op-amp non-inverting shape — input up, output down), voltage-shunt (the inverting shape — both down), current-series (input up, output up), current-shunt (input down, output up).

The standard method of analysis is to identify the topology from those two questions, account for the feedback network's loading at each port, compute A and β, and let the closed-loop formula do the rest.

What you should now be able to explain or do

Derive the closed-loop gain formula and state what it approaches when loop gain is large. Classify any feedback circuit by asking the sampling question and the mixing question. Predict all four impedance outcomes from first principles rather than from a memorised table. State how much distortion and bandwidth improve for a given loop gain.

Check yourself