The three op-amp rules
What are the three rules that let you analyze any negative-feedback op-amp circuit quickly?
| Level | ● screening |
| Track | General board |
| Really testing | The foundation for every op-amp follow-up. |
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Say this first: Treat the op-amp as ideal while it has negative feedback and is not clipped: (1) the voltage between its two inputs is driven to zero, so V+ ≈ V−; (2) the inputs draw no current; (3) so write KCL at the inverting input and solve for Vout.
Then explain: These come from infinite open-loop gain and infinite input impedance. They fail when there is no negative feedback (comparator), when the output saturates at a rail, when the signal is beyond the GBW, or when slew-rate limited.
Follow-ups: Derive the inverting gain: (0 − Vin)/R1 = (Vout − 0)/Rf → Vout = −(Rf/R1)·Vin.
Going deeper
Where rule 1 really comes from. Vout = A·(V+ − V−). With A = 100,000 and Vout = 5 V, the inputs differ by only 50 µV — "zero" for any board you will ever build. Note that it is the feedback that forces this, not the op-amp alone: cut the feedback path and the same part slams into a rail.
Worked example. Non-inverting stage, R1 = 1 kΩ to ground, Rf = 9 kΩ. Rule 2 says no current enters the − input, so V− = Vout·1/10. Rule 1 says V− = Vin. So Vout = 10·Vin. With finite gain the exact result is G = 10/(1 + 10/A): at A = 100,000 the error is about 0.01%.
Where people go wrong
- Using rule 1 on a comparator or a Schmitt trigger — positive feedback or no feedback, so the inputs are not equal.
- Thinking rule 2 applies to the output. The output can source and sink real current — up to its limit.
- Forgetting the rails: once the output clips, both rules are off and the "virtual ground" disappears.
Say it in the room: "I'll treat it as ideal while it has negative feedback and stays linear — then I'll check gain-bandwidth, swing and slew."
More like this in the book
This is AN-01 from Hardware Engineer Interview Questions. The book has 16 questions on analog & op-amps and 141 in all, each answered the same way: what to say first, how to explain it, the numbers worth quoting and the follow-ups that come next.
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