Op-Amps, Feedback & Active Filters
Ideal vs real op-amp behaviour, the four feedback topologies, gain-bandwidth trade-off and Butterworth/Chebyshev active filters.
Key formulas
f_max (full-power) = SR / (2π · V_peak)
Slew-rate limit: A 0.5 V/µs op-amp with a 5 V peak sine tops out near 16 kHz — the classic 'why is my sine a triangle' answer.
poles at ω_c·(cos 112.5° ± j·sin 112.5°), Q = 1/√2
2nd-order Butterworth pole locations: Equal-radius circle placement gives the flat passband; Sallen-Key realises it with two resistors and two capacitors.
Cheat sheet
- ▸Ideal op-amp rules: infinite open-loop gain (forces virtual short), infinite input impedance (no input current), zero output impedance.
- ▸Inverting gain = −Rf/Rin; non-inverting gain = 1 + Rf/R1; follower gain = 1 (impedance buffer).
- ▸Negative feedback trades gain for bandwidth: GBW (gain-bandwidth product) stays roughly constant — gain 100 amp has 1/100 the bandwidth.
- ▸Feedback topologies: series-shunt (voltage amp), shunt-series (current amp), series-series (transconductance), shunt-shunt (transresistance). Detect by what is sampled at output and mixed at input.
- ▸Slew rate limits large-signal speed: max undistorted sine frequency f = SR / (2π·Vpeak). Below that, gain-bandwidth dominates.
- ▸Butterworth = maximally flat (all poles equally spaced on the s-plane circle); Chebyshev trades ripple for a steeper initial roll-off.
- ▸Virtual ground only exists in inverting configuration with the + input grounded — a measurement point, not a physical node you can load.
Inverting vs non-inverting amplifier
| Aspect | Inverting | Non-inverting |
|---|---|---|
| Gain | −Rf/Rin (phase-inverted) | 1 + Rf/R1 (in-phase) |
| Input impedance | Rin (set by the input resistor) | Very high (op-amp input) |
| Input node | Virtual ground at − input | Signal drives + input directly |
| Common-mode swing | None (node fixed) | Full — needs rail-to-rail input for large swings |
Top 4 campus interview questions
MCQ mastery quiz
1. The gain-bandwidth product of a voltage-feedback op-amp is roughly…
2. An op-amp with SR = 0.5 V/µs outputting a 10 V-peak sine is distortion-free up to about…
3. Series-shunt feedback mixing and sampling corresponds to a…
4. Which filter type is maximally flat in the passband?
5. A unity-gain follower is used mainly to…