--- title: "Slew-rate check for four input signals" subject: "Advanced Electronics" chapter: 2 key: "semester_4/advanced_electronics:slew-rate-multiple-signals" source: https://www.bctengineer.com/q/semester_4/advanced_electronics/slew-rate-multiple-signals site: BCT Engineering --- # Slew-rate check for four input signals Advanced Electronics · Chapter 2: Operational Amplifier Characterization - Asked in: 2071 Chaitra, 4+3 marks - Video: [Op-Amp Slew Rate Explained (with Examples)](https://www.youtube.com/watch?v=2DFIr6t1hbc) — ALL ABOUT ELECTRONICS - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_4/advanced_electronics/slew-rate-multiple-signals - Whole chapter: https://www.bctengineer.com/md/semester_4/advanced_electronics/chapter-2 ## Question The op amp in the given figure has slew rate of 0.5 V/μS. The input signals are as follows: V1 = .01 sin 10⁶t, V2 = .05 sin (350 × 10³)t, V3 = .1 sin (200 × 10³)t, V4 = .1 sin (50 × 10³)t. [Figure: inverting amplifier: Vin through 10 KΩ to the inverting input, feedback resistor 330 KΩ from output V0 to the inverting input, non-inverting input grounded.] Determine whether the output will get distorted due to slew rate limitation? Find the new value of feedback resistor such that none of the signals gets distorted. ## Short answer For the inverting amplifier (gain 33), V2 and V3 require slopes 0.578 V/µs and 0.66 V/µs, exceeding the 0.5 V/µs slew rate, so they distort. To avoid distortion, gain must be ≤25, so feedback resistor ≤250 kΩ. ## Answer Given: inverting amplifier with R1 = 10 kΩ, Rf = 330 kΩ, so |Av| = 330/10 = 33. SR = 0.5 V/µs = 0.5 × 10⁶ V/s. For an input Vp sin ωt, the output is 33·Vp sin ωt and its maximum slope is ω × 33 × Vp. The output is undistorted only if this is ≤ SR. #### Check each signal | Signal | Vp (V) | ω (rad/s) | Output peak (V) | ω·Vm (V/µs) | Distorted? | |---|---|---|---|---|---| | V1 | 0.01 | 10⁶ | 0.33 | 0.330 | No | | V2 | 0.05 | 3.5 × 10⁵ | 1.65 | 0.578 | Yes | | V3 | 0.1 | 2 × 10⁵ | 3.3 | 0.660 | Yes | | V4 | 0.1 | 5 × 10⁴ | 3.3 | 0.165 | No | ```text V1: 10⁶ × 33 × 0.01 = 0.33 × 10⁶ V/s < 0.5 → OK V2: 3.5×10⁵ × 33 × 0.05 = 0.5775× 10⁶ V/s > 0.5 → distorted V3: 2×10⁵ × 33 × 0.1 = 0.66 × 10⁶ V/s > 0.5 → distorted V4: 5×10⁴ × 33 × 0.1 = 0.165 × 10⁶ V/s < 0.5 → OK ``` **V2 and V3 will be distorted** by slew-rate limiting; V1 and V4 will not. #### New feedback resistor For each signal the maximum gain allowed is Av(max) = SR/(ω·Vp): ```text V1: 0.5×10⁶ / (10⁶ × 0.01) = 50 V2: 0.5×10⁶ / (3.5×10⁵ × 0.05) = 28.57 V3: 0.5×10⁶ / (2×10⁵ × 0.1) = 25 V4: 0.5×10⁶ / (5×10⁴ × 0.1) = 100 ``` The smallest limit is 25 (set by V3), so the gain must be ≤ 25: ```text Rf ≤ 25 × R1 = 25 × 10 kΩ = 250 kΩ ``` **Answer: V2 and V3 are distorted; use Rf ≤ 250 kΩ** (e.g. a standard 240 kΩ or 220 kΩ) so that none of the signals is distorted. (This treats each signal applied separately, which is the usual reading; if all four were applied together, the slopes could add and a still smaller gain would be needed.) ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. For R1 = 10 kohm and Rf = 330 kohm, the inverting amplifier gain magnitude is: A. 33 B. 34 C. 3.3 D. 330 Answer: A. |Av| = Rf/R1 = 330/10 = 33. (Key point: Gain) 2. The output of a sine of peak Vp is undistorted only if: A. omega x Vp >= SR B. omega x Av x Vp <= SR C. Av x Vp <= SR D. omega/Av <= SR Answer: B. The output peak is Av Vp and the max slope is omega times that. (Key point: Distortion test) 3. With SR = 0.5 V/us, which signals are distorted? A. V1 and V4 only B. All four C. V2 and V3 only D. None Answer: C. Required slopes: V1 0.33, V2 0.578, V3 0.66, V4 0.165 V/us; only V2 and V3 exceed 0.5. (Key point: Which signals distort) 4. The maximum gain allowed by the worst signal (V3) and the resulting Rf are: A. 28.57 and Rf <= 285.7 kohm B. 100 and Rf <= 1 Mohm C. 50 and Rf <= 500 kohm D. 25 and Rf <= 250 kohm Answer: D. Av(max) = SR/(omega Vp); V3 gives 0.5e6/(2e5 x 0.1) = 25, the smallest, so Rf = 25 x 10k. 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