---
title: "Maximum peak input for undistorted output"
subject: "Advanced Electronics"
chapter: 2
key: "semester_4/advanced_electronics:slew-rate-max-peak-input"
source: https://www.bctengineer.com/q/semester_4/advanced_electronics/slew-rate-max-peak-input
site: BCT Engineering
---

# Maximum peak input for undistorted output

Advanced Electronics · Chapter 2: Operational Amplifier Characterization

- Asked in: 2068 Chaitra, 2+5 marks
- 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-max-peak-input
- Whole chapter: https://www.bctengineer.com/md/semester_4/advanced_electronics/chapter-2

## Question

Define Slew Rate of an operational amplifier. An amplifier has a bandwidth of 20KHz and closed loop gain of 20. Find the maximum peak input signal that can be applied to obtain undistorted sine wave output. Assume SR = 1V/μs.

## Short answer

Slew rate is the maximum output voltage rate of change, SR=(dVo/dt)max. For a sine wave, Vm=SR/(2πf); with SR=1 V/µs and f=20 kHz, Vm=7.958 V. Dividing by closed-loop gain 20 gives maximum peak input 0.398 V.

## Answer

#### Slew rate
**Slew rate (SR)** is the maximum rate of change of output voltage per unit time that an op-amp can produce, SR = (dVo/dt)max, usually in V/µs (0.5 V/µs for the 741). For a sine output Vm sin 2πft, the maximum slope is 2πf·Vm, so the output is undistorted only if 2πf·Vm ≤ SR.

#### Maximum peak input
Given: bandwidth (highest signal frequency) f = 20 kHz, closed-loop gain = 20, SR = 1 V/µs = 10⁶ V/s.

```text
Maximum undistorted output peak:
  Vm = SR / (2πf)
     = 10⁶ / (2π × 20 × 10³)
     = 7.958 V
Maximum peak input:
  Vin(peak) = Vm / gain = 7.958 / 20
            = 0.398 V
```

**Answer: maximum peak input ≈ 0.398 V (398 mV)**, giving a 7.96 V peak output at 20 kHz. A larger input would make the output slew-rate limited (triangular) at the top of the band.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Slew rate is:
   A. The maximum rate of change of the output voltage
   B. The maximum output voltage
   C. The unity-gain frequency
   D. The rate of change of input offset
   Answer: A. SR = (dVo/dt)max in V/us. (Key point: Slew rate definition)

2. A sine output is undistorted if:
   A. f*Vm >= SR
   B. 2*pi*f*Vm <= SR
   C. Vm/f <= SR
   D. 2*pi*Vm <= f
   Answer: B. Max slope of Vm sin(2 pi f t) is 2 pi f Vm. (Key point: Undistorted condition)

3. With SR = 1 V/us and f = 20 kHz, the max undistorted output peak is:
   A. 15.9 V
   B. 0.398 V
   C. 7.96 V
   D. 79.6 V
   Answer: C. Vm = 10^6/(2 pi x 20000) = 7.958 V. (Key point: Max output)

4. With gain 20, the maximum peak input is:
   A. 7.96 V
   B. 0.159 V
   C. 1.59 V
   D. About 0.398 V
   Answer: D. 7.958/20 = 0.398 V. (Key point: Max input)

## Related in Advanced Electronics

- [Slew-rate check for 40 dB amplifier at 20 kHz](https://www.bctengineer.com/question.md?key=semester_4%2Fadvanced_electronics%3Aslew-rate-40db-20khz) — Advanced Electronics, chapter 2
- [Voltage follower square-wave output with slew rate](https://www.bctengineer.com/question.md?key=semester_4%2Fadvanced_electronics%3Avoltage-follower-square-wave) — Advanced Electronics, chapter 2
- [Maximum Vp for undistorted output (1 kΩ/33 kΩ)](https://www.bctengineer.com/question.md?key=semester_4%2Fadvanced_electronics%3Aslew-rate-1k-33k-vp) — Advanced Electronics, chapter 2, asked 2×
- [Slew-rate check for four input signals](https://www.bctengineer.com/question.md?key=semester_4%2Fadvanced_electronics%3Aslew-rate-multiple-signals) — Advanced Electronics, chapter 2
- [Offset definitions; closed-loop output resistance](https://www.bctengineer.com/question.md?key=semester_4%2Fadvanced_electronics%3Aoffset-closed-loop-output-resistance) — Advanced Electronics, chapter 2, asked 2×
- [Slew-rate distortion check, 330 kΩ/10 kΩ inverter](https://www.bctengineer.com/question.md?key=semester_4%2Fadvanced_electronics%3Aslew-rate-330k-10k) — Advanced Electronics, chapter 2

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