---
title: "Maximum Vp for undistorted output (1 kΩ/33 kΩ)"
subject: "Advanced Electronics"
chapter: 2
key: "semester_4/advanced_electronics:slew-rate-1k-33k-vp"
source: https://www.bctengineer.com/q/semester_4/advanced_electronics/slew-rate-1k-33k-vp
site: BCT Engineering
---

# Maximum Vp for undistorted output (1 kΩ/33 kΩ)

Advanced Electronics · Chapter 2: Operational Amplifier Characterization

- Asked in: 2072 Chaitra, 3+3+1 marks; 2071 Shrawan, 3+3+1 marks (asked 2 times)
- 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-1k-33k-vp
- Whole chapter: https://www.bctengineer.com/md/semester_4/advanced_electronics/chapter-2

## Question

In a closed-loop inverting configuration of an op-amp, the input resistance and the feedback resistance are 1 KΩ and 33 KΩ respectively. (i) Determine the value of Vp for an undistorted output if an input to the circuit is Vin = Vp sin(2πft), where f = 1 kHz and slew rate = 0.6 V/μs. (ii) If the value of Vp is assumed to be 5V, state two possible remedies in the circuit to have an undistorted output.

## Short answer

Gain = 33. For undistorted output, 2πf·33Vp ≤ SR ⇒ Vp ≤ 0.6×10⁶/(2π×1000×33) = 2.89 V. For Vp = 5 V, reduce Rf to ≤ 19.1 kΩ (gain ≤ 19.1) or use an op‑amp with SR ≥ 1.04 V/µs.

## Answer

Given: inverting amplifier, R1 = 1 kΩ, Rf = 33 kΩ, f = 1 kHz, SR = 0.6 V/µs.

```text
Closed-loop gain |Av| = Rf/R1 = 33
Output: vo = -33 Vp sin(2πft),  peak Vm = 33 Vp
```

#### (i) Maximum Vp for undistorted output
For a sine wave the maximum slope of the output is 2πf·Vm. To avoid slew-rate distortion:

```text
2πf·Vm ≤ SR
Vm(max) = SR/(2πf)
        = 0.6 × 10⁶ / (2π × 1000)
        = 95.49 V
Vp(max) = Vm/33 = 95.49/33 = 2.894 V
```

**Answer: Vp ≤ 2.894 V (about 2.89 V)** as far as slew rate is concerned.

Note: with a ±15 V supply the output cannot exceed about ±13 V anyway, so in practice clipping (saturation) limits Vp to about 13/33 ≈ 0.39 V before the slew-rate limit is reached.

#### (ii) Vp = 5 V: remedies
With Vp = 5 V, Vm = 33 × 5 = 165 V and the required rate is 2π × 1000 × 165 = 1.037 V/µs > 0.6 V/µs, so the output is distorted. Two remedies:

1. **Reduce the closed-loop gain:** gain ≤ 95.49/5 = 19.1, i.e. **Rf ≤ 19.1 kΩ** (with R1 = 1 kΩ); in practice the gain must also be small enough to keep the output within the supply (e.g. gain ≤ 2.6 for ±13 V swing, Rf ≤ 2.6 kΩ).
2. **Use an op-amp with a higher slew rate:** SR ≥ 1.037 V/µs (e.g. LF351, 13 V/µs).

Other options: reduce the input amplitude (attenuate before the amplifier) or reduce the frequency.

## Check yourself

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

1. What condition avoids slew-rate distortion for a sine output?
   A. Vm ≥ 2πf SR
   B. f Vm ≥ SR
   C. 2πf Vm ≤ SR
   D. 2πf ≥ SR
   Answer: C. Max slope of Vm sin(ωt) is ωVm. (Key point: Condition)

2. What is Vm(max) for f = 1 kHz and SR = 0.6 V/µs?
   A. 0.6 V
   B. 95.5 V
   C. 6 V
   D. 9.5 V
   Answer: B. 0.6×10^6/(2π×1000) = 95.49 V. (Key point: Max output)

3. What is Vp(max) with gain 33?
   A. 0.39 V
   B. 2.89 V
   C. 33 V
   D. 95.5 V
   Answer: B. 95.49/33 = 2.894 V. (Key point: Max Vp)

4. Which is a valid remedy for Vp = 5 V?
   A. Increase Rf
   B. Reduce SR
   C. Reduce gain (Rf ≤ 19.1 kΩ) or use an op-amp with SR ≥ 1.04 V/µs
   D. Increase the frequency
   Answer: C. Required slope is 1.037 V/µs > 0.6, so lower gain or higher-SR op-amp. (Key point: Remedies)

## Related in Advanced Electronics

- [Maximum peak input for undistorted output](https://www.bctengineer.com/question.md?key=semester_4%2Fadvanced_electronics%3Aslew-rate-max-peak-input) — Advanced Electronics, chapter 2
- [Input impedance of inverting op-amp](https://www.bctengineer.com/question.md?key=semester_4%2Fadvanced_electronics%3Ainverting-input-impedance) — Advanced Electronics, chapter 2
- [Offset/bias definitions; closed-loop input resistance](https://www.bctengineer.com/question.md?key=semester_4%2Fadvanced_electronics%3Aoffset-bias-closed-loop-input-resistance) — 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×
- [Find coefficients of op-amp summing circuit](https://www.bctengineer.com/question.md?key=semester_4%2Fadvanced_electronics%3Asumming-amplifier-coefficients) — Advanced Electronics, chapter 1

## Related in other subjects

- [Transfer function of op-amp with Rs ∥ C feedback](https://www.bctengineer.com/question.md?key=semester_3%2Fcontrol_systems%3Atf-opamp-rs-c-r1-r2) — Control Systems, chapter 2
- [Non-inverting op-amp voltage gain](https://www.bctengineer.com/question.md?key=semester_1%2Ffundamental_of_electrical_and_electronics_engineering%3Anon-inverting-amplifier-gain) — Fundamental of Electrical and Electronics Engineering, chapter 6
- [Transfer function of op-amp phase-shift circuit](https://www.bctengineer.com/question.md?key=semester_3%2Fcontrol_systems%3Atf-opamp-allpass-r1-c-r2) — Control Systems, chapter 2, asked 2×
- [Ideal op-amp properties; non-inverting gain](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Aopamp-props-noninverting-gain) — Basic Electronics Engineering, chapter 4, asked 3×