---
title: "Op-amp properties and differentiator"
subject: "Basic Electronics Engineering"
chapter: 4
key: "semester_2/basic_electronics_engineering:opamp-props-differentiator"
source: https://www.bctengineer.com/q/semester_2/basic_electronics_engineering/opamp-props-differentiator
site: BCT Engineering
---

# Op-amp properties and differentiator

Basic Electronics Engineering · Chapter 4: The Operational Amplifier and Oscillator

- Asked in: 2071 Magh, 2+4 marks; 2069 Bhadra, 2+4 marks (asked 2 times)
- Video: [Differentiator - Operational Amplifier | Basic Circuits #15 | Electronics Tutorials](https://www.youtube.com/watch?v=P5rrkTI3hZw) — CircuitBread
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_2/basic_electronics_engineering/opamp-props-differentiator
- Whole chapter: https://www.bctengineer.com/md/semester_2/basic_electronics_engineering/chapter-4

## Question

State any four important properties of ideal Op-Amp. Draw the circuit diagram of a differentiator using Op-Amp and show that the output is the derivative (differentiation) of the input signal.

## Short answer

Ideal op-amp: infinite open-loop gain, infinite input resistance, zero output resistance, infinite bandwidth. Differentiator: input through C to inverting input, feedback Rf. Virtual ground: i = C dVin/dt = -Vo/Rf => Vo = -RfC dVin/dt. So output is derivative.

## Answer

#### Four properties of an ideal op-amp
1. Infinite open-loop voltage gain.
2. Infinite input resistance (zero input current).
3. Zero output resistance.
4. Infinite bandwidth, infinite CMRR and zero offset voltage.

#### Differentiator using op-amp
```text
               +-----[ Rf ]-----+
               |                |
          C    |     |\         |
 Vin o----||---+-----|- \       |
                     |   >------+----o Vo
               +-----|+ /
               |     |/
              GND
```
The input Vin is connected through a capacitor C to the inverting input; the feedback resistor Rf connects the output to the inverting input; the non-inverting input is grounded.

#### Proof
- The inverting input is at virtual ground, V− = 0.
- Current through the capacitor: i = C d(Vin − 0)/dt = C dVin/dt.
- No current enters the op-amp, so the same current flows through Rf: i = (0 − Vo)/Rf = −Vo/Rf.

Equating:

C dVin/dt = −Vo/Rf

**Vo = −RfC dVin/dt**

So the output is proportional to the derivative of the input, with a minus sign (180° phase shift). The scaling factor is the time constant RfC.

Example: for a sine input, Vin = Vm sin ωt, the output is Vo = −RfCωVm cos ωt. A square wave input gives spike (pulse) outputs, and a triangular input gives a square wave.

**Practical note:** the gain increases with frequency and amplifies noise, so a small resistor in series with C and a small capacitor in parallel with Rf are added to limit the high-frequency gain.

## Check yourself

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

1. How is the op-amp differentiator connected?
   A. Capacitor C at the input to the inverting terminal, Rf as feedback
   B. Resistor at the input, capacitor as feedback
   C. Both resistors
   D. Input at the non-inverting terminal
   Answer: A. Vin passes through C into the inverting input, with Rf from output to that input and the non-inverting input grounded. (Key point: Circuit layout)

2. Which current flows through the capacitor?
   A. i = C dVin/dt
   B. i = Vin/C
   C. i = C Vin
   D. i = Vin dt/C
   Answer: A. With the inverting node at virtual ground, i = C d(Vin - 0)/dt. (Key point: Capacitor current)

3. What is the output voltage?
   A. Vo = -Rf C dVin/dt
   B. Vo = +Rf C dVin/dt
   C. Vo = -(1/Rf C) ∫Vin dt
   D. Vo = Rf Vin
   Answer: A. Equating C dVin/dt = -Vo/Rf gives Vo = -Rf C dVin/dt. (Key point: Output)

4. What does a triangular input produce?
   A. Square wave
   B. Sine wave
   C. Spikes only
   D. Constant dc
   Answer: A. The derivative of a constant-slope ramp is a constant, alternating in sign, so a square wave. (Key point: Waveform behaviour)

## Related in Basic Electronics Engineering

- [Op-amp properties and integrator](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Aopamp-props-integrator) — Basic Electronics Engineering, chapter 4
- [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×
- [Ideal op-amp properties; inverting gain](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Aopamp-props-inverting-gain) — Basic Electronics Engineering, chapter 4, asked 3×
- [Properties of ideal op-amp](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Aideal-opamp-properties) — Basic Electronics Engineering, chapter 4, asked 2×
- [Op-amp properties and summing amplifier](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Aopamp-props-summer-v1-2v2-3v3) — Basic Electronics Engineering, chapter 4
- [Op-amp properties; square wave generator](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Aopamp-five-props-square-wave) — Basic Electronics Engineering, chapter 4

## Related in other subjects

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- [Output voltage of two op-amp IA](https://www.bctengineer.com/question.md?key=semester_4%2Fadvanced_electronics%3Atwo-opamp-ia-output) — Advanced Electronics, chapter 4
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- [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