---
title: "Voltage gain of non-inverting op-amp"
subject: "Basic Electronics Engineering"
chapter: 4
key: "semester_2/basic_electronics_engineering:opamp-noninverting-gain"
source: https://www.bctengineer.com/q/semester_2/basic_electronics_engineering/opamp-noninverting-gain
site: BCT Engineering
---

# Voltage gain of non-inverting op-amp

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

- Asked in: 2067 Chaitra, 3 marks; 2068 Magh, 4 marks (asked 2 times)
- Video: [Operational Amplifier: Non-Inverting Op-Amp and Op-Amp as Buffer (Op-Amp as Voltage Follower)](https://www.youtube.com/watch?v=uyOfonR_rEw) — ALL ABOUT ELECTRONICS
- 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-noninverting-gain
- Whole chapter: https://www.bctengineer.com/md/semester_2/basic_electronics_engineering/chapter-4

## Question

Derive the voltage gain of the non-inverting amplifier using an ideal op-amp.

## Short answer

Use virtual short: V- = V+ = Vin. V- = Vo R1/(R1+Rf). Equate: Vin = Vo R1/(R1+Rf). So Av = Vo/Vin = 1 + Rf/R1. Gain positive, ≥1.

## Answer

A **non-inverting amplifier** uses an op-amp with negative feedback to give an output in phase with the input and a gain set by two resistors.

#### Circuit and derivation
```text
              |\
 Vin o--------|+ \
              |   >------+------o Vo
         +----|- /       |
         |    |/        [Rf]
         |               |
         +---------------+
         |
        [R1]
         |
        GND
```
R1 is connected from the inverting input to ground and Rf from the output to the inverting input (negative feedback). The input Vin is applied directly to the non-inverting terminal.

**Derivation** (ideal op-amp)
- No current enters the op-amp inputs.
- Virtual short: V− = V+ = Vin.
- The voltage at the inverting node is set by the divider R1, Rf: V− = Vo × R1/(R1 + Rf).

Equating V− = Vin:

Vin = Vo R1/(R1 + Rf)

**Av = Vo/Vin = 1 + Rf/R1**

The gain is positive (the output is in phase with the input) and always at least 1. For Rf = 0 or R1 = ∞ (open), the circuit becomes a unity gain buffer (voltage follower), Av = 1.

Example: R1 = 1 kΩ, Rf = 9 kΩ gives Av = 1 + 9 = 10. The input resistance is very high (equal to the op-amp input resistance) and the output resistance is very small.

## Check yourself

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

1. Where are R1 and Rf connected in the non-inverting amplifier?
   A. R1 from inverting input to ground, Rf from output to inverting input
   B. R1 in series with Vin, Rf to ground
   C. Both at the non-inverting input
   D. Rf from non-inverting input to ground
   Answer: A. They form a voltage divider on the output that feeds the inverting input (negative feedback). (Key point: Feedback network)

2. What is the voltage at the inverting node used in the derivation?
   A. V- = Vo R1/(R1 + Rf)
   B. V- = Vo Rf/(R1 + Rf)
   C. V- = 0
   D. V- = Vo
   Answer: A. The divider gives V- = Vo R1/(R1 + Rf), and virtual short sets it equal to Vin. (Key point: Derivation step)

3. For R1 = 1 kΩ and Rf = 9 kΩ, what is the gain?
   A. 9
   B. -9
   C. 10
   D. 0.1
   Answer: C. Av = 1 + Rf/R1 = 1 + 9 = 10. (Key point: Gain)

4. What are the phase and input resistance of this amplifier?
   A. In phase, very high input resistance
   B. 180° out of phase, input resistance R1
   C. In phase, input resistance R1
   D. 180° out of phase, very high input resistance
   Answer: A. Input goes to the non-inverting terminal, so output is in phase and the input resistance is that of the op-amp, very high. (Key point: Phase and impedance)

## Related in Basic Electronics Engineering

- [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×
- [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
- [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×

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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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- [Input impedance of inverting op-amp](https://www.bctengineer.com/question.md?key=semester_4%2Fadvanced_electronics%3Ainverting-input-impedance) — Advanced Electronics, chapter 2