---
title: "Wien bridge RC oscillator, Barkhausen criteria"
subject: "Basic Electronics Engineering"
chapter: 4
key: "semester_2/basic_electronics_engineering:wien-bridge-barkhausen"
source: https://www.bctengineer.com/q/semester_2/basic_electronics_engineering/wien-bridge-barkhausen
site: BCT Engineering
---

# Wien bridge RC oscillator, Barkhausen criteria

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

- Asked in: 2069 Bhadra, 4+2 marks
- Video: [How Oscillator Works ? The Working Principle of the Oscillator Explained](https://www.youtube.com/watch?v=XVS8Puf4tiw) — 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/wien-bridge-barkhausen
- Whole chapter: https://www.bctengineer.com/md/semester_2/basic_electronics_engineering/chapter-4

## Question

Describe the operation of Wien bridge RC-sinewave oscillator. State Barkhausen criteria.

## Short answer

The Wien bridge oscillator uses a non-inverting op-amp and series-parallel RC network providing positive feedback with 0° phase shift at f₀=1/(2πRC). With gain slightly above 3, oscillations start and amplitude is stabilised by a non-linear element. Barkhausen criteria: |Aβ|=1 and loop phase shift 0° or 360°.

## Answer

#### Wien bridge RC oscillator

It is a sine wave oscillator for audio frequencies. It uses a non-inverting op-amp amplifier with a Wien (lead-lag) RC network as positive feedback.

```text
           +------[ Rf ]-------+
           |                   |
 GND--[R1]-+        |\         |
           +--------|- \       |
                    |   >------+----o Vo
           +--------|+ /       |
           |        |/         |
           |                   |
           +--[ R ]--||--------+
           |         C     (series R-C arm)
         +-+-+
         |   |
        [R] === C   (parallel R-C arm)
         |   |
         +-+-+
           |
          GND
```

**Parts**
- The series R-C and parallel R-C arms (with the same R and C) give the positive feedback to the non-inverting input.
- Rf and R1 give negative feedback that sets the amplifier gain A = 1 + Rf/R1.

**Operation**
1. At low frequencies, the series C acts almost as an open circuit, so the feedback is small and leads in phase. At high frequencies, the parallel C almost shorts the non-inverting input to ground, so the feedback is small and lags in phase.
2. At only one frequency, f₀ = 1/(2πRC), the phase shift of the network is exactly 0° and the feedback factor is at its maximum, β = 1/3.
3. The amplifier is non-inverting (0° phase shift), so at f₀ the total loop phase shift is 0°.
4. With gain A = 3 (Rf = 2R1), the loop gain Aβ = 1 and a stable sine wave at f₀ is produced. Initially, noise starts the oscillation, with A slightly more than 3.
5. The amplitude is stabilised by using a lamp or a diode-resistor network in the Rf path, so that the gain falls when the output grows.

Frequency: **f₀ = 1/(2πRC)**

#### Barkhausen criteria

1. |Aβ| = 1 (loop gain unity).
2. Phase shift around the loop = 0° or 360°.

## Check yourself

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

1. What is the network phase shift at f0 = 1/(2πRC)?
   A. 0°
   B. 90° lead
   C. 90° lag
   D. 180°
   Answer: A. At f0 the lead-lag network gives exactly 0° and maximum β = 1/3. (Key point: Phase at f0)

2. Why is the op-amp non-inverting in the Wien bridge oscillator?
   A. It gives 180° so it cancels the network
   B. It increases input resistance only
   C. It gives 0° phase shift so the total loop phase is 0° at f0
   D. It lets Rf be removed
   Answer: C. Network 0° plus amplifier 0° satisfies the phase part of Barkhausen. (Key point: Amplifier type)

3. How does oscillation begin, and what gain is used?
   A. Noise starts it, with A slightly more than 3
   B. A signal source is required, with A = 1
   C. Noise starts it with A less than 3
   D. It needs A = 0 initially
   Answer: A. A slightly above 3 makes Aβ slightly above 1 so noise grows into oscillation. (Key point: Starting oscillation)

4. How is output amplitude stabilised?
   A. A larger capacitor is added
   B. The supply is reduced
   C. A lamp or diode-resistor network in Rf reduces gain as output grows
   D. Rf is made zero
   Answer: C. The gain drops when amplitude rises, holding Aβ at 1. (Key point: Amplitude stabilisation)

## Related in Basic Electronics Engineering

- [Barkhausen criteria; Wien bridge frequency](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Abarkhausen-wien-derive-frequency) — Basic Electronics Engineering, chapter 4
- [Wien bridge oscillator circuit and operation](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Awien-bridge-draw-explain) — Basic Electronics Engineering, chapter 4, asked 4×
- [Barkhausen criteria and square wave generator](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Abarkhausen-square-wave-generator) — Basic Electronics Engineering, chapter 4

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- [Barkhausen criteria and RC oscillator using op-amp](https://www.bctengineer.com/question.md?key=semester_3%2Felectronics_devices_and_circuit%3Abarkhausen-rc-opamp-oscillator) — Electronics Devices and Circuit, chapter 5