---
title: "Barkhausen criteria and RC oscillator using op-amp"
subject: "Electronics Devices and Circuit"
chapter: 5
key: "semester_3/electronics_devices_and_circuit:barkhausen-rc-opamp-oscillator"
source: https://www.bctengineer.com/q/semester_3/electronics_devices_and_circuit/barkhausen-rc-opamp-oscillator
site: BCT Engineering
---

# Barkhausen criteria and RC oscillator using op-amp

Electronics Devices and Circuit · Chapter 5: Signal Generator and Waveform-Shaping Circuits

- Asked in: 2072 Chaitra, 2+1+4 marks
- Video: [BARKHAUSEN CRITERIA, WEIN BRIDGE, AND PHASE SHIFT OSCILLATOR](https://www.youtube.com/watch?v=YpKGCwkt5Xk) — Prof. Barapate's Tutorials
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/electronics_devices_and_circuit/barkhausen-rc-opamp-oscillator
- Whole chapter: https://www.bctengineer.com/md/semester_3/electronics_devices_and_circuit/chapter-5

## Question

State Barkhausen criteria for sinusoidal oscillator. Is this principle applicable to RC oscillator using op-Amp? Why? If yes, determine the frequency of oscillations and the gain of the amplifier circuit.

## Short answer

Barkhausen criteria: |Aβ| = 1 and total phase shift 0°/360°. Yes, RC oscillators using op-amps satisfy this. For a phase-shift oscillator, f ≈ 0.065/(RC) and gain ≥ 29; for a Wien-bridge, f = 1/(2pi RC) and gain = 3.

## Answer

**Barkhausen criteria:** An amplifier with feedback produces sustained sinusoidal oscillation at the frequency for which the loop gain Aβ satisfies both:

1. **Magnitude condition:** |Aβ| = 1 (loop gain is exactly unity)
2. **Phase condition:** the total phase shift around the loop is 0° or 360° (positive feedback), that is, ∠Aβ = 0°, 360°, ...

Here A is the amplifier gain and β is the feedback factor.

#### Is the principle applicable to RC oscillators using an op-amp?
**Yes.** An RC oscillator is still a feedback system: an op-amp amplifier (gain A) and an RC feedback network (factor β). The oscillation condition is the same: loop gain |Aβ| = 1 with total phase shift 0° (360°) at one frequency. The RC network provides the frequency selectivity (it has the right phase only at one frequency), instead of an LC tank. The op-amp supplies the gain and needed phase (inverting or non-inverting). 

#### Frequency and gain
Two common op-amp RC oscillators:

**(a) RC phase-shift oscillator (inverting amplifier + three RC sections)**

The three-section network gives 180° phase shift and an attenuation of 29 at one frequency. With the inverting amplifier of 180°, the total is 360°.

**f = 1/(2π √6 RC) ≈ 0.065/(RC)**

Required gain: |A| = Rf/R ≥ **29**

**(b) Wien-bridge oscillator (non-inverting amplifier + Wien network)**

The network gives β = 1/3 and 0° phase at ω = 1/RC.

**f = 1/(2π RC)**

Required gain: A = 1 + Rf/R1 = **3** (Rf = 2 R1; slightly more than 3 to start the oscillation).

**Example:** R = 10 kΩ, C = 10 nF: phase-shift f = 650 Hz with gain 29; Wien f = 1.59 kHz with gain 3.

## Check yourself

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

1. Is the Barkhausen criterion applicable to op-amp RC oscillators?
   A. Yes, they are feedback systems that need |Aβ| = 1 and 0° phase
   B. No, only LC oscillators
   C. No, op-amps have no gain
   D. Only for crystal oscillators
   Answer: A. An RC oscillator is an amplifier plus RC feedback network, so the same condition applies. (Key point: Applicability)

2. What gain is required in the RC phase shift oscillator?
   A. 3
   B. 29
   C. 1
   D. 44.5 for op-amp
   Answer: B. The network attenuates by 29, so |A| = Rf/R ≥ 29. (Key point: Phase shift gain)

3. What gain is required in the Wien bridge oscillator?
   A. 3
   B. 29
   C. 1/3
   D. 6
   Answer: A. β = 1/3, so A = 1 + Rf/R1 = 3. (Key point: Wien gain)

4. Which pair of frequencies is correct (phase shift, Wien)?
   A. 1/(2πRC), 1/(2π√6 RC)
   B. 1/(2π√6 RC), 1/(2πRC)
   C. both 1/(2πRC)
   D. both 1/(2π√6 RC)
   Answer: B. The phase-shift oscillator runs at 1/(2π√6 RC) and the Wien at 1/(2πRC). (Key point: Frequencies)

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