--- title: "Barkhausen criteria and oscillation principle" subject: "Electronics Devices and Circuit" chapter: 5 key: "semester_3/electronics_devices_and_circuit:barkhausen-criteria-principle" source: https://www.bctengineer.com/q/semester_3/electronics_devices_and_circuit/barkhausen-criteria-principle site: BCT Engineering --- # Barkhausen criteria and oscillation principle Electronics Devices and Circuit · Chapter 5: Signal Generator and Waveform-Shaping Circuits - Asked in: 2068 Baisakh, 4 marks; 2070 Chaitra, 2 marks (asked 2 times) - Video: [Oscillators & Barkhausen Criterion - Basic Introduction](https://www.youtube.com/watch?v=skDVcnVwK3A) — The Organic Chemistry Tutor - 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-criteria-principle - Whole chapter: https://www.bctengineer.com/md/semester_3/electronics_devices_and_circuit/chapter-5 ## Question State Barkhausen criteria and explain the principle of oscillation. ## Short answer Barkhausen criteria: |Aβ|=1 and 0°/360° phase. Oscillation starts from noise; the feedback network selects one frequency meeting the phase condition. Initially |Aβ|>1, amplitude grows until nonlinear limiting makes |Aβ|=1, sustaining oscillation. ## 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. #### Principle of oscillation An oscillator converts dc power into ac of a fixed frequency without any input signal. It consists of an amplifier, a positive feedback network, and a frequency-determining network (LC, RC or crystal). ```text +---------+ Vs=0 -->| A |----+----> Vo +---------+ | ^ | | +-----+ +---| β |<-+ +-----+ ``` 1. At switch-on, the noise and the turn-on transient present in the circuit have components of many frequencies. 2. The amplifier amplifies these. The feedback network passes back a fraction β in phase (0° or 360° for only one frequency fo). So only that component is reinforced. 3. At first, the loop gain is slightly above 1 (|Aβ| > 1), so the amplitude grows exponentially. 4. As the amplitude increases, the amplifier saturates or a limiter reduces the gain, until |Aβ| = 1. The amplitude then becomes constant: a sustained oscillation of frequency fo. With closed-loop gain Af = A/(1 − Aβ): when Aβ = 1 the denominator is zero, so the gain is infinite, which means an output exists with no input. If |Aβ| < 1 the oscillation dies out; if |Aβ| > 1 (and not limited) the output is distorted. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What starts oscillation when the circuit is switched on? A. An external input signal B. Noise and the turn-on transient containing many frequencies C. A battery pulse only D. The load resistor Answer: B. Noise has all frequencies; the one with correct phase is reinforced by positive feedback. (Key point: Start of oscillation) 2. Why must |Aβ| be slightly above 1 initially? A. So the amplitude grows exponentially from noise B. So the oscillation dies out C. To reduce distortion D. To make the phase 180° Answer: A. |Aβ| > 1 makes the amplitude build up until limiting. (Key point: Initial loop gain) 3. How does the amplitude become constant? A. Saturation or a limiter reduces gain until |Aβ| = 1 B. The feedback is disconnected C. β increases without limit D. The frequency changes Answer: A. As amplitude rises the gain falls, settling at |Aβ| = 1. (Key point: Amplitude stabilisation) 4. What does Aβ = 1 mean for the closed-loop gain Af = A/(1 - Aβ)? A. Af = 0 B. Af = 1 C. Af is infinite, i.e. output exists with no input D. Af = A Answer: C. The denominator becomes zero, so an output can exist without any input. 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