--- title: "Barkhausen criteria and Wien bridge oscillator" subject: "Electronics Devices and Circuit" chapter: 5 key: "semester_3/electronics_devices_and_circuit:barkhausen-wien-bridge" source: https://www.bctengineer.com/q/semester_3/electronics_devices_and_circuit/barkhausen-wien-bridge site: BCT Engineering --- # Barkhausen criteria and Wien bridge oscillator Electronics Devices and Circuit · Chapter 5: Signal Generator and Waveform-Shaping Circuits - Asked in: 2081 Bhadra, 1+1+3 marks; 2074 Ashwin, 2+6 marks (asked 2 times) - 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-wien-bridge - Whole chapter: https://www.bctengineer.com/md/semester_3/electronics_devices_and_circuit/chapter-5 ## Question State Barkhausen criteria for oscillation. Draw Wien bridge oscillator circuit to generate sine wave and derive the frequency of the generated sine wave. ## Short answer Barkhausen criteria: |Aβ|=1 and 0°/360° phase. The Wien bridge oscillator uses a Wien network (series R‑C, parallel R‑C) for positive feedback. It oscillates at f₀ = 1/(2πRC) and requires an amplifier gain of 3 (Rf = 2R1). ## 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. #### Wien bridge oscillator circuit ```text +-----[ Rf ]-----+ | | +-----+-----(-)\ | | >-----+------o Vo | +-----(+)/ | [R1] | | | +---[R]---[C]----+ series arm: Vo to (+) GND | +---[R]--+ | | +---[C]--+ | GND parallel arm: (+) to ground ``` The series arm (R in series with C) joins Vo to the (+) input, and the parallel arm (R in parallel with C) joins the (+) input to ground. Rf and R1 form the gain-setting divider at the (−) input. - Positive feedback: series R-C from the output to the (+) input, and parallel R-C from the (+) input to ground (the Wien network). - Negative feedback: the divider Rf and R1 (sets the closed-loop gain). #### Frequency of the generated sine wave The feedback factor of the Wien network (with equal R and C) is β = Vf/Vo = 1 / [3 + j(ωRC − 1/(ωRC))] - At ω = ωo = 1/(RC): the reactive part is zero, so β = 1/3 and the phase shift is 0°. - Barkhausen condition: the loop gain Aβ must be unity with 0° phase, so the amplifier gain must be A = 1 + Rf/R1 = 3 → **Rf = 2 R1** - **Frequency of oscillation:** **fo = 1 / (2π R C)** (If the arm values are unequal, with Ra and Ca in the series arm and Rb and Cb in the parallel arm: fo = 1/(2π √(Ra Rb Ca Cb)).) To start the oscillation, the gain is made slightly above 3 (Rf slightly more than 2R1), and the amplitude is limited by a nonlinear element (a lamp or a diode network in the feedback). Example: R = 10 kΩ, C = 16 nF gives fo ≈ 1 kHz. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What magnitude condition does the Barkhausen criterion impose on loop gain? A. |Aβ| = 1 B. |Aβ| = 0 C. |Aβ| = 3 D. |Aβ| < 1 Answer: A. Sustained oscillation requires the loop gain to be exactly unity (in practice slightly above 1 to start). (Key point: Barkhausen magnitude) 2. At ω = 1/(RC) what are the feedback factor and phase of the Wien network? A. β = 1/29, 180° B. β = 1/3, 0° C. β = 3, 0° D. β = 1/3, 180° Answer: B. The reactive term vanishes so β = 1/3 with 0° phase shift. (Key point: Wien network at resonance) 3. What gain does the amplifier need, and what resistor relation gives it? A. A = 29; Rf = 29R1 B. A = 3; Rf = 2R1 C. A = 1; Rf = 0 D. A = 3; Rf = 3R1 Answer: B. Aβ = 1 needs A = 1 + Rf/R1 = 3, so Rf = 2R1. (Key point: Gain requirement) 4. What is the Wien bridge oscillator frequency for equal R and C? A. 1/(2π√6 RC) B. 1/(2πRC) C. 1/(2π√(LC)) D. 1/(1.386 RC) Answer: B. fo = 1/(2πRC). 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