--- title: "Wien-bridge oscillator working" subject: "Electronics Devices and Circuit" chapter: 5 key: "semester_3/electronics_devices_and_circuit:wien-bridge-oscillator" source: https://www.bctengineer.com/q/semester_3/electronics_devices_and_circuit/wien-bridge-oscillator site: BCT Engineering --- # Wien-bridge oscillator working Electronics Devices and Circuit · Chapter 5: Signal Generator and Waveform-Shaping Circuits - Asked in: 2082 Shrawan, 6 marks; 2080 Bhadra, 4 marks; 2079 Bhadra, 2+4 marks; 2078 Bhadra, 1+3+2 marks; 2074 Chaitra, 6 marks; 2069 Chaitra, 2+3+3 marks; 2068 Baisakh, 6 marks; 2071 Chaitra, 6 marks (asked 8 times) - Video: [Wien Bridge Oscillator (using op-amp) Explained](https://www.youtube.com/watch?v=gbUXbaxvX94) — ALL ABOUT ELECTRONICS - 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/wien-bridge-oscillator - Whole chapter: https://www.bctengineer.com/md/semester_3/electronics_devices_and_circuit/chapter-5 ## Question Explain the working principle of Wien-Bridge oscillator with circuit diagram and necessary expressions. ## Short answer A Wien-bridge oscillator uses an op-amp with a positive feedback RC network that provides zero phase shift at f₀ = 1/(2πRC). To sustain oscillation, the non-inverting gain must be exactly 3, requiring Rf = 2R₁. ## Answer A Wien-bridge oscillator is an audio-frequency RC oscillator which uses an op-amp (non-inverting amplifier) with a Wien-bridge network as the positive-feedback path. It gives a low-distortion sine wave. #### Circuit diagram ```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). #### Working and expressions 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 is the oscillation frequency with equal R and C in the Wien network? A. fo = 1/(2π sqrt(6) RC) B. fo = 1/(2π RC) C. fo = 1/(RC) D. fo = 2π RC Answer: B. The reactive term vanishes at ω = 1/(RC), so fo = 1/(2π RC). (Key point: Frequency of oscillation) 2. At fo, what are the Wien network's feedback factor and phase shift? A. β = 1/29, 180° B. β = 1/3, 0° C. β = 3, 0° D. β = 1/3, 180° Answer: B. With the imaginary part zero, β = 1/3 with 0° phase, so a non-inverting amplifier closes the loop. (Key point: Feedback factor) 3. What amplifier gain is needed for sustained oscillation? A. A = 29 B. A = 1 C. A = 3, i.e. Rf = 2 R1 D. A = 1/3 Answer: C. Barkhausen requires Aβ = 1, so A = 3 = 1 + Rf/R1, hence Rf = 2R1. (Key point: Gain condition) 4. How are oscillations started and the amplitude kept stable? A. Gain slightly above 3 initially; a nonlinear element (lamp or diodes) limits amplitude B. Gain below 3; a capacitor limits amplitude C. Gain exactly 3 with no limiter D. Gain of 29 with a zener Answer: A. Slightly more than unity loop gain lets oscillations build up from noise, and a nonlinear element reduces gain as the amplitude grows. 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