--- title: "Op-amp astable multivibrator" subject: "Electronics Devices and Circuit" chapter: 5 key: "semester_3/electronics_devices_and_circuit:opamp-astable-multivibrator" source: https://www.bctengineer.com/q/semester_3/electronics_devices_and_circuit/opamp-astable-multivibrator site: BCT Engineering --- # Op-amp astable multivibrator Electronics Devices and Circuit · Chapter 5: Signal Generator and Waveform-Shaping Circuits - Asked in: 2083 Baisakh, 8 marks; 2075 Chaitra, 8 marks; 2071 Shrawan, 4 marks (asked 3 times) - Video: [Astable Multivibrator (using op-amp) Explained](https://www.youtube.com/watch?v=T7T3At9N9dk) — 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/opamp-astable-multivibrator - Whole chapter: https://www.bctengineer.com/md/semester_3/electronics_devices_and_circuit/chapter-5 ## Question Define the term multivibrator. Explain the operation of op-amp based astable multivibrator for square wave with the help of circuit diagram and waveforms and also determine its frequency of oscillation. ## Short answer Output toggles between ±Vsat as capacitor voltage crosses ±βVsat, where β = R1/(R1+R2). Period T = 2RC ln[(1+β)/(1–β)], so frequency f = 1 / {2RC ln[(1+β)/(1–β)]}. Produces a square wave. ## Answer #### Multivibrator A multivibrator is a regenerative circuit with two states in which the output switches between them. It has three types: **astable** (no stable state, free-running square wave), **monostable** (one stable state, gives a single pulse when triggered) and **bistable** (two stable states, flip-flop). #### Op-amp astable (square-wave) multivibrator ```text +--------[ R ]--------+ | | | |\ | +-------|-\ | | | >----+-----+---o Vo (±Vsat) [C] +---|+/ | | | |/ | GND +--+--[R2]---+ | [R1] | GND ``` The inverting input is connected to the output through R and to ground through C. The non-inverting input receives a fraction of the output from the divider R1, R2 (positive feedback). β = R1/(R1 + R2) #### Operation 1. Suppose the output is at +Vsat. The voltage at the (+) input is +βVsat. The capacitor charges toward +Vsat through R. 2. When vC reaches +βVsat, the (−) input becomes higher than (+), and the output switches to −Vsat. Now the (+) input is −βVsat. 3. The capacitor discharges and then charges toward −Vsat, until vC reaches −βVsat; then the output switches to +Vsat again. 4. The cycle repeats, giving a square wave while the capacitor voltage is an exponential triangular-like wave between ±βVsat. ```text Vo +Vsat ____ ____ | | | | ------------| |____| |____ -Vsat vC +βVsat /\ /\ ------------ / \ / \ <- exponential \/ \/ -βVsat ``` #### Frequency of oscillation During charging, vC rises from −βVsat to +βVsat, towards Vsat: vC(t) = Vsat − (Vsat + βVsat) e^(−t/RC) At t = T/2, vC = +βVsat: βVsat = Vsat − Vsat (1 + β) e^(−T/2RC) → e^(−T/2RC) = (1 − β)/(1 + β) T/2 = RC ln[(1 + β)/(1 − β)] **T = 2RC ln[(1 + β)/(1 − β)], f = 1/T = 1 / {2RC ln[(1 + β)/(1 − β)]}** With β = R1/(R1 + R2): the expression becomes T = 2RC ln(1 + 2R1/R2). Special case: R2 = 1.16 R1 (β = 0.462) gives ln(...) = 1, so f = 1/(2RC). **Example:** R = 10 kΩ, C = 0.1 µF, R1 = R2 → β = 0.5, ln(3) = 1.0986, T = 2 × 10⁴ × 10⁻⁷ × 1.0986 = 2.2 ms, f = 455 Hz. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Which statement describes an astable multivibrator? A. It has two stable states like a flip-flop B. It has one stable state and gives one pulse when triggered C. It has no stable state and free-runs as a square wave generator D. It needs an input clock to switch Answer: C. An astable switches continuously between two quasi-stable states without any trigger. (Key point: Astable definition) 2. In the op-amp astable, at what capacitor voltage does the output switch from +Vsat to -Vsat? A. +Vsat B. +βVsat C. 0 V D. -βVsat Answer: B. While the output is +Vsat, the (+) input is +βVsat; when vC reaches it, the (-) input exceeds (+) and the output flips. (Key point: Switching threshold) 3. What is β in the op-amp astable circuit? A. R2/(R1 + R2) B. R1/(R1 + R2) C. R/(R + R1) D. 1/RC Answer: B. The divider R1, R2 feeds back β = R1/(R1 + R2) of the output to the non-inverting input. (Key point: Feedback fraction) 4. What is the period of oscillation? A. T = RC ln[(1 + β)/(1 - β)] B. T = 2RC ln[(1 + β)/(1 - β)] C. T = 2RC ln[(1 - β)/(1 + β)] D. T = 0.693 RC Answer: B. Charging from -βVsat to +βVsat takes T/2 = RC ln[(1 + β)/(1 - β)], so T is twice that. (Key point: Period formula) 5. For R = 10 kΩ, C = 0.1 µF and R1 = R2 (β = 0.5), what is the approximate frequency? A. 455 Hz B. 4.55 kHz C. 1 kHz D. 159 Hz Answer: A. T = 2RC ln3 = 2 x 10^-3 x 1.0986 = 2.2 ms, so f is about 455 Hz. 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