Oscillators and Multivibrators
What this domain tests
Oscillator conditions, RC and LC oscillator frequency expressions, and the three multivibrator types including 555-timer versions. Frequency calculations and state-count questions are the usual numericals.
Core rules
- Barkhausen criterion: loop gain Aβ = 1 with total loop phase shift of 0° or 360°. In practice the loop gain is kept slightly above 1 so oscillation starts, and nonlinear limiting brings it back to 1.
- RC phase-shift oscillator: three identical RC sections give 60° each; f = 1/(2πRC√6), and the amplifier must supply a gain of at least 29.
- Wien bridge oscillator: f = 1/(2πRC) with amplifier gain of at least 3; the lead-lag network gives zero phase shift at resonance.
- Colpitts uses a capacitive divider, Hartley a tapped inductor; both give f = 1/(2π√(LC)). A crystal gives the highest Q and best frequency stability.
- Astable multivibrator has no stable state and runs freely producing a square wave; monostable has one stable state and gives a single pulse of width 1.1RC; bistable has two stable states and acts as a flip-flop.
- 555 astable: f = 1.44/((R1 + 2R2)C), duty cycle = (R1 + R2)/(R1 + 2R2), always above 50 %.
Worked example
A Wien bridge oscillator uses R = 10 kΩ and C = 0.01 µF. f = 1/(2π × 10⁴ × 10⁻⁸) = 1/(6.283 × 10⁻⁴) ≈ 1592 Hz. For sustained oscillation the non-inverting gain must be 1 + Rf/R1 = 3, so Rf = 2R1.
Traps that cost marks
- Writing Aβ = 1 as exactly the starting condition instead of slightly more than 1.
- Using 45° per section (that would need four sections) instead of 60°.
- Expecting a standard 555 astable to give exactly 50 % duty cycle.
- Confusing pulse width 1.1RC (monostable) with the astable frequency formula.