Oscillator criteria (Barkhausen)
A loop oscillates at the frequency where its total phase shift is 360° and keeps oscillating only if its loop gain there is at least 1. The Wien network gives zero phase shift at f₀ = 1 ÷ (2πRC) and passes exactly β = ⅓, so the amplifier needs a gain of at least 3.
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How it works
Phase condition: the Wien network is in phase only at f₀ = 1.592 kHz, where it passes β = ⅓.
Gain condition: Aβ = 3.20 ÷ 3 = 1.067 — above 1, so it grows until the op-amp clips.
Try it on the bench
- Try R_f = 2.0 kΩ: exactly 3, in theory. In practice it either creeps up or dies away: that is why real Wien oscillators regulate their gain (see the lamp-stabilised version).
Parts on the bench
- 2 × Bench power supply
- NE5532 low-noise op-amp
- 4 × Resistor
- 2 × Film capacitor
In the course
Electronics Engineering, module “Oscillators and timing”.