Wien-Bridge Oscillator

Active analog

A non-inverting op-amp wrapped in a Wien $RC$ network. When the loop gain crosses unity at exactly one frequency, thermal noise is amplified into a clean sinusoid; a nonlinear gain limiter parks the amplitude on a stable limit cycle. The phase portrait shows the oscillation being born — a Hopf bifurcation you can trigger with a knob.

Live circuit OSCILLATING (limit cycle), 1.59 kHz

Drag a value tag to change that part. Click a wire to clip a probe on.

Causal signal trace paused

Amplify a perturbation Noise at the op-amp input is the seed; loop gain decides whether it grows.

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Step 1 / 5 Amplify a perturbation

Notebook: 12 parts and 15 wires, modelled as second-order loop with amplitude limiting

Recommended lab 9 of 18

Use loop gain and phase to predict oscillator startup or decay.

Builds on: Dynamic RC Low-Pass Filter

Predict, then test

Set amplifier gain just below $3$ . What happens to a small disturbance at $f_0$ ?

Commit before the explanation appears. This is a prediction, not a quiz score.

Governing model

f_0 = \dfrac{1}{2\pi RC} \;\cdot\; A\beta = 1 \text{ (Barkhausen), gain } = 3

Parts

op-amp gain stage
series + shunt $RC$ bridge
$R_f/R_g$ gain setting
amplitude-limiting element

Limits of the model

gain $2.8$ – $3.2$
$f_0$ from $RC$
Hopf onset at gain $=3$

Diagnosis challenge The fault is hidden. Work it out from the changed outputs first.

Notebook: 12 parts and 15 wires, modelled as second-order loop with amplitude limiting

Set amplifier gain just below 333. What happens to a small disturbance at f0f_0f0​?

Set amplifier gain just below $3$ . What happens to a small disturbance at $f_0$ ?