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 · mode=full 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.

t_{\mathrm{stage}}=\htmlData{math-slot=value}{\mathtt{0.00}}\,\mathrm{s}

step 1 / 5 Amplify a perturbation

Notebook · 12 parts · 15 wires · 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

structural inventory

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

boundaries

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

diagnosis challenge Fault identity withheld: infer it from the changed outputs first.

Notebook · 12 parts · 15 wires · 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 $f_0$ ?