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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.

12 components · 15 connections · second-order loop with amplitude limiting

recommended lab 9 of 11

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.

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

control console

The Wien network passes exactly one frequency with zero phase shift and a $\lvert H(j\omega_0)\rvert=\tfrac13$ loss — so the amplifier must supply a gain of 3 to close the loop and sing.

A=\htmlData{math-slot=value}{\mathtt{0.00}}

R=\htmlData{math-slot=value}{\text{10.00 kΩ}}

C=\htmlData{math-slot=value}{\text{10.00 nF}}

switchboard · fault injection

inject hidden fault

test bed · mode=full

Wien-Bridge Oscillator

instrumentation rack

Barkhausen classifier OSCILLATING (limit cycle)

f_0=\htmlData{math-slot=value}{\text{1.00 kHz}}

\mu=\htmlData{math-slot=value}{\mathtt{-0.00}}

A_o\approx\htmlData{math-slot=value}{\mathtt{0.00}}

v_o

\mathrm{d}v_o/\mathrm{d}t

birth of the limit cycle

v_o(t)

diagnostic probe