Lissajous figures as a phase detector
Feed one sine into the X input of a scope and a second into Y. When the frequencies are related by a small integer ratio the trace closes on itself, and the shape encodes the phase difference between the two signals.
Setup
With equal frequencies the parametric curve is
Measurements
Bench readings from a 1 kHz reference against a shifted copy, using the ratio of the y-axis crossing to the peak amplitude.
| Run | Set φ (deg) | Crossing / peak | Measured φ (deg) | Error |
|---|---|---|---|---|
| 01 | 30 | 0.497 | 29.8 | −0.2 |
| 02 | 45 | 0.711 | 45.3 | +0.3 |
| 03 | 60 | 0.868 | 60.2 | +0.2 |
| 04 | 90 | 1.000 | 90.0 | 0.0 |