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

x=Asin(ωt+φ),y=Bsin(ωt)x = A\sin(\omega t + \varphi),\quad y = B\sin(\omega t)

Measurements

Bench readings from a 1 kHz reference against a shifted copy, using the ratio of the y-axis crossing to the peak amplitude.

RunSet φ (deg)Crossing / peakMeasured φ (deg)Error
01300.49729.8−0.2
02450.71145.3+0.3
03600.86860.2+0.2
04901.00090.00.0