A few days ago, I saw this:
At first sight, this would seem to be an impossibility. However, it might be possible, but it depends to the facilities that your single channel 'scope has. You will need either:
1. An external trigger input, or
2. An external X input.
Using an external trigger input:
Connect the trigger input and the Y input to one of the voltages you wish to compare, set the trigger up as normal and position the trace, noting the position. Leaving the trigger input on that voltage, transfer the Y input to the second voltage and note the difference. This should give you a reasonable indication of phase difference, but an accurate measurement will be difficult.
Using an X-Y display:
Connect the X input to one voltage, the Y input to the second voltage, and switch the timebase to external. Adjust the channel gains to give a suitable display. If the two voltages are exactly in phase, the resulting picture will be a straight line at 45° (or -45°). If there is a small phase difference, which hopefully will be the case, then the line will spread into an ellipse. The ratio of the width (or height) of the ellipse on the zero axis to the overall width (or height) is the sine of the phase difference.
The presence of harmonics might shift the zero crossing point ((for the external trigger method or, indeed, for a dual-channel oscilloscope), or will mean the line is not straight in the case of the X-Y plot.
Drifting off-topic a little, I’ve found that the most reliable and consistent method of measuring phase difference is to record a large number of data points over one cycle, then to extract the phase of the fundamental wave using Fourier. The hardware is a dual-channel sound card, in a set-up described in the test reports for the transformers, and a software 'scope to digitise the waveforms, from whence the data is imported into a spreadsheet to do the maths. Phase is ‘absolute’ in terms of the data set, but it is the difference between two traces that is important. Careful attention to detail is needed to minimise and account for phase errors in the test rig.
I’ve recently discovered a library for LibreOffice Calc that does all the Fourier maths.
Apologies for the website design - I suggest using your browser developer tools to change the background colour and make it readable.
Also, a minor error in the instructions: The key stroke to enter the array formula is Ctrl-Shift-Enter, not Ctrl-Enter as written.