X-Y

When the "X-Y" control is on, the horizontal deflection (X) of the electron beam is not controlled by the sawtooth generator in the CRO but by the signal connected to channel 2. The vertical deflection (Y) is determined by the signal connected to channel 1. Both input signals can be added if needed ("Add"), so the sum of both channels can deliver the vertical signal.

From the combination of different signals "Lissajous" figures can be created. They enable the user to determine the phase and the frequency ratio between two input signals. The following images show examples:

The horizontal signal frequency is twice the vertical frequency. You can see the lines touch the left and right edge at two locations. The phase is 270°.
At 0° and 180° the crossing point is located at the center of the screen.
For values larger 180° it is located left of center.
For values less than 180° it is located right of center.

The signal frequencies are identical. You can see the curve touches the right and left edge at one location only.
When a circle (or at least an oval perpendicular to one of the axis) is created, the phase must be 90° (or 270°), because the axis perpendicular to one another for the horizontal and vertical signals deliver data according to a sinewave and matching cosine.