Two signals f_a and f_b are given as the input to EX-OR to measure phase difference. The average output voltage will be:

Concept:

The Truth-Table for an X-OR Gate is:

If digital ‘0’ is 0 V and digital ‘1’ denotes 5 V.

Then, for a 0°/360° phase shift between f_a and f_b, the output Y will be as shown:

Now, if we shift f_b slowly in the positive direction, the average value of the result (Y) will increase gradually until the phase shift between them reaches π radians (180° )

i.e for a phase shift of 180° (π radian), the output voltage will be as shown:

Now, as the phase shift between f_a and f_b is further increased by more than 180°, the average output voltage will start to decrease gradually.

The waveform of the Average Value of Y will be therefore as shown;