Phase and Group Delay

Cuthbert Nyack

A signal passing passing through a circuit usually comes out with a phase shift f radians. The ratio -f/w has units of seconds and represents the phase delay.
For wave groups the group delay is defined as -df/dw. The difference between the 2 is illustrated by the applet below. The phase vs frequency is shown by the magenta line. The gradient of the central portion of this plot can be changed by changing "p" to show the meaning of group delay.
If m is changed from 10 to 20(other parameters constant), phase shift of carrier changes from 5 to 10rad/s. Since the carrier frequency is 10rad/s, this means a delay of 0.5s which is easily verified by the time marker.
As m changes from 10 to 20rad the group delay changes from 2.5 to 5s which can be verified by the time marker. If p changes from 0 to 1 with m at 10, the group delay changes from 0 to 5s.

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