Re: Phase and Group Velocity
watertreader said:
Hi,
Is there any good explanation for phase and group velocity? any example for in terms of communication and AM wave signal?
Thanks
Here is some information on phase and group delay:
1.)
Phase delay: If a block has a transfer function which incorporates a frequency dependence, this will cause a phase shift (mostly with negative slope) between input and output. Then, the phase delay is defined as
Tp=- φ/ω. In words: thats the delay of each point of the corresponding sinewave - and for a continuous sinusoidal signal the delay of the complete signal.
2.)
Group delay: It is defined only for a group of frequency componenets which are close together with respect to its mean value (narrow band signal). A good example is an amplitude modulated signal having a tight and limited spectrum around the carrier. After some mathematical manipulations (rather involved with series expansion) it is shown that the delay of the SIGNAL CONTENT (in case of AM: the envelope of the modulation signal) is identical to the following expression:
Tg=-dφ/dω. This is called "group delay".
From the definition it is clear that the slope of the phase function must be constant if no distortions are allowed - that means: phase must be a linear function of frequency (in the band of interest).
It is interesting to note that Tg can be negative, if the phase slope is positive.
This can be (and has been) measured and can be shown also via simulation.