amdx wrote:
Can someone explain how these two relate in a waveguide.
My limited understanding is, group velocity is slow near cutoff and
increases as frequency increases to almost c.
I don't know the difference between group velocity and phase velocity.
Thanks, Mike

Phase velocity is the velocity of a constant phase point. For example,
if you look at a point where the voltage or current wave crosses zero
going in the positive voltage or current direction, it moves down the
waveguide at the phase velocity. In a waveguide, the phase velocity is
always greater than the speed of light c. It approaches c at very high
frequency, and increases without bound as cutoff is approached.

The group velocity is the speed at which information can be moved. In
other words, a change in the signal (e.g., turning it on or off or
changing its amplitude) propagates at the group velocity. In a
waveguide, the group velocity approaches c at very high frequency and 0
at cutoff.

Mathematically, vp = c/sqrt(1 - (f/fc)^2)
vg = c * sqrt(1 - (f/fc)^2)

where vp is the phase velocity, vg is the group velocity, f is the
frequency, and fc is the cutoff frequency. These equations are valid for
TE and TM modes in hollow waveguides.

A medium in which the phase velocity varies with frequency is called a
dispersive medium, and all hollow waveguides are in this category. Phase
and group velocities are the same in non-dispersive media such as
coaxial cable.

Kraus uses a caterpillar as an example: The humps on the caterpillar's
back move at the phase velocity, but the caterpillar moves at the group
velocity.

Roy Lewallen, W7EL