Waveguide - Group Velocity, Phase Velocity, Cut off Frequency & Impedance

Group Velocity

It is the velocity of electromagnetic waves in the waveguide. Group velocity is denoted by the symbol Vg. Group velocity is less than velocity of electromagnetic waves in free space.

Phase Velocity

It is the velocity which the electromagnetic waves changes it phase in the waveguide during propagation. Its symbol is Vph. Group velocity and phase velocity of the electromagnetic waves is the same in free space.

Cut Off Frequency

It is the frequency which cannot be propagated through the waveguide. Its symbol is fc.

Formulas

Fc = c/2a

Here fc stands for cut off frequency C stands for velocity of Electromagnetic waves in free space. Which is 3 x 10⁸ m/s. a stands for broad dimension of waveguide?

λg =  wave length of the electromagnetic waves inside the waveguide.
f   = frequency in free space
c   = velocity of electromagnetic wave in free space
fc = cut off frequency

The broad dimension of the waveguide is 5cm. find its cut off frequency.

Fc = c/2a
Fc = 3x10¹⁰ cm / 2 x 5 cm
Fc = 3 x 10⁹ Hz
Fc = 300 MHz
F = 3 GHz

Impedance (Zo) of waveguide

The characteristics impedance (Zo) is known as the impedance infinity of long waveguide. If the load which is connected with the waveguide is terminated with its characteristic impedance, then the whole energy is consumed by the load nad no reflected enery is transferred back towards the source.

Here

Zo = Characteristic impedance of waveguide
λg = waveguide length (the wave length of the frequency travelling through waveguide)
λo = Wave length of the operating frequency

Here

fc = cut off frequency of the waveguide
f = operating frequency in free space