Group speed of wave in rectangular waveguide¶

The group speed of a wave in a rectangular waveguide depends on the ratio of the wavelength of the signal to the critical wavelength of the waveguide and the electromagnetic properties of the insulator within the waveguide.

Notation:

\(c\) (c) is speed_of_light.

group_speed¶: group_speed of the wave in the waveguide.

Symbol:: v_g
Latex:: \(v_\text{g}\)
Dimension:: velocity

relative_permittivity¶: relative_permittivity of the insulator.

Symbol:: epsilon_r
Latex:: \(\varepsilon_\text{r}\)
Dimension:: dimensionless

relative_permeability¶: relative_permeability of the insulator.

Symbol:: mu_r
Latex:: \(\mu_\text{r}\)
Dimension:: dimensionless

wavelength¶: wavelength of the signal.

Symbol:: lambda
Latex:: \(\lambda\)
Dimension:: length

critical_wavelength¶: Critical wavelength of the system. See Critical wavelength of waveguide.

Symbol:: lambda_c
Latex:: \(\lambda_\text{c}\)
Dimension:: length

law¶

v_g = c * sqrt(1 - (lambda / lambda_c)^2) / sqrt(epsilon_r * mu_r)

Latex:: \[v_\text{g} = \frac{c \sqrt{1 - \left(\frac{\lambda}{\lambda_\text{c}}\right)^{2}}}{\sqrt{\varepsilon_\text{r} \mu_\text{r}}}\]