Phase speed of wave in rectangular waveguide¶

The phase 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.

phase_speed¶: phase_speed of the wave in the waveguide.

Symbol:: v
Latex:: \(v\)
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 = c / sqrt(epsilon_r * mu_r * (1 - (lambda / lambda_c)^2))

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