Wave resistance of coaxial waveguide

A coaxial waveguide is an electrical cable consisting of a central conductor and a shield arranged coaxially and separated by an insulating material or an air gap. It is used to transmit radio frequency electrical signals. The wave resistance of a coaxial waveguide depends on the radius of the outer conductor and the radius of the inner conductor, as well as on the relative permittivity and the relative permeability of the insulator material.

Notation:

1. \(\mu_0\) (mu_0) is vacuum_permeability.

2. \(\varepsilon_0\) (epsilon_0) is vacuum_permittivity.

resistance

electrical_resistance of the wave in the waveguide.

Symbol:

R

Latex:

\(R\)

Dimension:

impedance

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

outer_radius

radius of the outer conductor.

Symbol:

r_o

Latex:

\(r_\text{o}\)

Dimension:

length

inner_radius

radius of the inner conductor.

Symbol:

r_i

Latex:

\(r_\text{i}\)

Dimension:

length

law

R = sqrt(mu_0 * mu_r / (epsilon_0 * epsilon_r)) / (2 * pi) * log(r_o / r_i)

Latex:

\[R = \frac{\sqrt{\frac{\mu_0 \mu_\text{r}}{\varepsilon_0 \varepsilon_\text{r}}}}{2 \pi} \log \left( \frac{r_\text{o}}{r_\text{i}} \right)\]