Attenuation coefficient in metal

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 specific resistance of a coaxial waveguide depends on the diameter of the outer conductor and the diameter of the inner conductor, as well as on the relative permeability and the relative permittivity of the insulator material, the surface resistance of the outer conductor and the surface resistance of the inner conductor.

attenuation_coefficient

attenuation_coefficient in metal.

Symbol:

alpha

Latex:

\(\alpha\)

Dimension:

1/length

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_surface_resistance

Surface electrical_resistance of the outer conductor.

Symbol:

R_o

Latex:

\(R_\text{o}\)

Dimension:

impedance

inner_surface_resistance

Surface electrical_resistance of the inner conductor.

Symbol:

R_i

Latex:

\(R_\text{i}\)

Dimension:

impedance

outer_diameter

diameter of the outer conductor.

Symbol:

d_o

Latex:

\(d_\text{o}\)

Dimension:

length

inner_diameter

diameter of the inner conductor.

Symbol:

d_i

Latex:

\(d_\text{i}\)

Dimension:

length

resistance

Constant equal to \(420 \Omega\).

Symbol:

R_0

Latex:

\(R_0\)

Dimension:

impedance

law

alpha = sqrt(epsilon_r / mu_r) * (R_i / d_i + R_o / d_o) / (pi * R_0 * log(d_o / d_i))

Latex:

\[\alpha = \frac{\sqrt{\frac{\varepsilon_\text{r}}{\mu_\text{r}}} \left(\frac{R_\text{i}}{d_\text{i}} + \frac{R_\text{o}}{d_\text{o}}\right)}{\pi R_0 \log \left( \frac{d_\text{o}}{d_\text{i}} \right)}\]