Specific 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 specific 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 permeability of the insulator material, frequency of signal and specific conductivity of conductor.

specific_resistance

electrical_resistance of coaxial waveguide per unit length.

Symbol:

R

Latex:

\(R\)

Dimension:

impedance/length

absolute_permeability

absolute_permeability of the insulator.

Symbol:

mu

Latex:

\(\mu\)

Dimension:

inductance/length

angular_frequency

angular_frequency of the signal.

Symbol:

w

Latex:

\(\omega\)

Dimension:

angle/time

specific_conductance

electrical_conductance per unit length.

Symbol:

G

Latex:

\(G\)

Dimension:

conductance/length

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(w * mu / (2 * G)) / (2 * pi) * (1 / r_i - 1 / r_o)

Latex:

\[R = \frac{\sqrt{\frac{\omega \mu}{2 G}}}{2 \pi} \left(\frac{1}{r_\text{i}} - \frac{1}{r_\text{o}}\right)\]