Attenuation coefficient in metal in rectangular waveguide for transverse electric waves

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

Conditions:

1. Waves propagating in the waveguide must be transverse electric waves.

2. Second index \(n \ge 1\).

attenuation_coefficient

attenuation_coefficient in metal.

Symbol:

alpha

Latex:

\(\alpha\)

Dimension:

1/length

surface_resistance

electrical_resistance of the surface.

Symbol:

R_s

Latex:

\(R_\text{s}\)

Dimension:

impedance

first_index

The first index shows how many half-wavelengths fit across the width of the cross section.

Symbol:

m

Latex:

\(m\)

Dimension:

dimensionless

second_index

The second index shows how many half-wavelengths fit across the height of the cross section.

Symbol:

n

Latex:

\(n\)

Dimension:

dimensionless

width

Width, or first dimension of the cross section. See length.

Symbol:

a

Latex:

\(a\)

Dimension:

length

height

Height, or second dimension of the cross section. See length.

Symbol:

b

Latex:

\(b\)

Dimension:

length

medium_resistance

electrical_resistance of the medium filling the waveguide.

Symbol:

R

Latex:

\(R\)

Dimension:

impedance

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

alpha = 2 * R_s / R / (a * sqrt(1 - (lambda / (2 * lambda_c))^2)) * ((1 + a / b) * (lambda / (2 * lambda_c))^2 + (1 - (lambda / (2 * lambda_c))^2) * a / b * (a / b * n^2 + m^2) / ((a / b * n)^2 + m^2))

Latex:

\[\alpha = \frac{2 \frac{R_\text{s}}{R}}{a \sqrt{1 - \left(\frac{\lambda}{2 \lambda_\text{c}}\right)^{2}}} \left(\left(1 + \frac{a}{b}\right) \left(\frac{\lambda}{2 \lambda_\text{c}}\right)^{2} + \frac{\left(1 - \left(\frac{\lambda}{2 \lambda_\text{c}}\right)^{2}\right) \frac{a}{b} \left(\frac{a}{b} n^{2} + m^{2}\right)}{\left(\frac{a}{b} n\right)^{2} + m^{2}}\right)\]