Coaxial Cable Loss due to Loss Tangent

Electrical losses in a coaxial cable create heat in the outer and center conductors and are the two main types of coaxial cable loss, skin-effect loss and dielectric loss, respectively. This heat, or loss, can be calculated with the understanding of the following concepts.

What is Skin Effect Loss?

In coaxial cable, skin effect is the movement of an alternating electric current (AC) whereby the current density is greater near the surface of the conductor and lessens within the conductor.  Skin effect is the decline in current density and the skin depth is a measure of the depth at which the current density falls to 1/e of its value near the surface. Over 98 percent of the current flows within a layer 4 times the skin depth from the surface. At high frequencies, the skin depth becomes much smaller. Skin effect loss usually occurs at high frequencies when the signal reaches and moves along the surface of the inner conductor, which causes additional RF losses at higher frequencies.

A skin depth calculator can be found here.

Resistance per unit length is the ratio of specific resistance or resistivity to the area of cross-section of given conductor in Ohm per meter. With skin-effect loss, the resistance per unit length, Rl, and the inductance per unit length, Ll, increase with the square root of the frequency.

Skin effect losses are resistive, caused by the narrowing of the conduction path. In calculating loss, loss per unit length includes the skin effect loss and dielectric loss.

What is Dielectric Loss?

Dielectric conduction loss is caused when the insulating material inside the transmission line absorbs energy from the electromagnetic field developed between the inner and outer conductors. Dielectric loss explains the amount of dissipation of electromagnetic energy or heat of a dielectric material. It is often described in terms of either the loss angle δ or the corresponding loss tangent tan δ. Both refer to the phasor in the complex plane whose real and imaginary parts are the resistive (lossy) component of an electromagnetic field and its reactive (lossless) counterpart. The ratio of two quantities is defined in term of Tan.

What is Loss Tangent?

Loss tangent is the ratio at any specified frequency between the real and imaginary parts of the impedance of the capacitor. A large loss tangent refers to a high degree of dielectric absorption. Loss tangent is the ratio between the imaginary and real parts of the complex permittivity where the permittivity of dielectric is given by:

ε =ε_re − jε_im

When this formula is drawn on an x-y plane, the tangent of the angle between the real and the imaginary quantity is discoverable which can be described as:

tanδ = ε_im/ε_re

Which means the ratio of the imaginary part to the real part of the permittivity is found to be another quantity, i.e. the loss tangent, which is used to express the losses in a dielectric material. In other words, it is the ratio of the imaginary part to the real part or the tangent of the angle between the complex number and the real axis.  This angle is the loss angle and the tangent is called the loss tangent.  Thus, the value of the loss tangent describes how lossy a material is, such that it either represents a very lossy material or a very good conductor.

Measurement of loss using sinusoidal excitation at a particular frequency yields the product of skin effect and dielectric loss functions or the sum of the skin effect and dielectric losses in units of dB. Once the skin-effect loss is derived, the portion of loss attributable to dielectric losses may be estimable.