Fields and Waves I: Cable Information
Last Updated 12 December 1996
To better approach design projects involving transmission lines, I am collecting information on coaxial and other cables. Information will be updated whenever something interesting comes along.
The Characteristic Impedance of the Line Does Not Represent Loss!
How to Find R, L, G, and C for Actual Cables:
Below you will find a variety of information on some common transmission lines.
The information is given in the same form as you will find if you check the sources I have used (mostly catalogs). When you analyze the lines, you will need
to know the resistance R, conductance G, inductance L, capacitance C per unit
length. Only the capacitance per unit length is usually given. However, since
most cables are used at a megahertz and above, the characteristic impedance
quoted is real and thus can give you inductance, since you know the capacitance. That leaves the resistance and conductance. The conductance can be
determined from either the conductivity (usually given as resistivity) or the loss tangent (also given as the power factor or the dissipation factor -- at low loss conditions, these are equivalent)
of the insulating material. You can apply the principle called the conductance
analog of capacitance to find G from C. For nearly all modern cables, G is so
small that it can be neglected. For phone lines used until recently, G was
quite large and thus needed to be included in any analysis. Please note that most commercially useful insulators have Finally, the resistance can be found
from the attenuation or from the cable geometry. You should know how to
calculate the D.C. resistance per unit length due to the current flow in the
center conductor and the shield. (Here the conductivity used is that of the wires and is, thus, usually the conductivity of copper or aluminum.) Also, at higher frequencies, you can apply
the surface impedance expressions that incorporate the skin effect. However,
you are better off at higher frequencies to use the attenuation data.
Source:NATIONAL WIRE and CABLE CORPORATION
Attenuation (dB/100ft) @ Hz
RG-8A/U D.C. Resistance per km for center cond = 6.1 ohms, shield = 3.9 ohms
(Note that attenuation data in catalogs usually applies to higher frequencies.
At audio frequencies, you should consider
using the D.C. resistance since the skin effect is not important.)
PE = Polyethylene PF = Power Factor
PE-HD eps=2.34 from 60 to 3e9 Hz PF = .0002
Remember that the power factor (PF) is essentially the same as the loss tangent for low loss materials.
Source: Times Wire and Cable
Polyethylene eps=2.3; PF = 0.0003; rho (resistivity) = 1e14 ohm-m
Teflon eps=2.1; PF = 0.0003; rho = 1e17 ohm-m
Source: "Electrical Communication" by Albert
Paper Insulated Telephone Lines (All parameters are per loop mile.)
R=86 ohms, L=0.001 henry, C=0.062 microfarad, G=1.4 micro-mhos
phase velocity 47,600 miles per second, attn: 1.07 dB per mile,
alpha=0.123, beta=0.132
Source: Zahn's book on Electromagnetics
Normal air has a conductivity at the surface of the earth of 2e-14 S/m. This value can be used for air insulated cables, if no other values can be found.
Source: Miner's book on Electromagnetics
Foamed polystyrene has a dielectric constant of 1.03 and a loss tangent of less than 2e-4.
Some Possibly Useful Cable Links
Please note that there are a variety of claims made by the manufacturers listed above that may or may not have any substance. You will have to judge for yourself.