# Coaxial Cables

The coaxial cable is
perhaps the most important piece of equipment used when performing this lab. We used
a model RG-58U coaxial cable during our experiment. The RG notation stands for Radio
Guided because the cable is optimal for carrying radio waves ranging in frequency
from 3Hz to 3000Ghz^{1}. The U stands for General Utility. Our
coaxial cable is comprised of an inner conductor of wound copper surrounded by a
polyethelene dielectric. On top of the insulating polyethelene layer, there is an
outer conductor of braided copper and then finally a black PVC jacket. These layers
can be seen in the picture below:

whatis.com

The inner conductor of
copper wire is .455 mm in radius while the outer copper braid is 1.475mm.^{2}
These two properties are very important because they allow one to find the
characteristic impedance (Z_{o}) from the capacitance and inductance per unit
length of the cable. To find the Capacitance per unit length one must find the
electric field due to the inner copper conductor using Gauss's Law and then integrate this
expression to acquire an expression for the potential between the inner and outer
conductors. Using the relation C=Q/V it becomes possible to find an expression for
capacitance per unit length. For a full derivation click here.
Next, to find the Inductance per unit length one must first find the magnetic field due to
the inner conductor using Ampère's law. Relating the obtained expression for the
magnetic field to the flux of the B-field between the two conductors one can find the
inductance per unit length by the relationship L=Flux/I. To see the full derivation
click here. From these two pieces of information, it
becomes possible to find the characteristic impedance of a coaxial cable from Caltech's derived expression
Z_{o}=Sqrt[L/C]. Here L and C are the obtained values for Inductance and
Capacitance per unit length. Now that you are well versed in the properties of
coaxial cables proceed to see how they are applied in our experiment!

<<I'll go back to the Abstract thank you
I'll move onwards towards
experimental setup>>

#### References:

Dictionary of PC Hardware and Data
Communications Terms found at Http://www.ora.com/reference/dictionary/terms/C/Coaxial_Cable.htm

Http://bugs.wpi.edu:8-8-/EE535/hwk2cd97/yqin/sc4.htm