# 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 3000Ghz1.  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:

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 (Zo) 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 Zo=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!

#### References:

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

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