# factors influencing capacitance of a cable

I am out of my depth here so I am looking for a simple explanation. If you have twisted pair cables of differing makeup, varying in conductive material, diameter of the conductor, number of twists per meter and number of pairs in the cable. What if any effect the pairs capacitance.

This is in the sphere of telecoms.

EDIT:

C = (EoErA)/d

capacitance seems to be based on “Permittivity” which is a function of conductivity which would imply that it will differ by from copper to aluminium.

also the area of the conductor, so that conductors with a larger surface area have more capacitance.

and lastly the insulator and distance between the conductors will play a role.

Are there any effects that I am missing? does the number of pairs around the one tested make any difference?

EDIT: I seem to have misunderstood Permittivity it seems to be only to do with the insulator not the conductor.

• Permittivity is to do with the insulation materials between the conductors and not the conductivity of the conductors. Capacitance to ground is also something to consider as well as capacitance between conductors. – Andy aka Feb 11 '15 at 11:55
• Thanks, does that mean that the material used for the conductor plays no part? – Sam Feb 11 '15 at 12:16

Capacitance is a function of the spacing of the conductors and the dielectric constant (aka relative permittivity) of the insulating materials. All other things being equal, the capacitance between two wires will be proportional to the dielectric constant of the insulator.

A vacuum (and dry air) has a dielectric constant of 1. Insulating plastics have dielectric constants in around 2-4 generally.

The thicker the insulation, the wider spaced the wires will be, and thus the lower the capacitance per linear unit, again, all other things being equal.

You can approximate the capacitance of an unshielded twisted pair by:

C(pF/ft) = $\frac{2.2\epsilon }{log_{10}(\frac{1.3D}{f d})}$

Where

D is the diameter of of the wire including insulation (inches)

d is the conductor diameter (inches)

$\epsilon$ is the dielectric constant of the insulation

f is the stranding factor (about 1)

Here's another reference that gives a derivation of a similar approximation.

The resistance of the conductors does not directly affect the capacitance but it will have other effects on the performance, especially when the lengths are long. Look up the Heaviside condition for more on that.

• Re: Heaviside, the story of the first (and later) trans-Atlantic cable(s) is interesting. – George Herold Feb 11 '15 at 14:06
• Thank you, This seems to me to say that it would be hard to have a uniform pF/m of differing cable sections spanning 0.3mm to 1.2mm in conductor diameter. I am in a discussion regarding a ~10% error in measured distance (derived by capacitance) and data records on cable length. – Sam Feb 11 '15 at 14:55
• 10% is not much. Twisting is ignored in the above equation but a tight twist could significantly reduce the apparent length of the cable (thus increasing the pF/m of the twisted pair). I doubt the thickness of the insulator is controlled all that well too. – Spehro Pefhany Feb 11 '15 at 15:23
• Thank you for pointing out the what should have been obvious to me 'length of a conductor is greater than the length of a spiral' a twisted pair within a bundle which itself is twisted could easily account for the measured length being 10% greater than the observed. Time to see if I can get hold of spec sheets and the equations used. – Sam Feb 11 '15 at 16:57

When Insulated wires getting twisting, Capacitance also increase with respect to number twists even if you are increasing thickness.