Propeller Head Plaza Technical and scientific discussion of amps, cables and other topics.

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Takin this code puppy for a ride..coaxial wire equation example.

Posted by jneutron (A) on November 2, 2005 at 10:14:19

In Reply to: html codes posted by jneutron on November 1, 2005 at 09:54:02:

I used font size 5 in this, so I could see the symbols.

Ok..the eq's.ε is actually : ε₀ * .ε_r
the dielectric coefficient..

First, the capacitance of a coaxial line..

C = ^{(2 π ε)} / _{Ln (douter / dinner)}

Next, the inductance of a coaxial line..

L = (μ / 2 π) * Ln (d_outer / d_inner)

Re-arrange both equations, with Ln (d_outer / d_inner)
on one side:

Capacitance:

Ln (d_outer / d_inner) = ^{(2 π ε)} / _C

Inductance:

Ln (d_outer / d_inner) = ^{L 2 π} / _μ

Note: both equations equal the Ln ratio, so equate them..

^{(2 π ε)} / _C = ^{L 2 π} / _μ

The 2 π's
cancel:

ε / C = L / μ

Bring C to the right, μ to the left:

ε μ = C L

For free air, copper, silver, assumtion is μ = 1
This means that for a specific insulation type, the product of L and C will be a constant. Note that no where within that result, is the specific size of either conductors. ..they were cancelled out at the beginning of the analysis. This means, that L C will be geometry invarient for coaxial structures..the product L C will only be determined by the insulation.

For L and C in units per foot, this equation holds:

L * C = D.C. *1034, this is for L in nanohenries, C in picofarads.

DC is the dielectric coefficient relative.

When a cable is measured, giving an L and C, the product of those gives the EFFECTIVE DC, which provides the boundary line for that construction geometry, and the velocity of propagation...

With the LC graph of D.C. and the one of velocity, any cable measured can be quantified as to the utilization of the geometry.. In other words, how close it comes to coaxial cable when it comes to containing the magnetic and electric fields..

Cheers, John

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