At 02:40 PM 7/12/2006, K4SAV wrote:
>All this grounding talk has got me thinking again.
>
>Most of us know that the impedance of a wire is increased by its skin
>resistance, and that a wire with more skin area (such as a strap) will
>provide a lower impedance. But how much lower? I decided to break out my
>spread sheet I made for calculating these things and take a look. The
>data is tabulated below.
><snip>
>
>Calculated data:
>#4 wire, 10 ft length, L = 0.43 uH (straight wire in free space)
>Note: A wire in the ground will appear as a higher inductance than shown
>here, because of the decreased velocity factor of the medium.
>Z(L) represents impedance calculated from inductance only.
>
>Freq Z(L) DC res Skin res
>330 Hz 8.86e4 2.49e3 8.86e4
>920 Hz 2.47e3 2.49e3 1.48e3
>1660 Hz 4.46e3 2.49e3 1.99e3
>10 kHz 2.69e2 2.49e3 4.88e3
>100 kHz 0.269 2.49e3 1.54e2
>1 MHz 2.69 2.49e3 4.88e2
Interestingly, too. compare for a AWG10 wire, which has a DC resistance of
about 10e3 ohms for 10 ft. I would assume skin resistance would scale with
diameter (at least for higher frequencies) 6 gauges is half the diameter,
so at 1 MHz, call it 0.1 ohm. Inductance will be almost the same as for
AWG4, I think.
So if the wire is at all very long, the inductance will dominate, even for
a very thin wire.
I suppose this is important from the "limiting the voltage rise" part of
lightning protection, but still, the wire has to carry the current without
melting, but, there, we can see that an AWG 10 wire can take a fairly hefty
current without fusing, especially for a short pulse. (The figure you
usually see for fusing calculations is the "action" which is the integrated
current squared.. given in A^2*seconds)
Fusing current for AWG 10 copper for continuous current is about 400 amps.
But for a short pulse, if you plug 50 microseconds into the Onderdonk
equation, you get a fusing current of 56 kA for a AWG 16 wire. Fusing
current goes as the area in this equation, so an AWG 10, with 4 times the
area, would be 200+ kA.
Having blown up a fair number of wires ranging from AWG10 to AWG40 with
fast high current pulses, I'd say the real limit, on larger wire (>AWG16)
is going to be mechanical stresses on the wire from the magnetic field.
{google "quarter shrinking" and "exploding wires" for more info)
>I didn't have a spreadsheet already made up to calculate the skin
>resistance of a strap, but I do have one to calculate its inductance.
>Since the inductance is the predominate parameter, it's probable all you
>will need anyway. The calculations are for a strap thickness of 0.05
>inches, and a length of 10 ft. Since the thickness doesn't effect the
>inductance very much, it wasn't included as a variable parameter.
>Compare these numbers to a #4 wire, same length, which was 0.43 uH.
>
>Strap width Inductance uH
> 0.5 in 0.40
> 1 in 0.36
Given that a 0.5 inch wide strap is about the same as a wire.. what about
multiple wires in parallel.. If they are spaced apart far enough, the
inductances will be parallel.
>The formula for the wire inductance and strap inductance came from the
>Polyphaser book, Grounds for Lightning & EMP Protection.
>
>One other note of significance: None of these calculations include
>resonant effects. For wires that are long compared to the frequencies
>being considered, resonance effects can increase the impedance by a huge
>amount compared to an impedance value calculated from wire inductance.
>
>Jerry, K4SAV
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