[TowerTalk] Ground wire impedance

Gary Schafer garyschafer at comcast.net
Wed Jul 12 22:25:25 EDT 2006

> -----Original Message-----
> From: towertalk-bounces at contesting.com [mailto:towertalk-
> bounces at contesting.com] On Behalf Of Jim Lux
> Sent: Wednesday, July 12, 2006 5:36 PM
> To: K4SAV; towertalk at contesting.com
> Subject: Re: [TowerTalk] Ground wire impedance
> 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    8.86e-4    2.49e-3    8.86e-4
> >920 Hz    2.47e-3    2.49e-3    1.48e-3
> >1660 Hz   4.46e-3    2.49e-3    1.99e-3
> >10 kHz    2.69e-2    2.49e-3    4.88e-3
> >100 kHz   0.269      2.49e-3    1.54e-2
> >1 MHz     2.69       2.49e-3    4.88e-2
> Interestingly, too. compare for a AWG10 wire, which has a DC resistance of
> about 10e-3 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

I don't think resonance would be a problem with the frequencies involved
with lightning. If your ground lead is that long the inductance will be off
the chart already.

Although inductance may be the dominant factor at the AC frequencies don't
forget that there is also a large DC component in a lightning strike also.
It is still important to have very low DC resistance in the ground system as
well as low inductance. Even a fraction of an ohm resistance in the ground
lead or a connection can allow the voltage to rise hundreds or thousands of
volts because of it.

Gary  K4FMX

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