[TowerTalk] Conductive Concrete and Grounding

[Jim Lux]

At 12:18 PM 1/27/2005, K8RI on Tower Talk wrote:

>Trying to remember my theory... It's been a long time.


>I think of lightning as a poor square wave.  It has an fairly abrupt rise 
>time and a bit slower fall time as I recall.

Lightning stroke currents (in a target that's being hit) are typically 
modeled (and equipment is tested) with a so-called double exponential pulse:

y(t) = exp(-at)-exp(-bt)

typical rise time(10% to 90%) is 2 microseconds, fall time to 50% is 50 
microseconds.



>It's also complex, with changes in amplitude and usually consists of 
>multiple closely spaced strikes appearing as one flash that might flicker 
>a bit. It may even have several distinct separate flashes.

Most lighting is 3-4 strokes.  More at 
http://home.earthlink.net/~jimlux/lfacts.htm



>Even if the stroke were always in the same direction the rapid varying 
>amplitude would make it basically an AC signal.  If you pick the mean 
>current and then measure either side you will see substantial voltage 
>swings which would be positive and negative in reference to that point.
>
>Taking the square wave of short duration.  Tom remembers this stuff much 
>better than I so he may need to expand (or correct).



>The theory part is a tad confusing as a perfect square wave consists of an 
>infinite series of harmonics.  If that sounds confusing you should try to 
>figure the band width of a network signal which is basically DC.  Yet, 
>it's DC only in the sense that it stays positive (I believe it's positive) 
>in reference to the common, or return path.  The faster the rise time, or 
>fall time the broader the signal.  Remember even CW is not zero band width 
>but depends on the sending speed as well as the characters being sent.

More that the bandwidth depends on the rise and fall time of the keying 
waveform, as well as the sending speed.


>The power for the perfect square wave would be a summation of an infinite 
>series, but in real life the lightening is a far cry from a perfect square 
>wave.  In that case the power is basically a summation with some limit and 
>the power drops off at a given rate with frequency.


Even square waves have decreasing power for odd harmonics.  A sawtooth 
(which is a better representation of a lightning stroke) has decreasing 
power for ALL harmonics.  But, a harmonic representation is not a very good 
one for lightning.

You've essentially got a single shot impulse here, so you probably don't 
want to use a harmonic series representation.

With the miracle of modern computation.. I built a waveform some 131072 
samples long, sampled at 1 nSec intervals, for a 1.5/50 microsecond 
impulse, then calculated the power spectrum.  Most of the power is down 
quite low.  By the time you get to even 1 MHz, you're already 60 dB down.

It's important to NOT confuse the spectral characteristics of the actual 
stroke current with the spectral characteristics of signals that may be 
induced by an adjacent stroke, or with the spectrum of the field radiated 
by the stroke a long way away.

The RF emissions (radiated) from the stroke does have a significant 
components well up into the tens of MHz. Partly because the "antenna" (i.e. 
the lightning stroke itself) is bigger (in wavelength terms) for higher 
frequencies.  Sure, the lightning stroke has a huge amount of power down at 
10kHz, but it's also a pretty poor antenna for that frequency.  It's a 
positively giant antenna for 20MHz or 50 MHz.  There are also some 
interesting spectral components coming from the stepped nature of the 
typical lightning stroke.

If you make a simple approximation and put in a 20dB/decade correction, the 
power vs frequency drops smoothly down to about -10dB at 1 MHz, sort of 
asymptotically converging to around -14dB from 3-4 MHz on out.  This is all 
relative to a +50dB for DC (the dominant component) The analysis had 
frequency bins about 7kHz wide.


And, when it comes to induced currents, it gets even more complex.  Then 
you have to take into account the frequency selectivity of the "victim 
circuit".