|To:||"K8RI on Tower Talk" <firstname.lastname@example.org>,<email@example.com>, "'Tower Talk List'" <firstname.lastname@example.org>|
|Subject:||Re: [TowerTalk] Conductive Concrete and Grounding|
|From:||Jim Lux <email@example.com>|
|Date:||Thu, 27 Jan 2005 14:02:40 -0800|
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.
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".
See: http://www.mscomputer.com for "Self Supporting Towers", "Wireless Weather Stations", and lot's more. Call Toll Free, 1-800-333-9041 with any questions and ask for Sherman, W2FLA.
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