Re: Zappers: Using white noise instead of one frequency

HEY - WAIT JUST ONE MINUTE...

I didn't like the way this thread ended, and it's been nibbling at me for a while (ok, 2 years). Anyway, it turns out that I'm right and you're wrong, so I'm putting this out as a public service. So there.

Your description of the energy in a white noise zapper is based on the converging series (harmonic relationships and rolloff) that is a part of all periodic waveforms (square wave, triangle, sawtooth, whatever). **But white noise is none of those things.** It is equal energy at each individual frequency, even if there are a million of them. Practical circuits don't have infinite bandwidth, so lets keep this limited to 1 MHz, twice the traditional zapper bandwidth. Also, no quibbling about real world devices - 9V batteries make 9V forever at any current I want, 555s and opamps make real 9V peak-to-peak outputs, etc. Real world devices are 2nd-order issues, an unnecessary complication of this basic analysis.

A 9V 50% square wave has many sinewaves inside of it. Here are a few:
composit - 9.00 Vp-p or 4.5 Vrms

Fundamental - 11.46 Vp-p or 4.05 Vrms

3rd harmonic - 3.82 Vp-p or 1.35 Vrms
(fundamental divided by 3)

5th harmonic - 2.29 Vp-p or 0.81 Vrms
(fundamental divided by 5)

41st harmonic - 0.28 Vp-p or 0.099 Vrms
(fundamental divided by 41)

etc.

An analog white noise zapper doesn't have a fundamental frequency and a few harmonics, it has all frequencies and equal voltage at all of them. If you compare the two circuits' output spectra, at some harmonic the steadily decreasing square wave harmonic voltage value will drop below the constant white noise value. At all frequencies above that crossover, the white noise zapper will make more energy that the square wave zapper. So the way to optimize the white noise circuit is to make this crossover frequency as low as possible.

White noise is a pretty ugly waveform on a scope with all kinds of peaks and valleys. According to the math, some of the peaks can be 10 or 100 times what looks like the average value (called the rms value) of the waveform. The math of white noise predicts this, and high quality circuits confirm it. This could be a problem, because with only 9V of battery for the p-p output, preserving peaks that are 10 times the rms value means the rms value would have to be only 0.9V, a pretty small signal. But the high peaks are rare, so clipping them off doesn't change the white noise "purity" very much.

How much? Ask Analog Devices, one of the great names in analog electronic components.

http://www.analog.com/static/imported-files/tutorials/MT-048.pdf

In their tutorial MT-048 (page 5), they list the relationship between how often peaks happen vs the rms value of the signal. Turns out that if you turn up a 9 Vp-p white noise signal until you are clipping off only 1.2% of the peaks, the rms value will be 20% of the p-p value, or 1.8 Vrms. As shown in the short table above, this is greater than the 3rd harmonic of a 9 V square wave. So a white noise zapper will put out **significantly** more energy than a standard 555 zapper at all harmonics, and 44% of the fundamental.

BTW, that lower fundamental is were the energy for all of those other frequencies comes from. Basically, it's spectrum shaping. A Clark zapper has a huge fundamental, very low energy at all harmonics, and only 7 or 13 harmonics in the standard zapper bandwidth (and only 100 harmonics in a newer 2.5 KHz design). A white noise zapper has a smaller fundamental, way more energy at all higher frequencies, and over 470,000 of them.

Let's look at some practical values. For a 2.5 KHz (2500 Hz) zapper, the 3th harmonic is 7.5 KHz and the 41st harmonic is a little over 100 KHz. In a standard squarewave zapper, each harmonic is smaller than any ones below it. For example, the 41st harmonic is 7.3% of the 3rd harmonic value. BUT for a white noise zapper with a 99% clipping level, the energy at the same freq as the 41st harmonic would be larger than the energy at the same freq as the 3rd harmonic, and increase of over 900%. So a white noise zapper will put out much more energy than a standard zapper at all of the equivalent squarewave harmonic frequencies, and an almost infinite number of frequencies between them.

Caution - the increase in high frequency energy might be enough to cause electrical burns. Based on postings here, burns are rare with a standard zapper. It might be the case that for a white noise zapper the output has to be turned down even more that in the example above for safety. Cutting the output by 50% still would put out more energy at the higher harmonics than a 555 type.

Got Got GOT to love analog electronics.

ak