Re: Duty cycle and Even Harmonics

Than you for your detailed explanations, dsss27.
I will put this topic on my priority list, and will continue to trust my instruments and simulators in the mean time.
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To parazapper
For what I remember of wave form theory, ANY wave form with a periodic cycle is the sum of the periodic event (the fundamental), and many harmonics of this fundamental, with particular amplitude and phase characteristics, This is why a C5 musical note made by a piano, a trumpet or a flute, will have same fundamental, but harmonics will make a different, distinctive sound

http://en.wikipedia.org/wiki/Harmonic

“A harmonic of a wave is a component frequency of the signal that is an integer multiple of the fundamental frequency.”

With this definition of harmonic, it MOST be a direct relation (an integer multiple) between every frequency you found, and the “main” frequency.

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When you explain:
=> using 1.3333333 kHz as suggested, t = 750 usec.
t-high = 750 usec*0.75 = 562.50 usec freq = 1777.777/2 = 888.8885 Hz
t-low = 750 usec*0.25 = 187.50 usec freq = 5333.333/2 = 2666.666 Hz
odd, t-low is the 3rd harmonic of t-high.
t-high harmonics are 888.8885, 2666.6655, 4444.4425, 6222.2195, 7999.9965, 9777.7735, 11555.55, 13.333.327, ...
t-low harmonics are 2666.666, 7999.998, 13333.332, ...
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I translate that
888.8885, 2666.6655, 4444.4425, 6222.2195, 7999.9965, 9777.7735, 11555.55, 13.333.327, ...
and 2666.666, 7999.998, 13333.332, ...
most have a direct relation (an integer multiple) with 1.333kHz.
In this particular example, some have this relation, others no. Something wrong?
Ho! By the way! There is some magic on your numbers :
2666.6655, 7999.99, 13333.3, are even harmonics of 1333.333 (:-)

I respect very much your integrity and your zapper’s expertise.
But with harmonic’s topic, I prefer to continue working with my theory and what my instruments shows me, as long as it match the theory supporting their numbers.
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In any case, when I build 33 different frequencies, one after the other, in a narrow sweep, this looks in an oscilloscope like a pulse train of width modulation, making an incredibly complex wave form to study (at my level) with even more additional harmonics.

My final point in this is that I’m making an astonishing amount of harmonics, many of them in the pathogen band. Odd? Even? A LOT could be the good answer I look for.
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And finally, to answer again Ascarillena
I continue to maintain that :
“Almost any duty cycle on a square wave, but a PERFECT 50/50 will produce some or many even harmonics.”
And I continue to believe that it is possible to make more than odd harmonics only, with a square or pulsed repetitive wave, in purpose.

I will be back with this topic, when personally convinced, one way or another, and with irrefutable arguments to offer.