Nick wrote:
Not sure why you are taking the 2nd harmonic of your heater frequency, so lets start with a heater 60kHz signal and lets start with a 18kHz audio tone from your music. That will produce a sum and difference of 42kHz and 78k. Thats great you say, neither are audible. However, you seem to be ignoring that the maths produces a series, not a single term a you suggest, you will also get 24k, 6kHz which will be audible. You will also get much more complex terms. Its all clear in wiki
"So the output contains sinusoidal terms with frequencies at the sum i1 + i2 and difference i1 - i2 of the two original frequencies. It also contains terms at the original frequencies and at multiples of the original frequencies 2i1, 2i2, 3i1, 3i2, etc.; the latter are called harmonics, as well as more complicated terms at frequencies of Mi1 + Ni2, called intermodulation products."
This all happens before the transformer, so even if the transformer is band limited the terms in the audio band will get out. I am not making this up, I tried it 8 or more years ago, the intermod is audible.
But you will just .ignore this as before.
I am not going to ignore, but I am getting tired and bored...
I am mentioning the 2nd harmonic because the first is nulled and what remains is the 2nd, as suggested by "yours" Dimitry. Maybe he is wrong, too?
Besides the fact that we are trying to combine a sine wave with an imperfect square wave, and the standard math does not explain the case (much more complicated calculation), and the fact that music is not a sine wave, the bottom line can be expressed as the magnitude of the resulting harmonics.
Thus, what is the magnitude of those harmonics, of which some are audible frequencies?
Once we establish the magnitude, we may guess whether they are audible, and under which conditions. Something that is 80dB below can easily be heard on efficient enough speakers, if amplified enough, without interfering signals (amplifier distortion, tube hiss... and why not, music playing?).
The reason why I an really getting bored is trying to prove that pigs can't fly - while everyone knows that they can if we shoot them from a large enough cannon!
Now the fact that we are not actually engaging in pigs shooting instead of plain farming, and that this is an unlikely activity obviously does not subtract validity or entertainment quality to a pig shoot contest?
If I was selling HF AC, I would probably indulge this further and try to dissuade the opponents. But I am neither selling nor in a position to sell, thus I must ask myself:
why such hard opposition - is it care for the wellbeing of fellow DiYers who might damage their hearing with audible HF AC artifacts and heterodyne byproducts - or the possibility that those hearing impaired DIYers (who have tried HF AC heating and thus damaged their hearing) might choose to forget about DC, thus making obsolete the various fancy voltage controlled current source solutions (current servo) that are considered top notch although even the authors acknowledge the basic flaw of DC heating (difference in potential i.e. bias between rhe two ends of the filament), and the solutions are horribly inefficient in electric terms (just rectifying means a loss of at least 62%, and there are additional losses in smoothing, regulation, current setting...) as well as thermal terms (a lot of heat being generated, depending on the heater requirements).
But since I am not (selling), I am frankly beginning to loose motivation: you are certainly going to win this war of attrition. No news from the heaters front: fancy commercial DC solutions reign supreme because DIYers have little knowledge and a lot of confidence, besides a lack of imagination and vision. After all, it's just a hobby they pursue for the sake of making stuff on their own in their spare time (it is more important to do something than accomplish something).
