Re: Of notches, coupling and frequency splitting

["Tesla list" <tesla@xxxxxxxxxx>]

Original poster: acmq@xxxxxxxxxxxxxxxx 

> Original poster: Finn Hammer <f-h@xxxx>
>
>
>
> All,
>
> Just to remind, this thread is about waveforms that oscillates at 2
> different frequencies simultaneously, (like the current waveform in a
> tesla coil tank circuit) and what it looks like on a scope.
>
> With input from Steve Conner, on the 4HV forum, I was encouraged to
> look at not only the + - peaks, but also the zero crossings.
> http://home5.inet.tele.dk/f-hammer/sawtoothnotchtable.jpeg
> This data suggests that the primary current waveform is a sine wave
> with a slight sawtooth tilt to it. Also, at the notches, a phase
> reversal takes place, which increases the frequency during 1-2 cycles.
>
> If his is it: the rising 1/4 portion of the wave is shorter in
> duration than the falling 1/4 portion, then it makes sense to me that
> the wave oscillates at 2 frequencies simultaneously.
>
> The transition from leading phase to lagging phase at the notches,
> with the associated rise in frequency, should show up in the FFT
> plots but I can`t see how it does..
>
> Comments?
>

The oscillations at two frequencies are exactly equivalent to a modulated
oscillation at one frequency:

cos(a)*cos(b) = 0.5*(cos(a+b)+cos(a-b))

The difference in time in the rising and falling sections are due to
losses, that put different exponential decays in the two components. Can
be also due to nonlinearities, in a practical measurement or modeling that
includes these effects. The phase transition at the notch is natural, and
is evident at the left side the formula. it does not appear in the
spectrum.

Antonio Carlos M. de Queiroz