RE: Critical rise time

["Tesla list" <tesla@xxxxxxxxxx>]

Original poster: "Leigh Copp" <Leigh.Copp@xxxxxxxxxxx>

Hi Robert,


Original poster: "Bob (R.A.) Jones" <a1accounting@xxxxxxxxxxxxx>

Hi Leigh,
 > Original poster: "Leigh Copp" <Leigh.Copp@xxxxxxxxxxx>
 >
 >
 > Just a thought with regard to the comment that "Rise time implies
 > waveform shape, that is "fo"." I think that you meant the frequency
 > -content-, and not fo.
 >
 > The sum of the Fourier components of the wave each impart their own
 > contribution on the rise time. The bandwidth of the system can be
 > calculated as 0.35/risetime, but this would be the highest frequency
 > components only. Fo of the system, as has been well discussed in this
 > group, is 1/(2*pi*sqrt(L*C)). The higher order harmonics of the
system
 > however, are what contribute to the "steepness" of the wave front.
These
 > are going to be multiples of fo.

If you make the usual assumptions of a lumped approximations, perfect
sync
sg and no losses you just have two components.
Linear losses just give the components exponential skirts.

<LC> - I agree. First approximation only.

 > The current we are applying to our TC's is resonant at some fo and
 > modulated by our spark gap (which itself is very rich in 3nth order
 > harmonics) and it's own pulse rise time. Rotary spark gaps or SSTC's
are
 > modulating by the break rate additionally.
 >
 > If anyone is brave enough to apply the convolution theorem to that
one
 > the actual system bandwidth can be expressed in terms of break rate
and
 > fo.
 >

Modulating or more accurately repeating at the break rate is the same as
convolving (in the time domain) by a series of impulses with a period
equal
to the break rate. Which is the same as multiplying the spectrum by a
series
of impulses. Which just turns the continues spectrum of a single break
into
a discrete one with components separated by the break frequency.

<LC> It's been a while since I looked at this properly, so entertain me
for a moment; would repeating at the break rate not (by definition) be
the same as modulation by a pulse train? So it then becomes the
convolution of a pulse train and the resonant frequency of the tank.
(assuming as we stated above, lumped parameters in the TC).

I agree the spectrum of a self excited burst mode SSTC could be tricky.

<LC> I guess in the case of the SSTC with feedback you would have to
either assume steady state operation, (or use chaos theory as in the
higher order simulation of a phase locked loop).



Robert (R. A.) Jones
A1 Accounting, Inc., Fl
407 649 6400