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Re: Critical rise time



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.

> 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.

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

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