RE: Critical rise time (RE: Terry's New Plane Wave Antenna)

["Tesla list" <tesla@xxxxxxxxxx>]

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

Hi Gerry,

OK - I understand what you meant now. This merely assumes that the wave
shape is sinusoidal.

I was including the BPS as a manner of exemplifying the general case,
where rise time is a function of the overall wave shape, which is going
to be determined by the frequency components of the whole enchilada.

On to your question however: I believe that the slope of a single half
cycle -is- the rise time that will govern the voltage at the output. The
voltage is n*(d(phi)/dt), and d(phi)/dt is proportional to di/dt.

I'm not sure how this relates to the rise time vs. breakdown time
relationship however.

Leigh


-----Original Message-----
From: Tesla list [mailto:tesla@xxxxxxxxxx]
Sent: January 14, 2006 10:03 AM
To: tesla@xxxxxxxxxx
Subject: Re: Critical rise time (RE: Terry's New Plane Wave Antenna)

Original poster: "Gerry  Reynolds" <gerryreynolds@xxxxxxxxxxxxx>


Hi Leigh,

Actually, I really did mean the frequency "fo".  I was speaking maybe
a little too loosely and thinking in time domain not the fourier
spectrum considering BPS repetition.  My thinking for the question
was confined to a single bang.  Given that, the slope of a sine wave
is a function of its frequency and (what I left out) its
amplitude.  My main question was trying to determine if the growth in
the sinewave envelope (ringup) was the determining factor (affected
by coupling) or just the slope of a single sinewave half cycle.  It
sounds like you are including the BPS info in the risetime
definition.  What I think I heard from the answer was the slope of a
single half cycle is the determining risetime.  Someone correct me if
this is wrong.

Gerry R




>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.
>
>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.
>
>Leigh
>
>
>
>-----Original Message-----
>From: Tesla list [mailto:tesla@xxxxxxxxxx]
>Sent: January 13, 2006 2:28 AM
>To: tesla@xxxxxxxxxx
>Subject: Re: Critical rise time (RE: Terry's New Plane Wave Antenna)
>
>Original poster: "Gerry  Reynolds" <gerryreynolds@xxxxxxxxxxxxx>
>
>Thankyou Marco,
>
>Maybe someday one can quantify this range of rise times by a range of
>frequencies.  Im now wondering if the "critical rise time" is fixed
>or dependent on some other factors.
>
>Gerry R
>
>
> >Original poster: "Marco Denicolai" <marco.denicolai@xxxxxxxxxx>
> >
> >Hi Gerry,
> >
> > > -----Original Message-----
> > > From: Tesla list [mailto:tesla@xxxxxxxxxx]
> > > Sent: Friday, January 06, 2006 19:04
> > > To: tesla@xxxxxxxxxx
> > > Subject: Re: Terry's New Plane Wave Antenna
> > >
> > > Original poster: "Gerry  Reynolds" <gerryreynolds@xxxxxxxxxxxxx>
> > >
> > > Hi Marco,
> > >
> > > What you are saying is one can get the rise time of the topload
> > > voltage too small for optimum streamer formation???
> >
> >Yes. The optimal rise time is often called "critical rise time". It
is
>the
> >one for which time-to-crest is equal to time-to-breakdown.
>Time-to-crest
> >means time for the waveform to reach its maximum value. Sorry for the
>odd
> >words but this is the naming often used in the literature.
> >
> > > If so, does
> > > this relate directly to "fo" of the coil (rise within one RF
cycle)
> > > or to the coupling coefficient "k" (affects the peak to peak
> > > rise).
> >
> >Rise time implies waveform shape, that is "fo".
> >
> > > Also, I presume there is an upper limit on the rise time for
> > > optimum streamers as well.
> >
> >Probably, I mean for TC kind of bangs. For single surge pulses (like
>those
> >used in classical literature) using larger rise time gives, of
course,
> >larger time to breakdown.
> >
> > > What other factors affect these boundary
> > > constraints??
> >
> >I hope to shed some light on this in my PhD work, if it ever gets
done
>:)
> >
> >Best Regards
> >
> >
>
>