Critical Rise Time
a Tesla List discussion
definitions: convolution - an integral that expresses the amount of overlap of one function over another function
Date: Sun, 15 Jan 2006 12:35:22 -0700 - Subject: Re:vv Critical rise time - Original poster: "Bob (R.A.) Jones"
Hi Leigh,
> Original poster: "Leigh Copp"
snip
> 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 [sic]
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
than becomes the
convolution of a pulse train and the resonant
frequency of the tank. (assuming as we stated above, lumped parameters
in the TC).
No to repeat a particular waveform is not the same as modulation if modulation
means multiplication. Repeating a particular waveform is equivalent to
convolution with a train of
impulses with a period equal to the rep rate. I suspect that you are
thinking about a continuous waveform and are chopping it up.
>
> 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).
I believe that modern SSTG operate in small (relative to transient decay) bursts
so the start transient is significant i.e. they never achieve the steady state
response that can be easily obtained from the transfer function. So there would
be very significant errors in assuming steady state.
Robert (R. A.) Jones -
A1 Accounting, Inc., Fl
Date: Mon, 16 Jan 2006 06:55:40
-0700 - Subject: RE: vv Critical rise
time, - Original poster: "Leigh Copp"
Hi Bob,
I know we are getting down to semantics here, but if modulation -is-
multiplication, I think we are modulating. In breaking the circuit (with, insert
switching method of choice here) we are effectively
multiplying the waveform alternately by 1, or 0.
Put another way, repeating a waveform is no different than the digital
modulation employed on many of the communication methods we use today. One
amusing example I saw was that of a blanket modulating a smoke stream.
If we resort to the IEEE definitions, essentially any variation of any parameter
of a waveform or signal is considered as modulation.
Now that's twice I have resorted to pulling out the IEEE purple book :). -
Leigh
Date: Mon, 16 Jan 2006 16:24:17
-0700 - Subject: Re: vv Critical rise
time, - Original
poster: "Bob (R.A.) Jones"
Hi Leigh,
I don't have any difficulty in getting down to semantics so long as it helps our
understanding.
Try this analogy.
If we have a line (continuous repeating wave) we can modulate it into a dashed
line.
If we have an "A" (finite non repeating wave form) we can convolve it with a
train of impulses to get a string of "A"s.
In the analogy above the "A" is equivalent to the impulse of the Tesla coil. Which is a finite non repeating waveform i.e. two beating cosines decaying. I don't see how you can modulate an "A" to get a string of "A"s. When I
have time I will sketch the waveforms and spectrums and get Terry to
temp it. That will probably help. What waveform are you proposing to
modulate to get the final waveform of the coil
Date: Tue, 17 Jan 2006 17:00:29
-0700 - Subject: RE: vv Critical rise
time, - Original
poster: "Leigh Copp"
Hi Bob,
Excellent analogies by the way.
What I was suggesting was that the impulse of the Tesla coil is being modulated
by the break rate of our gap, or switch. Essentially I was treating the
resonance of the TC as a continuous wave, and ignoring the discharge pattern for
the purposes of examining the "modulation" of the relatively high fo of the TC
by the much lower break rate. This is not a valid assumption of course,
since if the TC is serving its purpose it will be discontinuous (or as you
stated, will have finite duration) all on it's own, not counting the pulses on
the primary side, since we are regularly discharging from the top load.
Thinking about this a bit more, our break rate is synchronous with our discharge
rate, so you are right in that modulation was not the best choice of
terminology.
I was not proposing to modulate a waveform necessarily. The original question
was regarding the definition of, and contributing factors to rise time, and my
point was merely that any non-sinusoidal wave form's rise time is determined by
higher order harmonic content, and that modulation of any kind would be a
contributing factor to this higher order content.
Deliberately modulating the input the [sic] affect the ring up? That's an interesting
idea. I am thinking that the frequency at which we can modulate our power
devices however, is much too low relative to fo to achieve much wave shaping. -
Leigh
go to www.pupman.com and check the January 2006 archive for more