Re: Resonant Voltage Formula

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: "Gerry Reynolds" <gerryreynolds-at-earthlink-dot-net> 

Hi Jim,

Yeh thats what I meant to say.  Anyway, thanks for the energy balance
explaination.   Maybe if one was interested in only the early portions of
the ringup, they could do a straight line approximation.

Gerry R

 > Original poster: "Jim Lux" <jimlux-at-earthlink-dot-net>
 >
 > It's actually exponential rise and decay, not logarithmic..
 >
 > They're both for the same reason.. Take the decay case first.. it's
easier.
 > The rate of energy loss is proportional to the amount of energy in the
 > system (that is, you lose a constant "percentage" each cycle).
 > This forms a simple differential equation f' = -kf (where the ' indicates
a
 > derivative.. df/dt = -k *f)  and the f=exp(-kt) is a solution to this.
 >
 > The increment/rise/charging is a bit different... the loss is the same,
but
 > each cycle you are adding energy, until the energy lost = the energy added
 > (i.e. everything balances)... this makes it df/dt = k1 - k2f  (the k1 is
the
 > amount you're adding, the -k2f is the amount lost each cycle..)
 >
 > So, the solution for this one winds up being of the form ka *(1 -
exp(-kat))
 >
 >
 > ----- Original Message -----
 > From: "Tesla list" <tesla-at-pupman-dot-com>
 > To: <tesla-at-pupman-dot-com>
 > Sent: Saturday, July 10, 2004 8:54 PM
 > Subject: Re: Resonant Voltage Formula
 >
 >
 >  > Original poster: "Gerry Reynolds" <gerryreynolds-at-earthlink-dot-net>
 >  >
 >  > Hi Steve,
 >  >
 >  > The logrithmic decay is be cause the energy loss per unit time
decreases
 > as
 >  > the signal decays.  Im wondering on ramp up, if one can say the rate of
 >  > energy pumped in is constant and deduce the envelope of the sinewave.
 > Maybe
 >  > you can scope the ringup and make an approximation.
 >  >
 >  > Gerry R.
 >  >
 >  >  > Original poster: "Steve Conner" <steve.conner-at-optosci-dot-com>
 >  >  >
 >  >  >  >The quantiti [pi/Q] in "Vpeak = Vmax(1-exp(-n*pi/Q))" is known as
the
 >  >  >  >"logarithmic decrement" of the waveform.
 >  >  >
 >  >  > The original poster was not asking about how the waveform decays
 >  > naturally,
 >  >  > but how it rings _up_ when the resonance is forced by a SSTC-like
 > driver.
 >  > I
 >  >  > must admit that I don't know a simple formula for this one :(
 >  >  >
 >  >  > Steve C.
 >  >  >
 >  >  >
 >  >
 >  >
 >
 >