# Re: [TCML] capacitor charge time?

```Jay,

The charging of the capacitor with the mA source will indeed take many mS to
reach sufficient voltage.

The DISCHARGE of the capacitor into the low impedance of the primary
inductance is much faster (no its not chaotic, it follows the rules of
E&M).  You can figure out the peak current by knowing 1) the peak charging
voltage and 2) the impedance of the primary L (or C) at Fres.  In your case
the 9nF cap has 54 ohms impedance at 328khz, so at a peak charge voltage of
17kV, the peak discharge current will be 315A.  Yes, this is a very
different order of magnitude than the charging current which peaks at 60mA,
and this is why tesla coils work so well at making sparks (there is a huge
amount of power delivered to the spark over a tiny amount of time).

The result discharging current is basically a decaying sinusoid at the Fres
of the tank.  Coupling to the secondary circuit ultimately changes this to
being a damped sinusoid of 2 close frequencies (causing a beating pattern).

Good info:

http://www.richieburnett.co.uk/operation.html#operation

Steve

On Sat, Oct 24, 2009 at 12:52 PM, <jhowson4@xxxxxxxxxxx> wrote:

> Thanks for the explanation Steve
> But I am still a little foggy
> for the capacitor charging the input current decides on the time. which is
> what that equation gets me.
> suppose i have a 12kv 60ma supply and a cap of 9nf
> if i just let that charge all by it self the charge time is 2ms.
> but wait i am using an ac supply so 1/f=T and the period is .017ms and a
> quarter of that is .0042ms meaning that my capacitor does charge in one
> quarter of a wave length.
>
> but lets look at the other side now my coil has a resonant F of 328khz so
> its period is 3us and a quarter wave is .76us.
>
> so really my cap only have 76us to become charged before it is forced to
> discharge; completely changing the first paragraph.
> the charge after charging by the power supply could be 46nC thus the
> voltage across the cap at this time would be umm this cant be right 5v.
> Q/C=V 46nC/9nF =~5v
>
> Steve this makes no sense to me
> does this mean that the discharging of the capacitor is chaotic and does
> not follow the resonant frequency
> or am i missing another critical idea that makes is all work out.
> even in your explanation how can something charge on a ms scale at ma and
> discharge on a ns scale at ka.
>
>
> John "Jay" Howson IV
>
> ----- Original Message -----
> From: "Steve Ward" <steve.ward@xxxxxxxxx>
> To: "Tesla Coil Mailing List" <tesla@xxxxxxxxxx>
> Sent: Monday, October 19, 2009 12:37:49 PM GMT -05:00 US/Canada Eastern
> Subject: Re: [TCML] capacitor charge time?
>
> In the case of a constant current source (or even otherwise as long as you
> can do some calculus)
>
> Q = C*V = I*t
>
> Assuming the charging is limited purely by R is not valid in most tesla
> coil
> charging systems. Generally its limited by some inductive impedance at
> 60hz. The impact of this impedance on charging the capacitor is
> non-obvious, particularly as the capacitor is discharged at various phases
> along the 60hz mains cycle. Using spice would be a good option to gain more
> insight. Most tesla coilers dont bother to dig this deep and just pick a
> ballast (inductor) that gets their average charging current within an
> acceptable value.
>
> To get at your original idea... the resonant behavior of the tesla coil is
> damped and long gone before you really even start to charge up the
> capacitor
> again. You are dealing with time scales and power levels that are on very
> different magnitudes. The capacitor charging is in the 10's of mA and mS
> range, while the resonant discharge is in the 100s of Amps and 10's of uS
> range. Interestingly enough, the DRSSTC is a solid-state approach to
> driving a TC where the tank capacitor is always in a state of being
> "charged
> up" by a special power source that can keep up with the 100's of Amps and
> can switch polarities along with the resonant frequency of the system,
> somewhat along the lines of your idea in question.
>
> Steve
>
> On Thu, Oct 15, 2009 at 6:26 PM, <jhowson4@xxxxxxxxxxx> wrote:
>
> > Hey guys.
> > I was explaining the tesla coil to one of my physics friends (we are both
> > sophmores) and he asked a question that i could not answer.
> >
> > I was asked if it would be a good idea to match the time required to
> charge
> > a capacitor to (1/4) of the resonant frequencies period. with the general
> > idea that the capacitor would be completely charged when the resonant
> wave
> > form was at a max or a min, thus maximizing efficiency.
> >
> > sounds like a good idea to me.
> >
> > But when we went to try and do an example calculation we realized that
> our
> > standard RC capacitor charging equation would not work because our
> current
> > output from the transformer was fixed and would only decrease after the
> cap
> > charging current became less than or equal to our source current.
> >
> > and this spawns my question. how does one calculate the charge time of a
> > capacitor with a fixed source voltage and current.
> >
> > does the capacitor ignore the fact that the transformer is current
> limited
> > and draw that initial huge current anyway. or is there some other special
> > equation that accounts for a limited source current and fixed source
> > voltage.
> > or are we both just missing something.
> >
> >
> > t=-CR ln(IR/V) derived from I=V/R e^(-t/RC)
> >
> >
> > thanks for the help
> > Jay Howson
> > _______________________________________________
> > Tesla mailing list
> > Tesla@xxxxxxxxxx
> > http://www.pupman.com/mailman/listinfo/tesla
> >
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