Re: Balancing L/C Sizes

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

Original poster: "William Swanson by way of Terry Fritz <twftesla-at-uswest-dot-net>" <swansontec-at-yahoo-dot-com>

Hi Matt!
By coincidence, this is the exact problem I was trying
to figure out yesterday! Basically, the energy in a
capacitor is equal to the voltage squared times one
half of the capacitance, while the energy in an
inductor is equal to the current squared times one
half of the inductance. In a perfect world, we could
use any values of inductance and capacitance that we
wanted, since there would be no particular limit on
how much current or voltage we could operate at. The
problem is that in reality there are very real limits,
especially on current. These limits are what determine
the sizes of the coils and toploads that we should use
on a TC.

The reason the limits are tougher on current is
because the resistance of the wire causes enormous
losses at high current. Running even a few hundred
amps through a wire of modest size can generate
hundreds of watts of wasted heat energy. Since the
losses in a piece of wire are equal to the current
squared times the resistance of the wire, it is far
more effective to reduce current than to focus on the
resistance of the wire when designing a coil. The key
to reducing current is, of course, to increasing
inductance, since twice the inductance means only
1/2^0.5 times the current for the same energy, which
means 1/2 the losses. Therefore, the efficiency of a
coil is directly proportional to its ratio of
inductance to resistance.

Picking a topload isn’t as tricky, since most of the
losses of a capacitor occur when it breaks down the
surrounding dielectric. We want this breakdown in
Tesla coil work, since it results in streamers and
sparks. Therefore, simply stick with the
tried-and-true rules of thumb for picking a topload.

My conclusion is that the inductance/capacitance ratio
for your coil isn’t really all that important if you
pick a good sized torroid using the handy rules of
thumb, and to optimize your coil’s
inductance/resistance ratio as far as it will go. In
this connection, I would also like to point out that
wire gauge shouldn’t make much of a difference, since
you can get twice as many turns with wire that is half
as thick. Since twice as many turns means four times
the inductance, while half as thick wire makes four
times the resistance, the inductance/resistance ratio
stays the same no matter how small your wire is.

-William

--- Tesla list <tesla-at-pupman-dot-com> wrote:
> Original poster: "by way of Terry Fritz
> <twftesla-at-uswest-dot-net>" <Mddeming-at-aol-dot-com>
> 
>  Hi All! 
>         A short while ago, there was a very good
> explanation of LC 
> oscillation posted using the analogy of pouring
> water from one container 
> (electrical field in capacitor) to another container
> (magnetic field in coil) 
> and back again. It was mentioned that you would, of
> course, not want to use a 
> bucket and a thimble. 
> This started me thinking (danger, danger) that just
> as there is an 
> appropriate size capacitor to store a given amount
> of energy, 0.5CV^2, there 
> should also be an appropriate size coil such that
> the field of the coil could 
> absorb the energy being transferred to it from the
> cap, so as not to empty 
> the "bucket" into the "thimble". While the primary
> coil is more of a transfer 
> device, (funnel) than bucket, it seems that there
> must be some sort of 
> min/Max size constraint, but I can't recall any
> discussion of an energy 
> storage equation for a coil. Likewise, the secondary
> can be looked at as a 
> device to "funnel" charge into the topload and
> ultimately to the streamers. 
> It seems to me that there should be some sort of
> calculable optimal range of 
> sizes out of the infinite combinations of L & C for
> any frequency. It is 
> somewhat hinted at in the "rules of thumb" about
> power, coil size, and 
> topload size, but I can't seem to find anything
> definitive. Perhaps some of 
> the theoreticians could elucidate, or a historian
> could point me to a thread 
> I missed? 
> 
> Seeking light and lightning in the hills, 
> 
> Matt D.
> 
> 


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