Re: Math help...

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

Original poster: "Bert Hickman by way of Terry Fritz <twftesla-at-qwest-dot-net>" <bert.hickman-at-aquila-dot-net>

Josh and all,

That's an excellent question, Josh - and it goes to show that very few
things are truly simple in coiling... :^)

Malcolm is correct. Previous experiments have measured primary tank
capacitor voltage during a complete primary-secondary-primary energy
transfer cycle. These have shown that the efficiency of the first
primary-to-secondary transfer (from an initially charged tank capacitor to
a fully resonating secondary) can indeed exceed 90%. However, this makes no
statement regarding how efficiently we were able to charge the tank cap
from the mains supply in the first place. For that, we need to talk a bit
more about capacitor charging circuits...

Most Tesla coils use AC charging circuits for simplicity. However, these
charging circuits are NOT RC circuits but instead are RLC circuits, and
these are dominated by inductive reactance. The inductive reactance comes
either from the built-in internal leakage inductance of the NST
transformer(s), or from external inductive ballasting that's purposely been
inserted into the mains primary circuit in the case of externally-ballasted
systems powered by MOT's or distribution transformers. Even though an NST
may have relatively high secondary winding resistance, this is still
dwarfed by much larger inductive reactance. For example, while a 15/60 NST
may have 4000 - 6000 ohms of winding resistance (R) between HV bushings
(varies by vendor), it has the equivalent of 250,000 ohms of inductive
reactance (X), a level that's 40-60 times as large! 

Because of the lower secondary winding resistance of an MOT or Pig, the
ratio of X/R is typically even greater than NST's when they are inductively
ballasted. Although there are also some nonlinear core effects, the
charging system behaves "mostly" like an LC circuit. And the charging
efficiency of an LC circuit will be much higher than a simple RC circuit,
since energy stored in the system's inductance can be efficiently
transferred to the tank cap or sent back into the mains. In contrast,
energy dissipated by a series resistor is permanently lost as heat. An
excellent and more detailed explanation of inductive ballasting was
recently provided to the TC Mailing List by Richie Burnett. 

The bottom line is that, with inductive ballasting you can achieve very
high charging efficiencies (90-95%) for transferring energy from incoming
mains power to the tank cap. Thus, you can get very high system efficiency
(incoming mains power versus output streamer/leader air incineration). With
inductive charging, overall system efficiency could be in the range of 81 -
85% if we were able to successfully quench at the first primary current
"notch". 

Now Luc's DC charging system is completely different than the above
examples. Luc specifically asked about how much power would be dissipated
in the water series resistors as a function of R, C, Vcap and break rate.
Luc is using a relatively low impedance HV DC power supply (since the DC
storage caps have significantly more capacitance than the tank caps). And
he has purposely inserted relatively large water resistors in the HV
outputs in order to limit the charging current to the tank cap. Because of
parasitic wiring inductance, this can also be considered as an RLC circuit
. However, in this case the lumped resistance is MUCH larger than the
inductive reactance, and we can safely approximate it by a simple RC
circuit. And, for an RC circuit, the BEST you will ever see at the tank cap
is 50% of the energy supplied by the incoming mains. Hence, the TC's output
at the secondary can be no better than about 45% of incoming mains power. 

Hope this clarifies the situation a bit... :^)

-- Bert --
-- 
Bert Hickman
Stoneridge Engineering
Email:    bert.hickman-at-aquila-dot-net
Web Site: http://www.teslamania-dot-com


Tesla list wrote:
> 
> Original poster: "David L Wilson by way of Terry Fritz
<twftesla-at-qwest-dot-net>" <daveandcynthia-at-juno-dot-com>
> 
> > Luc,
> >
> > It can be shown that if a capacitor is charged through a resistor,
> > and if
> > the charge time is sufficient to virtually fully charge the cap
> > (Tcharge >
> > 3RC), then the series resistor will dissipate the SAME amount of
> > energy as
> > the energy that ends up being stored in the capacitor. Knowing this
> > simplifies the problem a bit.
> >
> 
> Wow!  Since all TC's have at least some stray resistance in the wiring of
> the tank circuit, does this mean any Tesla Coil can never be more than
> 50% efficient?  It seems so if the same amount of energy delivered to the
> tank capacitor is dissipated in the wiring.  Would someone correct me if
> this is wrong, as I am a little confused by it.
> 
> Sincerely,
> 
> Josh Wilson