Re: DC Tesla Coil

From: 	Antonio Carlos M. de Queiroz[SMTP:acmq-at-compuland-dot-com.br]
Sent: 	Sunday, January 04, 1998 2:52 PM
To: 	Tesla List
Subject: 	Re: DC Tesla Coil 

Alfred C. Erpel wrote:

>     I would like to discuss an example.
>     Let's assume a capacitor of .000000084 Farads and a primary of .00003
> Henrys. This circuit has reasonable values for a TC and will resonate at
> 100,000 hz. Let us assume a transformer of appropriate size feeding the
> capacitor and a helical primary coil of 5 inch radius and 10 inch height. A
> 13 turn coil will give an inductance of .00003 Henrys. This primary coil
> will be about 34 feet long. If I use number 8 stranded wire at .0006 ohms
> per ft., the total resistance of my primary will be .0204 ohms.
>     This inductor (primary) has a time constant (L/R) of .00147 seconds
> (assuming no resistance in the capacitor). This would be the amount of time
> it takes the magnetic field to grow to 63% of its final potential value
> assuming there is enough current available. The amount of time for 1 cycle
> of 100,000 hz is .00001 so if their was enough current available for 1 time
> constant it would take 147 times longer than 1 cycle.

A note: The time constant for an LC tank is 2L/R. You may think that in half
of the time the energy is in the capacitor, not in the inductor, and so it
takes twice longer to dissipate the energy. The spark gap also contributes
with extra resistance.

> 1) It seems that maximum power will resonate thru a tank circuit when the
> potential energy storage of the capacitor equals the potential energy
> storage of the inductor. i.e. when .5CV^2 = .5LI^2
> Is this true?

No. All the energy that the tank has is the energy that was initially in the
capacitor. Different inductance or capacitance values just change the resonance
frequency (and the time constant, taking into account the resistance).

> 2) I don't believe in the example circuit above that there is even close to
> enough energy to fully *charge* the primary. How would you calculate this
> value and the amount of time it would take to transfer into the primary. Is
> this the reason it doesn't matter that a time constant (above) is 147 times
> longer than 1 cycle?

See a paper in the American Journal of Physics, Vol. 65 (8), August 1997,
page 744.
Or use the program that I wrote to simulate two coupled RLC tanks:
> 3)How does the fact that as the primary is establishing its magnetic field,
> it is also inducing current in to the secondary affect this scenario. Aren't
> we theoretically hoping that most of energy being transferred into the
> primary won't go into building a field, but will be induced into the
> secondary?

The effect is that the energy in the primary circuit, instead of simply
decaying exponentially to zero due to dissipation in the circuit resistances,
oscillates between the primary and secondary circuits, decaying as before.
The primary capacitor voltage decreases with an almost cosinusoidal envelope,
while the secondary capacitor (the toroidal terminal) voltage increases with
an almost sinusoidal envelope, reaching the maximum value when the primary
energy reaches zero (at this moment the spark gap shall open). The time
required for the complete transfer depends on the coupling between the
two coils (See eq. 11 in the mentioned paper).
The theory mentioned above covers all this.

Antonio Carlos M. de Queiroz