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# Re: DC Tesla Coil

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From: 	Antonio Carlos M. de Queiroz[SMTP:acmq-at-compuland-dot-com.br]
Sent: 	Sunday, January 04, 1998 6:02 PM
To: 	Tesla List
Subject: 	Re: DC Tesla Coil

Alfred C. Erpel wrote:

>     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 there is more energy in the capacitor than in the inductor, and so it
takes twice longer to dissipate the energy. The spark gap also contributes
with extra resistance. With your values, the amplitude of the oscillation
will take 0.00294 seconds to decay to 37% (1/e) of the initial value.

> 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?

(??)
To understand correctly what happens, 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 and see the
waveforms:
ftp://coe.ufrj.br/pub/acmq/teslasim.zip

> 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 of the coupling 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, while
decaying much 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 (the ideal instant to open the spark gap). The time
required for the complete transfer depends on the coupling between the
two coils, and is practically independent on time constants. The expression below
gives the approximate time (taken from the above mentioned paper, eq. 11). fr
is the resonance frequency of both circuits and k is the coupling coefficient.
The expression seems correct for low k values (<0.5).

0.5              1
T~=--------------------------*----
1             1       fr
---------- - -----------
(1-k)^0.5     (1+k)^0.5

The maximum secondary voltage is, at most (ignoring losses):

Vc2max=Vc1(0)*sqrt(L2/L1)

Exactly what would be obtained with an ideal transformer (that would be very
difficult to construct with the required insulation and coupling).

Antonio Carlos M. de Queiroz
mailto:acmq-at-compuland-dot-com.br
http://www.coe.ufrj.br/~acmq

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