[Prev][Next][Index][Thread]

0.5*C*V*V vaild? (Was Output Voltages and Voltage/Length)


----------
From:  Mark S. Rzeszotarski, Ph.D. [SMTP:msr7-at-po.cwru.edu]
Sent:  Friday, February 06, 1998 1:23 AM
To:  Tesla List
Subject:  Re: Is 0.5*C*V*V vaild?  (Was Output Voltages and Voltage/Length)

Hello All,
        I have stayed out of this voltage/length discussion until now, but
have really enjoyed the dialogue!
        I have done considerable modelling of tesla coils and helical
resonators, examining the theoretical voltage rise under non-breakout
conditions.  I have also built a series of tesla coils with back-to-back
LED's placed every 2 inches along the length of the coil with various H/D
configurations to examine the voltage rise in these rather heavily damped
coil systems.  Several observations are notable:
1.  The voltage distribution goes from a minimum at the base to a maximum at
the top when tuned to the quarter wavelength of the coil system, even in a
damped coil system.
2.  Adding a toroid or sphere to the top tends to linearize the voltage rise
somewhat, so that the turn-to-turn voltage stress is lessened especially
near the top of the coil.
3.  If you want accurate measurements of the voltage at the top of the coil,
your probe better have very little capacitance.  I can visually affect the
LED voltage distribution of a coil from 6 feet away by waving a hand.  This
is in a heavily loaded, lossy coil system.  Measurements with a vector
impedance meter on a coil without LED's demonstrate that the impedance is
affected by moving about at distances of greater that 12 feet for a 16 inch
tall by 4 inch diameter coil.  Typical oscilloscope probes have 10-30 pF of
capacitance, which greatly affects the readings unless you have a huge coil
system with a Csec of perhaps 10-20 times this or more.
4.  The Corum brothers suggest that the voltage rise in a helical resonator
can be rather astronomical.  I disagree.  My measurements of the maximum
possible voltage at the toroid tend to agree with the equation:
Vsec(max) = Vpri x SQRT(Cpri/Csec), or the equivalent:
Vsec(max) = Vpri x SQRT(Lsec/Lpri), which is essentially the lumped circuit
model.
        There is an interplay of energy storage between the capacitance (1/2
Csec V^2) and the inductance (L dIsec/dt), (as well as an interplay between
the primary and secondary systems while the spark gap is conducting).
Trying to quantitate coil energy is fruitless, since it is a dynamic system.
In addition, when the sparks break out, the corona field around the toroid
adds significant capacitance to the system, thereby lowering the resonant
frequency, (as well as adding another unknown capacitance quantity).  The
intensity of the sparks depends on the available energy stored in the
secondary during ringdown and the resonant frequency.
Oscilloscope traces of firing coils demonstrate that the coil rings down
completely between eack primary spark.  If the resonant frequency is low,
this ringdown takes longer, and the spark ion paths persist a bit longer so
that they can be re-used during successive discharges, thereby lengthening
the spark.
        I feel that any quantitation of voltage/length for a tesla coil
should include specification of the number of breaks per second as well as
the resonant frequency, since these factors also play an important role in
determining what happens.  If you really need an equation, I suggest 8400
volts/inch for a tesla coil.  Anything higher than this is speculative at best.
Regards,
Mark S. Rzeszotarski, Ph.D.