Re: Simulation of a conventional Tesla coil

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

Original poster: "Dr. Resonance by way of Terry Fritz <teslalist-at-qwest-dot-net>" <resonance-at-jvlnet-dot-com>


These equations were originally developed for spark gap transmitters and I
always assumed they were analagous to a Tesla RC circuit with log decrement.

Dr. Resonance


 > Original poster: "Malcolm Watts by way of Terry Fritz
<teslalist-at-qwest-dot-net>" <m.j.watts-at-massey.ac.nz>
 >
 > Hi DC,
 >
 > On 19 May 2003, at 11:36, Tesla list wrote:
 >
 >  > Original poster: "Dr. Resonance by way of Terry Fritz
 > <teslalist-at-qwest-dot-net>" <resonance-at-jvlnet-dot-com>
 >  >
 >  >
 >  > Since you can see the wavetrain on a storage scope, and knowing the
decay
 >  > rate is directly related to circuit resistance, why not just calculate
the
 >  > current?
 >  >
 >  > The resistance of all circuit components can be measured (so low with
large
 >  > dia copper tubing or wire it is almost negligible) except for the
higher
 >  > resistance of the sparkgap.
 >  >
 >  > The sparkgap presents a problem, but by subtracting the resistance of
other
 >  > components from the total resistance you will have the resistance of
the
 >  > operating sparkgap.  Total circuit resistance is directly related to
the
 >  > decrement (decay) factor of the wavetrain.
 >  >
 >  > Total current, I rms, in a spark oscillator circuit is:
 >  >
 >  > I rms  =  3.14 * E * C *  sqr ((N * F) / d
 >  >
 >  >      I rms = rms current in Amperes
 >  >
 >  >      E = Voltage on capacitor at the commencement of each wavetrain
 >  >
 >  >      F = Freq. in Hz
 >  >
 >  >      N = Number of sparks/second
 >  >
 >  >      d = decrement (decay) factor of wavetrain   (related to
resistance)
 >  >
 >  >
 >  >
 >  >
 >  > The logarithmic decrement factor is calculated by:
 >  >
 >  >
 >  >      d = 3.14 * R * sqr (C / L)
 >  >
 >  >      d = log. decrement factor
 >  >
 >  >      R = circuit resistance in Ohms
 >  >
 >  >      C = capacitance in Farads
 >  >
 >  >      L = inductance in Henries
 >  >
 >  >
 >  > The above equation is solved for resistance.  This gives total circuit
 >  > resistance of an operating LC circuit.
 >
 > The problem is that a circuit with a sparkgap in it exhibits a linear
 > decrement so you can't use the logarithmic RC formula to derive a
 > value for gap resistance.
 >
 > Malcolm
 >
 >  > The actual decrement factor can be determined by viewing the waveform
on a
 >  > storage scope:
 >  >
 >  >      d = (log n) * A1 / A3  =  A2 / A4  = A m/ An
 >  >
 >  >      d = decrement factor   (typical value would be 0.25 with a total
 > circuit
 >  > resistance of 5 Ohms)
 >  >
 >  >      A1 = Amplitude of first wave (positive peak)
 >  >
 >  >      A2 = Amplitude of first wave (negative peak)
 >  >
 >  >      A3 = Amplitude of second wave (positive peak)
 >  >
 >  >      A4 = Amplitude of second wave (negative peak)
 >  >
 >  >
 >  > When I get my scanner running I will scan a waveform drawing which more
 >  > clearly illustrates how the decrement value is directly measured on a
 >  > waveform.
 >  >
 >  > The pos. amplitude of the first wave is the value measured from 0 to
the
 >  > first positive peak.   The neg. amplitude of the first wave is the
lower
 >  > section measured from 0 to the first neg. peak.
 >  >
 >  > You essentially are developing a value for the actual circuit
resistance
 >  > which is directly dependent on the rate of decay of the waveform.  The
 >  > decrement is a ratio of the first peak to the second peak to the third
peak,
 >  > ... ad infinitum.  This decaying value is related directly to the
 >  > resistance.
 >  >
 >  > Tesla didn't have a method of directly seeing these waveforms but with
 >  > modern storage scopes than can freeze this waveform we can take direct
 >  > measurements of these amplitude ratios and then calculate the decrement
 >  > factor.  The measured decrement factor is then used directly into the
two
 >  > equations to find the actual total resistance of the operating LC
circuit.
 >  > After measuring the DC resistance of the circuit and subtracting this
value
 >  > (almost negligible) from the actual total resistance of the operating
 >  > circuit we end up with the actual resistance of the operating sparkgap.
 >  >
 >  > Many experimenters have assumed that the resonant circuit peak
discharge
 >  > potential is E rms x 1.4.   It's not.  Under resonant conditions the
peak
 >  > discharge voltage of the capacitor is E rms x 2.2 (see below).  This
assumes
 >  > max. spacing on the sparkgap so the cap doesn't fire early.
 >  >
 >  > Also, if the sparkgap is at a wide spacing, or in the case of the RSG
type
 >  > gap, and, if the capacitor recharging current is a high value, then:
 >  >
 >  >      Ep = 1/2 * 3.14 * Emax which is equal to = 2.22 * Erms
 >  >
 >  >      Ep = peak voltage to which capacitor is charged just before firing
 >  >
 >  >      E max = E rms (of transformer) * 1.4  =  E rms * sqr 2
 >  >
 >  >      E = E rms voltage of transformer
 >  >
 >  > The above equation assumes the transformer can provide a high current
to
 >  > completely recharge the capacitor to full value before it fires.
 >  >
 >  > Dr. Resonance
 >  >
 >  > Resonance Research Corporation
 >  > E11870 Shadylane Rd.
 >  > Baraboo   WI   53913
 >  >
 >  >
 >  > -- snip --
 >  >
 >  >  > It would be interesting to revisit spark gap voltages and currents
now
 >  > that
 >  >  > the equipment is so much better...
 >  >  >
 >  >  > Cheers,
 >  >  >
 >  >  >          Terry
 >  >
 >  >
 >  >
 >
 >