Re: Simulation of a conventional Tesla coil

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

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
 >
 >
 >