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The Tesla coil: Genius or folly?

16 Jan 2014  | Steve Taranovich

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The iron core transformer output voltage will drop to zero while the input remains the same as long as the arc is occurring. The transformer current becomes limited by the equivalent series impedance of RS + jXS shown in figure 5.

Now let's look at the lumped circuit model of the shorted Tesla coil for analysis (figure 6)

Figure 6: The lumped circuit model of the shorted Tesla coil where R1 and R2 are the effective resistances of the air-cored transformer primary and secondary respectively.

Figure 6 shows M as the mutual inductance between the primary and the secondary of the transformer.

When the gap arcs over, C1 stores all of the energy at first, but as time goes on C1, L1, C2, L2 and M share the total energy, which will decrease due to R1 and R2 resistances. If the design is done properly, by the setting of particular values of C1, L1, C2, L2 and M then all of the energy in C1 will be transferred to the secondary at once at time t1. At t1 there is no voltage on C1 and no current in L1. If the gap opens at t1 then energy cannot get back to the primary which causes no current storage in L1 and hence the capacitor will not be charged.

Subsequently the secondary becomes an RLC circuit and C2 and L2 will have non-zero initial conditions. The circuit will now resonate at a frequency set by C2 and L2 values. S with an open gap, the secondary of the Tesla coil is a classic RLC circuit and as we would expect, has a damped sinusoid output.

If we set the gap to arc over at a voltage near the peak of the 60Hz sinusoid, then there will be only one pulse each half cycle (120 pulses/second) being supplied to the air-cored transformer. So if the secondary is designed for a 240kHz resonant frequency then each pulse will need to supply enough energy to sustain an oscillation in the secondary for 2,000 cycles. Dr. Johnson found that the arc only lasts for 10 us which is only 2 or 3 cycles of the output waveform.

The genius of Nikola Tesla is realised by those who try to complete Tesla's experiment in Colorado Springs or Wardenclyffe on Long Island, New York. However, that will not stop engineers from trying. I'm looking forward to more efforts like Dr. Johnson's and his students.

A mini Tesla coil using a DC voltage input8
The electrical engineering faculty members at UTeM Malaysia, put together a pretty neat design for a Tesla coil with better mobility, being less bulky than typical designs. Their goal was to generate a high frequency current with a medium voltage, that is, 2.5kV on the secondary with an unusual 24VDC at the primary input side instead of an AC voltage as is typical with most designs.

The proposed mini Tesla coil uses all the same components as a traditional Tesla coil such as the toroid, primary and secondary coils, spark gap and capacitor. On big difference is that the mini-design does not use a rotary of sphere gap, but instead a contactor of a relay since conventional spark gaps would not work with a 24 VDC input.

The 24 VDC is not enough to fire the gap across the relay contactor since a one millimeter gap needs 3 kV to generate an arc. Instead, the arc is created by opening and closing the gap very quickly. During the opening and closing of the relay, the 24V will charge the tank capacitor which will in turn transfer energy to the primary of the transformer.

Guiding high voltage arcs in the Tesla coil
Finally, let's take a look at a technique guiding the high voltage arcs of the Tesla coil by using laser-induced plasma filaments in air5.

A terawatt femtosecond laser was used to guide high-voltage arcs in the air using plasma filaments. A high-voltage electrode, set at the top of a Tesla coil voltage elevator, emanates arcs to a grounded node.

Extremely short, pulsed laser beams, having energy in the mJ region, have non-linear propagation in air. Long plasma filaments, also known as Birkeland currents (Much of Nikola Tesla's research and experimentation was in the plasma region of guided energy and power) having electron density of 1016 – 1018 cm-3 are able to be generated due to dynamic competition between the non-linear Kerr self-focusing (which eventually collapses the beam) and plasma de-focusing (which tends to halt the collapse of a beam). The laser ionizes the air and causes this effect.

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