Tesla Coil Case Study

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In essence, Tesla coils are a high-voltage, resonant transformer circuits. They consist of the six major components (Behrend 1), namely: Primary transformer Tank capacitor Spark gap Primary coil Secondary coil Toroid Figure 1: Tesla coil (diagram)
A primary transformer is a step-up transformer that takes the line voltage of the AC source and steps it up to a range between 12 kV and 50 kV at 60 Hz (Johnson 4). The efficiency of this transformer is largely dependable on the construction of its core. The iron from which the core is made has to be of a high permeability (amount of magnetization within the iron when immersed into a magnetic field) and a low retentivity (portion of residual magnetic field upon the removal of the magnetizing
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The logic behind it is given as follows. When the magnetic flux drops with the current, it will not become zero as the current drops to zero, but it will be dependant on the residual magnetic field. The residual magnetic field of an open circuit is much less than with the closed circuit of iron (Haller and Cunningham 4). Given that the electromotive force in the secondary winding is directly proportional to the drop in the magnetic field, it follows that there is a larger drop of the magnetic field for the straight core, thus, the electromotive force will be larger.
A tank capacitor is the component within the circuit which is responsible for storing a huge quantities of an electrical energy in an electric field. It can be visualised as a type of a „sponge“, slowly „soaking up“ the electricity for a couple of milliseconds, then „squeezed hard“ so that the previously soaked up electricity is discharged in a few microseconds („How Tesla Coils Work“). Also, it forms the LC circuit with the primary coil. Due to the efficiency purposes, this LC circuit has to be tuned to the same frequency as the LC circuit composed from the secondary coil and the toroid (Behrend
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Therefore, by simple logic, one should look for a suitable dielectric material, the area of the plate as large as possible, and the distance between the plates as smaller as possible. Also, one should take into account the breakdown voltage of the used material and maybe some other limiting factors. Figure 2: MMC (Multi-Mini Capacitor)
A spark gap is, as the name indicates, a gap or an open circuit between two wires in the circuit, which becomes short circuited when there is a sufficient voltage build-up on its electrodes. This happens when the capacitor has excerted all its energy on the coil, thus, there is a maximum charge in the coil, which causes a spark that makes a short circuit in the spark gap.
Essentially, a spark gap is a switch between the primary transformer and the primary coil. When there is an open circuit, a capacitor will charge from the primary transformer and, consequently, when there is a short circuit, a capacitor will discharge on the primary coil. Figure 3: Static type spark

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