# TCBA - Tesla Coil Builders Association

Devoted to the construction, operation and theoretical analysis of the Tesla coil

# TCBA Volume 10 - Issue 1

## Page 14 of 18

### Electrical Engineering Department, California State University Long Beach, 1250 Bellflower Blvd., Long Beach, CA 90840-8002

[This paper involves the design and construction of a device for obtaining very high voltages at high frequency. The device, which is basically a high voltage/frequency resonant transformer, is known as a Tesla coil, the paper is specifically written around a five-kva unit designed and built in 1989. Covered topics include Tesla coil fundamentals, design, and implementation of design. The tank circuit components, secondary coil power control and instrumentation are described and functions discussed. The actual operation of the coil is discussed at the end of the paper.]

This paper is a physical and operational description of a large Tesla coil, a type of high frequency resonant transformer used to generate high voltages. It was invented by the noted scientist and engineer Nikola Tesla in the late nineteenth century. The Tesla coil circuit is a tuned LC resonant circuit. Both the primary and secondary parts of the circuit have inductive and capacitive components: the primary being capacitively dominant and the secondary inductively dominant.

The maximum energy is transferred(1) when L1C1 = L2C2: where

• L1 = primary inductance (small)
• C1 = primary capacitance (large)
• L2 = secondary inductance (large)
• C2 = secondary capacitance (small)

As the circuit is energized, the primary transformer charges the primary capacitor C1 until such a point that the voltage becomes great enough to jump across the spark gap. This energy enters the primary inductor and is coupled to the secondary inductor via mutual induction.(2) The mutual inductance of the system is governed by:(3)

Where M is the mutual inductance of the system and k is the coefficient of coupling between the primary and secondary.

As the energy of the capacitor is depleted, the spark gap ceases; the oscillations quickly damp out in the primary circuit as the secondary oscillates at its resonant frequency.(4) The output voltage can be roughly approximated by:(5)

Where V1 is the primary voltage and V2 is the secondary terminal voltage. This would be accurate if complete energy transfer between the primary and secondary occurred. None the less, it can be used for rough calculations. It can be seen that the voltage will be high at the secondary. The primary capacitance is 1 x 10E -7 farads and the secondary capacitance is on the order of 1 x 10E -11 farads.

A discharge on this order is long, thick, noisy, and has a charge density that can make it quite dangerous.

The project designed here was not based upon any particular design; the starting parameter was the ac line power capacity. Five kva was chosen as a good maximum power level because it was small enough to be obtained from most 220 volt electrical service plugs yet large enough to get good results.

The power transformer was custom built to match the power input required. It has a 220 volt input and draws about 30 amperes. The secondary supplies 15,000 volts at 0.40 amps. The transformer was made as a self-limiting high reactance saturable-core type. This eliminates the need for series reactance to limit the input current. It has primary taps for use at lower powers, and a heavily potted secondary to minimize breakdown. The transformer is built to withstand as high as 300 volts rms on the input.