# Designing a Tesla Coil

#### Article By : How to Design a Tesla Coil Before people knew about electricity, many natural phenomena appeared as supernatural events caused by angry gods. Fortunately, people today know physics laws and they can operate with them according to their needs without problems.

A Tesla coil is a resonant circuit composed by two LC circuits, inductively coupled. In other words, it’s a transformer with a primary circuit and secondary circuits that can raise the electrical voltage to produce sparks. Under normal conditions, the air can be considered an insulator. A voltage applied between two isolated points does not cause the passage of any electrical current. If the voltage is increased, the electric field can become intense enough to receive the energy for ionizing other particles. The phenomenon is amplified with a progressive increase in moving ions. An electric current is established with heating of the area that causes further ionization of the air. A highly ionized gaseous channel is created, which acts as an electrical conductor, capable of sustaining an electric arc. The spark has an intense glow in a very short duration on a zigzag path, with a detonating sound. Lightning is a spark of great intensity. To trigger the spark, the electric field must exceed the rigidity threshold of the dielectric. For standard air, it’s about 3 kV/mm, but it decreases easily with humidity. To produce a spark of 10 cm, you must supply a voltage of about 300,000 V (300 kV).

Length of spark
With this very general formula, you can measure the voltage between two conductors by measuring the length of the sparks. When a potential difference is applied between two electrodes, an electric field is formed:

E = V * d

Where “V” is the voltage and “d” is the distance between the electrodes. For each material, there is a value, known as the breaking point, which represents the minimum electric field necessary to trigger a spark. To generate a spark of 1 cm, it is necessary to apply 30 kV. To know the voltage between two electrodes, simply multiply the length of the spark (in centimeters) by 30 kV, at a temperature of 25°C with dry air. This method works with two spherical electrodes. The value may vary based on pressure and humidity. As shown in Figure 1, it is really hard to generate big sparks. For a spark of 10 cm, it needs a voltage of 300,000 V, and for a spark of half a meter, you must supply about 1,500,000 V — really very dangerous.

Figure 1: Graph of the length of spark vs. voltage

It’s very impressive how nature can produce very big lightning bolts of millions of volts!

How does it work?

We know that a Tesla coil, created by Nikola Tesla, is a special resonant transformer with two coupled coils. A Tesla coil transformer operates differently than a traditional transformer with an iron core. In a conventional transformer, the two coils generate a voltage gain, which depends on the ratio of the number of turns. In a Tesla coil, on the other hand, the gain can be much larger because it is proportional to: √L2/L1.

The right balance between the individual parts allows a coupling capable of generating an electromagnetic wave suitable of lighting a luminescence lamp. It has an air core. Its operating frequency is between 50 KHz and 30 MHz. The coil transfers energy from the primary to the secondary. The voltage produced on the secondary increases until all the energy of the primary circuit has been transferred to the secondary one. The system is based on an RLC group and on a sinusoidal generator, as shown in Figure 2. An RLC circuit is an electrical circuit consisting of a resistor (R), an inductor (L), and a capacitor (C), connected in series. The transformer on air steps the input voltage up 100× to create a high voltage. After a few seconds, the voltage is high enough to fire the spark gap. The capacitor and the primary coil of the second transformer then form a resonant circuit. The secondary transformer coil is attached to a toroid, representing capacitor connected to ground. It also forms a resonant circuit with the same resonant frequency. The energy is gradually transferred from the first circuit to the second, then the spark gap stops conducting, leaving all the energy in the toroid circuit. Once the spark gap stops conducting, it takes a while for the voltage to build up enough for it to fire again.

Figure 2: An RLC circuit and the graph of its output, in the domain of frequency

The example of the figure consists of a resistor of 10 Ω (it determines the Q factor of circuit), a capacitor of 47 pF, and an inductor of 20 mH. To calculate the frequency of resonance of the circuit (in the example, it’s 164,155.78 Hz) you can use the formula shown in the box. If the RLC circuit is supplied exactly at its resonance frequency, on the inductor, we obtain a much higher voltage than that which is applied to the input. In these conditions, the circuit is, for the voltage generator, a perfectly resistive load. For these characteristics, we understand that the construction of the coils cannot be random but must be the result of precise and accurate calculus and formulas.

General schematic

Figure 3 shows a general but fully working schematic of a Tesla coil. The spinterometer and the capacitor (tank) can be mounted according to two different configurations. Let’s illustrate its components. The construction is not hard, but it requires care.

Figure 3: General schematic of the Tesla coil

The transformer T1 increases and elevates the input voltage to about 10 kV. This component is usually used to illuminate advertising signs with neon. You cannot use a traditional transformer. The capacitor C1, a Leyda’s bottle or a high-voltage capacitor, is connected in parallel to the secondary of the transformer. C1 charges and discharges its voltage at the frequency of the input voltage. It’s interesting to note that the input voltage can be also a DC voltage (but without the first transformer). When the difference of the potential on C1 exceeds the limits imposed by the spinterometer, a spark occurs between its terminals and a strong current flows through L1, discharging the capacitor. The spark closes the circuit. L1 and L2 are two components of a transformer — L1 is the primary and L2 is the secondary. On the terminals of L2, a very high voltage will be present. The power of the current on the coils depends on the capacity of C1. You can connect several capacitors in parallel. It’s very important that this component be suitable for the used voltages. On the other hand, you can connect in series and in parallel many capacitors to obtain the requested operative voltage.

Construction

As said before, the transformer T1 works as elevator of the input voltage. Be careful when handling it. As shown in Figure 4, the primary coil L1 is made with a thick wire wrapped around to plastic support with a diameter of 25 cm. The construction of L2 is very tedious. You can use a long plastic tube with a diameter of 12 cm. For optimal performance, it’s a good idea to treat the support with a plastic paint. The coil is composed by 2,000 turns of enameled wire of 0.4 mm (26 AWG).

Figure 4: Design and measurements of the coils

The capacitors must be chosen and built with care. You cannot use normal capacitors. The difference of potential is very high and the components could be destroyed. It can follow the project of a Leyden jar or you can connect together many polyester capacitors in series/parallel to obtain the maximum amount of capacity and voltage of at least 15,000 V. The capacitors must not be polarized. You can build a very efficient capacitor using two aluminum foil glued to a glass plate, in the opposite faces. With the dimensions of 50 × 50 cm, and a thickness of glass of 3 mm, you can get a capacitor of 7,378 pF. Glass has a very high dielectric constant. Anyway, this capacitor can be smaller. Figure 5 shows different examples of high-voltage capacitors.

Figure 5: Different examples of high-voltage capacitors

The spinterometer is a very easy component and is very important. It is a device used to generate electrical discharges in the air through two electrodes. It consists of two spheres. The distance between the terminals can be progressively reduced until the intensity of the electric field exceeds the dielectric rigidity value of the air and a spark occurs. You can see an example of a spinterometer in Figure 6.

Figure 6: Example of a spinterometer

During the construction, pay attention to insulate the critical parts of the circuit.

Use

When the construction is done, you can soon test the device. Be careful with any operations. The setup must be executed without electric connection. The sparks could be very painful. When the device is turned off, you can adjust the distance between the two spheres of the spinterometer to get a spark. To adjust the spark, move the two spheres away about 5 cm apart. Then approach the electrodes in small steps, turning off the device each time. The power of the sparks is proportional to the capacity of the capacitor. Once you get the sparks in the spinterometer, the secondary coil is ready to produce a special effect. From its top, you can produce large sparks, approaching metal objects to the sphere on the coil. You must keep them with a long insulated handle (wood or plastic). The length of the sparks (electric arcs) is proportional to voltage across the secondary coil. Don’t touch any part of the circuit with your hands. A spark of 20 cm is a very good result.

Tuning

The Tesla coil is similar to a radio receiver. It has to tune to the resonance frequency to get the best performance from it. To improve the efficiency of the device, we suggest the following solutions:

• Increase or decrease the number of turns of the primary coil.

• Increase or decrease the number of turns of the secondary coil.

• Move closer or further away the two spheres of the spinterometer among them by some millimeters (remember to switch off the power).

• Increase as much as possible the capacity of the tank of capacitors.

• Change the connection on different circles on the primary coil, as shown in Figure 7.

• Use good quality materials and good components.

Figure 7: You can improve the coupling of the LC circuit by changing the value of inductance of the primary coil with a different position of the connection.

Conclusion

There are many solutions to build a Tesla coil. This is probably the easiest one. Be careful while you work with these circuits, as the voltage is very high. During the operation of the Tesla coil, a strong ozone smell is left in the air. Eventually, you can build a smaller version of the device and then you can increase the power of the Tesla coil. In Figure 8, you can see a complete Tesla coil. In it, we can distinguish (from left to right):

• the transformer (230 V to 10,000 V)
• the HV capacitor
• the spinterometer
• the two coils (primary and secondary)

Figure 8: A complete Tesla coil 