Tesla Coil Theory

This page describes the theory of tesla coils and you find basic information about how a tesla coil works. The page only deals with principle function. Calculations needed for the design are in the design page.
What is a Tesla Coil?
What can you do with a Tesla Coil?
The inventor: Nikola Tesla
How does it work?
Information on important details
RF ground
Sparkgap information
Toroid information
About corona effects
About the skin effect
Different types of coils
Tesla magnifier systems
Bipolar tesla coils
Twin coil systems
Solid state coil systems
Basics
Capacitors
Inductivities
LC-Circuits
Some documents

What is a Tesla Coil?

A tesla coil is a special kind of transformer. It is an air cored transformer, that means no iron core is needed. Primary and secondary coils are mounted concentric. Voltage does not depend on the ratio of windings in secondary and primary, instead the voltage rise depends on resonance effects between primary and secondary. The secondary acts as receiver for the energy in the primary. The so called quarter wavelength theory, which means, that the secondary is wound to the quarter wavelength of the resonance frequency in the meantime has been disproved, although my coil is still built to that theory.
Resonance frequencies are typically between 50kHz and 500kHz. Output voltages may reach several 100 kV. If enough energy is feeded, voltage may rise up to the megavolt range. If voltage reaches a certain level, sparks will break out and form artificial lightning.

What can you do with a Tesla Coil?

People often ask: Why do you build a tesla coil? What's the sense? What can you do with it? For me it is the construction itself that makes a lot of fun and is a challenge to get it up and running. And of course the result of all that work are beautiful arcs and sparks - hopefully ;-).
Besides this you can also learn a lot about what Nikola Tesla worked on about 100 years ago.
Tesla coils have real applications in industry and in entertainment. There exist commercial companies dealing with that stuff. See my links page for references.
All in all, this is a very fascinating hobby and a challenge to get it working. I'm already looking forward to my next larger model.

The inventor: Nikola Tesla

Nikola Tesla was born on July 9/10, 1856 in Smiljan, Croatia. He was one of the most productive inventors. He emigrated to the United States in 1884 and worked for the Westinghouse Electric Company in Pittsburgh. Tesla was the man who predicted the future of alternating current (AC), opposite to the direct current (DC) systems propageted by Edison. In 1891 the tesla coil was patented. In fact, the tesla coil is the first form of radio. The difference is, that Tesla wanted to transport energy for the purpose of energy transport via a wireless media. Our radios and TV sets are also nothing else than receivers of energy, which is produced at high frequency at the sender and received by our antennas. The difference is the low power at the receiver side, as only information is needed to be transported. Tesla was successful in his research, but never got enough funding to complete his work.
In 1943, Tesla was officially recognized as the inventor of the era of wireless energy transport, which made him the official inventor of radio, not Marconi. Most people don't know that and Marconi is still the name in mind when talking about the invention of radio.
Nikola Telsa died on Jan. 7, 1943, in New York City.
For further information see my links page.

How does it work?

This chapter describes how a tesla transformer works. Only the simple type of transformer is discussed. The basic circuit of a Tesla Coil is very simple and only consists of few parts. Following diagram shows the simplest circuit. This diagram omits some parts like safety sparkgaps and the filter circuit needed for protection purposes.


The transformer is used to convert the mains voltage of 220V to a high voltage of 8kV to 15kV or even higher for very large coils. Different types of transformers may be used. See the transformer chapter. Beginners typically use neon sign transformers and so did I. The picture shows a center tapped neon transformer.
The high voltage of the transformer output charges the capacitor through the primary winding. This charging lasts until the breakdown voltage of the sparkgap is reached. At this point, the sparkgap begins to fire and acts as a very fast switch which now closes the red painted so called primary tank circuit. This primary tank circuit acts as a resonant LC circuit with its resonance frequency determined by the L and C values of primary coil and capacitor.

The energy stored in the capacitor is now transferred to the secondary. The secondary also builds an LC ciruit together with the toroid on its top. This toroid plays the role of the capacitor. The secondary circuit must be in tune with the primary circuit to allow for proper energy transfer. As the energy in the secondary increases now very fast, a resonance is created in the secondary, with its base connected to the RF ground. This ground is a dedicated ground for this purpose. Never connect to your utilities ground. The maximum voltage is found at the top of the secondary, at the toroid. If the toroid is not too big, this voltage will lead to a spark breakout, which consumes the energy supplied by the primary. The energy in the primary tank will decrease and the voltage will be too low to keep the sparkgaps arc running. The capacitors will be charged in the next half wave until the sparkgap will breakdown again.
The same mechanism repeats every half cycle using the sparkgap as some kind of automatic switch.

Information on important details

RF Ground

For proper operation of a coil, it is important to have a good RF ground. At the bottom of the secondary there are flowing very high currents of several amperes, depending on the power level of the coil. These currents are of high frequency, too. RF ground must therefore be of very low impedance and also be dedicated for your coil use. Never connect a tesla coil to the normal house ground. This may result in destruction of electrical equipment and even cause damage to the electrical installation. The good ground connection also is needed for a good performance of the coil.

Sparkgap information

The main spargkap is a very important detail of the whole system. There exist different types of sparkgaps. See the design page for a short description and an overview, which type to select. This chapter will explain some important terms used when talking about sparkgaps.
A sparkgap can be seen as a very fast switch (microseconds range for closing a circuit). It also has very low loss, especially if the current is high and the gap is low distance. Quenching is an essential detail in sparkgap technology. It is about extinguishing the arc in a sparkgap. Starting an arc is much easier than stopping. There are 2 electrodes of a given shape and distance. When applying a voltage, an electrical field is setup. This field depends on the shape of the electrodes and the voltage applied (see also corona info). At a certain level of voltage, this field will be too strong and a breakdown will occur. When the sparkgap is firing, the current produces a lot of heat and hot ions, which are a very low resistance path. When you decrease voltage now, there are still lots of hot ions in the gap. This results in a far lower voltage needed to fire the gap. Either, the gap will not switch off, which will prevent the capactitor from being loaded again, or the voltage of the next ignition will be much lower, resulting in less energy stored in the capacitor. By removing hot ions as fast as possible from the gap, you can achieve, that your gaps stay clean. Quenching is the term for this. For example, you can blow an airflow through the gaps. For techniques of quenching, see the design page.
Dwell time also is used often in sparkgap terminology. This applies to rotary sparkgaps, where the design allows to control the time, for which electrodes are in a position to allow firing the gap.

Toroid information

As mentioned above, the secondary coil needs a capacitive load on its top to build an LC circuit. This capacitive load is built by a metal object connected to the upper end of the secondary. The object forms one "plate" of this capacitor, while the other side is the surrounding environment.
This object may be of any shape, but the toroid form prevents breakout of sparks for higher voltages than for example a simple sphere form. This is because of the shape of the electric field around the toroid. Formulas can be found in the design page and construction hints are in the construction page.
The capacity of the toroid together with the secondary coil inductance forms the secondary LC circuit. In addition to the capacity of the toroid there is also a self capacity of the secondary coil, which has to be taken into account.

About corona effects

Corona occurs when the voltage on an object exceeds the breakdown voltage of the medium it is contained in, for example air. Corona effect depends on the form of the object. In general, the smaller the radius, the earlier corona discharges will happen. Corona effects are seen as some blue light around the object. It is an unwanted effect, as this always means losses of energy. These losses lead to warmup, which for example in capacitors may be destructive. Reducing corona can be done by introducing smooth forms instead of sharp corners. This reduces the electrical field strength, and higher voltages will be needed for corona discharges to start. Another means to reduce the effect is to immerse the object into oil. This is done for example with capacitors and transformers.

About the skin effect

While DC and low frequency AC will use the complete cross section of the wire for current flow, this is no longer true for high frequencies. For high frequencies the so called skin effect occurs. This effect is caused by the fact, that within the wire, the currentflow induces a magnetic field from the center to the outer wire diameter. For high frequencies, this field is changing very fast. As changing magnetic fields induce voltages, this fastly changing field itself induces voltages within the wire. The current caused by these voltages overlays the actual main current, resulting in higher current at the outer diameter, while current in the center of the wire is reduced.
This means, that at high frequencies, the current in a wire will only use the outer regions (the skin) of the wire, while inside the wire, almost no current will flow. The effect depends on the magnetic permeability of the wire material.
The picture on the left explains the skin effect. The red arrow is the main (AC!) current flow through the wire. This current induces a magnetic field indicated by the blue ellipse. This field itself will induce currents, because it is changing. These currents are shown by the violet circles. The direction of these currents will be opposite in the center and therefore decrease the resulting current, while at the outer range of the wire the current will be increased.
The depth of current penetration into the wire can be calculated by

where is the frequency of the current, is the electrical conductivity of the wire and is the permeability of the wire material.

Different types of coils

There exist different types of coils. The basic type is the one in discussion in this page. Other types are for example the bipolar type, the twin coil systems and the magnifier systems. Here is a short description, but no further details. Maybe, I will start building these types of systems at a later time.

Tesla magnifier systems

Magnifier systems use a third coil (called the tertiary), which is coupled to the secondary and placed in some distance. This tertiary carries the toroid and is connected with its base to the top of the secondary. There is no magnetic coupling of the tertiary to the secondary. This means also, that energy from the tertiary may not be fed back into the primary tank.

Bipolar tesla coils

The bipolar version is a 1/2 wave type of tesla coil. The secondary is mounted horizontally, and the primary is centered at the secondary. The secondary produces voltage peaks at its discharge electrodes at both ends, which stay open. The voltage in the center is zero. The primary sometimes exists only of a pair of taps on the secondary.

Twin coil systems

Twin coil systems use 2 identical secondary coils with toroids, but wound in opposite direction. Their primaries are constructed the same way and fed by the same currents, i.e. they are in the same tank circuit, but winding direction is different for both coils. This type of coil may produce long discharges between both toroids.

Solid state coil systems

The solid state coil systems use solid state elements, i.e. transistors etc. instead of a sparkgap as switch. This works up to certain levels of power, but the good old sparkgap is still the only way to achieve the really high power levels needed for the big coils.

Basics

This chapter provides some general basics for the theoretical background in a very short form.

Capacitors

Capacitors are used to store energy in form of an electrical field between 2 elements of different electrical charge. These elements may be of any shape, for example 2 aluminium plates parallel to each other with some fix space. This fix space may be just air. If it is filled with some material, the capacity will change. This material is called the dielectricum and the change of capacity is reflected in the so called dielectric constant, which is the ratio of the capacity with the dielectricum in between and the capacity with air. Different materials have different dielectric constants.
The capacity of the above 2 parallel aluminium plates can be calculated as follows:

C is the capacity in Farad, A is the overlapping area of the plates in square meters, d is the distance of the plates in m, = dielectric constant, = dielectric number of the material between the plates. For multiple plates stacked alternately, this formula changes to

where n is the number of plates used.
For calculating the capacity of a PE plate stack capacitor, also the following formula may be used:

This formula is found on most tesla webpages. C is the capacity in pF, A is the area of the plates in square centimeters, n is the number of plates, d is the distance in mm.
Important: this formula is only valid for PE polyethylene dielectricum!.

Capacitors in series and in parallel circuits

Capacitors may be combined in series or parallel. The result of this is a new value of capacity.
Parallel connection
When connecting capacitors in parallel, the resulting capacity is the sum of all capacities.

Series connection
When connecting capacitors in series, the resulting capacity is calculated as follows:

Inductivities

Inductivities are also able to store energy. Energy is stored in a magnetic field. The inductivity of a coil depends on several factors. Also the form of the coil has influence. The easiest calculation may be done for coil forms, which have a magnetic field flow, which is closed, for example a single layer coil wound in a toroid form. When you spread this coil form, you get a cylinder coil form. For very long coils, i.e. the length is much longer than the diameter, the formula to calculate the inductivity is very simple:

A is the cross section of the coil in square meters, l is the length of the coil in meters. The factor is the magnetic field constant: 1,256637 exp-6 H/m. The factor is the permeability number of the material in the magnetic field of the coil, i.e. the core of the coil.
Using single layer coils with shorter length, a correction factor needs to be introduced. This is shown in the following graph:

With the new factor included the formula is changed to

The product of and is also called the permeability of of a material.
In tesla coil applications, the secondary will typically have a range for d/l of 0,2 to 0,33, i.e. the coil will be seen as an almost very long coil, with factor K ranging from about 0,87 to 0,91, as indicated by the blue area in the graph.
For the calculation of the inductivity of a single layer coil, also the so called Wheeler equation exists. This is as follows:

In this formula, L is the inductance in microhenry, R is the radius of the coil in inches, N is the number of turns and H is the height of the coil in inches.

Inductivities in series and in parallel circuits

Inductivities may be combined in series or parallel, too. The result is a new value of inductivity.
Parallel connection
When connecting inductivities in parallel, the resulting inductivity is calculated as follows:

Series connection
When connecting capacitors in series, the resulting inductivity is the sum of all inductivities.

LC-Circuits

When combining capacitors and inductivities in a single circuit, we get so called LC-circuits. These circuits show resonance effects at a given frequency. These effects are used in every radio for tuning to a sender. When feeded with an input at resonance frequency, a parallel LC-circuit shows a behaviour called resonant rise. This means, that both elements, the capacitor and the inductivity have the same reactance at this frequency and the circuit begins to oscillate. The cacapcitor gets loaded and stores the energy. When loaded, it begins to discharge via the inductivity. The current now builds up a magnetic field, which itself stores the energy now. This field breaks down and creates a current in the other direction. This current again charges the capacitor. When the capacitor is charged, the same game happens again. This would be endless, but as the components have losses (resistance of wires, dielectric losses), the wave will be damped and lose energy.
The energy feeded into the LC-circuit may be provided by a magnetic field with a special frequency. This is done by radio senders. Energy is transported via the air and very small amounts of this energy are catched by an antenna and feeded to an LC-circuit in your radio. When tuning to a sender, you just vary the capacity of the LC-circuit, which results in a change of the resonance frequency. You also could change the inductivity value to tune your radio.
The tesla coil uses the same effect. You have the primary circuit, which may be frequency adjusted by tapping the primary inductivity, while your capacitor has a fixed value. The primary acts as the sender and its magnetic field is coupled into the secondary, which acts as the receiver.

Some documents

In this section, you find some documents I have written. They are in zipped MS Word format for download and will be available soon.

Toroid diameter ratios About the influence of the ratio of inner and outer diameter of the toroid on the capacity.
Max voltage expectation About the maximum voltage to be expected for a tesla coil system.
© 1999 by Herbert Mehlhose