Editing Tesla coil (section)

==Operation==
[[File:Teslova cívka v provozu.JPG|thumb|upright=1.3|Homemade Tesla coil in operation, showing [[brush discharge]]s from the toroid. The high [[electric field]] causes the air around the high-voltage terminal to [[ionization|ionize]] and conduct electricity, allowing electricity to leak into the air in colorful [[corona discharge]]s, [[brush discharge]]s and [[streamer discharge|streamer arcs]]. Tesla coils are used for entertainment at science museums and public events, and for special effects in movies and television.]]
[[Image:Tesla coil circuit.svg|thumb|Unipolar Tesla coil circuit. ''C2'' is not an actual capacitor but represents the capacitance of the secondary windings ''L2'', plus the capacitance to ground of the toroid electrode ''E''.]]

A Tesla coil is a [[radio frequency]] [[electronic oscillator|oscillator]] that drives an air-core double-tuned [[resonant inductive coupling|resonant transformer]] to produce high voltages at low currents.<ref name="Tilbury1"/><ref name="Haddad"/><ref name="Naidu"/><ref name="Sprott"/><ref name="Anderson"/><ref name="Denicolai"/> Tesla's original circuits and most modern coils use a simple [[spark gap]] to excite oscillations in the tuned transformer. More sophisticated designs use [[transistor]] or [[thyristor]]<ref name="Haddad"/> switches or [[vacuum tube]] [[electronic oscillator]]s to drive the resonant transformer.

Tesla coils can produce output voltages from 50&nbsp;[[kilovolt]]s to several million volts for large coils.<ref name="Haddad"/><ref name="Sprott"/><ref name="Denicolai"/> The alternating current output is in the [[low frequency|low radio frequency]] range, usually between 50&nbsp;kHz and 1&nbsp;MHz.<ref name="Sprott"/><ref name="Denicolai"/> Although some oscillator-driven coils generate a continuous [[alternating current]], most Tesla coils have a pulsed output;<ref name="Haddad"/> the high voltage consists of a rapid string of pulses of radio frequency alternating current.

The common spark-excited Tesla coil circuit, shown below, consists of these components:<ref name="Naidu"/><ref name="Denicolai2"/>
* A high-voltage supply [[transformer]] ''(T)'', to step the AC mains voltage up to a high enough voltage to jump the spark gap. Typical voltages are between 5 and 30 kilovolts (kV).<ref name="Denicolai2"/>
* A [[capacitor]] ''(C1)'' that forms a tuned circuit with the [[primary winding]] ''L1'' of the Tesla transformer
* A [[spark gap]] ''(SG)'' that acts as a switch in the primary circuit
* The Tesla coil ''(L1, L2)'', an air-core double-tuned [[resonant transformer]], which generates the high output voltage.
* Optionally, a capacitive electrode (top load) ''(E)'' in the form of a smooth metal sphere or [[torus]] attached to the secondary terminal of the coil. Its large surface area suppresses premature air breakdown and arc discharges, increasing the [[Q factor]] and output voltage.

===Resonant transformer===
{{Further|Resonant inductive coupling}}
{{Further|Transformer types#Resonant transformer}}The specialized transformer used in the Tesla coil circuit ''(L1,L2)'', called a [[resonant transformer]], oscillation transformer, or radio-frequency (RF) transformer, functions differently from ordinary transformers used in AC power circuits.<ref name="Gerekos"/><ref name="Gottlieb"/><ref name="BurnettOperation"/> While an ordinary transformer is designed to ''transfer'' energy efficiently from primary to secondary winding, the resonant transformer is also designed to ''temporarily store'' electrical energy. Each winding has a [[capacitance]] across it and functions as an [[LC circuit]] (resonant circuit, [[tuned circuit]]), storing oscillating electrical energy, analogously to the way a [[tuning fork]] stores vibrational mechanical energy. The [[primary winding|primary coil]] ''(L1)'' consisting of a relatively few turns of heavy copper wire or tubing, is connected to a [[capacitor]] ''(C1)'' through the [[spark gap]] ''(SG)''.<ref name="Haddad"/><ref name="Naidu"/> The [[secondary winding|secondary coil]] ''(L2)'' consists of many turns (hundreds to thousands) of fine wire on a hollow cylindrical form inside the primary. The secondary is not connected to an actual capacitor, but it also functions as an LC circuit, the inductance of ''(L2)'' resonates with stray capacitance ''(C2)'', the sum of the stray [[parasitic capacitance]] between the windings of the coil, and the capacitance of the [[toroid]]al metal electrode attached to the high-voltage terminal. The primary and secondary circuits are tuned so that they have the same [[resonant frequency]],<ref name=":0">{{cite journal |last=Cvetić |first=Jovan M. |date=October 2016 |title=Tesla's High Voltage and High Frequency Generators with Oscillatory Circuits |journal=Serbian Journal of Electrical Engineering |volume=13 |issue=3 |pages=301–333 |doi=10.2298/SJEE1603301C |s2cid=55561957 |doi-access=free}}</ref> so they exchange energy, acting like a [[coupled oscillator]]; during each spark the stored energy rapidly oscillates back and forth between the primary and secondary.

The peculiar design of the coil is dictated by the need to achieve low resistive energy losses (high [[Q factor]]) at high frequencies,<ref name="Sprott"/> which results in the largest secondary voltages:

* Ordinary power transformers have an [[magnetic core|iron core]] to increase the magnetic coupling between the coils. However at high frequencies an iron core causes energy losses due to [[eddy current]]s and [[hysteresis]], so it is not used in the Tesla coil.<ref name="BurnettOperation"/>
* Ordinary transformers are designed to be "tightly coupled".  Both the primary and secondary are wound tightly around the iron core.  Due to the iron core and close proximity of the windings, they have a high [[mutual inductance]] ''(M)'', the [[coupling coefficient (inductors)|coupling coefficient]] is close to unity 0.95&nbsp;– 1.0, which means almost all the magnetic field of the primary winding passes through the secondary.<ref name="Gerekos"/><ref name="BurnettOperation"/> The Tesla transformer in contrast is "loosely coupled",<ref name="Haddad"/><ref name="BurnettOperation"/> the primary winding is larger in diameter and spaced apart from the secondary,<ref name="Naidu"/> so the mutual inductance is lower and the coupling coefficient is only 0.05 to 0.2.<ref name="BurnettCouplingCoefficient"/><ref name="Sprott"/> This means that only 5% to 20% of the magnetic field of the primary coil passes through the secondary when it is open circuited.<ref name="Haddad"/><ref name="Denicolai2"/> The loose coupling slows the exchange of energy between the primary and secondary coils, which allows the oscillating energy to stay in the secondary circuit longer before it returns to the primary and begins dissipating in the spark.
* Each winding is also limited to a single layer of wire, which reduces [[proximity effect (electromagnetism)|proximity effect]] losses. The primary carries very high currents. Since high-frequency current mostly flows on the surface of conductors due to [[skin effect]], it is often made of copper tubing or strip with a large surface area to reduce resistance, and its turns are spaced apart, which reduces proximity effect losses and arcing between turns.<ref name="BurnettParts"/><ref name="Gerekos1"/>

{{Multiple image
| total_width       = 400
| image1            = Homemade Tesla coil closeup.jpg
| caption1          = Unipolar coil design widely used in modern coils. The primary is the flat red spiral winding at bottom, the secondary is the vertical cylindrical coil wound with fine red wire. The high-voltage terminal is the aluminum [[torus]] at the top of the secondary coil.
| image2            = Bipolar Tesla transformer 1908.jpg
| caption2          = Bipolar coil, used in the early 20th century. There are two high-voltage output terminals, each connected to one end of the secondary, with a spark gap between them. The primary is 12 turns of heavy wire, which is located at the midpoint of the secondary to discourage arcs between the coils.
}}

The output circuit can have two forms:

* ''Unipolar'': One end of the secondary winding is connected to a single high-voltage terminal, the other end is [[ground (electricity)|grounded]]. This type is used in modern coils designed for entertainment. The primary winding is located near the bottom, low potential end of the secondary, to minimize arcs between the windings. Since the ground (Earth) serves as the return path for the high voltage, streamer arcs from the terminal tend to jump to any nearby grounded object.
* ''Bipolar'': Neither end of the secondary winding is grounded, and both are brought out to high-voltage terminals. The primary winding is located at the center of the secondary coil, equidistant between the two high potential terminals, to discourage arcing.

===Operation cycle===
The circuit operates in a rapidly repeating cycle in which the supply transformer ''(T)'' charges the primary capacitor ''(C1)'' up, which then discharges in a spark through the spark gap, creating a brief pulse of oscillating current in the primary circuit which excites a high oscillating voltage across the secondary:<ref name="Anderson"/><ref name="Denicolai2"/><ref name="BurnettOperation"/><ref name="Gerekos5"/>
# Current from the supply transformer ''(T)'' charges the capacitor ''(C1)'' to a high voltage.
# When the voltage across the capacitor reaches the [[breakdown voltage]] of the spark gap ''(SG)'' a spark starts, reducing the spark gap resistance to a very low value. This completes the primary circuit and current from the capacitor flows through the primary coil ''(L1)''. The current flows rapidly back and forth between the plates of the capacitor through the coil, generating radio frequency oscillating current in the primary circuit at the circuit's [[resonant frequency]].
# The oscillating [[magnetic field]] of the primary winding induces an oscillating current in the secondary winding ''(L2)'', by [[Faraday's law of induction]]. Over a number of cycles, the energy in the primary circuit is transferred to the secondary. The total energy in the tuned circuits is limited to the energy originally stored in the capacitor ''C1'', so as the oscillating voltage in the secondary increases in amplitude ("ring up") the oscillations in the primary decrease to zero. Although the ends of the secondary coil are open, it also acts as a tuned circuit due to the capacitance ''(C2)'', the sum of the [[parasitic capacitance]] between the turns of the coil plus the capacitance of the toroid electrode ''E''. Current flows rapidly back and forth through the secondary coil between its ends. Because of the small capacitance, the oscillating voltage across the secondary coil which appears on the output terminal is much larger than the primary voltage.
# The secondary current creates a magnetic field that induces voltage back in the primary coil, and over a number of additional cycles the energy is transferred back to the primary, causing the oscillating voltage in the secondary to decrease ("ring down"). This process repeats, the energy shifting rapidly back and forth between the primary and secondary tuned circuits. The oscillating currents in the primary and secondary gradually die out due to energy dissipated as heat in the spark gap and resistance of the coil.
# When the current through the spark gap is no longer sufficient to keep the air in the gap ionized, the spark stops ("quenches"), terminating the current in the primary circuit. The oscillating current in the secondary may continue for some time.
# The current from the supply transformer begins charging the capacitor ''C1'' again and the cycle repeats.

This entire cycle takes place very rapidly, the oscillations dying out in a time of the order of a millisecond. Each spark across the spark gap produces a pulse of damped sinusoidal high voltage at the output terminal of the coil. Each pulse dies out before the next spark occurs, so the coil generates a string of [[damped wave]]s, not a continuous sinusoidal voltage.<ref name="Anderson"/> The high voltage from the supply transformer that charges the capacitor is a 50 or 60&nbsp;Hz [[sine wave]]. Depending on how the spark gap is set, usually one or two sparks occur at the peak of each half-cycle of the mains current, so there are more than a hundred sparks per second. Thus the spark at the spark gap appears continuous, as do the high-voltage streamers from the top of the coil.

The supply transformer ''(T)'' secondary winding is connected across the primary tuned circuit. It might seem that the transformer would be a leakage path for the RF current, damping the oscillations. However its large [[inductance]] gives it a very high [[electrical impedance|impedance]] at the resonant frequency, so it acts as an open circuit to the oscillating current. If the supply transformer has inadequate [[short-circuit inductance]], radio frequency [[choke (electronics)|choke]]s are placed in its secondary leads to block the RF current.

===Oscillation frequency===
To produce the largest output voltage, the primary and secondary tuned circuits are adjusted to [[resonance]] with each other.<ref name="Sprott"/><ref name="Anderson"/><ref name="Gerekos"/> The [[resonant frequency|resonant frequencies]] of the primary and secondary circuits, <math>\scriptstyle f_1</math> and <math>\scriptstyle f_2</math>, are determined by the [[inductance]] and [[capacitance]] in each circuit:<ref name="Sprott"/><ref name="Anderson"/><ref name="Gerekos"/>
:<math>f_1 = {1 \over {2\pi \sqrt {L_1 C_1}}} \qquad \qquad f_2 = {1 \over {2\pi \sqrt {L_2 C_2}}}\,</math>

Generally the secondary is not adjustable, so the primary circuit is tuned, usually by a moveable tap on the primary coil L<sub>1</sub>, until it resonates at the same frequency as the secondary:
:<math>f = {1 \over {2\pi \sqrt {L_1 C_1}}} = {1 \over {2\pi \sqrt {L_2 C_2}}}\,</math>

Thus the condition for resonance between primary and secondary is:
:<math>L_1 C_1 = L_2 C_2\,</math>

The resonant frequency of Tesla coils is in the low [[radio frequency]] (RF) range, usually between 50&nbsp;kHz and 1&nbsp;MHz. However, because of the impulsive nature of the spark they produce broadband [[radio noise]], and without shielding can be a significant source of [[radio frequency interference|RFI]], interfering with nearby radio and television reception.

===Output voltage===
[[File:Teslacoil.jpg|thumb|upright=1.5|Large coil producing 3.5 meter (10 foot) streamer arcs, indicating a potential of millions of volts]]

In a resonant transformer the high voltage is produced by resonance; the output voltage is not proportional to the turns ratio, as in an ordinary transformer.<ref name="BurnettOperation"/><ref name="Gerekos3"/> It can be calculated approximately from [[conservation of energy]]. At the beginning of the cycle, when the spark starts, all of the energy in the primary circuit <math>W_1</math> is stored in the primary capacitor <math>C_1</math>. If <math>V_1</math> is the voltage at which the spark gap breaks down, which is usually close to the peak output voltage of the supply transformer ''T'', this energy is
:<math>W_1 = {1 \over 2}C_1V_1^2\,</math>

During the "ring up" this energy is transferred to the secondary circuit. Although some is lost as heat in the spark and other resistances, in modern coils, over 85% of the energy ends up in the secondary.<ref name="Anderson"/> At the peak (<math>V_2</math>) of the secondary sinusoidal voltage waveform, all the energy in the secondary <math>W_2</math> is stored in the capacitance <math>C_2</math> between the ends of the secondary coil
:<math>W_2 = {1 \over 2}C_2V_2^2\,</math>
Assuming no energy losses, <math>W_2\;=\;W_1</math>. Substituting into this equation and simplifying, the peak secondary voltage is<ref name="Sprott"/><ref name="Anderson"/><ref name="BurnettOperation"/>
{{Equation box 1 |indent =: |cellpadding=0 |border=1 |border colour=black |background colour=transparent |equation=<math>V_2 = V_1\sqrt{C_1 \over C_2} = V_1\sqrt{L_2 \over L_1}.</math>
}}
The second formula above is derived from the first using the resonance condition <math>L_1 C_1\;=\;L_2 C_2</math>.<ref name="BurnettOperation"/> Since the capacitance of the secondary coil is very small compared to the primary capacitor, the primary voltage is stepped up to a high value.<ref name="Anderson"/>

The above peak voltage is only achieved in coils in which air discharges do not occur; in coils which produce sparks, like entertainment coils, the peak voltage on the terminal is limited to the voltage at which the air [[electrical breakdown|breaks down]] and becomes conductive.<ref name="Anderson"/><ref name="BurnettOperation"/><ref name="BurnettParts"/> As the output voltage increases during each voltage pulse, it reaches the point where the air next to the high-voltage terminal [[ionization|ionizes]] and [[corona discharge|corona]], [[brush discharge]]s, and [[streamer discharge|streamer arcs]] break out from the terminal. This happens when the [[electric field]] strength exceeds the [[dielectric strength]] of the air, about 30&nbsp;kV per centimeter. Since the electric field is greatest at sharp points and edges, air discharges start at these points on the high-voltage terminal. The voltage on the high-voltage terminal cannot increase above the air breakdown voltage, because additional electric charge pumped into the terminal from the secondary winding just escapes into the air. The output voltage of open-air Tesla coils is limited to a few million volts by air breakdown,<ref name=":0"/> but higher voltages can be achieved by coils immersed in pressurized tanks of [[transformer oil|insulating oil]].

===Top load or "toroid" electrode===
[[File:OneTeslaTS DRSSTC Tesla Coil closeup.jpg|thumb|Solid state DRSSTC Tesla coil with pointed wire attached to toroid to produce [[brush discharge]] ]]

Most Tesla coil designs have a smooth spherical- or [[toroid]]al-shaped metal electrode on the high-voltage terminal. The electrode serves as one plate of a [[capacitor]], with the Earth as the other plate, forming the [[tuned circuit]] with the secondary winding. Although the "toroid" increases the secondary capacitance, which tends to reduce the peak voltage, its main effect is that its large-diameter curved surface reduces the [[potential gradient]] ([[electric field]]) at the high-voltage terminal; it functions similarly to a [[corona ring]], increasing the voltage threshold at which air discharges such as corona and brush discharges occur.<ref name="Denicolai5"/> Suppressing premature air breakdown and energy loss allows the voltage to build to higher values on the peaks of the waveform, creating longer, more spectacular streamers when air discharges finally occur.<ref name="BurnettOperation"/>

If the top electrode is large and smooth enough, the electric field at its surface may never get high enough even at the peak voltage to cause air breakdown, and air discharges will not occur. Some entertainment coils have a sharp "spark point" projecting from the torus to start discharges.<ref name="Denicolai5"/>