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Tesla Coil Theory
www.GardenBallistics.co.nr
James Kelly 2008
Contents: Tesla coil theory
Introduction
Getting started
The Tesla coil
How a Tesla coil works
The components of a Tesla coil
Mains voltage supply + Variac
Mains RFI/EMI filter
High voltage power supply
Power factor correction (PFC)
RF RC low pass filter + safety spark gaps
Grounding
Static Spark gap
Resonant matching of the primary and secondary circuits
Tank capacitor
Primary coil + strike rail
Secondary coil + Top load
Theory of a Tesla coil
Introduction
A Tesla Coil is a device invented by the scientist Nikola Tesla (1856-1943). It is a high voltage,
high frequency, resonant transformer capable of producing many thousands of volts in the form
of lightening like discharges. It was primarily built for experiments investigating x-rays, high
frequency alternating current phenomena, electrotherapy, and wireless power for electric power
transmission. With this coil, Tesla was able to generate voltages of such magnitude, they would
shoot out of the apparatus as bolts of lightning!
Today, Tesla Coils are mainly built by amateur enthusiasts all over the world for the sole reason
of the exhilarating thrill of producing their very own lightning.
Getting started
The first question you should probably ask yourself is “What size of Tesla coil should I build?”
This depends on how much money you are willing to spend and how easily you can get hold of
the materials and components needed. I personally would advise starting off with a small Tesla
coil as a “first attempt model” to get yourself familiar with designing, building and using a Tesla
coil. This will allow you to make mistakes and learn valuable lessons when you come to build a
larger, more proficient model in the future. These devices are not easy to design and build; they
require a lot of patience and attention to detail to obtain an effective, high performing Tesla coil
that’s worth the time and money spent on the project.
The Tesla coil
There are many types of Tesla coil and there is no specific definition for a particular design that
represents a true Tesla coil. The main types are DC resonant charging, AC resonant charging,
solid state Tesla coils. I am concentrating on an AC resonant charging Tesla coil, one of the
most common design types utilised by enthusiasts.
The basic circuit diagram for an AC resonant charging Tesla coil is shown below.
Neon Sign
Transformer
Mains
Voltage
AC
~
~10,000V
240V
Tank
Capacitor
High voltage,
high frequency
discharge
Toroidal
Top load
Secondary
Coil
Static
Spark Gap
Primary
Coil
RF
Ground
RF
Ground
A Tesla coil is made up of a small number of major parts. Firstly, a high voltage power supply
is needed to convert 240 volts AC mains voltage up around 10,000 volts AC. These are usually
neon sign transformers (NST’s). A high voltage tank capacitor is required to store charge in
the circuit and a high voltage switch in the form of a static spark gap is needed to pulse
switch the charge in the capacitor through the primary coil. A secondary coil supporting a
metallic toroid or top load is coupled with the primary.
How a Tesla coil works
As the capacitor charges from the high voltage power supply, the potential across the static
spark gap electrodes increases until the air between the spark gap ionises allowing a low
resistance path for the current to flow through; the ‘switch’ is closed. Once the capacitor has
discharged, the potential across the spark gap is no longer sufficient to maintain ionised air
between the electrodes and the ‘switch’ is open. This happens hundreds of times a second
producing high frequency (radio frequency) AC current through the primary coil.
The capacitor and primary coil produces an LCR (inductor-capacitor-resistor) circuit that
resonates at a high resonant frequency. The secondary coil and top load also create an LCR
circuit that must have a resonant frequency equal to the resonant frequency of the primary
circuit. The high resonant frequency coupling of the primary coil with the secondary coil induces
very high voltage spikes in the secondary coil.
The top load allows a uniform electric charge distribution to build up and lightning like strikes are
produced from this to a point of lower potential, in most cases ground.
The coupling between the primary and secondary coils do not act in the same way as a normal
transformer coil would but works by high frequency resonant climbing or charging to induce
extremely high voltages. The true physics is still not completely understood but can be modelled
experimentally.
The components of a Tesla coil
A realistic Tesla coil requires many other additional components than described above to
operate efficiently and safely. The complete circuit diagram of my Tesla coil is shown below.
Power factor
correction Neon Sign
Variac
capacitor Transformer
RF mains
filter
Tank
Capacitor
Simplified Terry
filter
Toroidal
Top load
~
Static
Spark Gap
LINE
AC
LOAD
Capacitance
between top
load and RF
ground
Mains
Ground
RF
Ground
Mains
Ground
RF
Ground
Primary
Coil
Secondary
Coil
RF
Ground
Below, I will describe in detail each component needed, how they work and why they are
needed.
Mains voltage supply + Variac
This is simply the main electricity socket in your house which supplies 240VAC @ 50Hz in the
UK and 120VAC @ 60Hz in the U.S.
A variable transformer (or variac) is often used in line with the mains supply to allow a variable
input for the high voltage power supply. It allows for different power outputs of the Tesla coil and
allows you to gradually turn the Tesla coil up to full power. Simply turning on a Tesla coil at full
power can put a large strain on it components.
Mains RFI/EMI filter
A mains or line filter is a commercially available device that filters
out radio frequency noise and electromagnetic interference from
a voltage line. They are often used in household appliances to
filter out interference from the mains side line and stopping the
interference from getting into the appliance which can potentially
cause damage to the device. In the case of using it in a Tesla
coil circuit, it must be wired in reverse. In other words, the line
and load terminals need to be wired the other way round – line
for load and load for line. This is because we need to prevent
radio frequency produced by the Tesla coil from entering the
mains side line which can damage anything plugged into your house and neighbours houses
mains sockets. An RFI/EMI filter is a must! The casing of the RFI mains filter should be
connected to the mains ground (NOT the RF ground).
High voltage power supply
There are a number of alternative power supplies that can be used for Tesla coils. The most
common power supply used is a neon sign transformer (NST). These are used to power neon
gas tubes for commercial sign purposes. Their voltage output can vary from about 2,000V to
15,000V and can have a current output from about 10mA to 120mA. There are two different
types of NST the older iron cored and the newer switch mode NST. For Tesla coil use the older
type is ideal as they have their own built in current limiting magnetic shunt, are secondary
midpoint grounded, have no GFI ground fault protection, they can survive high radio frequency
current and can run indefinitely in short-circuit and no-load conditions. They are very resilient to
harsh electrical conditions – great for Tesla coils! The newer switch mode NST’s are not ideal
for Tesla coil use as they have built in GFI ground fault protection, short circuit protection and
their components cannot withstand high frequency radio currents – they will simply be fried if
they work at all under Tesla coil conditions!
NST – 10,000Volt @ 60mA
Microwave Oven Transformer
Pole-Pig Transformer
Other high voltage power supplies that can be utilised for Tesla coil use are Ignition coils from
cars, oil burner igniters, fly-back transformers, microwave oven transformers, medical X-ray
transformers and power distribution transformers, also known as pole-pig transformers.
Power factor correction (PFC)
Power factor correction is provided by a non-polar capacitor in parallel with the mains supply
voltage lines. PFC shifts the voltage-amperes (VA) rating of the high voltage power supply used
closer to its actual input and/or output power and reduces the draw current of the transformer.
Reducing the current is beneficial as the size and rating of the components used in the circuit
can be less, e.g. switches, RFI filter etc. Without PFC the circuit components would have to
stand twice the current or more. Also large power losses due resistance in the wires can be
reduced this way P  I 2 R .


To calculate the capacitance needed for 100% PFC you first need to calculate the transformer
input impedance either from the values written on the transformer or using a multimeter with
impedance measurement function. Then using Z 
Now using C 
1
Z
V
, calculate a value for the impedance.
I
where   2f , calculate a value for the capacitance.
Note that this is the theoretical PFC capacitance value for the transformer only and may not
produce the optimal value for the PFC for spark gap Tesla coil circuits as the operational
frequency of the spark gap affects the power factor as well. Some neon sign transformers
already have built in PFC capacitors.
RF RC low pass filter + safety spark gaps
High voltage radio frequency (RF) RC-style low
pass filters are the NST’s protection circuit. They are
another essential component to ensure the NST
does not get damaged from the harsh electrical
conditions of the Tesla coil circuit. They filter out
high frequency radio currents and high voltage
peaks from the primary circuit, stopping them from
getting to the NST where the RF current and high
voltage peaks will damage the internal windings and
kill your NST.
There are many designs for an NST protection circuit that use various combinations of resistors,
capacitors and inductors (chokes). Some people implement circuits that use inductor chokes for
filtering out RF currents and high voltage peaks. I personally believe that this is not a good idea
because while they are effective at isolating the NST from the tank resonant frequency, they do
subject the NST to high voltage peaks at the resonant frequency of the LC network. Damping
resistors can help somewhat to completely eliminate these high voltage peaks but these series
resistors would have to have such a high resistance that they would waste far too much power
to be useful.
However, there is a well known RC low pass filter circuit that has been used by many Tesla coil
enthusiasts and has proven very effective of time. This circuit is called a Terry Filter named after
the person that developed it Terry Fritz. Below is the circuit diagram of the Terry Filter for 9kV,
12kV and 15kV Tesla coils.
The safety spark gaps are used as a final resort to protect your NST from high voltage peaks
produced in the primary circuit of the Tesla coil. These safety spark gaps need to be set with an
air gap distance between their electrodes such that, using only your NST across them, they only
just don’t arc.
Also notice how the NST’s centre tapped ground of the secondary windings are connected. This
ground line must be connected to an RF ground separate to the mains ground. A large metal
pole in the ground is ideal for this. DO NOT connect this ground to mains ground as this is
extremely dangerous!
Grounding
In Tesla coils there two types of ground point, the mains ground and the RF ground. Mains
ground is simply the ground pin on and mains supply. The RF ground is a separate ground to
mains usually obtained by connecting to a large metallic rod rammed deep into the ground
outside.
The only things that should be grounded to the mains ground are the components and devices
on the mains side (before the HV transformer) that are safe to touch such as switches, dials,
RFI/EMI filter ground etc.
The high voltage secondary side of the HV transformer (primary circuit side) must not be
grounded at all as seen in some schematics. However, the centre midpoint grounded NST
connection should be connected to RF grounded.
The Tesla coil secondary circuit should be grounded directly to a low impedance, low
inductance RF ground from the bottom of the secondary coil. This separate ground will
adequately sink RF current and voltage. If the mains ground was used, the high voltage high
frequency would easily damage electrical equipment in your house connected to the mains and
will even bypass mains surge protectors.
The thickness of the mains ground wire is likely be too thin if used as a RF ground, having
considerably large impedance at the high frequencies present. The high impedance is not ideal
as the secondary coil would not be properly grounded and the wire could suffer from a voltage
drop of the order of ~10+kV resulting to corona discharge from the wire some distance along its
length – potentially lethal to anything nearby, be it electrical equipment or a person. A high
impedance ground will also shift the zero voltage node along the wire to a place close to the
solid ground. This will cause a phase shift in the secondary circuit possibly resulting in
breakouts occurring from any point along the secondary coil, not just from the top load.
Static Spark gap
The static spark gap is a simple high voltage switch that
is very easy to make and operate. As the tank capacitor
charges from the high voltage power supply, the potential
across the static spark gap electrodes increases until the
air between the spark gap ionises allowing a low
resistance path for the current to flow through; the ‘switch’
is closed. Once the capacitor has discharged, the
potential across the spark gap is no longer sufficient to
maintain ionised air between the electrodes and the
‘switch’ is open. This happens hundreds of times a
second producing high frequency (radio frequency) AC current through the primary coil.
A high voltage spark gap becomes very hot during operation and the ionised air surrounding the
spark gap will keep the switch closed for longer than desired. It is therefore common for a static
spark gap to made up of many smaller spark gaps aligned in series this will reduce the heat
produced and dissipate the heat created more effectively. It is also common practice to integrate
a fan to quench the spark gap which will blow away the ionised air quickly and help to keep the
electrodes cool. Quenching the spark gaps allow the ‘switch’ to be open and closed quicker
which will allow the primary circuit to produce higher firing frequency pulses.
A more advanced spark gap is the rotary spark gap where multiple
electrodes on a rotating disc pass two fixed electrodes. The rotating
disc is powered by a synchronous motor to allow an easy method of
varying the spark gap firings. This also helps to keep each electrode
cool as there are many electrode where only two on the rotating disc
are firing at one time. An ideal material to use for the spark gap
electrodes is tungsten rods as they resist ware and tarnishing due to
prolonged use in spark gaps.
Resonant matching of the primary and secondary circuits
The primary circuit of the Tesla coil consists of the high voltage tank capacitor, the spark gap
switch and the primary coil (inductor). The secondary circuit consists of the secondary coil
(inductor), the top load and RF ground.
Both circuits have the form of a series LCR circuit which resonates at a particular resonant
frequency governed by the component part values. There will be a capacitance (C), an
inductance (L) and a resistance (R). The capacitance in the secondary circuit comes from the
self-capacitance of the top load and the capacitance of the top load with RF ground. The
resistance in both circuits come from the resistance of the parts used in the circuits. The circuit
will resonate at its resonant frequency when the sum of the capacitance and inductance
impedances equal zero. The resonant frequency of an LCR circuit is given by the equation
0  2f 0 
1
LC
where  0 is the resonant frequency in radians per second and f 0 is the
resonant frequency in Hertz. The resistance of the circuit acts as a damping factor to the
resonance of the circuit and in most circumstances can be neglected for use in
Tesla coil circuit design.
The primary and secondary circuits of the Tesla coil must have the same resonant frequency to
enable high frequency resonant charging between the primary and secondary circuits which
results in the extremely high induced voltage in the secondary circuit.
The resonant frequency of both the primary and secondary circuits should be in the range of
about 100kHz to 1MHz. Operation at a lower frequency allows for lower heat losses and is
therefore better for high power output and bigger diameter coils.
Tank capacitor
The tank capacitor consists of a high voltage
capacitor rated at about two or three times the
RMS voltage rating of the high voltage
transformer, so if you have a NST rated at
10,000 VAC its RMS voltage would be
~14,000VAC, so the tank capacitor must be
able to withstand ~40,000 volts. This is because
the primary circuit can have many very high
voltage peaks present when in operation which
can damage a too lower rated capacitor. The
tank capacitance usually varies between about 1nF to about 50nF depending on the resonant
properties of the primary circuit design.
There are a number of alternative methods for obtaining high voltage capacitors.
A very common method of producing such a capacitor is to create an array of smaller rated
capacitors, known as an MMC (Multi Miniature Capacitor). The individual capacitors are set in
parallel and series combinations to get the desired voltage and capacitance rating. The
following two equations are used for calculating the combined total capacitance parallel and
series arrays:
C parallel  C1  C 2  C3  ...
C series 
1
1
1
1


 ...
C1 C 2 C3
Adding capacitors in series, effectively doubles their voltage rating, whilst adding capacitors in
parallel has no effect on the voltage rating. High voltage (~1,000V) polypropylene capacitors are
usually used for MMC types of tank capacitor. This method can be quite expensive due to the
number of capacitors needed, depending on the design some can have over 100 individual
capacitors.
Another method is to buy a few higher voltage rated (~10,000V) ceramic capacitors (~1nF) and
set these up in parallel and series combinations to obtain the required ratings. This is another
type of MMC but can be cheaper due to the smaller number of capacitors needed. This is the
style I have used on my Tesla coil. I have used four 20,000V, 1nF ceramic capacitors, two in
series and two sets of these pairs in parallel to obtain ratings of 40,000V and 1nF for my tank
capacitor.
Another method is to roll or build your own high voltage capacitor using aluminium foil and
sheets of polypropylene, however this method can be hard to obtain an accurate capacitance
and produce an efficient capacitor.
Primary coil + strike rail
There are three main types of primary coil (inductor):
spiral, helical and inverse conical. Helical coils are
wound into a helix of equal diameter. Spiral coils (or
pancake coils) are wound into a flat spiral. Helical coils
are wound into a vertical helical spiral. Inverse conical
coils are wound into a conical spiral with an inclined
angle of 30° to 45°.
The primary and secondary coils need to be loosely
coupled inductively (normal mains transformers have
high coupling between separate coils to get better
performance and efficiency) to allow the secondary to undergo resonant climbing to very high
voltages.
The helical coil is generally not recommended over the other designs as it is not as efficient due
to a too larger inductive coupling between the secondary coil, preventing efficient resonant
climbing. It is also higher, increasing the chances of top load discharge to its upper windings
which can damage the components of the primary circuit especially the tank capacitor. The
inverse conical coil and spiral coil are far more common and both can be used in small and
medium power Tesla coils. For larger high power (1000W and over) Tesla coils the spiral
primary coil design is best. I personally prefer the spiral coil design for all power ranges of Tesla
coil due to its simplicity and no obvious difference in efficiency from that of the inverse conical
coil design.
The coil is made from hollow copper tubing (micro bore) with a diameter of about 6-8mm. A
frame is constructed to support and fix the copper coil in place. The frame is usually made from
sheets of a good insulator like polypropylene (plastic chopping boards are a good source for
this).
There is a reason for using hollow tubing known as the skin effect. The current density within a
conductor depends of the frequency of the current. Alternating current within a conductor tends
to have a higher current density at its surface than at its centre. As the frequency of the current
increases so does the density of the current towards the surface of the conductor. The diagrams
below try to illustrate the effective current density within the cross section of a rod like
conductor.
Low frequency
High frequency
So for higher frequencies, the centre of the conductor is not used or available for the current to
pass through. Using a solid conductor is just wasteful not required, so for high frequency
applications tubing is ideal for use as a conductor.
The skin depth can be calculated using the following equation (SI units):

1
f
Where f is the frequency of the current in the conductor, μ is the relative permeability of the
conductor material and σ is the electrical conductivity of the conductor material.
The reason for using a relatively large conductor for the primary coil is to minimise the
impedance and resistance for the high frequency. Also, not only would a solid copper tube be
very expensive but it would also be extremely hard to form into a spiral shape.
The skin effect also causes the effective resistance of the conductor to increase with the
frequency of the current. The skin effect is basically due to eddy currents induced in the
conductor by the AC current.
The equations for each coil design are shown below for calculating the approximate theoretical
inductance.
Spiral / Pancake coil
L
NR 2
8 R  11H
L = inductance of coil in micro-Henry’s (µH)
R = average radius of the coil in inches, measured
from the centre of the coil to the mid point between
the inner winding and outer winding.
N = number of turns.
W = width of the windings in inches, measured from
the inner winding to the outer winding.
Helical coil
L
NR2
9 R  10 H
L = inductance of coil in micro-Henry’s (µH).
N = number of turns.
R = radius of coil in inches, measured from the
centre of the coil to the middle of the outer wire/s.
H = height of coil in inches.
Inverse conical coil
L1 
NR 2
9 R  10 H
L2 
NR 2
8R  11H
L  L12 sin 2 x   L22 cos 2 x 
L = inductance of coil in micro-Henry’s (µH).
L1 = helical inductance factor.
L2 = spiral inductance factor.
N = number of turns.
R = average radius of coil in inches, measured from
the centre of the coil to the mid point between the
inner/lower winding and the outer/upper winding.
H = vertical height of the coil in inches.
W = width of windings in inches, measured from the
inner/lower winding to the outer/upper winding.
x = inclination angle of the coil in degrees.
(Pictures and equations obtained from: http://alumnos.elo.utfsm.cl/~bikers/TCC.html)
The primary coil is located underneath the secondary coil and top load which leaves it
susceptible to discharge strikes when in operation which can easily damage the components of
the primary circuit. These discharges can easy break the tank capacitor and filter components
that are not designed to withstand such high frequencies and high voltage. To protect the
primary coil and circuit a strike rail is placed above the primary coil. This strike rail is located
usually about 2 inches above the highest winding of the primary coil and directly above the outer
winding of the primary coil to intercept any discharges that could be drawn to the primary coil.
The strike rail is directly connected to RF ground via a low inductance, low impedance thick wire
or more commonly a thick metallic strip. The strike rail is made from a length of copper tubing
similar to the primary coil material. The strike rail should NOT be a completed loop (i.e. it must
be an open loop), and should have a gap of about 2 or 3 inches. This is to stop the strike rail
from experiencing any inductive effects from the primary and secondary coils which would
effectively draw out energy from your circuit and ground it.
Secondary coil + Top load
The secondary coil is a large single layered coil often made with
magnet wire. The form of the coil is usually a PVC drainage pipe.
This pipe needs to be completely free from moisture and needs to be
smooth. Leaving the pipe out in the sun for a few hours will remove
most of the moisture. It must then be coated inside and out with
polyurethane varnish to seal it from moisture. Each end of the pipe
must also be sealed off either with commercial PVC pipe end caps or
home made PVC end caps. Magnet wire is usually used for the
windings and need to wound very tightly with no kinks or gaps. This
process can take a very long time by hand and the process must be
done with care. Once the coil is wound each end of the windings can
be temporarily clamped and the whole coil needs to be coated with a
few coats of polyurethane varnish until a smooth finish is obtained.
The approximate dimensions for the secondary coil are the height of the coil should be about 5
to 7 times the diameter of the pipe used and the number of turns on this pipe should be about
1000. A good starting diameter for a Tesla coil is around 60mm to 80mm. I believe it is easier to
design and make the secondary coil and top load first and build the other components of the
Tesla coil around these components as the other components can be adjusted more easily
whereas the secondary coil and top load are fixed once built.
The top secondary winding is directly connected to a top load discharge terminal usually in the
form of a toroid or sometimes a sphere. The bottom secondary winding is directly connected to
an excellent RF ground connection.
I don’t recommend a sphere as the top load they are not as efficient at shielding the top of the
secondary coil from a large magnetic field which prevents discharge from the top windings. The
toroid also looks a lot more impressive in my opinion.
A toroid can be constructed from flexible aluminium air duct hose (used for air conditioning and
extraction). The flexible hose is cut and bent into a toroid and fixed together using epoxy resin.
The toroid is more efficient with a smooth metallic finish and so it is a good idea to cover the
toroid with aluminium tape to provide this smooth finish.
The secondary coil has an inductance and due to the high frequencies used it also has a self
capacitance. The toroid itself acts a single plate of a virtual capacitor with the air being the
dielectric and the ground/Earth acting as the second plate of the virtual capacitor.
The inductance of the secondary coil is calculated using the same equation above for the helical
primary coil.
The self capacitance of the secondary coil is given using the Medhurst equation. This equation
is only an approximation but is sufficiently accurate to allow an inaccuracy of only a few picofarads.
Medhurst equation:
C  0.29 L  0.41R  1.94
R3
L
Where C is the self capacitance in pico-farads, L is the length of the coil in inches and R is the
radius of the coil in inches.
The capacitance of the toroid is approximated by the following equation:

D 
C  1.41.2781  2  D2 D1  D2 
D1 

Where C is the capacitance of the toroid in pico-farads, D1 is the total outer diameter of the
toroid in inches and D2 is the diameter of the cross section of the toroid in inches, i.e. the
diameter of the tubing used for the toroid.
The total capacitance of the secondary coil and toroid is not quite the sum of the two but about
80% to 90% of their sum, so an efficiency factor is introduced to their sum. This is due to their
close proximity which causes the toroid to shield some of the secondary coil surface area from
ground reducing their self capacitance. This is not too important as this discrepancy can be
overcome by tuning the primary coil with the secondary later.
Radio
Frequency
mains filter
AC
~
Neon Sign
Transformer
Mains
Ground
Tank
Capacitor
Simplified Terry
filter
Toroidal
Top load
Capacitance
between top
load and RF
ground
Static
Spark Gap
LINE
~
LOAD
Power factor
correction
RF mains capacitor Neon Sign
Transformer
filter
RF
Ground
RF
Ground
Primary
Coil
Secondary
Coil
RF
Ground