exploring the high-voltage tesla coil
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Abstract—The purpose of this paper is to outline the basic
theory of Tesla coil operation, discuss the use of different
mathematical equations that can be used to analyze a Tesla coil,
demonstrate that a functional Tesla coil can be built from
materials that are either readily available or that can be
improvised, provide experimental results of the research
conducted, and discuss methods for improving the design of
future Tesla coils.
Index Terms—Air core transformer, High voltage, LC circuit,
Tesla coil
I. INTRODUCTION
ikola Tesla invented the Tesla Coil to study the properties
of high voltage, high frequency electricity. According to
[1], “The Tesla coil is a combination of two circuits. Each
circuit has a coil of wire, both wound together around a hollow
tube. One of the coils is made of heavy wire and has just a few
turns around the tube. The other circuit’s coil is made of finer
wire wound many times around the tube. When an alternating
current passes through the coil of heavy wire, it produces a
magnetic field. The magnetic field induces current in the fine
wire.” Variations of the Tesla coil were used in early radios
including the one “invented” by Marconi. Although the Tesla
coil was extremely important to the early transmission and
reception of radio signals, today it is used primarily to
investigate the effects of high voltage, high frequency
electricity. It is this aspect of the Tesla coil that shall be
explored in this paper.
II. BASIC TESLA COIL THEORY
A Tesla coil is a type of transformer. It differs from
traditional transformers in a few important ways. It has an air
core instead of an iron core. The primary coil is mounted
concentric with the secondary coil. Output voltage depends
upon the resonance effects between the primary and the
secondary, instead of the ratio of windings between them.
The Tesla coil needs a high voltage input. This can be
accomplished with a traditional iron core transformer. The
input voltage for a medium sized Tesla coil should be in the
range of 8-15 kV. To avoid confusing this transformer with
the Tesla coil throughout the paper it shall be referred to as the
NST (Neon Sign Transformer, because that was the high
voltage input that was used for this particular experiment).
Whenever the terms primary and/or secondary are used, they
are referring to the primary and/or secondary coils of the Tesla
coil (not the NST), unless specifically stated otherwise.
The capacitor, spark gap and primary coil make up what is
commonly referred to as the primary tank circuit (See Fig. 1).
The high voltage input provided by the NST charges the
capacitor after passing through the primary windings of the
coil. At some point the breakdown voltage of the spark gap is
reached, the spark gap arcs over to close the tank circuit. The
purpose of the spark gap is to act as a very fast switch. The
primary tank circuit may be analyzed as a resonant LC circuit.
As was mentioned earlier the spark gap acts as a very fast
switch, closing the primary tank circuit for a few microseconds
every time it fires. It should fire very rapidly. The distance
between the two terminals of the spark gap must be set so that
it is close enough to rapidly arc over, but far enough away so
that a constant arc is not produced.
The bottom end of the secondary coil is connected to an RF
ground dedicated for its use. The secondary coil is
concentrically inside of the primary coil. The top of the
secondary coil is connected to a metal sphere or toroid to give
it a capacitive load. The metal sphere or toroid forms one
plate of the capacitor. The ground forms the other plate, and
the atmosphere acts as the dielectric. This capacitance along
with the inductance of the secondary coil forms a second LC
circuit.
An LC circuit is any circuit that contains both capacitors
and inductors. An LC circuit will show resonance effects for a
given frequency. The resonance frequency is the frequency at
which the capacitor and the inductor have the same reactance.
When an LC circuit has an input at resonance frequency it
demonstrates an effect called resonant rise and the circuit will
Exploring the High-Voltage Tesla Coil
N
Grady L. Cutrer, III April 25, 2005
Fig. 1. The Tesla coil consists of two LC circuits; the Primary tank circuit is
outlined in red [2].
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oscillate. The capacitor is charged by the NST and stores this
energy. This energy will begin to discharge into the primary
coil. The current in the primary coil will build up a magnetic
field which will now be storing the energy that was stored by
the capacitor. The magnetic field created by the primary coil
will breakdown and creates a current in the opposite direction.
This current once more charges the capacitor and the cycle
repeats. This cycle would be infinite if the entire circuit were
constructed of ideal components. The real circuit has losses so
the real cycle is dampened.
A Tesla coil can be modeled as two LC circuits. The
primary tank circuit (the capacitor, primary coil, and spark
gap) makes up one LC circuit. The frequency of the primary
tank circuit may be adjusted by changing the connection points
on the primary coil. The secondary coil, its RF ground, and
the discharge terminal make up the second LC circuit. An LC
circuit can receive energy from a magnetic field at or near its
resonance frequency. The magnetic field provided by the
primary tank circuit is used to energize the LC circuit of the
secondary coil, RF ground, and discharge terminal. The
secondary coil amplifies this energy and will discharge it either
as an arc of electricity to a grounded object or as a corona into
the surrounding air if no grounded object is present [2].
III. DESIGN AND EXPERIMENTATION
There are two main objectives for this experiment. The first
objective is to demonstrate that a functional Tesla coil can be
constructed from materials that are either readily available or
that can be improvised. The objective for the second part of
the experiment is to explore the properties of high voltage,
high frequency electricity.
PART A – DESIGNING THE TESLA COIL
The high voltage input that the Tesla coil required was
provided by a luminous tube transformer (NST). The NST
was provided by a friend in the neon sign business. The NST
has an input of 120 V, 6 A, and 60 Hz. The output of the NST
is 12000 V, 0.060 A (60 mA), and 60 Hz.
The capacitor was one part of the needed equipment that
had to be improvised. A commercially available capacitor that
could hold the charge needed at a voltage this high is not only
hard to find but quite expensive. The capacitor was
constructed with glass functioning as the dielectric. The first
generation of these capacitors used mason jars lined on the
inside and the outside with aluminum foil (commonly referred
to as a Leyden jar). These capacitors would only function for
a short period of time before the glass became too hot and
shattered. The second generation solved this problem by using
a solution of sodium chloride in water to function as the inner
plate. In addition to preventing the glass from breaking (due
to the fact that water has a high specific heat and conducts the
heat away from the glass) this allowed the use of bottles, which
could not be lined on the inside with aluminum foil. The
bottles also had considerably more surface area which
increased capacitance. The bottles were lined on the outside
with aluminum foil to provide the other plate. The formula for
calculating capacitance is
0( ) /C A dκ= ∈ , (1)
where C is capacitance in Farads, κ is the dielectric constant
of the material (estimated to be 7.6), 0∈ is the permittivity of
free space, A is the surface area in square meters, and d is the
plate separation in meters [3]. The capacitance was estimated
to be 0.00075 µF for one bottle by using (1). Eight of these
bottles were connected in parallel to form the capacitor bank.
The capacitor bank has an estimated total capacitance of 0.006
µF. The formula for calculating the energy stored by a
capacitor is
21
( )2
E C V= ∆ , (2)
where E is the energy stored in Joules, C is the capacitance in
Farads, and ∆V is the difference in electric potential between
the two plates [3]. The energy stored by the capacitor bank
when fully charged was estimated to be 0.432 J by using (2).
The primary coil was designed from copper refrigerator
tubing using an inverse-conical-helix form. The primary coil
has a maximum radius of 0.077 m, an average radius of 0.06
m, it is 0.05 m tall, has a 45° angle of rise, and is tapped after
4 turns of tubing. According to [2], the inductance may be
approximated by using
2 2
1 2
2
1
2
2
( sin( )) ( sin( ))
( ( / 0.0254))
8( / 0.0254) 11( / 0.0254)
( ( / 0.0254))
9( / 0.0254) 10( / 0.0254)
L L L
N RL
R W
N RL
R H
θ θ= +
=+
=+
, (3)
where L is the inductance in micro Henries, θ is the angle of
elevation of the coil, R is the average radius of the coil in
meters, W is the maximum radius of the coil in meters, and H
is the height of the coil in meters. The inductance was
estimated to be 1.96 µH by using (3).
The secondary coil was constructed by winding AWG#20
magnet wire on a 2” PVC core. The secondary coil is .532 m
tall, and has a radius of 0.03 m. It has 692 turns of wire. The
Wheeler formula [ 2L in (3)] estimates the inductance of the
secondary coil to be 3035.35 µH.
The discharge terminal was constructed from two metal
bowls placed together so that the shape approximates a sphere.
The spark gap consists of two metal bolts placed inside a
PVC housing. It is designed so that the distance between the
two bolts can be adjusted. It is enclosed in PVC because when
the coil is in operation the spark gap is very bright and very
loud.
The NST and the secondary coil each had a dedicated RF
ground which was achieved by driving a metal pipe several
feet into the earth. There was a third RF ground constructed
using this same technique that was used to ground a movable
metal object. This grounded object was placed 0.15 m
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(measured linearly from closest points) away from the
discharge terminal.
A variac was placed in between the NST and the main line.
This provided a convenient way to turn the coil on and off. It
also allowed precise control over the input voltage and thus the
output voltage of the Tesla coil. The variac that was used has
an input of 115 V and an output voltage that was variable from
0-130 V. This is also useful for setting the rate that the spark
gap fires.
All components were assembled using Fig. 1 as the circuit
diagram (See Fig. 2 for a photograph of the set up). Maximum
sustained arc length achieved was 0.15 m (See Fig. 8 for a
photograph of the arc). According to [4], the formula
0.765 ( )
.0254
LkV = × , (4)
where kV is kilovolts and L is arc length in meters, can be used
to estimate the output voltage of a medium-sized Tesla coil.
The overall output of the Tesla coil was estimated to be
225,000 V by using (4).
PART B – PROPERTIES OF HIGH VOLTAGE, HIGH
FREQUENCY ELECTRICITY
In the presence of high frequency, high voltage electricity
many materials lose their ability to act as an insulator. This
was observed by attaching an insulated wire to the discharge
terminal. When this was brought near a ground visible coronal
discharge could be seen leaking through the insulation. Once
this was brought a little closer the electricity arced directly
through the insulation, generating enough heat to melt it.
Nikola Tesla dreamed of a world where it would be possible
to transmit electricity wirelessly. He was actually able to do
this. He constructed a giant Tesla coil that was able to light up
200 light bulbs and run a motor from 25 miles away [1]. This
experiment was repeated on a much smaller scale. A
fluorescent light bulb was placed so that it stood vertically
with the bottom in contact with the earth at a distance of 1.0 m
from the secondary coil. Voltage was controlled by the variac
and slowly increased from a starting point of 0 V. As soon as
the input voltage was high enough to cause the spark gap to
fire the bulb started glowing (See Fig. 10). As the input
voltage was stepped up further the bulb would glow brighter.
Experimentation showed that the bulb did not even need to be
touching the ground, and at maximum power the light would
light up even at distances approaching 2 meters. This works
because the alternating electric field is so strong near the Tesla
coil that it is able to excite the gas atoms inside the fluorescent
tube without a wire connection.
High voltage, high frequency electricity tends to flow over
the surface of a conductor instead of flowing through the core.
This was experimentally verified in the past with a much
smaller coil by allowing the coil to arc to the hand. Only the
slightest sensation of being shocked was detected. Due to the
much greater output of this coil this could not be safely
investigated during this experiment. Although theoretically
the electricity should flow over the surface of the skin and not
“shock” the body, there is a very real danger of being burned
by the intense heat produced by the arc at the point of contact.
IV. DISCUSSION
The Tesla coil utilized in this experiment was designed to be
constructed from materials that were readily available and
inexpensive. This placed many limitations on the coil.
Household wire was used to make the connections within
the circuit. Wire designed to carry high voltages would have
been used in an ideal situation.
The NST is a popular choice for the high voltage source that
a Tesla coil requires; however, there are other types
transformers available that can dramatically raise the output of
a Tesla coil.
The least efficient component that caused the most
significant reduction in final output voltage was determined to
be the capacitor bank (See Fig. 4). The capacitors that were
used limited the overall output of the coil. Salt-water-bottle
capacitors are very inefficient and leak current. This could be
seen as corona discharge around the capacitor bank. The only
reason that this type of capacitor was selected is due to the fact
that they are inexpensive, and the materials required for their
construction are readily available. In addition to being
inefficient, the capacitance of this type of capacitor is very low
when compared to the optimal capacitance. The formula
max
1
2 ( )( / )C
f V Iπ= , (5)
where Cmax is the maximum capacitance in Farads, f is the
frequency in Hertz, V is the voltage, and I is the current, can be
used to find the capacitance where the reactance of a capacitor
and a transformer match for a given frequency [2]. The
maximum capacitance was calculated to be 13.263 µF by using
(5). Recall that the total capacitance of the capacitor bank
used was calculated to be 0.006 µF. Substituting these values
into (2) it can be seen that the capacitor bank is only storing
0.05% of the energy that an ideal capacitor would store (for
this particular transformer in an ideal circuit). The dielectric
value of the glass (used to calculate the capacitance) was
estimated. The dielectric value of glass can vary from a value
of 4 to 10. Due to this significant degree of variation the value
of 7.6 was chosen because it is roughly between the two
extremes. It would be advisable to use a different type of
capacitor if possible.
Obviously (4), which was used to estimate the output
voltage, is only an approximation due to the fact that arc
length is dependant on many factors of which voltage is one.
Atmospheric conditions such as pressure, temperature, and
especially humidity would have significant influence on arc
length.
Lack of the equipment necessary to measure the actual
values of capacitance of the capacitor bank, inductance of the
primary and secondary coils, and output voltage of the
secondary coil prevented further analysis.
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V. CONCLUSION
The experiment proved quite successful in demonstrating
that a functional Tesla coil can be constructed from materials
that are either readily available or that can be improvised. The
experiment also demonstrated several properties of high
voltage, high frequency electricity. Methods of improving the
overall output and efficiency of the Tesla coil have been
discussed and will be investigated in future rebuilds of the
Tesla coil.
APPENDIX
SPECIFICATIONS OF THE ELECTRICAL COMPONENTS USED IN CONSTRUCTION OF
THE TESLA COIL
Note that “(*)” indicates that the value has been estimated.
NST
Manufacturer: Jefferson Electric; Bellwood,
IL
Type: Outdoor, non-weatherproof
luminous tube transformer,
midpoint ground
Input: 120 V, 6 A, 60 Hz
Output: 12000 V, .060 A, 60 Hz
Variable Control (Variac)
Manufacturer: Calrad; Japan
Model: VC-5
Input: 115 V, 5 A
Output: 0-130 V, 575 VA
Capacitor Bank
Type: 8 parallel salt-water-bottle
capacitors
Capacitance: 0.006 µF (*)
Primary Coil
Type: Copper tubing wound into an
inverse-conical helix
Turns: 0-8 depending on where the
connections are made, was
tapped at 4 turns for this
experiment
Inductance: 1.96 µH (*)
Secondary Coil
Type: AWG#20 magnet wire wound
on a 2”PVC core
Turns: 692 (*)
Inductance: 3035.35 µH (*)
Maximum secondary output: 225,000 V (*)
PHOTOGRAPHS
Fig. 2. Photograph of the equipment as it was assembled for this experiment.
Fig. 3. Different angle of equipment set up.
Fig. 4. Close up view of the capacitor bank.
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Fig. 5. This shows the distance between the discharge terminal and the
grounded object, which was 0.15 m (15cm) in this photograph.
Fig. 6. This shows the coronal “streamers” emanating from the discharge
terminal. The coil is operating at slightly below the power necessary for it to
arc to the grounded object to the right. Notice the streamers on the grounded
object also.
Fig. 7. Similar to Fig. 6. except that a longer exposure time was used to take
the photograph.
Fig. 8. The input voltage is increased with the variac and the maximum
sustained arc length of 0.15 m (15cm) is obtained.
Fig. 9. The input voltage was barely lowered until the arc dissipated, but the
intense electric field between the discharge terminal and the grounded object
is visible.
Fig. 10. Demonstration of wireless illumination of a fluorescent lightbulb.
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Fig. 11. Beautiful display of intense sustained arcs. In this photograph the
grounded object is significantly closer to the discharge terminal.
ACKNOWLEDGMENT
Grady L. Cutrer, III thanks Mike Elliot for providing the
NST, Lambert Electric Motor Service for providing the
magnet wire used to wind the secondary coil, and the late
Grady L. Cutrer, Sr. for years of inspiration and for teaching
me how to build my first Tesla coil.
REFERENCES
[1] Encarta Online Encyclopedia. “Tesla, Nikola.” Retrieved April 21,
2005. Available: http://encarta.msn.com
[2] H. Mehlhose. “Tesla Coil Theory”. Herb’s Tesla Coil Page. Retrieved
April 21, 2005. Available:
http://home.wtal.de/herbs_teslapage/index.html
[3] R. A. Serway, J. W. Jewett, Jr. Physics for Scientists and Engineers.
California: Brooks/Cole-Thomson Learning, 2004, ch. 26, 32.
[4] J. H. Couture. “Voltage/Length”. Retrieved April 21, 2005. Available:
http://www.pupman.com/listarchives/1998/january/msg00387.html
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