1

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].

2

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

3

(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.

4

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.

5

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.

6

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