# Spark Gap Tesla Coil

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## Introduction: Spark Gap Tesla Coil

This is a tutorial on how to build a Spark Gap Tesla Coil with a Faraday cage dress.

This project took me and my team (3 students) 16 working days, it costs around 500 USD, I will assure you that it will not work from the first time:), most important part is that you have to understand all the theory behind and know how to deal with the components that you choose.

In this instructable, I will take you through all the theory behind, the concepts, the formulas, a step by step building for all the parts. If you want to build smaller or larger coils the concept and formulas will be the same.

The requirements for this project:

- Knowledge in: Electrical, electronics, electromagnetic and lab equipment

- Oscilloscope

- Neon Sign transformer; 220V to 9kV

- High voltage capacitors

- Copper cables or copper pipes

- Wood to build your chassis

- PVC pipe for the secondary coil

- Flexible metallic pipe for the Toroid

- A small 220V electric Fan for the spark gap

- Aluminum papers and mesh for the Faraday cage dress

- Insulated wires for the secondary

- Neon Lamps

- Voltage Regulator if you do not have a stable 220VAC

- Connection to ground

- A lot of patience

## Step 1: Introduction to the Spark Gap Tesla Coil

A Tesla coil is a resonate transformer containing a primary and secondary LC circuit. Designed by inventor Nikola Tesla in 1891, the two LC circuits are loosely coupled together. Power is supplied to the primary circuit through a step-up transformer, which charges a capacitor. Eventually, the voltage across the capacitor will increase sufficiently to short a spark gap. The capacitor will discharge through the spark gap and into the primary coil. The energy will oscillate back and forth between the primary capacitor and primary coil inductor at high frequencies (typically 50 kHz- 2 MHz). The primary coil is coupled to an inductor in the secondary circuit, called the secondary coil. Attached to the top of the secondary coil is a top load that provides capacitance for the secondary LC circuit. As the primary circuit oscillates, power is induced in the secondary coil where the voltage is multiplied many times. A high voltage, low current field develops around the top load and arcs of lightning discharge in a sweet display of awesomeness. The primary and secondary LC circuits must oscillate at the same frequency to achieve maximum power transfer. The circuits in the coil are usually "tuned" to the same frequency by adjusting the inductance of the primary coil. Tesla coils can produce output voltages from 50 kilovolts to several million volts for large coils.

## Step 2: Theory

This section shall cover the complete theory of operation of a conventional Tesla coil. We will consider that the primary and secondary circuits are RLC circuits with low resistance, which accords with reality.

For the aforementioned reasons, internal resistance of the component is not represented. We will also replace the current-limited transformer. This has no impact regarding pure theory.

Note that some parts of the secondary circuit are drawn in dotted lines. This is because they are not directly visible on the apparatus. Regarding the secondary capacitor, we’ll see that its capacity is actually distributed, the top load only being "one plate" of this capacitor. Regarding the secondary spark gap, it is shown in the schematic as a way to represent where the arcs will take place.

This first step of the cycle is the charging of the primary capacitor by the generator. We’ll suppose its frequency to be 50 Hz. Because the generator(NST) is current-limited, the capacity of the capacitor must be carefully chosen so it will be fully charged in exactly 1/100 seconds. Indeed, the voltage of the generator changes twice a period, and at the next cycle, it will re-charge the capacitor with opposite polarity, which changes absolutely nothing about the operation of the Tesla coil.

When the capacitor is fully charged, the spark gap fires and
therefore closes the primary circuit. Knowing the intensity of the breakdown electric field of air, the width of the spark gap must be set so that it fires exactly when the voltage across the capacitor reaches its peak value. The role of the generator ends here.

We now have a fully loaded capacitor in an LC circuit. Current and voltage will thus oscillate at the circuits resonant frequency, as it was demonstrated before. This frequency is very high compared to the mains frequency, generally between 50 and 400 kHz.

The primary and secondary circuits are magnetically coupled. The oscillations taking place in the primary will thus induce an electromotive force in the secondary. As the energy of the primary is dumped into the secondary, the amplitude of the oscillations in the primary will gradually decrease while those of the secondary will amplify. This energy transfer is done through magnetic induction. The coupling constant k between the two circuits is purposefully kept low, generally between 0.05 and 0.2.

The oscillations in the primary will thus act a bit like an AC voltage generator placed in series on the secondary circuit.

To produce the largest output voltage, the primary and secondary tuned circuits are adjusted to resonance with each other. Since the secondary circuit is usually not adjustable, this is generally done by an adjustable tap on the primary coil. If the two coils were separate, the resonant frequencies of the primary and secondary circuits would be determined by the inductance and capacitance in each circuit

## Step 3: Distribution of Capacitance Within the Secondary Circuit

The secondary capacitance Cs is really important to make the tesla coil work, the capacitance of the secondary coil is necessary for the calculations of the resonate frequency, if you do not take all parameters into account you will not see a spark. This capacitance consists of many contributions and is difficult to compute, but we’ll look at its major components.

The highest fraction of the secondary capacitance comes from the top load. Indeed, we have a capacitor whose "plates" are the top load and the ground. It might be surprising that this is indeed a capacitor as these plates are connected though the secondary coil. However, its impedance is quite high so there’s actually quite a potential difference between them. We shall call Ct this contribution.

Turns of the secondary coil.

The other big contribution comes from the secondary coil. It is made of many adjacent turns of enameled copper wire and its inductance is therefore distributed along its length. This implies there’s a slight potential difference between two adjacent turns. We then have two conductors at different potential, separated by a dielectric: a capacitor, in other words. Actually, there is a capacitor with every pair of wires, but its capacity decreases with distance, therefore one can consider the capacity only between two adjacent turns a good approximation.

Let’s call Cb the total capacity of the secondary coil.

Actually, it’s not mandatory to have a top load on a Tesla coil, as every secondary coil will possess its own capacity. However, that a top load is crucial for having beautiful sparks.

There will be extra capacity form the surrounding objects. This capacitor is formed by the top load on one side and conducting objects (walls, plumbing pipes, furniture, etc.) on the other side.

We’ll name the capacitor of these external factors Ce.

As all these "capacitors" are in parallel, the total capacity of the secondary circuit will be given by :

Cs = Ct + Cb + Ce

## Step 4: Conception and Construction

In our case we used an automatic voltage regulator to maintain the voltage input for the NST at 220V

And it contains a built in AC line filter (YOKOMA ELECTRIC WORKS.,LTD. In japan-Model AVR-2)

This instrument could be found in X-Ray machines or bought directly from the market.

The high voltage transformer is the most important part of a
Tesla coil. It is simply an induction transformer. Its role is to charge the primary capacitor at the beginning of each cycle. Apart from its power, its ruggedness is very important as it must withstand terrific operation conditions (a protection filter is sometimes necessary).

The neon signs transformer (NST) which we are using for our tesla coil, characteristics (rms values) are the following:

Vout = 9000 V, Iout = 30 mA

The output current is, in fact, 25mA, 30mA is the peak which drops to 25 mA after starting.

We can now compute its power P = V I, which will be useful to set the global dimensions of the Tesla coil as well as a rough idea of its sparks’ length.

P = 225 W (for 25 mA)

NST Impedance = NST Vout ∕ NST Iout =9000/ 0.25=360 KΩ

## Step 5: Primary Circuit

Capacitor:

The role of the primary capacitor
is to store a certain quantity of charge for the coming cycle as well as forming an LC circuit along with the primary inductor.

The primary capacitor is usually made of several dozen caps wired in a series / parallel configuration called a Multi-Mini Capacitor (MMC)

The primary capacitor is used with the primary coil to create the primary LC circuit. A resonate sized capacitor can damage a NST, therefore a Larger Than Resonate (LTR) sized capacitor is strongly recommended. A LTR capacitor will also deliver the most power through the Tesla coil. Different primary gaps (static vs. sync rotary) will require different sized primary capacitors.

Cres = Primary Resonate Capacitance (uF) = 1 ∕ (2 * π * NST Impedance * NST Fin)=1/ (2*π*360 000 * 50) =8.8419nF

CLTR = Primary larger-than-resonance (LTR) Static Capacitance (uF) = Primary Resonate Capacitance × 1.6

= 14.147nF

(this could slightly differs from an approximation to another, recommended coefficient 1.6-1.8 )

We used a 2000V 100nF capacitors, Nb= Cunit/Cequiv= 100nF/0.0119 uF= 9 Capacitors. So for exactly 9 caps we have Ceq= 0.0111uF= MMC capacitance.

Think about connecting high power, 10MOhms resistors in parallel to each capacitor for safety.

Inductance:

The role of the primary inductor is to generate a magnetic field to be injected into the secondary circuit as well as forming an LC circuit with the primary capacitor. This component must be able to transport heavy current without excessive losses.

Different geometries are possible for the primary coil. In our case we will adapt the flat archimed spiral as a primary coil.This geometry naturally leads to a weaker coupling and reduces the risk of arcing in the primary: it is therefore preferred on powerful coils. It is however rather common in lower power coils for its ease of construction. Increasing the coupling is possible by lowering the secondary coil into the primary.

Let W be the spiral’s width given by W = Rmax − Rmin and R its mean radius, i.e. R = (Rmax + Rmin)/2, both expressed in centimeters. If the coil has N turns, an empirical formula yielding its inductance L in microhenrys is:

Lflat =(0.374(NR)^2)/(8R+11W).

For the helic shape If we call R the radius of the helix, H its height (both in centimeters) and N its number of turns, an empirical formula yielding its inductance L in microhenrys is: Lhelic =(0.374(NR)^2)/(9R+10H).

These are many formulas that you can use and check, they will give close results, the most accurate way is to use the oscilloscope and measure the frequency response, but the formulas are also necessary for building the coil. You can also use simulation software like JavaTC.

Formula 2 for flat shape: L= [0.25*N^2*(D1+N*(W+S))^2]/[15*(D1+N*(W+S))+11*D1]

where N: number of turns, W: wire diameter in inches, S: wire spacing in inches, D1: inner diameter in inches

Input data of my Tesla Coil:

Inner radius: 4.5 inches, 11.2 turns, 0.25 inches spacing, wire diameter=6 mm, outer radius= 7.898 inches.

L using Formula 2=0.03098mH, from JavaTC= 0.03089mH

Therefore, primary frequency: f1= 271.6 KHz (L=0.03089 mH, C=0.0111MFD)

Lab experience (primary frequency tuning)

and we obtained resonance at 269-271KHz, which verify the calculation, see Figures.

## Step 6: Spark Gap

The function of the spark gap is to close the primary LC circuit when the capacitor is sufficiently charged, thus allowing free oscillations inside the circuit. This is a component of prime importance in a Tesla coil because its closing/opening frequency will have a considerable influence on the final output.

An ideal spark gap must fire just when the voltage across the capacitor is maximal and re-open just when it falls down to zero. But this is of course not the case in a true spark gap, it sometimes does not fire when it should or continues to fire when the voltage has already diminished;

For our project, we used a static spark gap with two spherical electrodes (built using two drawer handles) which we designed manually. And it could be adjusted manually also by rotating the spherical heads.

## Step 7: Secondary Circuit

Coil:

The function of the secondary coil is to bring an inductive component to the secondary LC circuit and to collect the energy of the primary coil. This inductor is an air-cored solenoid, generally having between 800 and 1500 closely wound adjacent turns. To calculate the number of turns that have been wound, this quick formula will avoid a certain fastidious work:

Wire gauge 24 = 0.05 cm, PVC diameter 4 inches, number of turns=1100 spires, height needed=1100 x 0.05= 55 cm = 21.6535 inches. => L= 20.853 mH

where H is the height of the coil and d the diameter of the wire used. Another important parameter is the length l we need to make the entire coil.

L=µ*N^2*A/H. Where µ represents the magnetic permeability of the medium (≈ 1.257 · 10−6 N/A^2 for air), N the number of turns of the solenoid, H its total height, and A the area of a turn.

The top load acts like the upper "plate" of the capacitor formed by the top load and the ground. It adds capacity to the secondary LC circuit and offers a surface from which arcs can form. It is possible, actually, to run a Tesla coil without a top load, but performances in terms of arc length are often poor, as most of the energy is dissipated between the secondary coil turns instead of feeding the sparks.

Toroid Capacitance 1 = ((1+ (0.2781 − Ring Diameter ∕ (Overall Diameter))) × 2.8 × sqrt ((pi × (Overall Diameter × Ring Diameter)) ∕ 4))

Toroid Capacitance 2 = (1.28 − Ring Diameter ∕ Overall Diameter) × sqrt (2 × pi × Ring Diameter × (Overall Diameter − Ring Diameter))

Toroid Capacitance 3 = 4.43927641749 × ((0.5 × (Ring Diameter × (Overall Diameter − Ring Diameter))) ^0.5)

Average Toroid Capacitance= (Toroid Capacitance 1 + Toroid Capacitance 2 + Toroid Capacitance 3) ∕ 3

So for our toroid :inner diameter 4”, outer diameter=13”, spacing from the end of the secondary winding= 5cm.

C=13.046 pf

Secondary Coil Capacitance:

Secondary Capacitance (pf)= (0.29 × Secondary Wire Winding Height + (0.41 × (Secondary Form Diameter ∕ 2)) + (1.94 × sqrt(((Secondary Form Diameter ∕ 2) 3) ∕ Secondary Wire Winding Height))

Csec= 8.2787 pF;

It’s also interesting to know the (parasitic) capacitance of the coil .Here also the formula is complicated in the general case. We’ll use the value yielded by JAVATC ("Effective shunt capacitance" without top load) :

Cres = 6.8 pF

Therefore, for the secondary circuit:

Ctot=8.27+13.046=21.316pF

Lsec=20.853mH

Lab experiments results:

See pictures Above for the procedure of testing and testing results.

## Step 8: Resonance Tuning

Setting the primary and secondary circuits at resonance, have them share the same resonant frequency is of prime importance for good operation.

The response of an RLC circuit is the strongest when driven at its resonant frequency. In a good RLC circuit, the response intensity falls sharply when the driving frequency drifts from the resonant value.

Our resonant frequency= 267.47 kHz.

Tuning methods:

The tuning is generally done by adjusting the primary inductance, simply because it’s the easiest component to modify. As this inductor has wide turns, it is easy to modify its self-inductance by tapping the final connector at a certain place in the spiral.

The simplest method to achieve this adjustment is by trial-and-error. For this, one begins to tap the primary at a point supposedly close to the resonant one, lights the coil, and evaluates arc length. Then the spiral is tapped a quarter of turn forward/backward and one re-evaluates the result. After a few tries, one can proceed with smaller steps, and will finally get the tapping point where the arc length is the highest. Normally, this tapping

point will indeed set the primary inductance such as both the circuits are at resonance.

A more precise method would involve an analysis of the individual response of both the circuits (in the coupled configuration, of course, i.e. without physically separating the circuits) with a signal generator and an oscilloscope.

Arcs themselves can produce some extra capacitance. It is therefore advised to set the primary resonant frequency slightly lower than the secondary, in order to compensate for this. However, this is noticeable only with powerful Tesla coils (which can produce arcs longer than 1m).

## Step 9: Voltage at Secondary-Spark

Paschen's Law is an equation that gives the breakdown voltage, that is, the voltage necessary to start a discharge or electric arc, between two electrodes in a gas as a function of pressure and gap length.

Without getting in detailed calculation using the complex formula, for normal conditions it requires 3.3MV to ionize 1m of air between two electrodes. In our case we are having arcs about 10-13cm so it will be between 340KV and 440KV.

## Step 10: Faraday Cage Dress

A Faraday cage or Faraday shield is an enclosure used to block electromagnetic fields. A Faraday shield may be formed by a continuous covering of conductive material or in the case of a Faraday cage, by a mesh of such materials.

We designed four layers, grounded, wearable faraday cage as shown in the picture (used materials: Aluminum, cotton, leather). You can test it also by putting your mobile phone inside, it will lose signal, or placing it in front of your tesla coil and put some neon lamps inside the cage, they will not illuminate, then you could put it on and try it.

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