TESLA COIL DESIGN

There are many programs to calculate the physical dimensions of a Tesla Coil System (transformer, primary
coil & capacitor, secondary coil and its discharge terminal; but I believe there are a lot of people who will want to calculate
themselves each parameter, thus having full control of the general design process.

Here you'll find a straightforward
approach (don't fool yourself thinking a program gill give better results, because inside there's nothing more than formulas, usually
the same you are looking here).

__Note__:I've introduced new ideas to estimate the physical dimensions of the secondary coil as a function of the input power. This was done analyzing dozens of actually working Tesla Coils . Reports given by friends who've used this approach show Tesla coils working without problems and giving a satisfactory performance.

One of the new concepts I've introduced was "Available Transformer Power per Cubic-Inch of 2ry Coil Volume"
or AVP, thus:

where:

PWR = neon transformer power in watt

a

D = 2ry coil diameter in inches

This fancy coefficient remains almost constant (aprox. 2.5 Watt/in

The starting input will be the **neon xfmr** we have at hand, thus for the given neon transformer we
know:

**V _{x}** [kv] = transformer output

**I _{x}** [mA] = transformer output

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To match transformer and capacitor impedances we need:

therefore the matching capacitor will have a capacity of:

and if AC mains line frequency is

These formulas were obtained from regression of dozens of tesla coils ...

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From these approximate (*) values we adopt

where @ means adopted value from the suggested (*) value; therefore:

secondary coil height:é

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Now we may calculate de number of turns of secondary:

é **N _{2}** =

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Its value is derived considering that the actual wire length

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and as f = c / l where c = speed of light = 300000 km/s or 9.84 10

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= 0.4181

= 4.5

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we should select a sphere or toroid that has this capacity in [pF].

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**FOR A SPHERE OF DIAMETER d**

**C**[pF] =**k . d**

where k = 1.4142 for d [in] , and k = 0.556 for d [cm]

**FOR A TOROID OF OUTER DIAMETER***D*AND CROSS SECTION DIAMETER*d*

**C**[pF] = k. ( 1.2781 – [d / D] ) . SQR( pd .[D-d] )

where SQR= Square Root

In both cases, k = 1.4142 for d [in] , and k = 0.556 for d [cm]

Some assumptions must be made here, i.e.: for a normal helix we define:

If **D _{1}** =

If **D _{1}** =

From

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Let's use a neon transformer of 12kv / 30 mA, therefore:

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From these approximate (*) values we adopt

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therefore the secondary coil height:

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Now we may calculate de number of turns of secondary:

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**FOR A SPHERE OF DIAMETER d = 9.2 in = 23 cm**

**C**=_{ TOP}**13.9**pF

Some assumptions must be made here, i.e.: for a normal helix we define:

**D _{1}** =

threfore:

so:

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