PowerLabs Tesla Coil Design Guide

 It is interesting to note how the ever increasing number of Tesla Coil enthusiasts coming into the hobby tends to ask very similar, if not equal questions about how to design a Tesla Coil. The somewhat more advanced hobbyists attempting to better understand these devices also tend to ask similar questions about their principle of functioning. There are many web pages on the web explaining how a Tesla Coil works, and several more also explain how one can design and build one. Most certainly there are also a lot more pages to come which will address those issues likewise. POWERLABS aims to unite Tesla Coil Design, Construction, and Theory, all in one concise page. If I am successful I hope this will serve to answer many of the questions beginners have about coils, and will also help people in general understand the workings of such coils. The final goal of this file is to provide everything one would need to know in order to design an excellent Tesla Coil and modify it to his/her liking. I will provide mathematical equations only when absolutely necessary, and for now the topic of computer modeling, so vital if one is to obtain the maximum possible output, will be left aside. I will attempt the split up the different sections of a coil so as to give each one through treatment. The Tesla Coil drawing to the right of this text is there for reference as to what each part looks like. Note I didn’t use a picture because there are no two equal Tesla Coils: The fact that they are home made and often make use of whatever materials become available makes them vary in power, dimensions, proportions, and so on. Remember: The paths to success are many; I am just outlining the parameters here.

 Secondary Coil

 The Secondary Coil is at the heart of any Tesla Coil system. It is the long thin solenoid between the primary and the top load which develops voltages in the orders of hundreds of thousands or even millions of volts which are, of course, the objective of a Tesla Coil. Because it sees such a high voltage across it, the secondary coil must be properly sized and insulated. And because it operates at very high frequencies, the RF (“Radio Frequencies”) flowing through the wire will tend to dissipate some of their energy on the surrounding insulation. The High Voltage leakage through the insulation and the RF dissipation factor together form what is known a the “Q” of the secondary. The Q is a measure of how many times an oscillation will pass through it before it decays to 1/2 of its original magnitude. Of course, the higher the Q, the less energy the coil is dissipating, and therefore the more energy makes it to the sparks. High “Q” values are obtained by choosing the best insulation materials. We start by the coil form:
The coil form is the tube around which the secondary wire (the coil itself, so to speak) is wound. In order to have the lowest possible leakage resistance, it must be an excellent insulator. Most plastics will work here, so long as they don’t have any carbon or moisture incorporated onto them. The RF dissipation factor of the plastic will therefore decide which one is best. PE (Polyethylene) has the lowest RF dissipation factor of any plastic, but its far too malleable to hold a tightly wound coil. UHMW (Ultra High Molecular Weight) PE would work, but I have never seen pipes sold from that material. PP (Polypropylene) has almost as low a dissipation factor as PE, and is structurally strong enough to hold a tightly wound coil. It is, therefore, the best possible choice of material. Many other plastics will work almost as good as PP, Teflon (PTFE) to name one. However, these plastics will not be mentioned as their price and availability are prohibitive. Also note that Teflon has the coefficient of friction of any substance, and therefore any winding wound around it will eventually unwrap. Perhaps the second best choice after PP would be acrylic. Acrylic has a higher dissipation factor than PP, but it is not so high as to require the form to be varnished prior to use, and it also does not absorb any moisture, making any drying process unnecessary. Acrylic also makes some great looking coil forms, but price is a problem for larger coils.
Finally there is PVC. This is the material that is most often used, as PVC pipes are used extensively in pipelines and water drainage systems, making them so easily available at home improvement stores (while all the other plastics need to be obtained through a plastics supplier). Although PVC is not a bad choice in itself, it has drawbacks: Pipes made from that material sometimes have carbon in them so as to make them less sensitive to UV light by exposure to the sun. Black PVC is therefore useless for our purposes. The gray or white PVC must be used therefore. Its tendency to absorb some water when exposed to weather for a long time means that old PVC pipes should be avoided. When using PVC it is important to sand the pipe thoroughly so as to remove all traces of dirty and writings, and it is advisable to give it a layer of varnish prior to winding.
Some coils have also been wound on cardboard tubes. The need to bake it at 100C for hours so as to drive off any moisture, and than give it several coats of varnish inside and out to prevent further water absorption makes it a lot of work to end up with an inferior coilform material.
Once the coilform has been chosen and prepared as necessary, it should be sealed (I.E. Capped on both sides) so as to prevent sparks from running down the inside of the form and ruining it. Normal pipe caps can be used, but better looking results can be had by machining round disks and gluing them on top of the pipe.
Now, lets get into the dimensions of the pipe:
First, the pipe’s walls should be as thin as possible. This makes good sense since all materials dissipate RF to some extent and the more material you have surrounding the RF windings, the more losses you’ll have. The coil should be built with a D/H (Diameter-to-height) ratio of between 1:3 and 1:6. A lower D/H ratio gives the coil higher inductance for the same wire length, and since a high inductance is what gives the coil a high output voltage, this is desirable. However, there is more to high output than a high inductance: First, the coil should have between 800 and 1200turns. Going above or below those values seems to decrease output (either due to increased resistance, or due to too low inductance). Wire size is chosen based on the number of turns and the length of the coil. So the next obvious question is of course how do we choose the coil length.
As a general rule, the more power going into a tesla coil, the longer its sparks will be (although there is a lot more to long sparks than just raw power!). By using the equation

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 Tesla Coil Calculations:

You can calculate this as Ip = Vc.SQRT(Cp/Lp) by a conservation of energy argument where Vc is the cap voltage just prior to the gap firing. A full derivation of this is simple. Assume that at some point, all cap energy (electrostatic) ends up in the tank coil on the first quarter cycle of ring (magnetic). Equate 0.5Cp.Vc^2 = 0.5Lp.Ip^2 and the relation pops out with a little algebraic manipulation. The equation given amounts to cap voltage divided by the surge impedance of the tank.

Vpk = Vin * sqrt( sqrt (Ls/Cs) / sqrt(Lp/Cp) )
Vo = Vp SQRT(Ls/Lp)
Which equals to saying that
Vpk = Vin * impendance transformation