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So, You want to make a Tesla Coil…… Before I begin this explanation, I need to give credit to Matt Behrend. His website at: http://home.earthlink.net/~electronxlc/index.html was my main source of information. To start off, we will begin with our power source. In this example, we will use a 12kV, 60 mA source for all calculations. We will assume that we have 120V at 60Hz being fed to the transformer. Once we have our power source, we need to find the proper tank capacitor to match it. We first need to find the impedance, Z, (equivalent resistance) of the transformer. To find that, we use the equation: E Z I where E is the output voltage of the transformer in volts, and I is the output current in amps. For our example power source, we have: E 12000 Z 200,000 I .06 Now to determine what size capacitor to use to obtain resonance, we use the equation: C 1 2 * * F * Z where F is the frequency of your source (60Hz in America) and Z is your primary transformer impedance calculated above. Using our example, we have: C 1 1 1.33 *108 .0133F 2 * * F * Z 2 * * 60 * 200,000 Now that we have our calculated capacitance for resonance, we must analyze what type of spark gap to use. Since a perfectly resonant primary circuit can actually be harmful on your caps, it is best to go with a LTR (larger than resonant capacitance) To figure this out, you simply want a capacitance that is slightly larger than the calculated value. In our example, I would recommend a capacitance of about .016 to .019 uF. For our calculations, we will assume that we are going to use a tank capacitor of .016uF. We will next move on to our secondary coil. There are a few key things to keep in mind when making this. You want to keep it proportional. Don’t make it real tall and skinny or real short and fat. For our example, we will use 4 inch PVC which has an outer diameter of 4.5 inches, wound with AWG 24 wire to a height of 25.5 inches. Also, when winding the coil, use one continuous wire, avoiding overlapping turns. Now that the secondary coil is wound, we will make a toroid for it. It is most economical (space practical) and has better performance if you use a doughnut style toroid, however spheres work well too. In this example, we will be using 4 inch dryer duct in a circle with inner diameter of 11 inches and outer diameter of 19 inches. With the secondary coil fully assembled, we can now determine the resonant frequency of this setup. We begin with determining the total number of turns in the secondary coil. To do this, we use the equation: T N *H where N is the number of turns per inch, and H is the height of the coil. Using our AWG 24 at a height of 25.5inches, we obtain: T N * H 46.3* 25.5 1180turns Using the number of turns, we can now find the total inductance of the coil. Using the equation: 2 L N * R 9 R 10 H where N is the number of turns, R is the radius, and H is the height. Using our example coil, we obtain: 2 2 L N * R 9 R 10 H 1180 * 2.25 9 * 2.25 10 * 25.5 25609H Now we need to calculate the capacitance of out secondary coil. To do this, we have two different capacitances to figure out: the toroid, and the self capacitance of the windings. To start off, we will determine the self capacitance of the windings, using the equation: R3 C .29 L .41R 1.94 L Using our dimensions, we find our self capacitance to be: 2.253 C .29 * 25.5 .41* 2.25 1.94 9.61 pF 25.5 We now need to calculate the capacitance of the toroid. To do that, we will be using the equation: D C 1.41.2781 c Dc Do Dc Do Where Dc is the Cross Section Diameter of the toroid, and Do is the outer diameter ot the entire toroid. Using our designed toroid, we obtain: 4 C 1.41.2781 419 4 20.52 pF 19 We can now calculate the resonant frequency of our secondary coil system. To do this, we use the equation: F 1 2 LC The key to this is that L is in Henrys, and C is in Farads, so some unit conversions are required. Using our earlier calculated values, we obtain: F 1 2 (25609 * 10 ) * (9.61 * 10 6 12 20.52 * 10 12 181,186 Hz ) We now have our resonant frequency for our secondary coil. As mentioned earlier, a coil works best when the resonant frequency of the primary coil exactly matches that of our secondary coil. Since we already have our primary circuit capacitance, and know our goal frequency, we can now solve for the needed inductance of our primary coil. Using our above calculated numbers, we get: F 181186 1 2 LC 1 2 L * (.0133 *106 ) Solving for L, we find our desired inductance for our primary coil: L .0000580 H 58H Knowing that we now need to create a primary coil of 58uH, we have plenty of freedom here. Although not necessary, I would recommend making a flat pancake style. There are about an infinite combination of possibilities to make a flat coil that has this goal inductance. To find the inductance of your coil, use the following equation: L NR 2 8 R 11W where N is the number of turns, R is the average radius of the coil, and W is the width of the coil. In our example coil, we will be using .25 inch copper tubing, with .25 inch gap between turns. The radius from the center to the first turn is 6 inches. There are a total of 13.5 turns. With these numbers, we get: N 13.5 (6 (13.5 * (.25 .25))) R 6.375in 2 W 13.5 * (.25 .25) 6.75 L NR2 8R 11W 13.5 * 6.3752 8 * 6.375 11* 6.75 59.1H As you can see, the Inductance is not quite an exact match, but that is acceptable. We now have the dimensions of our coil, however for tuning reasons, it is a smart idea to add more turns. To be safe, I would wind at least 15 turns. This will allow for adjustment in the future, and will also allow for an exact tuned coil. The 13.5 turns is simply a good place to start. It will most likely need to be tapped in a different place, but that is half the fun of the coil….tweaking to achieve max output. Now we are left with our spark gap. To start off, you want to have a smaller gap. This will not put stress on your power supply. I would start with a spark gap of about .25 inches, and slowly increase the gap until you are satisfied with the output. This is a simple process to create a basic tesla coil. I would recommend that you double check your numbers with a program like WinTesla to ensure accuracy.