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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 *108  .0133F
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
 25609H
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  1.41.2781  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  1.41.2781    419  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 *106 )
Solving for L, we find our desired inductance for our primary coil:
L  .0000580 H  58H
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
NR2
8R  11W

13.5 * 6.3752
8 * 6.375  11* 6.75
 59.1H
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.