However, I wanted to learn about how Tesla Coils worked from this project. So I started researching Tesla Coils, and I want these blog posts to serve as a compilation of my research and design considerations as I fabricate a Tesla coil.

How do Tesla Coils Work?

The first question I asked before we started this project was: How do Tesla Coils work?

Tesla Coils make high voltage at high frequencies.

Tesla Coils are generally a two stage transformer, taking in the low voltage 60 Hz wall power, and converting it to millions of Volts at somewhere between 200 KHz to 4 GHz.

What does the most basic circuit look like?

How does a Tesla coil change the input frequency?

From a signals perspective, the first question I would have after reading the description would be, “how does the frequency change from 60 Hz to hundreds of kilohertz, or where does the non-linearity of this system come from?” (because linear systems cannot shift the frequency)

Transformers, Capacitors, and Inductors cannot change the frequency, it’s the spark gap.

In the primary side of a Tesla Coil, the spark gap introduces a non-linearity into the system.

There are three major pieces to the general Tesla Coil, as you can see in the above picture. The low voltage input from the wall to just past the high voltage transformer (yellow), the primary from the tank capacitor to the primary coil (green), and the secondary including the secondary coil and the toroidal top (red). The input charges the tank capacitor to a relatively high voltage (thousands of volts) still at 60 Hz until a spark gap breaks down. When this spark breaks down, it becomes a near zero resistance short circuit, which puts an impulse on the primary coil and causes the whole primary circuit to oscillate at it’s natural frequency, a function of the inductance of the primary coil, and the capacitance of the tank capacitor. The RLC (Resistor, Inductor, and Capacitor) circuit at resonance, creates a standing voltage wave that

You can read more about RLC circuits on Wikipedia here. The spark gap is the key to the non-linearity in this system.

How does a Tesla coil make millions of Volts?

The voltage increases from thousands of Volts to Millions of Volts because of resonance between the primary and secondary parts of the circuit.

The secondary side is another RLC circuit. The L is the secondary inductor, and the C is the torus on top. The R comes from the resistance of the windings on the coil. This low series self-resistance from the coil gives the secondary a high quality factor. The complete circuit occurs when air breaks down around the torus and current flows to the surrounding environment. The secondary is designed to naturally oscillate at the same frequency as the primary. Because they oscillate at the same frequencies, the voltage multiplies from the primary to the secondary. This is called a loosely coupled transformer.

Is the primary/secondary a normal transformer?

No. Because the windings of the primary are so far away from the windings of the secondary, and the core of the transformer is  air, it is considered a loosely coupled transformer. This means than the ratio of the windings of the secondary to the primary will not be exactly equivalent to the voltage gain. The voltage gain or ratio of secondary voltage to primary voltage is more affected by how well the primary and secondary resonate together, which happens when they are tuned to the same natural frequency.

Are there any other factors that affect the performance?

The secondary should have a length corresponding to the your design frequencies wavelength divided by 4, an antennae and transmission line rule. This is because on the secondary at resonance, a standing voltage wave is created on the length of the wire wrappings of the secondary coil. This standing wave will have a wavelength corresponding to the frequency it is resonating at, which ideally will be 4 times the length of the secondary coil wire.

where f is the frequency of oscillation, c is the speed of light (3E8m/s)

Note that the voltage maximum is where we want our length of wire to be, and it occurs at 1/4 of the width of the sine wave or the wavelength divided by 4.

Practical Applications

What does all of this mean for actually building a Tesla Coil?

This means that you should pick a frequency, I picked 600 kHz, for your Tesla Coil to operate at. Then you should calculate the wavelength, by taking the speed of light 3E8m/s divided by your frequency. Then you should divide this wavelength by 4 to get the length of your secondary coil wire in meters. My length was 125 meters. If you are using PVC to wrap your secondary around, pick a standard size outer diameter of PVC, (mine was 3″ PVC with an outer diameter of 3.5″) and calculate the number of turns by dividing your ideal wire length by pi*outer diameter in meters. 125/(.0889*pi) = 447.56 turns. If you want to be precise, you can also take into account the radius of the wire you are wrapping the PVC with, (mine was 26 gauge). Round up and you now know enough to make your coil.

When winding this coil, the turns should be close together, there should be no overlapping, and no kinks. When you are finished, you can measure the inductance of your coil, and compare to what this website says when you put in your coil dimensions.

In the next post, I will discuss the other half of the secondary, the torus on top, and how to calculate it’s dimensions so that your secondary oscillates at the design frequency.

What can I read to gain a better understanding?

Some other recommended Wikipedia readings are:

• Electrical Imedance
• Resonance of an RLC circuit
• Q-Factor

I found a php function which takes much of the hardest part of this problem and makes it easier. The function is version_compare().

—————————

What’s the problem? Say you have a version number such as 1.2.3 stored in a MySql database as a varchar, and you want to sort this version number. Without any decimals, here is the sorting descending:
+———+
| version |
+———+
| 9960 |
| 9952 |
| 9765 |
| 9764 |
| 10011 |
+———+
5 rows in set (0.00 sec)
It thinks 9960 > 10011
If you don’t have a decimal point this can be easily remedied by doing:
ORDER BY CAST(version AS UNSIGNED) DESC
But as soon as you put a decimal into the version, it ignores everything to the right of the decimal point.
My solution is a PHP sorting algorithm.
$versions is an indexed array that has this format, which could easily come from a database
array
0 =>
array
‘id’ => int 88
‘version’ =>
array
0 => int 0
1 => int 9
2 => int 10011
1 =>
array
‘id’ => int 87
‘version’ =>
array
0 => int 0
1 => int 9
2 => int 9960

// convert all values to ints
array_walk_recursive($versions, function(&$val, $i)
{
    if (is_string($val))
        $val = (int)$val;
});
// make to arrays the same length by padding them with 0s
function normalize($a, $b)
{
    $al = count($a);
    $bl = count($b);
    if ($al < $bl)
    {
        // add 0s to $a until they are the same size
        while (count($a) < $bl)
            $a[] = 0;
    }
    elseif ($al > $bl)
    {
        // add 0s to $b until they are the same size
        while ($al > count($b))
            $b[] = 0;
    }
    return array($a, $b);
}
//compare to integers and decide which one is bigger
// return 0 if they are equal
function check($a, $b)
{
    if ($a < $b)
        return 1;
    elseif ($a > $b)
        return -1;
    else
        return 0;
}
// sort the array
usort($versions, function($a, $b)
{
    // make sure the major_version arrays have the same length, pad with 0s to correct
    list($a['version'], $b['version']) = normalize($a['version'], $b['version']);
    for ($i=0; $i < count($a['version']); $i++)
        $check = check($a['version'][$i], $b['version'][$i]);
    return $check;
});

Vacuum ports and Adjustment Screws

My motorcycle has 4 inline carburettors, with a shared linkage, 3 adjustment screws between each pair of carbs, and the throttle connected in the middle.
The problem was that each carburettor wasn’t allowing the same amount of air through. This can be remedied with a tool called a manometer that measures the pressure difference at two points. Most multi carb setups have a small vacuum port between each carb and the engine, which is usually plugged with a screw. I took that screw out and found out it was an M5 x .8 metric thread. I then bought a hex bolt with that size, and drilled a hole down the center.

hex bolt with hole drilled through it

I then built the following tool from these plans, slipped the hex bolt into the end of the tube, filled it up with water, and balanced all of the cylinders. This took some trial and error, and I had to be careful that the carbs weren’t too far off or else there would be enough pressure to suck the water into the engine. I started on the right two cylinders, and adjusted the farthest right adjustment screw. I then moved left. When I was done, the problem was fixed, and the motorcycle was running perfectly.

DIY manometer

DIY Manometer

/**
 * Captures output from a function
 *
 * @param $callback is the name of the function
 * @return the output of the function
 */
function capture($callback)
{
    $args = func_get_args();
    array_shift($args);
    ob_start();
    if (count($args))
        call_user_func_array($callback, $args);
    else
        call_user_func($callback);
    $output = ob_get_contents();
    ob_end_clean();
    return $output;
}
$sidebar = capture('get_sidebar');
// or if it was a function you needed to pass arguments into
$title = 'Test';
$author = 'Nate Nuzum';
$header = capture('get_header', $title, $author);

// works in the newer version of php 5
$sidebar = capture(function()
{
    get_sidebar();
});
function get_sidebar()
{
    echo 'hello';
}
function get_header($title, $author)
{
    echo "{$title} {$author}";
}

Add the following to your .vimrc Set 100 to the max number of characters that you want in a line.

:nmap <c-a> ggVGgq
:setlocal textwidth=100

save and quit.

Open up a file to edit, press Control-A and voila!

<?php
// Disable the flash uploader
add_action('flash_uploader', 'disableFlashUploader');
function disableFlashUploader(){return false;}
?>

Iowa State has a high dollar deal with U.S. Bank that allows students to use their university id as a debit card. They have it set up such that, if you come to ISU, during your registration for classes, you automatically get routed into a line to sign up for a new U.S. bank debit card. And they make it seem like it is part of registering for ISU. A friend of mine called U.S. Bank about getting a loan. He asked them why he should get a loan from them if their rate wasn't that good. The service representative said, we have no reason to offer good rates, we make all of our money off of overdraft fees on college kids. Another friend of mine, over-drafted on accident. Each time she tried to use her debit card, for about 3 days, they charged her around $30. Her charges went up to over $500. We asked them why the card kept working if she was several hundred dollars in the negative, and the U.S. Bank employee replied, "We allow it to continue working to save the customer from the embarrassment of their card not working in the grocery store." I personally would much rather be slightly embarrassed by my debit card not working than to get charged hundreds of dollars in overdraft fees.

Two friends A and B meet every morning at the Grand Central Station around 7 am. Suppose the actual times they arrive are independent and uniformly distributed between 6:55 am and 7:05am. Let Z denote the time between arrivals, i.e. Z = time B arrives – time A arrives (can be negative!).
(a) What is the range of values of Z (i.e Im(Z))?
(b) Find the density of Z (derive a formula similar to the convolution formula derived in class).

The Solution

(a) The times for Z can vary from -10 to 10. Suppose friend A arrives at 6:55 and friend B arrives at 7:05. Z would = -10. The other way around will result in Z = 10
(b)

Define Random Variables

X = # of minutes (continuous) after 6:55 friend A arrives
Y = # of minutes (continuous) after 6:55 friend B arrives

Outline of Problem

• The probability distribution functions of X and Y are uniform (constant and area = 1)
• The convolution of the pdf’s of X and the negative of Y (X-Y) equal the pdf of Z
• The result should look closer to the normal curve because of the Central Limit Theorem

The two input pdf’s and the result of the convolution which is the pdf of Z

Performing the convolution

Note: a=10

Simulation

• Random number generator is a uniform distribution
• Histogram of Randbetween(0,10)-Randbetween(0,10) 2092 times divided by 2092
• Discrete version of this problem