Mini Tesla Coil
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The driver circuit:

This will be the circuit used for the ignition coil driver.
ignition coil driver circuit
This circuit was designed to not fry the 555 timer, this is because I noticed that having the ignition coil share a high voltage contact with a power connector made somewhat high voltages go back and into the 555 timer, thus frying it (I went through about 7 timers before I finally got this to work). So after desoldering a few unused boards, I found out that most of the IC's I removed were photocouplers and I thought that they could be used to isolate the frequency signal appart from the driver that connects to the ignition coil. In a way the photocoupler acted like a relay. For the photocoupler it does not have to be the cosmo 1010, I just used that one because that was the smallest photocoupler that I removed from the board. You can play around with the capacitor and resistor values to see what they do, but I found that this combination gives some of the largest arcs from the igntion coil. The ignition coil is not portrayed as connected to the driver circuit, but it is shown clearly where to connect in the schematic of the tesla coil itself. It is also essential that the 6 volt power source is separate from the 12 volt one, that is why there's a photocoupler, to completely isolate it. You can see that there is an "audio in" port on pin 5 of the 555 timer, that is optional, but in order to use it, you will have to change the capacitor from a 0.47uF electrolytic to a 0.1uF ceramic capacitor (it's the one with the number 104); all you have to do is connect the output of the audio device to this and connect the common wire to the negative on the 6 volt side, but try not to use anything expensive as I've been using a cheap CD player and it acts a bit weird now from being connected, so try not to use your $200 ipod touch or anything like that. The picture of a physical circuit is what the driver circuit looks like, and beside it is the transistor.

The Tesla coil circuit

This is the actual Tesla coil circuit. You can see the way the ignition coil has the inputs for the power that is outputted by the driver circuit.
main Tesla coil circuit
The first circuit is the one I used, a basic spark gap Tesla Coil with no additional safety features or regulators or anything. The circuit is wired in a way that you don't need to have a grounding connection at the base of the secondary, it's probably recommended but will make things harder and will pose a threat to any of your electronics that are plugged in.
The circuit in the middle is the most basic schematic of a solid state Tesla coil taken off electronsbefree, it is an off-line Tesla coil. I wanted to make one of these, but there isn't very much information on the internet about this one, and it also involves components that are somewhat pricey and that I don't currently have access to like IGBT's and high power MOSFET's.
The last circuit is a super simple solid state Tesla coil, it must be the most basic one I have ever seen, I think the owner of this image could be found here. I also wanted to make this one, but I don't have the resources to buy a nice high power MOSFET and the IXYDD414 chip.
The last picture is what my setup looks like. But I got my Tesla coil pretty solid state-ish because of the driver and being able to modulate the frequency with audio.

The Tesla coil components

Ignition Coil: Probably the most necesary component in a non-sstc type Tesla coil, but it doesn't have to be an ignition coil, just as long as it is something that can make a couple thousand volts. This is the component that supplies the high voltage that is necesarry to drive the unit. If you've ever seen or used an ignition coil, you know that there is only 3 connections, which is why I had to design that isolated driver circuit so you don't get inductive kickback mixed with high voltage signals.

Spark Gap: This component is one of the main timing mechanisms. This controls when the capacitor discharges across the primary coil. A drawback of this component is that it creates a lot of light, like an arc lamp. Another drawback is that it is incredibly loud, so this complicated some things when it came to playing music off this coil. To make this one, I just used a nail in a peice of wood and a screwdriver, and the screwdriver allowed me to adjust the distance of the gap.

Capacitor: This component controls the amount of power that can surge through the spark gap and into the primary coil. It stores a charge from the transformer or ignition coil in this case. When enough power has been stored, it is released through the spark gap. So the spark gap controls the frequency and the level of the power that goes through the primary, that is why it is important to be able to adjust the length of the arc.

Primary Winding: This is the component that turns the pulses of power into somewhat strong electromagnetic energy. It creates the pulses that the secondary then amplifies. This flat coil has to work in sync with the capacitor and the spark gap to make a frequency that corresponds with the secondary winding and the topload if it has one.

Secondary Winding: This is the part that amplifies the electromagnetic pulses from the primary winding and all the other components. This unit outputs high voltage at low current (low current considering the voltage that is outputted) hence the reason you can touch the arcs made by coils of this small size. On larger Tesla coils, the voltage is high enough to let out a fairly large ammount of current, so don't try touching too big of arcs. These also output a lot of electromagnetic energy so try not to let any electronics nearby, and on larger coils, unplug anything that is connected to the wall outlet unless the coil has it's own isolated power supply which I have never seen on large coils, only on small ones.

Action Photos

Here are some action photos of my tiny Tesla coil, I'm suprised that my iTouch didn't get fried, but on the videos you can see a little distortion.

The first 2 pictures are the streamers going through a standard 60 watt argon filled incandescent lightbulb. The last 2 pictures are a CFL without the circuitry and base, but there is enough electromagnetism going through the air to excite the phosphor in the bulb... wireless lighting.

Videos of my Tesla coil