Instructables
First things first, a disclaimer: 
I am not responsible for any bodily damage or property damage that is a result of one building or using this circuit. High voltage can be dangerous or lethal when used incorrectly, and it is up to the user of the circuit to use high voltage safety rules and maintain their own safety at all times.

Flyback transformers are some of the most commonly used high voltage supplies by hobbyists- mainly due to their relative simplicity and how easy they are to find. Every single CRT (big, heavy kind) TV that people are throwing out now has one, the bigger the TV the bigger the transformer.
But unlike many transformers that you find in electronics, which are designed to handle standard 60 hertz AC power, and are step down transformers, flyback transformers operate at much higher frequencies- around 16 khz or sometimes higher. Many modern flybacks also put out DC voltage. Older flybacks had AC power output, making them the ones you want. The AC flybacks can operate at higher power, since there are no rectifier/multiplier circuits built into them like the DC flybacks.
That being said, DC flybacks are easier to get. So for this project they are recommended. Make sure that the flyback transformer you are using has an air gap. This means that the core is not a loop all the way through, but is rather shaped like a C with the gap being about a mm thick. Almost all modern flybacks have an air gap, so if a new on is being used, checking is not necessary.

Now, onto the circuit. I am going to say right now this is not my circuit. I found it on the 4hv.org forums here. This Instructable is intended to take much of the theory presented in the thread and condense it into a quick how-to for beginners. 

This circuit uses the venerable 2n3055 transistor, which is loved/hated by flyback driver builders. Loved because it is so easy to get (even Radioshack sells them) and hated because they generally stink. They are prone to burning out, sometimes spectacularly. That being said, this circuit works incredibly well with it.

The bad reputation for the 2n3055 comes from it being used in the usual single-transistor flyback driver, which puts a lot of stress on the transistor. In this circuit, a few components have been added which dramatically increase the power that the circuit can put out. The theory of the circuit is discussed later in the Instructable. 
 
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lnp7119338 months ago

Great circuit, with just one issue I noticed: I had to reverse the connections to the feedback to get the circuit working. Is it just the way my circuit is set up or did other people find that too? I am using a 470 ohm resistor, a 25 ohm resistor, a 2n3055 transistor and a 1n4007 diode. Thanks for the circuit though, I am running it off of an old laptop charger XD

I am wondering about one more improvement, how about putting a second diode across the primary? what do you think?
Hi ! really really good tutorial, I have reached to 31kv by finding the best suiting cap. it was a 0.01uf ceramic 2kv one. anything higher or lower made the sparks shorter but that cap was making the circuit resonant. Anyway, I tried to increase the primary turns from 6 to 10 and while I had that cap, I flipped the power on, the arc started nicely at few mm and all of the sudden:

QUITENESS
Complete silence! , man I was mad, what happened, how? why? I don't know if its the flyback that fried or if it was the transistor. I checked the transistor and found that the Collector-Emittor was short circuited from inside, that is there was zero resistance between them! How did that happen, was it the cap capacitance? I tried many prim. turns before without trouble... but still shouldn't the diode cap save the trans. it seemed it did the opposite? ha?
Nice! I am creating a video of a complete beginner's guide to flyback drivers. Can I use your photo of the complete setup? I would put a caption at the bottom that says JoeBeau on Instructables.
JoeBeau (author)  clevelandstorms1 year ago
With that being said, however, this schematic is not my design, and i gave reference to it being the creation of the people at the 4hv forums.
JoeBeau (author)  clevelandstorms1 year ago
Sorry it took so long for me to respond. I've been busy with school and letting the hobbies slip slightly.
Sure you can. As long as proper credit is given, feel free to use my work.
rkorion1 year ago
If you put a variable capacitor, the frequency and the shape of the arc will be different.
well done, what are you going to use this for? tesla coils?
JoeBeau (author)  amandaghassaei1 year ago
I did build a quick and dirty TEA laser, but not much else with this yet. possibly a tesla coil in the near future