After the first attempt to build a Tesla Coil failed 10 years ago I finally fulfilled this childhood fantasy. Remembering the problems of obtaining high voltage capacitors and the like I went for the Solid State (No big capacitors and spark gaps, just transistors) approach this time. Not being the most skilled person when it comes to analog, and especially high frequency, circuits I started searching on the Internet. The design had to meet some requirements: It should run on a DC power supply (i.e. not mains power) and not need any exotic parts.
I finally settled for a circuit from this site (Mini Tesla Coil 3) and made my own PCB layout. This was the first PCB I made using a laser cutter to transfer the layout to the board. A blank copper-clad board was sprayed with two layers of black paint which was then etched away by the laser cutter. To completely burn away the paint the same image was lasered several times on the highest power. Afterwards the board was etched with HCl/H2O2.
The circuit uses an LC filter which has to be tuned to the resonant frequency of the secondary oscillator circuit. (If you choose to use it. I found that the circuit works just fine with out it. Apparently it is only necessary to filter any unwanted oscillations.) To measure the resonant frequency, connect a function generator to the lower end of the secondary coil and set it to a square wave output with 50% duty cycle. Then place a piece of wire parallel to the coil and hook it up to an oscilloscope (Also connect the grounds of function generator and oscilloscope.) Now increase the frequency of the square wave until you see a sine wave on the oscilloscope. When the sine wave has the biggest amplitude, you have found the resonant frequency. With a 9 Vpp square wave I measured a sine wave of about 90 Vpp. You have to do this procedure twice. Once with the topload and once without.
With the frequency you can now calculate the necessary values for the inductor and capacitor via the formula
Use available values to approximate your frequency as closely as possible.
The secondary coil has 1200 windings and was wound with 0.15mm enamelled copper wire on a Ø75mm PVC drain pipe. At each end the thin copper wire is routed to the inside of the pipe through small holes and soldered to a thicker wire. The holes are then sealed with hot glue. The pipe is mounted to a wooden base which also holds the posts that hold the primary coil. The Topload Capacity is a stainless steel ball which was sold as a home decoration item.
The primary coil is wound from Ø1mm copper wire. In my case it has about 8 windings of which a section can be selected with wire clamps. This makes quick adjustments possible. The driver circuit has four connections to the coils. One leads to the bottom of the secondary coil and is used as a feedback to measure the oscillations and drive the primary coil accordingly. This is done with the remaining wires. Voltage is applied alternately between wires 1-2 and 2-3 thus doubling the effective amplitude over the primary coil.
Here are some photos of sparks I made with my coil. You can generate quite interesting effects with light bulbs and other things filled with thin gas.