Voltage Multipliers
Transformers are not the only way one can boost voltage; another method to the madness is a Cockroft-Walton multiplier, or thes the Villard Cascade depending on your favorite dead scientist. “CWs”, as they are colloquially known, are a charge pump used to turn high voltage into very high voltage, a task in where transformers would not be suitable. Much like coupled inductors this circuit ‘trades’ current for voltage, but unlike a transformer, a CW outputs DC.
In reality it takes several more AC cycles for the capacitors to charge. How much the multiplier boosts the input voltage depends on the number of stages, and there is a simple formula for calculating such ideal voltage gain:[m]E_{out} = E_{in} * \sqrt{2} * n[/m]Where:[m]Eout[/m] is the output voltage[m]Ein[/m] is the RMS input voltageSay you have a 6 stage multiplier and you feed it 7kV. By using the formula above you can calculate that the theoretical maximum output voltage will be 59.397kV
The extremely high voltages make wire resistance for the most part irrelevant. Resultantly, the capacitors are capable of discharging in multi-kiloamp pulses; far more than the little diode at the end of the stack can handle. This means that during use you’ll need either a resistive load such as an x-ray tube, or if you just want to make sparks, a resistor in series with the output. Ohm’s law can help you determine what resistor you need, but expect it to be in the range of several million ohms. Remember that since there are very high voltages in place here there are also very high powers, so make sure your resistor is capable of handling the heat. A 1/4W resistor just ain’t gonna cut it!The super high voltages that a CW can produce are quite fun to play with. At these extreme potentials huge E-fields can be made, as well as plenty of ionic wind. Simply sitting next to an operating CW you can feel the field charge up your arm hair (if you have any), and there is no shortage of random electrostatic clicks and pops. Playing with a CW is quite an interesting experience.
How it works
A voltage multiplier consists of stages, each stage consisting of of 2 ultra-fast diodes and 2 high voltage capacitors. These stages are then stacked up to make the multiplier.