Transformers are not the only way to boost voltage; another method to the madness is a Cockroft-Walton multiplier, also known as the Villrad Cascade depending on your favorite dead scientist. CWs are used to turn high voltage into very high voltage, a task in where a transformer would not be suitable. Essentially it does the same job as a transformer boosting voltage while dropping current, but unlike a transformer a CW outputs DC rather than AC. A CW consists of stages, each stage consisting of of 2 ultrafast diodes and 2 high voltage capacitors. These stages are then stacked up to make a voltage multiplier.
In reality it takes several more AC cycles for the capacitors to charge up. How much the multiplier boosts the input voltage depends on the number of stages, and there is a simple formula for calculating the voltage boost:
Eout = Ein * √2 * n
Eout is the output voltage
Ein is the RMS input voltage
n is the number of stages in the multiplier
Say 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.
Why they suck
Like all good things in this world CWs aren’t perfect. The problem with the CW is as more current is drawn the voltage starts to sag considerably. This voltage drop can be counteracted by using either bigger capacitors or a higher frequency input, and the voltage drop can be roughly calculated using this formula:
Edrop = I / ( f * C ) * (2/3 * n³ + n² / 2 - n / 6)
Edrop is the voltage drop
I is the current drawn in amperes
f is the frequency in hertz
n is the number of stages
C is the size of the capacitors used in farads
This formula should definitely be taken with a grain of salt because while it makes sense in theory, the voltage drop in real life will be much higher. For example, I made a 4 stage CW that theoretically should have dropped only 1.4kV per mA; it actually dropped 20kV. That’s electronics for you.
As if voltage drop wasn’t enough, as current is drawn from the CW the output voltage starts to ripple. Once again there is a formula for calculating this;
Eripple = I / ( f * C ) * n * (n + 1) /2
Electrically CW’s blow, big time. Despite all their pitfalls they do work though, and until we find a better way of boosting high voltage they are all we’ve got. Both ripple and sag become bigger problems as the number of stages is increased, so it’s always ideal to use as few stages as possible and as high a frequency as practical in a CW. This means you’ll need a high voltage high frequency source such as an AC flyback transformer to power the multiplier.
Making One
Making a CW is a rather easy task since it’s such a simple circuit, so simple in fact that you don’t even need a PCB to do it. In the CW to the left I decided to use four stages, but because 30,000V capacitors are rather expensive I put two 15kV caps in series (hence why there are 16 capacitors instead of 8). A CW should be under oil to prevent excess corona losses, so I made this one thin enough to be fit inside a PVC pipe. How you make design and make your CW is your decision of course.
The extremely high voltages involved with CWs 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 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 figure out 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 extremely high voltages a huge electro-motive field 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 electrostatic clicks and pops. Playing with a CW is quite an interesting experience.
The sparks they can make aren’t half bad either.