If you need a high voltage, a voltage multiplier is one of the easiest ways to obtain it. A voltage multiplier is a specialized type of rectifier circuit that converts an AC voltage to a higher DC voltage. Invented by Heinrich Greinacher in 1919, they were used in the design of a particle accelerator that performed the first artificial nuclear disintegration, so you know they mean business.

Theoretically the output of the multiplier is an integer times the AC peak input voltage, and while they can work with any input voltage, the principal use for voltage multipliers is when very high voltages, in the order of tens of thousands or even millions of volts, are needed. They have the advantage of being relatively easy to build, and are cheaper than an equivalent high voltage transformer of the same output rating. If you need sparks for your mad science, perhaps a voltage multiplier can provide them for you.

## How Does It Work?

The multiplier circuit needs an AC power supply in order to work. For the sake of simplicity let´s assume that one side of the power supply is grounded and remains at zero potential, and the other varies between plus and minus U (100 V in the example). Here’s what happens:

1. Capacitor C1 charges through diode D1 at the voltage U (100 V) of the power supply, which is at its negative peak. Note that this leads the capacitor to be positive at its right side and negative at its left.  The yellow line indicates the direction of current flow
2. We now have +100 V at the upper side of the power supply, and this voltage adds to that of C1 that was charged in the previous step. Therefore capacitor C2 charges through D2 to 200 V, or 2U (100 V from the power supply plus 100 V from C2).
3. The charge stored in C1 was used in the previous cycle to charge C2, so C1 is now charging through D1 as in step 1. Also, capacitor C3 is charged through D3  to 2U. Why 2U? Because since C1 is discharged, point “a” in the schematic is at zero potential and C3 sees the 200 V of C2.
4. The power supply is again at its positive peak, and C2 is now being recharged as in step 2. At the same time, capacitor C4 charges to 200 V, because it is the potential difference that it sees: 400 V at its positive side (100 V of the supply plus 100 V of C1 plus 200 V of C3), and 200 V at its negative side, which is the potential of C2.

As we can see, we will end with 400 V between ground and the output (points a and b in the last figure), effectively quadrupling the supply voltage.

This is an idealized explanation, and as you may guess reality is always more complicated. For instance, capacitors do not charge instantly, therefore they do not reach the full voltage until several cycles have passed, depending on the charging current that the power supply can deliver.

The multiplier that we just discussed has two stages. Each stage is formed by two capacitors and two diodes and each one adds two times the voltage of the power supply, so for example a five-stage multiplier will have an output of ten times the input voltage. Note that each component in the circuit only sees at most twice the peak input voltage provided by the source, therefore you can use low voltage components and many stages to obtain a very high output voltage.

However, the output voltage will drop as soon as you connect a load to the circuit, according to this formula. Here we can see that we need high frequency and high capacitance in order to minimize voltage drop, and that this drop increases with current, and also very rapidly with the number of stages. In fact, since it depends on the cube of the number of stages, a multiplier with ten stages has 1000 times more voltage drop than one with a single stage.

Another situation that arises when very high voltages are present is corona discharge, which is an electrical discharge that arises when the strength of the electric field around a conductor is high enough. Corona acts as an unwanted load on the multiplier, reducing the output power. One way to minimize corona is to reduce the curvature in conductors, avoiding sharp corners, projecting points and small diameter wires. For this reason large diameter end points and conductors are used. This of course complicates the design of very high voltage multipliers but at the same time accounts for their impressive look, as in the feature image.

Making a voltage multiplier to obtain high voltage is a popular project and is pretty easy as long as the voltage is not too high for corona to start creating problems. All you need besides an AC power supply such as a neon transformer  are some high voltage diodes and capacitors. Practical uses include X-ray machines, photocopiers, air ionizers and microwave ovens, among others. At the high end of the spectrum are the multipliers used for research in particle accelerators, several meters in height, that can reach millions of volts.

The high voltage multiplier has a venerable history in particle accelerators, and even a Nobel prize in Physics was awarded for research that was possible thanks to it. However as new technology has arrived, in particular radio-frequency quadrupole systems, those magnificent multipliers have been retired. We sure will miss them, and of course that doesn’t stop you from building your own.