# Cockcroft-Walton Voltage Multiplier

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The Cockcroft-Walton (CW) Voltage multiplier is named for the Irish-British physicists John Douglas Cockcroft and Ernest Thomas Walton who used the circuit to generate very high voltages in their pioneering particle accelerator in 1932. They won a Nobel prize for this work and the name has been applied to this simple but elegant circuit ever since, even though they did not invent it. The true inventor was Swiss physicist Heinrich Greinacher, who has unfortunately been relegated to a footnote in history.

CW multipliers are still used quite a bit in situations where very high voltages at relatively low currents are needed, such as in photocopiers, photomultipliers, Geiger counters, ion generators, bug zappers and the like.

Figure 1 shows a two-stage CW multiplier. Each stage consists of two capacitors and two diodes. In this case stage one consists of capacitors C1 and C2, and diodes D1 and D2. The second stage consists of C3, C4, D3 and D4. The input to the circuit is an AC voltage which can be sinusoidal or in the form of a square wave. The output a DC voltage roughly four times the peak-to-peak input voltage.

Figure 2 shows how the multiplier works. For the purposes of this exercise, we will assume the input is a square wave centered on zero volts and with a 10V peak. This means in positive half-cycles the input voltage is +10V and in negative half-cycles it is -10V. We will ignore the diode voltage drops for the purposes of the analysis. I have also left the capacitor and diode designators off the diagram for clarity, but they are the same as Figure 1.

We’ll also assume that all of the capacitors are discharged when we start, so the voltages at nodes A through E are all zero. At step (i) the input voltage (node A) swings negative, charging C1 to 10V via D1. The voltage at node B remains zero.

When the input voltage swings positive in step (ii), node B is rises to 20V because the voltage on C1 is in series with input voltage. D1 is reverse biased, but D2 now conducts, charging C2 and therefore node C to 20V.

At step (iii) the input voltage reverses again, recharging C1 via D1 as before. D2 is reverse biased but D3 now conducts, charging C3 to 20V since node B is again at zero volts.

Now when the input voltage goes positive in step (iv) Node B is driven to 20V as before. This time, since C3 is charged to 20V, node D rises to 40V (the 10V input plus 10V across C1 plus 20V across C3). D4 now conducts charging C4 to 20V.

Subsequent cycles just continue this pattern. If there are more stages, the multiplication continues. In theory each stage adds another 20V to the output with the final voltage given by the peak-to-peak input voltage times the number of stages.

Figure 3 shows the waveforms we will see at each node. The output of each stage (nodes C and E) is a DC voltage. The intermediate nodes (B and D) have an AC component similar to the input node but offset by an increasing DC level. One of the benefits of this is that the capacitors and diodes in any stage only ever see the peak-to-peak voltage of the input across them (20V in our case), regardless of the output voltage.

That’s the simplified story. In reality you won’t get quite the output voltage that this analysis suggests. The diodes do have a forward drop that must be accounted for, and any load applied to the circuit will drag the voltage down as the source impedance of the multiplier is relatively high. Both effects get worse as more stages are added and there will eventually be a point where adding more stages won’t help.

These circuits typically aren’t therefore used with such low voltage inputs. More often than not they use multi-hundred-volt AC input with high-voltage diodes and capacitors to generate kilovolt outputs with very light loads. It’s not uncommon to see 10 or more stages under these circumstances. Figure 4 shows a typical commercially available example. This circuit is designed for a 120V AC input and has 17 stages for a notional 5.7kV.

References

Science and Technology. “Cockcroft-Walton Generator.” National Museums Scotland. Accessed February 26, 2022.
https://www.nms.ac.uk/explore-our-collections/stories/science-and-technology/cockcroft-walton-generator

“Cascade Generator Built at the Cavendish Laboratory | Science Museum Group Collection.” Accessed February 26, 2022.

“Cockcroft–Walton Generator.” In Wikipedia, January 16, 2022. https://en.wikipedia.org/w/index.php?title=Cockcroft%E2%80%93Walton_generator&oldid=1065936726.

“Eastern Voltage Research.” Accessed February 26, 2022. https://www.easternvoltageresearch.com/.

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