200kV Voltage Multiplier.

Help me finish this project.

 The Cockroft-Walton voltage multiplier was invented in the 30's by two men who gave it their names to serve as a way of producing very high voltages which would be unpractical to obtain from transformers due to the bulk of the insulation required. By using only capacitors and diodes, these voltage multipliers can step up relatively low voltages to extremely high values, while at the same time being far lighter and cheaper than transformers. They were, and still are, used in x-ray tubes, particle accelerators, electrostatic devices, and many other devices making use of very high voltages at DC values.
 Needing a high voltage DC source for its electrostatic research, PowerLabs searched all over the Internet trying to find a supplier. After a long exchange of e-mails with someone (whose name will not be disclosed) working for "Reynolds Industries", who seemed more interested in knowing who I was working for (he thought I was an industrial spy!) than in actually trying to sell me his products, and after having several of my e-mails ignored, with one final rude response attempting to sell me an 80kV 1mA cascade for 1000dollars, it was decided that PowerLabs should build its own cascade. The result is what you see below:

Here one of the individual capacitors used is seen with a rectifier (the thin white rod) placed next to it. All of the capacitors are TRW, and are rated for 9000V / 1nF each. Dimensions are 2cm (.8")diameter, 1cm (.4")width. Leads are 4.5cm (1.8")long. When charged to its full potential, each capacitor should store 0.4J, which of course translates into 1.62J for the whole bank when it is charged to its full potential (200kV). The total energy is kept at low levels so that it becomes possible to run very high duty cycles, charging the capacitors tens of thousands times every second. It is these very high duty cycles which make it possible to achieve a constant output from a cascade.
 Each rectifier is rated at 13kV, 5mA. Notice how short they are. The actual element is only 1cm long! Obviously, these will not reach their full potential in air without suffering arcovers. Under oil, it should be possible not only to push the system to its maximum high voltage limit, but also to go over the rectifiers' maximum current handling capabilities, as they will be cooled by the liquid surrounding them.

For this picture all 40 capacitors were lined up with the 40 rectifiers next to them.
 Both the capacitors and rectifiers were bought new, and are made in USA. The capacitors cost me $1.5 a piece (bulk buy of course), and the rectifiers were also $1.5 a piece (part of the deal). The whole system therefore cost $120 in parts, minus charger, enclosure, and oil.
 I plan on assembling them all inside a plastic pipe filled with clear non viscous silicone oil. Charging will be done by a flyback running at 30KHz, and outputting exactly 9kV at 10mA.

 Results: So far 6 stages have been installed and spark length is nearing 5cm (2"). As expected severe corona leakage is occurring and the input voltage has to be kept below 3kV otherwise sparkovers will occur. This will be solved as soon as the entire device is dipped in oil.
 2: The rectifiers keep blowing because my charging current is too high... I'll be installing some current limiting resistors for my next testing session. Spark length is now 12cm.

 Theory/Math:

 The output voltage (Eout) is nominally the twice the peak input voltage (Eac) multiplied by the number of stages,

 The voltage drop under load can be calculated as:

Edrop = I1/ (f*C) * (2 /3*n^3 + n^2/2- n/6)

where:
Iload is the load current
C is the stage capacitance
f is the AC frequency
n is the number of stages.

The ripple voltage, in the case where all stage capacitances (C1 through C(2*n)) may be calculated from:
Eripple = Iload/(f * C)*n*(n+1)/2

As you can see from this equation, the ripple grows quite rapidly as the number of stages increases (as n squared, in fact). A common modification to the design is to make the stage capacitances larger at the bottom, with C1 & C2 = nC, C3 & C4= (n-1)C, and so forth. In this case, the ripple is:
Eripple = Iload/(f*C)

For large values of n (>= 5), the n²/2 and n/6 terms in the voltage drop equation become small compared to the 2/3n³. Differentiating the drop equation with respect to the number of stages gives an equation for the optimum number of stages (for the equal valued capacitor design:

Noptimum = SQRT( Vmax * f * C/Iload)

Increasing the frequency can dramatically reduce the ripple, and the voltage drop under load, which accounts for the popularity driving a multipler stack with a switching power supply.

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 Last updated 03/04/05