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My HVG10 high voltage power supply puts out from 24kV to 75kV positive with respect to ground whereas I needed something that put out just a few thousand volts negative with respect to ground, positive with respect to ground and ground too. Luckily, my HVG10 contains a single circuit board immersed in mineral oil that is all that needed to be replaced in order to do this. Here's the resulting power supply.
Most voltage multiplier schematics you see are for positive output. To get both positive and negative output you need to add a second circuit in parallel with the positive output one but with the diodes reversed.
The squigly lines on the left in the diagram above represent an AC source, in this case a flyback transformer, which is part of the the input to the circuit board and everything to the right is the circuit board contents. A full schematic of an example of the input (non-voltage multiplier) side, of things can be found on this page about my 30kV power supply. Construction details for the high voltage power supplyI ordered the high voltage diodes and capacitors both from Information Unlimited, the same place that I bought the HVG10 power supply from many years ago. The diodes are their part number VG12 (12,000V, 10mA diodes, .625 x .13" rectangular epoxy coated, unmarked, 100 nanosecond fast recovery devices for use with high frequency switching circuits, avalanche diodes.) The capacitors are their part number .001m/20KV (0.001microfarad, 20kV ceramic disk capacitors.) Note that I didn't do any special calculations in selecting either of these parts. I simply looked for inexpensive high voltage, high frequency diodes and high voltage, non-electrolytic capacitors.
Two holes were drilled in the sides of the cap for the output wires. Two nylon bolts were stuck up through the top of the cap. I didn't want to have the HV- and HV+ steel output balls sitting directly on top of the cap since any dust accumulated on the cap would act as a conduction path between the two. So I raised them using the nylon bolts. The reason for making the output wires so long outside the cap was to make it easier to position the board inside the grey tube before putting the cap on top of the tube. I also made a plexiglas window in the top of the cap so that I could check that the output wires inside the cap were not close to each other.
Testing the high voltage power supplyI used my store bought 40kV Fluke HV probe connected to the oscilloscope's channel 1 to measure the negative and my homemade > 40kV HV probe connected to channel 2 to measure the positive, both relative to ground. As you can see from the following photos, the combination worked. The slight AC ripple on the upper line is noise picked up by the homemade probe from the 60Hz household AC lines. The result on the oscilloscope below is 2.84kV. This is the minimum voltage, which is around what I need this for. I haven't looked for the maximum. When the dial of the power supply is first turned up and voltage first appears, the voltage is higher. I then turn it down until around 2.8kV. If I go lower then the voltage quickly drops to zero.
A bit about the ground connection and safetyThe third steel ball is connected to ground. This isn't just for convenience. When the power supply is turned off, the voltage slowly goes to zero/ground. To make sure both positive and negative steel balls have reached zero/ground potential and are safe to touch, I have a long stick with a copper pipe taped to its end that I electrically connect the negative and positive balls to the the ground ball with one at a time as in the photos below. I keep the pipe in place for a few seconds to make sure they've reached ground potential since it may take a little time to drain capacitors. There is often a small arc when I do this. To be very safe, I touch the ground ball first before touching a HV one. If I touched a HV one first then the arc may find its way to ground through me instead of through the air to the ground ball.
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