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Chris,It's a very challenging design problem. And, the divider will be quite sensitive to changes in the surrounding E-field. Since TC sparks create shifting space charge regions with corresponding fluctuating E-fields in the surrounding air, accurate direct measurements can be done only if the Tesla coil is not actively creating streamers/leaders.
Many years ago, Marco Denicolai designed a compensated voltage divider to measure the output voltage of his large Tesla Coil. His divider used an aqueous resistor combined with E-field and distributed capacitance modeling. His divider was suspended from the ceiling directly above his TC toroid. His paper and some other information can still be found on his web site:
http://www.saunalahti.fi/~dncmrc1/wprobe/wprobe.pdf http://www.saunalahti.fi/dncmrc1/wprobe/hv_divider.htmThere are other methods for indirectly estimating the output voltage, but again these apply only to non-sparking TC's. These typically include E-field measurements or computing output from secondary base current measurements. A search of the Pupman archives will show many discussions over the years about pros and cons of various measurement approaches.
Bert Chris Boden wrote:
Ignoring limitations of cost and size, is it possible to build a large precision voltage divider (imagine something inside a 10' tall PVC pipe on a stand with a toroid in top) that would be able to accurately measure the output voltages of medium-sized Tesla Coils? Thoughts? Details? Design/method/parts suggestions? Has anyone ever done this before at the hobbiest level?
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