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One strategy for generating high voltages, without requiring excessive insulation on the transformers, is a cascade arrangement as described by Greinacher in 1920 (?). A cascade of transformers, each insulated at twice the stage voltage, is connected as shown in the following figure. The stage voltages are rectified and filtered with the filter capacitors connected in series to develop the desired output voltage.
The above figure shows the transfomers with iron cores, however, with the use of a higher frequency source (i.e. RF), air core transformers can be used with the attendant reduction in weight. In fact, any means of getting the power up the cascade can be used, providing the losses are acceptable and the insulation level is appropriate. A cascade of capacitors could also be used, in which case, the system starts to look like a classic Cockroft-Walton multiplier.
This scheme can also be used to generate high AC voltages, by omitting the rectifiers and filter capacitors, and connecting the stages together, essentially creating a cascade of autotransformers.
The significant design issue is that the "bottom" transformer must be sized to carry not only the power for the bottom stage, but also the N-1 stages above. One could design a system using ever decreasing transformer sizes, however, the economies of scale and convenience in building multiple identical sections means that the upper stages have over capacity.
A similar strategy, using a third, or tertiary winding on the transformers has also been used. This has the advantage that the power can be transmitted between stages using relatively low voltages, requiring fewer turns of thicker, easier to handle wire. The tertiary winding must be insulated from the other windings by the full stage voltage however. This strategy is of some use when inexpensive surplus transformers with an appropriate winding are available, an example of which is here.
Another form of the system is to use isolation transformers between the stages, insulated for the stage voltage, and a separate HV transformer at each stage, feeding the rectifiers and filters as appropriate.
Some examples of such cascades are here.
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