Understanding the Mechanics of a Cockcroft-Walton Generator

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The Cockcroft-Walton generator functions by using a series of capacitors and diodes to step up voltage in a multi-stage process. Each stage consists of a diode that rectifies the AC input and a capacitor that stores the charge, effectively increasing the voltage with each stage. The diodes allow current to flow in one direction, while the capacitors charge during the positive half-cycle and discharge during the negative half-cycle, resulting in a higher DC output. This mechanism enables the generator to produce high-voltage DC from a lower-voltage AC source. Understanding these interactions is crucial for grasping the generator's operation.
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I found this generator online and I was wondering how this setup works.

http://en.wikipedia.org/wiki/Cockcroft–Walton_generator

How do the different stages up the voltage into dc? and just how do the capacitors and diodes actually work together to do this?
 
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There's an explanation on http://www.blazelabs.com/e-exp15.asp.
 
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