Cockroft-Walton voltage multiplier circuits are sometimes called voltage multiplying ladders and with very good reason. Just look at this sketch:
We will examine the behavior of a x8 ladder using MultiSim 11 models as follows:
Note in these simulations that the peak-to-peak voltage excursions of the sine wave source and the square wave source are both 40 volts, but that number is chosen here only for convenient display.
There are four input channels on the MultiSim oscilloscope so we can look at the voltages at the top ends of capacitors C2, C4, C6 and C8 which are respectively x2, x4, x6 and x8 voltage multiplying points on these ladders. We see the following results:
We make the following observations:
1) Voltage multiplier outputs do not rise to their final values in zero time, but do so with time constants. There is a different time constant and settling time for each node and the higher the order of multiplication, the longer that settling time becomes.
2) The settling times for sine wave drive versus those for square wave drive are essentially the same. The settling times are not particularly waveshape sensitive.
Another way to analyze these circuits is with recursive differential equations.
Then click on this link for a discussion of the recursive differential equations method being applied to a specific voltage multiplier, a voltage doubler.
In point of fact, I just didn't have the patience to apply this method to voltage multipliers of larger x-values, but just looking at the x2 multiplier of the above URL, we see the following result for a sine wave drive.....
....and we see the following very similar result for a square wave drive:
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