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Dynamic Analysis of the Dickson Charge Pump

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R

ruma

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I am referring to the paper "A Dynamic Analysis of the Dickson Charge Pump Circuit" by T. Tanzawa & Tomaharu Tanaka. I am unable to understand the derivations for total charge supplied (Section II B). Why is the total charge consumed by an inverter k = total charge increase in capacitors C(K+1) to C(N). Also, how do we explain the final expression (15) where the kth capacitor has a multiplier k ?
 

I am unable to understand this either. This paper is so confusing. Could anybody help?
 

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