the efficiency of charge pump?

[kenddo]

hi all , i have calculated the efficiency of an rc loop , when charging the capacitor the efficiency η=(1-e^-t/RC)/2 ,the efficiency is allways less than 1/2! (η=Wc(t)/Wc(t)+WR(t)). if my conclusion is true the charge pump efficiency must be less than 50% ,but as far as i know the charge pump Efficiency (Typ) is 85(%) or above.
can u tell me the difference?

 

[kenddo]

WR(t)=CU²(1-e^2t/RC)/2
Wc(t)=CU²(1-e^t/RC)²/2
η=Wc(t)/(WR(t)+Wc(t))

 

[JPR]

kenddo,

You are correct in the efficiency of charging the capacitor from 0v. In a charge pump, the capacitor is NOT discharged completely, but is mostly left charged. This will allow the charging of the capacitor to be more like from 90% to 100% rather than from 0% to 100% (which gives max of 50%).

Using the 90% to 100% (actual result depends upon many factors). This means that the output is 90% of the input voltage (or more typically inverted at -90%). The efficiency in charging the transfer capacitor will now be 95%. The transfer of charge to the output capacitor will be at 90%, providing an overall efficiency of about 85%.

 

[kenddo]

Thank U JPR
You are right , I haven't thought about the initial condition

 

[funnynypd]

SMPS does has a high efficient on boost and step down.