SAR ADC switching energy calculation

[dirac16]

I am trying to calculate the switching power needed when moving between different switching positions in a capacitive DAC. The image below depicts the energy needed to go from a certain position to another for a conventional capacitive switching DAC. For example, in going from state A to B the paper claims a total of CVref^2 is required to be drawn from the reference generator. However what I found is only half this value. What is wrong with my calculation?

 

[gavanbash]

Hi
You can find your answer here

Request Rejected

 

[crutschow]

What is wrong with my calculation?

The energy stored by a capacitor is 1/2 CV² but it takes twice that energy to charge it through a resistive switch.
The other half of the energy is lost in the switch resistance (the value of the resistance makes no difference).

If you multiply the amount of charge going into the capacitor to charge it by the supply voltage to give the energy from the supply, you will see that it is twice the stored energy on the capacitor.