A charge of the first capacitor 202 is proportional to the voltage difference between the first node 361 and the second node 362. Therefore, the second capacitor 302 can be charged to a level for producing a voltage difference between the first node 361 and the second node 362 that corresponds to the desired charge change. In particular, the charge of the second capacitor 302 can be set as C2*(V0+ΔV). Therefore, the first and second pre-charge voltages 344 and 346 can be used to charge the second capacitor 302 to C2*(V0+ΔV) by setting a difference between the first and second pre-charge voltages 344 and 346 to be equivalent to the voltage difference V0 between the first node 361 and the second node 362 plus the change in voltage ΔV, or (V0+ΔV).
As a result, when the first and second pre-charge gates 322 and 324 open and the first and second transfer gates 326 and 328 close, an equilibrium between the first capacitor 202 and the second capacitor 302 is achieved whereby charge is transferred between the first and second capacitors 202 and 302 and the voltage change on first capacitor C1 equals to C2*ΔV/C1.