tpetar,
Sorry I did not mention. The purpose is to make the IC work in both AC only and 3V battery only condition. The requirement is to let IC generate regulated 3.3V for microcontroller. 10V (not regulated) is also needed for other use.
So the challenge here is to make it work in both 3V only and AC only. I don't want to make two separate circuits for these two conditions. They should share the same circuits.
In AC only condition, DC to DC booster is not needed because the voltage is already at 10V level. The regulator needs to be powered by the 10V not the 3V battery, because the battery voltage 3V is less than 3.3V. Band gap should be also powered by 3.3V.
In battery only condition, DC to DC is needed , and all the circuits can be powered by the battery, except the regulator because of the reason I mentioned above.
Thanks
Sean