If you rectify the line voltage, maybe grabbing peaks at 160 volts, and you need t0 provide 100 watts for 100 seconds, and your downstream switching regulator has a 40 volt dropout, how big a capacitor will you need?

For 100 seconds, and 100 watts, you need to store 10,000 joules (watt * seconds) OR MORE. At 40/160 dropout, or 25%, that is close to 100% nergy extraction, w'll ignore that 25% and compute what is needed.

Energy = 0.5 * C * V^2

and we manipulate

Energy / ( 0.5 * V * V) = C

10,000 / (0.5 * 160 * 160) = 10,000 / (0.5 * 25,600) = 10,00 / 12,800

C = 0.8 farads at 250 volt rating

If you rectify the line voltage, maybe grabbing peaks at 160 volts, and you need to provide 100 watts for 100 seconds, and your downstream switching regulator has a 40 volt dropout, how big a capacitor will you need?

For 100 seconds, and 100 watts, you need to store 10,000 joules (watt * seconds) OR MORE. At 40/160 dropout, or 25%, that is close to 100% energy extraction, w'll ignore that 25% and compute what is needed.

Energy = 0.5 * C * V^2

and we manipulate

Energy / ( 0.5 * V * V) = C

10,000 / (0.5 * 160 * 160) = 10,000 / (0.5 * 25,600) = 10,00 / 12,800

C = 0.8 farads at 250 volt rating