For a 11 watt device you could get a Panasonic 3400mah battery. I use one of those for 22 watts (but I think that is actually near the limit).
The SX chips (Siegelei 20w and Seven-22) hold their wattage up pretty well until the battery is empty.
The SX chips (Siegelei 20w and Seven-22) hold their wattage up pretty well until the battery is empty.