smps scheatics
I am not going to go into a lengthy analysis, but just explain the basic operation. Once you see this you will be able to work out the details.
When the AC is low (up to 120VAC) , Q1 is fired and the diode arrangement works as a voltage doubler. If the AC voltage is high (220VAC), Q3 will prevent Q1 from turning on and you will have normal full wave rectification.
HINT: D6 is just a bi-directional switch controlled by Q1, to analyze you can replace it by a switch between 2&3