There are two ways to construct the equivalent of an autotransformer. I will ignore for the m\oment the construction of the equivalent circuit using one isolation transformer, although that is the way most buck/boost configurations are constructed.
An autotransformer has one magnetic core and a single winding around that core which has at least three connection points: the two ends and a point in between them.
As with any transformer with multiple windings or winding sections, the voltage between any two points is proportional to the number of turns between those points. .
So lets take a hypothetical tranformer with 120 turns and a tap at the 100 turn point and apply 120 volts to the two ends, A and B. That sets the configuration as 1 volt per turn. And if the tap point, C is 100 turns from A the voltage A-C will be 100V. And the voltage C-B will be 20V. This is an autotransformer configuration that can be used to produce a lower output voltage.
Next, apply the 120V input to points A and B. That sets the voltage at 1.2V per turn. So the voltage from A to C will now be 144V. This is an autotransformer configuration that produces a higher output voltage.
Now note that there is no reason for the the wire guage to be the same from one end of the winding to the other. In our example, we will make the BC section of the winding 5 times the diameter of the AB section and revisit the second (boost) configuration. Ignoring magnetizing current, the current in AB will have to be 1/5 of the current in BC to satisfy the condition of power in = power out.
If the goal of the example is to provide 144V to a load which draws 1A, the transformer will only need to be rated for 24 Watts (120V times .2A on the input side, AB = 1A times 24V on the output side, BC.)
Instead of using a single winding wrapped continuously on a core, you can get exactly the same effect using an isolation transformer with a 5-1 turn ratio and connecting the two windings together in either a buck or a boost configuration.
