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A linear power supply regulates the output by measuring that output
and changing some parameter a tiny tiny amount so that it looks like
the output is either constant or changing a very tiny tiny amount.
The output transistor is operated in its linear region which often
consumes a lot of power that goes to waste as heat.
A switching power supply regulates the output by measuring the output
and changing some parameter a tiny tiny amount too, but instead
of changing the output a tiny amount too it simply regulates the pulse
width of the output transistor. A filter circuit at the output makes
the output look like it only changes a small amount, but a good scope
on the output will show some ripple that is the result of the constantly
switching output transistor.
The output transistor is operated as either fully on or fully off which
does not waste power because when a transistor is fully on it doesnt
waste that much power and when it is fully off it does not waste much
power either.
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