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These voltage regulators are really useful for IC circuits, but how much energy do they dissipate? For example, right now I am stepping down a 12V battery to 5V using a 7805; how would that compare to if I was using a transformer instead?
Now an unregulated supply (transformer + bridge rectifier + filter caps) vs. a regulated one may be what you meant.
In that case, remember that ALL transformers have a regulation spec. On smaller transformers it is usually worse than on large transformers; a 15VA transformer might be 20% while a 500VA one might be 5%. Either way, it's sucky regulation.
If you really need a stable voltage, the power loss across the regulator will simply be the voltage in - voltage out difference times the current through it*. But you can use switching regulators if you need higher efficiency, but these are harder to use and more expensive. A switcher will be capable of up to 90% effeciency or so, but they only operate well over say 20%-100% of their rated ouput power. At low % output power their efficiency becomes bad that sometimes a linear reg is better.
Duncan Amp Tools has a program called PSU Designer. Google for it, it's a real nice unregulated power supply simulation program that will let you try a lot of different power supply configs and lets you specify rated output voltage, current, regulation, use different diodes and rectifier configs, etc.
*Plus some super minor quiescent current - hardly significant unless you're using the new super LDO (<500mV dropout) regulators.
If you're going to use a transformer, I wouldn't use a 12V transformer, I'd go for a 9V transformer. Also for 1A of output current make sure the transformer is rated for 1.4A
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