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Advantages of switching P/S:
Higher efficiency, resulting in lower heat, resulting in smaller heatsinks.
Smaller transformers, smaller capacitors, smaller overall packages.
Disadvantages: higher output noise, higher and harder to fix EMI, some stability challenges, usually more expensive, magnetics are harder to design and build.
Advantages of linear supplies:
Low output noise and ripple, can be very tightly regulated, usually the stability is not a great issue, few EMI problems.
Disadvantages: bulky, large transformers and capacitors required, low efficienty, meaning large heatsinks.
Also, you can only obtain an output voltage that is lower than the input voltage, never higher.
Maxim had recently published a very nice app note "An Introduction to Switch-Mode Power Supplies" **broken link removed** . It has a list of pros and cons.
You can read the book "Power Supply Cookbook by Marty Brown" its initial pages makes you much aware of difference, it is also very good books for starting Power Supply. (you can download this book from this forum)
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