Why do opamps "rail" ?

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Of course that's what he means. The simple answer is that they're not perfect. It takes a small (usually microvolt or millivolt) DC "signal" between the + and - inputs to get the output to zero. It's spec'ed as the input offset voltage. Multiply this number by the open loop gain, and you get a big number which is typically greater than the supply volatge and that's where it "tries" to go. It stops at the rail.

"Latch-up" is a seaprate phenomenon, and that requires overdrive.
 
Here's a TL072 or similar.

Node B sits at 2Vbe:s + the drop over Re above negative rail. If an input is driven negative enough so that the gate junction of one of the JFET:s lets the input steal current from the current source then there won't be enough voltage at B to turn on the vas and the output will go to the positive rail.

For example, if IN+ is connected to negative rail, S will be 1Vbe above negative rail. B will be at about the same voltage, which isn't enough to turn on the VAS so the output will go positive instead of negative as expected.

The TL0xx series opamps input common mode range includes positive rail though!
 

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I had TL074 went to the rails before. It was wired as Unity Gain Buffers for a distribution amp as in one of their Application Notes. Initially on power up, no problems. Left it on overnight. Next morning, output was at one of the rails. Apparently, the output DC offset crept towards the rail as the opamp temperature increases.
 
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