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When I was searching Digikey for a ~6V to 3.3V Linear regulators, there was a minimum current column in the listing results. This kind of threw me because I didn't know that there was such a thing, or it was negligible. Since the uC in my design goes to deep sleep, this could be a problem. Do common regulators, like a LM1117-3.3 have this limitation? I didn't see it in the datasheet.

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According the the LM1117 datasheet, there is a typical minimum load current of 1.7mA (max 5mA) needed to maintain regulation. EDIT - this is for the adjustable version, I didn't notice you are using the fixed version, which has an internal resistor (which Steven mentions in his answer) to sink the minimum current required. So you will be okay, but the quiescent current (Typ. 5mA) is not great for a power conscious design, there are much better regulators out there if this is important.

Usually a linear regulator will require a minimum load current to maintain regulation, the reason being a typical linear regulator cannot sink current, only source it. Since there are usually other control currents that flow to the output pin, then even with the pass element off if there is no load the output voltage can rise above it's desired voltage because there is "nowhere for the current to go".
If you study the schematic in the datasheet you should be able to see how this happens.

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    \$\begingroup\$ +1 for mentioning that typical linear regulators can only source current, as this becomes a big deal if you have reverse currents. For example, with FPGAs, if you have a 2.5V aux input connected to a 3.3V output, better make sure your 2.5V rail can sink the reverse current, because the regulator probably won't! \$\endgroup\$
    – ajs410
    Sep 28, 2012 at 19:14
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The schematic on page 3 of the datasheet shows a resistor between output and ground, which will take care of the minimum load current for stable operation.

Note that some parameters are somewhat hidden in the datasheet's electrical characteristics, because they're not shown as parameters themselves, but as conditions for those parameters. For instance the 1.25 V reference voltage is specified for a minimum 10 mA load. It's a good idea to follow these conditions, otherwise the performance may be different from what's specified.

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Some current is always required to flow through the output stage, but sometimes this is drawn internally, so the application needs not worry about it.

This is the case of the LM1117 with fixed output voltage, and it is implied in the datasheet in the electrical characteristics section because it lists output voltage ranges for output currents greater or EQUAL to zero (and less than some upper value).

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As far as I can tell there's no output load current required to allow the LM1117-3.3 to maintain a regulated voltage. There is only a minimum load current for the adjustable version of the LM1117. It does have a max quiescent current of 15 mA, though. This may be an issue if you have a limited power source.

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