There are many types of LM, based on package and output voltage. But all the IC is rated for a maximum current of 1A. The below table will help you choose the right part number for your IC. The IC is popularly known for being used in Arduino boards to regulate 5V and 3. So if you are looking for a SMD component voltage regulator then this IC might be the right choice for you. If it a fixed voltage regulator just power the IC though the Vin pin and the regulated output can be obtained in the Vout pin.
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In general, if they only talk of tanatalum as AMS does they probably copied some old datasheet from somebody else. Any increase of the output capacitance will merely improve the loop stability and transient response. The ESR of the output capacitor should range between 0. Look in the LDO tag for some recent on-site examples; this one in particular has scope traces.
The NCP datasheet is most helpful in this regard: Frequency compensation for the regulator is provided by capacitor Cout and its use is mandatory to ensure output stability. A minimum capacitance value of 4. See Figures 12 and Higher values of output capacitance can be used to enhance loop stability and transient response with the additional benefit of reducing output noise. This is all they say, by the way: The circuit design used in the AMS series requires the use of an output capacitor as part of the device frequency compensation.
When the adjustment terminal is bypassed with a capacitor to improve the ripple rejection, the requirement for an output capacitor increases.
Without bypassing the adjustment terminal smaller capacitors can be used with equally good results. To further improve stability and transient response of these devices larger values of output capacitor can be used. These capacitors need to be placed as close as possible to, or below, the appropriate pins on the underside of the PCB. Between the MCU and the regulator you may have non-trivial inductance. The pros simulate the board in a rather expensive EM field simulator to figure out how much exactly.
Note that this EM simulation is only about the effect of the board, it does not include things like stability of voltage regs. That moves you to the left in graph in Fig 12 above.
Circuito Integrado AMS1117 - 1,8V