LM317: LM317DCY

Hello Shao,

You can determine the tolerance of your output voltage based on the following variables.
I will assume you need to use the LM317 across the datasheet temperature range.
In general, it is typical to assume a normal distribution for most parameters. 
The adjust current can be a worst case calculation, or you can also assume a normal distribution.

We would need more design details on the ADC application to offer a recommendation, such as current draw and temperature range.
However in general, ADC's are very noise sensitive and you will want an ultra low noise LDO.  You may also need to consider a precision reference if the tolerance is absolutely critical, such as in ADC's which use the power rail as the reference.  Please refer to TI documents slyt339.pdf, slyt355.pdf and slyt331.pdf for ADC voltage reference considerations.

1. Reference voltage, resistor feedback network and adjust current
Equation (1) in the datasheet gives the math to determine the output voltage based on the reference voltage, resistor feedback network and adjust current.
As the designer, you will be in charge of the resistor tolerances chosen.  Typically they are chosen as 1% or 0.1% resistors.  The reference voltage and tolerance is given in the datasheet in the "Electrical Characteristics" section.  For this component it is listed as a nominal of 1.25V with a minimum of 1.2V and maximum of 1.3V.  The adjust current is given as a nominal 50uA and a worst case 100uA.

2. Line regulation
Additional tolerance is given based on the variation in DC input voltage.
Section 6.5 "Electrical Characteristics" gives the maximum line regulation across temperature as 0.07 %/V.

3. Load regulation
Additional tolerance is given based on the variation in the DC output load current.
Section 6.5 "Electrical Characteristics" gives the load regulation as 70mV max for output voltages under 5V, or 1.5% of the output voltage for anything greater than 5V.

4. Line transients
If you have any line transient conditions, this may cause a perturbation on the output voltage.
This will often need to be characterized in your circuit based on your input filter, output filter and any additional compensation you add, such as feed foward capacitors or RC networks across the top setpoint resistor.

5. Input ripple
Typically the Power Supply Rejection Ratio (PSRR) is high enough that ripple on the input (such as that from another switching power supply feeding the LDO) is negligible.  The PSRR for this LDO at 10KHz is 60dB, for example, but it is only 20dB at 1MHz.

6. Load transients
If you have load transient conditions, this will cause a perturbation on the output voltage.  How much will depend on the magnitude and speed of the transient, the bandwidth of the LDO, and the output filtering or output capacitor(s) in the design.  This will often need to be characterized for your design.  Figures 3 and 4 give some examples of load transient response you may wish to review.

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Thanks,

- Stephen