LM317 adjustable voltage setting question

[gdecker1]

I'm reviewing the datasheet for the LM317 linear regulator, and it lists the equation for calculating voltage as:

VO = VREF (1 + R2/R1) + IADJ R2

If I plug in the numbers from my circuit (and neglect the error calculation), I get:

1.25 * (1+(1400/400))  = 5.625V

However, if I do a straight resistor-divider calculation assuming R1 = 400 and R2 = 1400, and assume 5.625V at the top of R1, I get Vref = 4.375. 

Swapping R1 and R2 (such at R1 = 1400 and R2 = 400) I get Vref = 1.25V with Vout = 5.625

Furthermore, most linear regulators with an adjust pin set the output using the equation 

VO = VREF (1 + R1/R2)

Which tracks with what I'm seeing in the math.

Is there a typo in the datasheet, or is there something significant I'm missing in how much current the ADJ pin has on it?

[Peter BENSCH · Accepted solution]

You have made a small error in your thinking, because the reference voltage of the LM317 is not measured against GND (in your schematic), but against the output – upside down, so to speak. This means that your simple voltage divider gives exactly the right result across the "upper" resistor.

The correction term R2*IADJ is intended to correct the error that can arise from the current flowing from the ADJ PIN in resistors with higher impedance values.

Does this answer your questions?

Regards
/Peter