Hi Team,
I'm designing a -15V power supply for my circuit with LM137.
My input is -15.5V. The maximum load current is about 500mA.
R1=120 Ohm and R2 is 1.31K
Is there any problem with the design?.
Also, I want to know 
Why capacitor C2 is required?. Is that for ripple rejection?.
What are the criteria for choosing resistor R1?.
The Maximum value of Iadj is 100uA
How to calculate Iadj?.
If Iadj is current to the adjust pin -1.25/120=10mA of current.
1. R1=120 Ohm and R2 is 1.31K is okay to use.
2. Why capacitor C2 is required?. Is that for ripple rejection?
According to the datasheet, the bypass capacitor on the adjustment terminal can discharge through a low current junction. Discharge occurs when either the input or the output is shorted. C2 is probably not required, but considering the age of this device, I would suggest following the datasheet configuration.
3. How to calculate Iadj? Iadj is used to calculate the Vout, and this is the leakage current of the adjustable pin.
4. If you would like to use R1 to calculate the biasing current, you will need to use (Vout - Vadj)/R1. Or you could use Vadj/R2.
You may see this dropout plot as shown in the datasheet. With 20mA of load, at room temp, the dropout is around 1.5V. 1V headroom may not be enough for the LDO to stay in regulation.
