Converting battery voltage 12 volts to -5,5 volts at about 3 mA
The MAX1720/MAX1721 chips are probably one of your easiest/cheapest solutions.  You will have to get +5 to +5.5V from your 12 V rail using a linear or buck converter first though.  This chip will simply invert the input voltage. With this single chip and a couple capacitors, you will have a negative voltage system for &lt; $2.  No separate PWM signal needed.



It is very efficient at 3mA:



The drawback of these types of solutions is that they are not really regulated, so if you have a large dynamic current load the voltage will change a lot.  For something low current like this project, this is pretty much ideal though.