Hi,
I need your OK to use the fixed outputs TPS73601 (or perhaps the TPS73615) – very low dropout voltage indeed ! - to create a DC Constant Current source (without having to incur into a large voltage drop across it), i.e. using their fixed output voltage across a fixed resistor as attached file.
Of course, the Zener voltage value will guarantee the dropout and all other design parameters will be strictly observed, etc..
Thanks,
Shlomi