A phantom power supply is only that and gives you a mic level signal. The B29L is a electret power supply plus a mic preamp.Slightly off topic but could the AKG C411l be used with this to power it?
Prodipe BP21 Phantom Power Supply | Ferre Musique | Reverb
BTW, these small capsules are all electrets and only need power for the FET to deliver a loadable signal, so 9-12 volts are usually enough. But I would not cross unless you know for sure that they are compatible (same voltage, same pin).
BTW, there is a C411PP that has a standard XLR connector and could be powered by standard phantom power. But then you only have a mic level signal.