I'm using a TPS63031 in an application that runs from a small 155 mAh battery. On average, the current consumption of my circuit is less than 10 mA, but even at its peak it never consumes more than 80 mA.
At first, I used the schematic on the first page of the datasheet, but noticed that the TPS63031 consumes an unacceptable amount of current even when no load is present. So then I decided to connect the PS/SYNC pin to ground. Now the output is an ugly sawtooth signal with approx. 3-400 mV peak-to-peak value. The frequency of the sawtooth waves seem to depend on the load. According to this thread this behaviour is to be expected from the chip in power save mode.
Unfortunately, this signal isn't an acceptable power supply for me: I have an MCU on the board whose UART experiences lots of frame errors while running from the TPS63031 and I also have an RF chip, and I'm afraid that the frequency of the sawtooth would screw up my RF performance.
I'm not a power management expert, so I'm curious, could I somehow filter the output of the TPS63031 to get a better power supply?