I am trying to design a battery powered remote controller that has the following components, TPS63802 (converter), AP9211 (battery charger/protection), Atmega328 (MCU), NRF24 (transceiver). The following circuit uses a push button to send a signal to the MCU to tell it to go to sleep or turn on. My questions is regarding the small current drawn my the MCU under sleep mode about (5uA-20uA depending on the sleep mode used) and how it effects the boost converter. More specifically will the Boost Converter be able to supply the 3.3v at such small currents and will the output be stable. Also this is my first time designing a battery powered device that doesn't have a physical switch that decouples the battery from the boost converter. Also is such a method recommend or are there better ways.
The front page of the datasheet shows operation down to light load; 80% at 100 uA load. Although the 2 A output seems excessive for a remote, this device is a reasonable choice. If TI has one that has a lower maximum output current, you will gain a little more efficiency at low loads because the gate charge in the power MOSFETs will be lower. Gate charge is all loss.
From page 16 (typos are TIs):
8.4.2 Power Save Mode Operation
Besides Continuos Conduction (PWM) Mode, TPS63802 features Power Safe (PFM) Mode operation to achieve high efficiency at light load currents. This is implented by pausing the switching operation depending on the load current.
This means at light load there will be ripple on the output. The converter will run for a few cycles and bring the output voltage up. The converter tuns off and the load (your uC in sleep state) draws the output back down. Page 17 of the datasheet has a drawing of this.
The TPS63802 will still draw current to run its circuitry. The datasheet quotes 11 uA.
The TPS63802 can certainly regulate the output at very low output currents.
It has a mode select pin that allows you to select between forced PWM mode (where the frequency will be constant but the efficiency low at light load) and PFM mode where the frequency will depend on load current at light load, but efficiency will be higher.
PFM mode would be the right mode for a battery powered application. The output ripple will be slightly higher, but to power an MCU in standby mode it won't make a difference.