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I'm trying to find a reliable way to connect my nRF52840 BLE-module to a 3.3V SD-card. The application is going to run on a lithium-ion battery and power is extremely budgeted.

The nRF52840 module can be powered in high-voltage mode by a supply between 2.5V and 5V and internally down-regulate that, BUT there is a 0.3V voltage drop. This means that the 3.3V will start drooping when the lithium-ion battery reaches 3.6 volts.

There is a solar-charging IC in my circuit (bq25570) which has a built-in configurable buck-regulator but that too has a voltage-drop of 0.2V, so the 3.3V will only be maintained until 3.5V.

I've been looking into buck/boost converters to regulate the voltage of BLE-module and SD-card to 3.3V, but seeing the poor efficiency at low currents (the nRF52840 consumes about 10uA when sleeping) I'm afraid battery-life will take a huge hit. I could only connect the buck-converter to the SD-card but when the battery is almost empty, the nRF52's SPI-lines will only be able to deliver up to 2.7V. What would be the most straightforward way around this?

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The nRF52840 module can be powered in high-voltage mode by a supply between 2.5V and 5V and internally down-regulate that

Nope. That regulator has 25mA maximum external output, SD card needs 100mA minimum in SPI mode.

The sd card operating voltage can down to about 2.7V - I recommend using an LDO with enable pin just for the card alone. Thus it can be switched off completely when not in use. I recommend 3.0V as output voltage.

The SD LDO output voltage and the NRF chip VDD voltage must match - the default 1V8 VDD level (when using REG0) would be waaay too low. See REGOUT0 in UICR.

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