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I am using M.2 LTE module in my design. The datasheet says "The host board shall provide 2.5 A peak current." What does this mean from supply current point of view??

Also, in the power consumption table it says 1629 mW max. That makes around 484 mA @ 3.3V.

What should I consider on power supply side 2.5A or 484mA??

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    \$\begingroup\$ If your PSU can't supply 2.5A your project won't work. (The lower figure may help you work out heatsinking or battery life, so it's not useless). \$\endgroup\$ – Brian Drummond Dec 3 '15 at 17:57
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    \$\begingroup\$ GSM specs call out a pulse of 577us every 4.6ms. During that pulse, there is typically ~2A of power consumed by a 3.3V GSM modem. Rough numbers there, but this is what I have found working with GSM modems. So you need to be able to handle the pulses which means you need a tight control loop or a lot of capacitance i.e. > 1000uF. \$\endgroup\$ – MadHatter Dec 3 '15 at 19:37
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You need to consider both. The supply must be able to provide brief current pulses of current of up to 2.5A. If you have the ability to supply 2.5A continuously then you are done. However if the supply cannot supply at least 2.5A continuously it must at least be able to supply the specified maximum average current on a continuous basis.

Take this user guide:

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