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I want to use multiple CR2032 batteries in parallel for higher capacity in a wireless RF remote (1.8-3.8 V working range for the RF MCU).

CR3032 is an option but I rejected it due to price and availability concerns. CR2032 cells are readily available and cheap.

Since primary cells shouldn't be charged, I feel that some circuit has to be in place to avoid it.

Is it feasible? If yes, what are my options?

Is there a standard part that I can put on each battery? This part should have a negligible voltage drop and should block reverse current.

Diodes are the standard parts that come to my mind but I fear they will take away a big chunk of operational capacity.

Below is the discharge graph of a typical coin cell:

cr2032 curves

Is it advisable to use a 220 mV schottky diode for reverse polarity and reverse current protection?

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Just wire them in parallel. nothing bad will happen.

Tell users not to mix fresh and depleted cells. (like every instruction manual does)

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I recently had this same issue and I found that putting the batteries is series and having an low-power buck-converter was quite feasible.

There is some extra price tag on it, and you have to be really picky about the regulator IC! With such small batteries the quiescent current from the IC can really damage your energy budget.

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Rough Idea to prevent a full cell unintentionally charging a depleted cell :

Add a p-type mosfet (sot23 or smaller) that enables the 2nd coin-cell when going to transmit for extra power & load sharing. you can add a 1k-ohm resistor parallel over the mosfet to provide equal battery life regarding sleep current.

If (both/all) cells are equipped with a p-mosfet, youd be able to protect each one.

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