Making battery powered device run off both AC and DC (battery backup).

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I have a vault that runs off 8 AAA batteries, but contrary to the specifications on the box the batteries do not last “over a year”. In fact they go dead every 2-3 months or so.
They make a unit now that comes with an AC adapter with battery backup but my unit is beyond its return period so I cannot exchange it.

So my question is can I adapt this so it runs off an AC wall adapter but also switches to DC during a power outage?
I realize I can hack into the battery holder compartment and solder in an AC adapter with matching output voltage but it’d be nice to have the battery backup as well because I’m pretty sure the keypad resets itself if power is interrupted. I also realize you can’t just use regular rechargeable batteries without a voltage regulation/cutoff circuit.

Any thoughts or ideas???
 
Just a single diode in series with the batteries is all that's needed if the power unit is unregulated - for a regulated one add a series diode from the PSU as well.

So battery/PSU connects to the two seperate anodes, and the output is from the two cathodes joined together.
 
Sounds simple enough. So the circuit would look like this (see attachment).

Also, what is keeping the unit from drawing off both sources?
 

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Sounds simple enough. So the circuit would look like this (see attachment).

Also, what is keeping the unit from drawing off both sources?
The AC source DC voltage would need to be slightly higher than the battery voltage so that the AC source supplies the power until the AC goes off.

You could also use rechargeable NiMH batteries and continually charge them with a low current (Duracell recommends no more than .0033 C, where C is the battery AH rating, to keep the battery charged indefinitely without damage).
 
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