hi there
welcome to the forums
what is a 23A battery ?
what is the device ?
what is its voltage and current requirements ?
lots more info needed so we can help you
Dave
In essence, all you need is to connect it up to the battery.
However, car electrical systems are noisy and you really need to filter the 12V so that you don't get large voltage spikes which will (potentially) disrupt or even destroy the wireless doorbell.
I would recommend that you connect a 220 ohm resistor in series with the +ve leas, and a 1000uF capacitor after that between +ve and -ve. These components will probably take up about as much room as the original battery.
220 ohm 1/4W or 1/2W (or higher power, but it will just be larger)
1000uF 16V or (preferably) 25V
There are other methods of doing this, but these parts can be obtained from pretty much anywhere that sells electronic parts.
Here is a schematic of what you want to do.
As has been mentioned, it is conventional to place the +ve rail at the top, an the negative at the bottom.
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It's also conventional to have the general flow from left to right. So inputs on the left, and outputs on the right.
This circuit will folow he input voltage, as you have measured. If you want a fixed 12 V output, you'll need a regulator (example). However, even a good low dropout regulator will require at least 12.5 V at its input pin.
Or simply place a 12V zener diode in parallel to the capacitor to protect from overvoltage. However, if your input voltage is below the zener voltage, so will be the output.
Generating a 12 V output from less than 12 V input will require a so called buck-boost regulator