A Sealed Lead Acid battery is by far the cheapest and most efficient kind of rechargeable battery to work with. There are very few rules to remember when it is used in a "standby" application like here.
Here is an concept schematic for a very simple and cheap powersupply suitable for the Soekris 4501 or similar which incorporates a sealed lead acid battery to provide battery backup.
Please note that the schematic is in no way complete, you will want to add a few decoupling capacitors, fuses etc. in various strategic places.
The first rule about sealed lead acid batteries is that they can be float charged by putting 2.25 to 2.30 V across each cell. For a 12V battery this is 13.50 to 13.80V. This voltage is measured at TP1 with a fully charged battery, and adjusted on the variable resistor.
The second rule is that the battery should never be charged with a current above approx a fifth of its rated capacity. For a 20Ah battery this means 4A max charge current. 3 terminal voltage regulators have a built in current limiter, choose a model which does not exceed the capacity of the battery. There is no harm in the regulators current limiter being less than the fifth of the batterys capacity, it only means that the battery takes longer to reach full charge.
The voltage at TP2 should be a tad higher than the voltage at TP1 plus the voltage drop in the rectifier bridge (typically .7V) plus the nominal voltage drop of the regulator (from 1V and up).
For a 12V battery, a 12VAC secondary transformer should work. The transformer must be rated at the maximum charge current plus the maximum load current. Make sure the voltage at Vout does not exceed the 20V max input of the Soekris 4501. If it does, a second voltage regulator can be introduced in the "upper leg".
Please notice that there is no circuit for temperature regulation of the float charge voltage. As long as the battery is at room temperature this is no problem. If the battery is exposed to large swings in temperature, without a charger which adjusts the float charge voltage accordingly, the lifetime will decrease drastically.
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