1) You want to use a so-called "deep cycle" battery (or batteries; see below). My recommendation is the Group 31 sized 8G31DT made by East Penn. Note that gel cells can be installed in occupied spaces; flooded cell lead acid batteries should not be.
2) Your battery (or bank of batteries wired in parallel) should be sized in two ways: for max current draw and for max energy withdrawal before recharging.
3) Max current draw (in amps) should not exceed 5% of nominal battery rating in Amp-Hours. (The 8G31DT is rated at a nominal 96 AH.) So figure out what your average current draw is and multiply that by 20. If the result is <100 AH one 8G31DT; if between 100 and 200 AH, two batteries in parallel; and so forth. (The usual rule of thumb is to assume a 95-5-5 (squelched receive-unsquelched receive-transmit) duty cycle. So figure out system's current draw squelched and multiply by .95; figure out unsquelched current draw and multiply by .05; figure out current draw on transmit and multiply by .05; add all three values and multiply by 20. This is the minimum size of the required bank in AH.)
4) Max energy draw from the bank should not exceed 50% of nominal capacity before being recharged. Using the average draw calculated above and multiply by the number of hours the system has to run on batteries and then multiply by two. This is the minimum size of the required bank in AH.
5) Don't scrimp on the charger. You want a multiple stage charger that is also capable of true zero current float stage. I'd recommend a Tru-Charge, sized (in amps) at 15-25% of the resultant bank size (in AH).
6) When you install this type of power supply, the radio is connected to the batteries and works on 12VDC. Charger is also connected to the batteries and left on. While AC is available, batteries will remain at full charge and load will be carried by the charger.
7) For what it is worth, I run Quantar stations (100W) on two or three 8G31DT batteries. Since Quantar requires 110VAC, these batteries are wired to a device called Heart Interface, which combines a 50A charger, a 1 KW inverter, and a fast (<18 msec) transfer switch. Primary function is to keep the Quantars from rebooting while the generator starts, stabilizes, and accepts load, but design spec was to carry Quantar for two hours (long enough if generator fails to get DPW up to station with a skid mount genset). In tests, system has exceeded the design basis easily. Total cost under $1,400.
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