The battery will supply very large current peaks and act to smooth the
supply. Amplifier output will depend a lot on voltage. A tenth volt
change will have a large effect on the output power.
I think you want to run the charger while operating the linear to keep
the battery up to peak voltage for more RF output and least cycling of
the battery.
The automatic charger is one that is voltage regulated for the optimum
full charge voltage to match the particular battery chemistry. A deep
cycle battery tends to have a lower full charged specific gravity and
that leads to a lower full charged voltage than a car starting battery.
A well regulated battery charger will naturally taper off to zero
current as the battery is charged. Many ordinary chargers are not so
regulated. I think 13.8 volts is about the right charge cut off voltage
for a deep cycle battery. 14.2 is optimum for the starting battery.
Some batteries will leak acid despite all precautions and that acid will
eat carpets, wood floors, and concrete floors. All batteries create some
hydrogen and oxygen when fully charged, also when loaded heavily. This
gas mix is the perfect proportion for the best bang, and it tends to be
wet with a bit of sulfuric acid so eats walls and such. The battery
ought to be in an acid proof container vented to the outside or even be
outside, though it looses a lot of capacity when cooled, which shouldn't
be a problem for you except on some mountain top.
73, Jerry, K0CQ
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