This is kind of low tech for here, but also more sophisticated than just a battery or trickle charger. Due to picking up on the amateur radio stuff (and it's all 12v) I decided to do what most do who have these "mobile" units used as home stations - buy a deep cycle battery to run it off of to handle the huge peak currents during transmit, and eliminate all chance of 60hz hum. But you got to keep the battery in good condition. Normally, a big lead acid battery is NOT something you want indoors. They fume, the fumes make trouble (and smell nasty). If you cycle them a lot, even the deep cycle marine types go bad. The sealed ones cost too much, and are even more sensitive to overcharge. So, what's an engineer to do?
Well, here's what I did. There might be something like this out there already, dunno - my fancy solar stuff does this, but at zillions of times more bucks. This was 100% out of my junkbox (and I could have done it better and still not bought parts).
According to Xantrex, deep cycle lead acid batteries have a tempco of around -21mv/C. In my case, I want to hold a battery at the highest possible voltage I can without getting into gassing and wasting power, since I'm off the grid, and don't need the gas (even the new flooded marine batteries are "maintenance resistant" - hard to add water.
This requires fairly close tempco matching. Turns out silicon diodes (1n4148 in this case) have around -2mv/C themselves, and that 17 of them work out with a standard LM-350 and around 10 milliamps to just the right voltage at temperatures around room temperature. Actually, it would be perfect with 10-11 diodes and a resistor in series, instead of getting the full set voltage (minus 1.25v for the regulator) from all diodes, but this is darned close and seems to be working out in real life. The 10 diodes plus resistor might be a little trickier to tune...
Simply - I used a 100 ohm pot (ex of tektronix, this is the good stuff) and a 47 ohm resistor between output and adj terminals, then the diodes to ground (note how I sensed the ground off the negative output, not someplace else). I added a diode backwards across the lm 350 in case someone hooks up the battery before powering the unit on, to save some low current junctions in the regulator from that abuse - having to quick charge the 4700 uf filter cap. I stole the xfrmr out of a 12v halogen desk lamp fixture I'd converted to LED. I could have used a larger xfrmr, at the cost of more losses due to core excitation current, and more drop across the regulator.
This circuit as shown (cheezy radio-crap bridge rectifier has a lot of forward drop) will not make big currents into the battery till the voltage drops pretty low. For this use, that's fine. For doing higher currents or holding the battery up well above 12.6v even under load, you'd want a higher voltage (maybe 15v) transformer, and/or shottky diodes in the bridge instead. But - then it would be less efficient the other 99.99% of the time when it's just floating and the supply itself is drawing more current than the battery(!). The way it is, the supply is kept near the battery, and if the supply heats up for whatever reason - the voltage goes down...reducing the current output and the heating. So I can hold this marine (johnson controls, sold at walmart) right at 13.7 or so volts, near-zero current, no gassing, for when the station is off, but always ready to go.