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So if the charger isn't built in. Is there a specific battery charger that you should use to charge your batteries? Do you just hook it up to the batteries like you would with any battery charger?
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Some years back, I read enough information about "proper" battery charging to make my head spin. It truly is a complicated operation if one wants the longest battery life possible. But I've also noticed that even if one has a perfect charging environment, you STILL have batteries fail earlier than perhaps they should just because the quality of things these days are not what they once were (or I can't afford the high quality stuff). So, I concluded that if I can get 4-5 years out of a battery bank, wonderful.
Some "experts" tell you that you really do need a very high amperage for recharge initially to recharge correctly. But very, very few people using solar panels actually have the ability for such high recharge amperage and yet they still get a decent life out of their batteries. I think this is because the most important thing for long life is to NOT run batteries down below 50% (12.06v).
The charging aspect is the most complicated of the three items being discussed. The unit you initially discussed indicated a 70 amp charge capability. You will have to take some time to consider HOW you will actually use your battery power and then how your applied charging methods are going to best serve to re-charge. Do you intend to draw your batteries down in a short period of time and then also have a short period of time before the next cycle ? If so, then you do need to consider a high amperage recharge environment.
If you intend to begin using power wisely (because you realize that power you have to make does not come easy, nor plentiful), then you can get by with what most are getting by with in smaller solar arrays and smaller shore chargers in parallel. You did not mention if you are including a solar option or not, but I almost think it is a must these days in order to keep things balanced, always getting something to compensate for any draw.
Yes, any charger simply connects in parallel with any other charge source with a few caveats. If a shore charger is plugged into the same circuitry as your battery powered inverted AC, then the charger turns on when your running without shore power. This just wastes power as the charger draws more than what it will put out (there is no perpetual motion). So you must find a way to power a charger only when on a true shore source.
Another issue is if you use any "coupling" methods from an alternator (like if this is for a vehicle). I always install a simple large solenoid that can couple my starting battery with my house battery bank. For one, it can help me start the truck if I got a dead battery, but also, if for some reason I had trouble charging the house batteries, I can charge via alternator.
BUT NOTE that solar people usually charge much higher than the 13-14.1 volts alternators generally provide, so you never want to join the two systems if the house is near the 15 volt mark for risk of over voltage to sensitive 12v gear turned on in the vehicle (backup cameras, stereos, etc). For me it is an emergency backup option.
When it comes to charger brands, it could be that NOCO is one you should research. It's what I have been using and I believe it does exactly what it should be doing. Because I have solar, I only need a charger when I am plugged in somewhere and have had a few days of no sun. In such case, I get by with a little 3.5a NOCO, and just watch that I do not take my batteries lower than I care to.
If you take on the task of reading about battery charging to perfection, I wish you well. Again, COMPLICATED ! But worth the understanding before you decide exactly what you should buy for your particular needs. Note that many of the old camper charger/power supplies never used any of these complicated methods... I guess people just replaced batteries more often.
Good Luck !