I guess it comes down to 'efficiency'. I can remember when inverters were 'motor-generators', before there was such a thing as an electronic inverter. They were large, noisy & needed periodic maintenance... replacement of brushes, bearings etc, but they produced the purest sine wave out there. The purest sine wave is still produced by something like this, a DC motor attached on the same shaft as an AC generator, which essentially rotates at the desired frequency & produces the desired voltage amplitude. Not unlike a common generator that uses a gasoline or natural gas fueled combustion engine to spin an AC generator. And remember that your household AC is a pure sine wave. Hence, most of the equipment, as in motor(s), you wish to run off the 'inverter' will run best & most efficiently on a pure sine wave. I'm sure there are newer AC motors out there these days that are optimized to run well on modified sine waves or PWM signals, but I would wager most of the AC motorized equipment used in our hobby prefers a pure sine wave. I think DC motors will increase in popularity in our hobby, since they are much easier to control and a lower voltage around water is always a good thing. So if you have a DC power supply & DC motor/pump, you don't need an inverter! One less piece of gear. Every time power is converted from one form to another, you lose some efficiency in the conversion process. Not a big deal necessarily, but for something that runs 24/7, like a return pump or powerhead, the more efficient, the greater the savings. That can be applied to your back up as well, run a DC motor off your 12 volt battery instead of using an inverter with a funky wave to run an AC motor and you'll probably get more running time during an outage.
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