Balanced DC output from a single 12v battery

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Here's the situation:
I'm building a boom box out of mostly parts I have laying around.

It's going to be a 2-channel thing using 1 class d amp ( Dayton Audio DTA-2 Class T Digital Audio Amplifier Module | 300-385 ) per channel. I'm using a pair of active crossovers in front of the amps to break things up.

I want to power the thing with some manner of sealed lead-acid batteries.

The problem is that the active crossovers I have on hand expect a balanced input (they can go as low as +/-5v). The amps don't require balanced voltage, so they can be powered directly by the battery, but I need balanced voltage for the crossovers.

What's the simplest/most efficient way to get some kind of balanced voltage?

The crossovers probably don't need too much power, maybe simple resistor divider to give me +/-6v?

If I use 2 6v batteries in series, can I center tap them and charge them in series (with a 12v charger)?
 
the PSU needs to be dual polarity. It is not correct to refer to this as "balanced".

Since the batteries and the amplifier are both completely isolated from the mains supply when portable, the voltages on the rails are "anywhere". It's only the relative voltage from rail to rail and from rail to audio ground that matters.

A virtual earth using resistors wastes battery power.
Use a very low current virtual earth generator.
 
There are DC-DC converter modules in DIP and SIP packages. Or, for essentially no cost you could use an MC34063 switching regulator to generate a negative voltage. Those chips are found in nearly every car cellphone charger and USB adapter. It might be wise to use a linear regulator as well. Produce -8V then use a 7905 to get -5 volts.

If you haven't bought the Dayton amps yet, why not try getting amps from eBay for 1/3 the price, including shipping? Just search for TA2024.
 
A couple of additions:

If measurements on a couple of randomly chosen car adapters are anything to go by, the 34063 won't waste too much power in overhead; one adapter was less than 5 mA, and that includes an LED. If there's enough ripple to be audible, you could follow it up with a negative linear regulator like a 7905 or 337, or perhaps just some RC filtering.

Regarding alternative amps, there are boards with Yamaha digital amp chips that look promising, and include practical features like clipping prevention. (That is, the chips support AGC and stuff, but I don't know if the boards are configured to use those features.) The YDA138 is in a larger chip package that would be easier to heat sink (and seems to include a headphone output); the YDA148 is much smaller. According to the data sheets, heat sinks are advised when using 4 ohm loads. Search for those chip numbers, or Yamaha digital amplifier.
 
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