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Does anyone have any idea how long you could run, say, the TP-LINK WR703N for on battery? It'd be neat to set one of these up at a small summer festival in a couple of months.

Buy one of those car cigarette-lighter USB charger thingies, and connect it between a car battery and the router. The WR702N (I presume similar to 703N) says "Powered through a micro USB port by an external power adapter or USB connection to a computer": http://www.tp-link.com/en/products/details/?model=TL-WR702N

A car battery is fast and easy to charge. I would guess a car battery would last 20 to 80 hours, depending on the the battery, the router, and the usage.

Alternatively most cigarette-lighter USB chargers can take under-voltage so you can easily hook up a LiIon laptop battery (nominally 10.8 Volts). Laptop batteries are great because they come with a laptop that can charge them very quickly.

A car battery gives you the option to use many other routers (maybe you have a suitable one lying around!). Routers often use a 12 Volt DC input, and although a direct connection between the battery and the device is theoretically the wrong voltage, in practice I myself would just connect it straight through without any qualms (unless it was an expensive or rare router!). The WR703N probably uses less power so would run longer, but maybe compromises on range?!

MR3020 and WR703N have nearly the same board.

I linked and described my observed runtime here: http://piratebox.aod-rpg.de/dokuwiki/doku.php/about/matthias

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