[SOLVED] Designing a power backup system for a router

Don't know if i had place this post in the proper thread section.

I am planning on to design a system to power my router. Unfortunately, there are shortcomings of electricity in our area and I want my router to operate 24/7. I have read the specs of the router and it requires 12v/1A | 12watts.

What I want to do now is to select a rechargeable battery so that I can power my router through it when my main electric power is cut-off. I thought about 3v7 LI-ION battery with a Boost converter but LI-ION can't provide me, ideally about 3.4A (12w/3v7) continuously. So should I connect two LI-ION in series (3v7x2) to drive Boost converter i.e (12/7v4 = 1.62A) or is there another better approach which can be both cost-efficient and suitable for the above purpose?

I need at-least 52Wh battery(s) to drive my router for at-least 3.5hours => (3.5h x 12w)/(80% effeciency of booster)

I would check two points:
- actual current consumption of the router
- supported input voltage range. Depending on the internal power supply topology it may work over a wider voltage range, possibly even without a boost converter.

actual current consumption of the router

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The max current it can consume ideally is 1A (mentioned on its charger).

Depending on the internal power supply topology it may work over a wider voltage range

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Should I use a variable power supply to find out the input voltage range ?

12v/1A

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Consider a marine or deep-cycle battery. May be found in an automotive, motorcycle, boating, or lawn-care shops.
You don't necessarily need to buy a new full-size automotive battery. However a half-used one could be just right for delivering 1A for a few hours. It could also power lights, etc., during a blackout.

To illustrate my point, I have router with a 12V/1.2A power supply. It actually runs with about half the current under typical operation conditions. And seems to accept input voltage down to 5 or 6 V (with respective higher input current, roughly constant input power, even decreasing by 10 or 20 %).

You see there can be some margin...

Let me find out the operating voltage range and cut-off voltage of my router along with the average current consumption under typical load. Then i will decide to choose b/w a small lead-acid battery or LI-ION batteries with Buck or Boost converter.