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 Small size 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 (3.7x2) to drive Boost converter i.e (12/7v4 = 1.62A) or there is another better approach which can be both cost-efficient and suitable for the above purpose?