I have a 12 V load that works by connecting an adapter from the AC socket and this adapter output 12v to the load. I decided to make a 12 v battery that can charged and the feed this load , all the work is done perfectly but the problem is that the battery when connected to the load its output voltage varies from 12 til 0 and the increase and continues like that, which may damage my load, so i think i should use a voltage regulator that outputs 12 v but it will work? if yes what kind of regulators i can buy?? Note : the load takes 1.2 A and the batteries are 4000 mAh
I would use a 8.4V LiPo battery pack rather than 12.6V.
An 8.4 will would use a DC-DC step-up boost converter.
A 12.8V would require a combination step-up/step-down converter.
Off the shelf solutions are few for a 1.2 A, 12V - 12V chargers and regulators.
But you already have a 12V battery pack.
You could use the versatile Linear Tech LT3652 Battery Charger
Input voltages from 5V to 32V
Will charge up to 2A
Works with Lead Acid, Li-ion, LiPo, and Li-phosphate.
Example 8.4V Li-ion charger powered with 12V AC adapter:
Example 12V Lead Acid charger powered with 5 VDC to 32 VDC :
Then for the output regulation the Linear Tech LTC 3111 12V 1.5A Buck-Boost DC/DC Converter
With low battery shut off.
If you want to switch between the AC adapter and battery without the voltage dropping to zero you can use a Linear Tech LTC4358 Ideal Diode Switch .
Or a Linear Tech LTC4412 Automatic Switch