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I am trying to run WiFi router from a 12v lead acid ups battery. To get a stable 12v output from the battery I used LM2596. Problem is output is always 8.28v-8.50v. No matter how many times I spin the potentiometer out put is 8.28v. Is this a wrong approach to get stable 12v dc from a 12v lead acid battery?

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LM2596 is a buck converter. It can only lower voltage. The parameter you are interested in is called "dropout voltage". To get stabilized 12V from an "approximate" 12V source you need a buck-boost converter.

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