How to get an analog signal 0 to 12 V DC based on reference 0 to 5 V DC?
You need feedback if you want an exact ratio of 12/5, an open loop transistor will not do this. I would use an opamp with a transistor amplifier. You could also look for an opamp that will output 55 mA (most won't) and leave out the transistor.

You need a rail-to-rail opamp so the output will go to ground. The supply voltage needs to be a few volts higher than 12V if you use a transistor.

Also see the "adding gain" section of this article:
https://www.allaboutcircuits.com/technical-articles/how-to-buffer-an-op-amp-output-for-higher-current-part-1/







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