How to build a linear LED driver that is dimmable?

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You might want to try TA’s Commander driver:

Texas Commander "TC" Constant current Opamp driver without PWM

Ok, I don’t have time for my normal long post explaining every little detail of this driver. Plus with all the advancements coming down the line in driver tech I see bigger and better things coming out this year anyways. Still this is a good concept and works great so it is worth posting it up. Basically while this was not the goal, this is an open source LD-3 driver. The difference being that the LD-3 has a better 4 layer PCB and can handle a bit more heat then this driver. The features and b…

Not in use in any light as far as I know, but it tested very well. It just tends to overheat in the mid-range amps (2-3 A). Your 1 A requirement sounds like a perfect fit. It has true linear regulation in 255 steps. It even works with most of the firmware around here if you do not need the DD mode or moon mode.