Below is the simulation of a two-transistor constant-current circuit for an LED.
It only requires an input voltage about 0.8V above the LED forward voltage to start controlling the current.
Above that point it the small current variation with input voltage is likely not noticeable in the LED output luminance.

It only requires an input voltage about 0.8V above the LED forward voltage to start controlling the current.
Above that point it the small current variation with input voltage is likely not noticeable in the LED output luminance.

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