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You're right that it's probably still detectable. But IEEE considers ~3+ kHz as "no risk." My interpretation is that it could be annoying but unlikely to cause an accident, etc.

Some of the really good LED dimming solutions I've seen that employ PWM are in the 30+ kHz range.

Of course, constant current dimming is the best, but it tends to be expensive.

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Dimming by reducing current in LEDs instead of PWM can be very non-linear with respect to light output, brightness can vary significantly between LEDs being given the same current (as is typical in a headlamp, with at least 4-8 individual LEDs being driven by a single driver), and temperature dependent, plus it can cause significant color shift. Long story short, reducing current for dimming groups of LEDs is largely non-practical.

Constant current dimming is used widely for mid-power LEDs in architectural applications. Usually there is a significant number of LEDs, in the 10s or 100s, such that individual variations would average out over the series. You have some color shift, usually toward greenish hues, but this is generally not a consideration.

It might be more of a problem in automotive applications, where for a headlight you use only a few high-power LEDs.

May still be less expensive if it reduces driver's weariness on the road by a few percent.

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