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Why is it important to control the current through an LED?

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A typical voltage-current relationship for an illumination-grade LED is shown in Figure 8. As seen in this figure, a slight change in voltage can result in very large changes in current. Since the light output of an LED is proportional to its current, this can result in unacceptable variation in light output. If the resulting current exceeds limits recommended by the manufacturer, the long-term performance of the LED can be affected, resulting in shorter useful life.

Figure 8. The relationship between forward voltage and current for illuminator LEDs.

Data based on literature from LumiLeds
The solid line is for normal operating parameters; the dotted lines are extrapolated.