LEDs are current driven devices. This means that the brightness of the LED is pretty much proportional to the current through it. At low currents, the forward voltage across a LED (and in fact almost any semiconductor diode) is proportional to the log of the current through it so the voltage rises sharply with applied current until, at higher currents, the voltage drop across the internal series resistance begins to dominate whereupon the voltage drop increases almost linearly with applied current. The corollary of this is that, until the internal resistance of the diode dominates, the current through the LED is exponentially related to the voltage applied across it. In other words, in this region of operation, a small change in voltage will cause a large change in current. In fact the same absolute voltage change of 'deltaV' volts in any given applied voltage 'Vd' will cause the same ratio change in the LED curent, for example doubling or halving it, irrespective of the actual value of Vd. The internal resistance of most low current (