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Assuming that each LED needs for example 3.5VDC to operate at 20 mA, the current drain would be 720 mA for the lot, and this would be the design current for when the 6V battery was fresh. The LEDs would dissipate 2.52 watts. If the LEDs were each connected to the 6V battery with a series resistor to limit the current, each of 36 resistors would be 260 ohms and the total wattage dissipated in the resistors would be 1.8 watts. In other words, the circuit would waste 41% of the energy in the resistors. The energy delivered to the LEDs would be 59% of the total input.
There were some small round surplus printed circuit boards, previously part of an I.R. illuminator available from BG Micro, that would hold the 36 LEDs, but the print was such that there were four circuits of of one resistor in series with nine LEDs. These four circuits were in parallel. This would require 3.5 * 9, or 31.5V.
In order to get this voltage, plus a bit more for the sake of current equalization and limiting, it was decided to build a small switching power supply of the 'boost' type. The power supply operates on 4.5 to 6.5 VDC input and delivers a well regulated 36VDC at 80 mA.
The LED current was measured and found to be about 30 mA. Since this was too much, a 48 ohm resistor was inserted between the power supply and the LED strings to bring the current to 20 mA. The 48 ohm resistor dissipates 0.3072 watt. The total wattage dissipated by the 220 ohm resistors is 0.352 watt. The LEDs dissipate 2.52 watts. The efficiency of the LED circuit is 78.9%. The efficiency of the power supply itself is 94%. The energy delivered to the LEDs is 74% of the total input.
It is understood that the power supply voltage could have been reduced slightly, and the 48 ohm resistor dispensed with. A power supply designed for a constant current could also have been used, but would have been more complex. Additionally, if the power supply has good enough voltage regulation, the 220 ohm series resistors could be reduced in value to 100 ohms and still balance the LED currents well.
This reduction in series resistance will reach a critical point, as the voltage across the LEDs changes materially with temperature, and it was found that out of the same batch of 50 LEDs, the voltage drop per LED varied over a 200mV range at a constant current of 20mA.
With the regulated switching power supply, the LED brightness remains constant over a longer portion of the lifetime of the battery because the battery current starts out lower when the battery is new. Lower currents allow more of the battery's Amp-Hour rating to be realized.
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