Note: ** This is a work in progress. The design is not entirely complete, nor has it been built yet. And may read more like a design-guide for engineers. (Sorry about that). Constructive suggestions and collaboration are welcome **
For more information on LED Grow-light design, see US patent #6921182 .
Step 1: Circuit Schematic
Start the circuit design by arbitrarily adding LEDs to a string. Add up the voltage of all the LEDs in a given string, and adjust the number of LEDs per string to get as close as possible to the power supply voltage without exceeding it. To do this it helps to mix and match LED colors in the string, since each color has a different voltage.
The main concern is that you don't exceed the LED's current rating.
Ohm's law says that the resistor value "R" in units of "ohms" that you should use is given by this equation:
R = (Vs - V_LEDs) / I_LED
Where Vs is the power supply voltage,
V_LEDs is the sum of the LED voltages in the string, and
I_LED is the current in amps that the LEDs are rated for
If V_LED is just slightly less than Vs then you will only need a very low value resistor, like 1 ohm or less, assuming a 1 amp string. You shouldn't need to drop more than a volt or two across the resistor. If you're dropping over 2.2 volts, why not just add another LED instead?
Just calculate the proper resistor value for each string, and after you've built the circuit, you can measure the current through each string with an ammeter to make sure the current does not exceed the LED's spec, especially when it is operating at its highest temperature. You can also calculate the current by measuring the voltage across the resistor and dividing by the resistance. (again, ohm's law).
The figure below shows a simple schematic example. 12 volt power supplies are very common and you should be able to find an extra one lying around that you can re-purpose for this, or you can acquire one from your favorite surplus distributor, for example allelectronics.com. In this example it should have a capacity of 2 Amps or more, or whatever is the sum of the current in each string.
The resistor values may need to be adjusted to limit the current in each branch to 1 amp, particularly given the LED's negative temperature coefficient, which may be as high as -4 mV/deg.C (check the "datasheet" pdf for the device). I'm also looking into using copper pcb-trace resistors (or "wirewound resistors"), mainly because copper has a positive temperature coefficient of resistance (about +0.4%/deg.C) which will help regulate current through the LEDs. So far the approach looks promising. Also, in theory this type of resistor is free (or under $1), simple (amenable to DIY), and high-power, which is ideal for our design goals. In theory, if the LED and copper resistor are solidly connected to the same heatsink, and so are at essentially the same "case temperature" (although not necessarily the same "junction temperature", but I will gloss over that for now), then we can calculate what minimum value of resistance we need so that the overall temperature coefficient is above zero, so there is less risk of "thermal-runaway" that could damage or destroy one or more LEDs. For example, for a 1 Amp LED, we would want at least 1 volt drop across the resistor, so that by Ohm's law, the +0.4%/deg.C resistor would yield +4 mV/deg.C, thus canceling the LED's -4 mV/deg.C. Also by Ohm's law to get 1 volt drop at 1 Amp, requires a 1 ohm resistor. This part can be bought for under a dollar, or can be made , for example with 2.5' of #36 wire, or 4' or #34 wire, etc. (Table_of wire sizes)