Oh brother! ... they just don't make engineers like they used to....and not magazine editors either I see. OK off my soap box.
So if one of the strings goes into current limiting....what will happen.... well if the main LED driver is a constant current source, say of 700mA, then it will keep increasing the output voltage until it can get to 700mA. As per the article, the circuit limits current to 455mA. However, the LED driver is putting out maximum voltage. The voltage has to be somewhere, so it is going to be on the left transistor...which is going to be hot and need a significant heat sink. That is something to keep in mind.
There is another way of doing the current limit that quite simple though perhaps not as flexible. All you need to do is put two forward biased diodes between the base of each transistor in the current mirror and ground. These are pennies each. This will limit the maximum voltage on the base of the transistor to approximately 1.4V. You could play with a standard diode and a schottky to get to 1.2V, but 1.4V works well.
Assuming 0.7V for Vbe of the current mirror transistor, then the maximum current in any chain is limited to (1.4-0.7)/1.5 = 470mA. 1.5 is the value of the resistor. Practically the limit is going to be lower than 470mA. You can extend this to as many chains as you want.
Note that the minimum hFe for the BD139 at 350mA is likely on the order of 30-35 (not typical, but what you may actually encounter). That means for 350mA, you are going to need on the order of 10mA into the base. With the 680ohm transistor between the last LED and the base, you will need a 680ohm * 0.010Amps = 6.8 volts extra! That means worst case you need 6.8V across this resistor, 0.7volts Vbe, and 0.5V or so across the 1.5ohm resistor or about 8 volts extra!!!
I would pass on their current limit scheme, get rid of the 680ohm resistors (but keep the 1.5 it is essential for current matching), and then use the two series connected diodes in the base to limit current.
Next I would consider closely reviewing what I have written and see if I am right or I have lost my mind (I could have made a mistake in my math). Assuming I have not, may want to consider a note to LEDS Magazine suggesting better peer review.
Semiman
I've replaced a couple 4' fluorescent fixtures in the kitchen with a motley collection of warm and neutral white LEDs. This batch is being run off 2 40W Xitanium drivers—each running 3 strings of 6 LEDs. I've voltage-matched the strings at operating temperature (3.07V-3.74V LED voltages), and they're well balanced as is, but I like the idea of having a current mirror just in case—and to turn off the string if one LED burns out.
I've used the current mirror shown in figure three http://www.ledsmagazine.com/features/6/2/2 to good success with two strings but when I add a third or fourth string, the circuit no longer shuts down when one LED opens. I've tried putting the highest vF string first, last, random—doesn't work. Works fine with two strings.
Any ideas or other circuits come to mind?
Thanks
PS The lights look great, BTW.