To clarify, here I meant the series replaced by parallel strings, like this:
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There is a term called "tolerance stacking" which usually refers to small tolerances adding up to larger tolerances, but in a series circuit it actually has the opposite effect of adding up to smaller tolerances.
Confused?
OK, let's assume that the voltage tolerances for your individual diodes are 0.1V and that your average diode is 3.0V. That means individual diodes could be as high as 3.05V or as low as 2.95V – a spread of 0.1V.
(This is a real-world example, because most Vf bins are 0.1V for 3030 diodes but can be as high as 0.2V for 3535 and other high-powered diodes.)
Now that 0.1V represents a potential difference of 3.4%. And that is the difference you could expect (worst-case scenario) between each of those diodes in parallel. Meaning a 3.4% diffrence in voltage requirements which will draw current away from the higher Vf diodes to the lower Vf diodes – resulting in an imbalance (and potential thermal runaway) between all 8 diodes.
Now let's place those diodes in series. Even though there is a potential difference of 3.4%, we would expect the law of averages to even out the voltages the more diodes we place in series.
So, 8x3.0V = 24V. The maximum voltage would be 8x.3.05V = 24.4V. The minimum would be 8x2.95V = 23.6V A difference of 0.8V or 3.4%.
However, the chances of having maximum and minimum voltages at the end of each series string are highly unlikely – and less likely as you increase the number of diodes in series.
Indeed, you would expect those averages to even out, for the most part, with perhaps only 0.2-0.3V difference between each series string. If there is a 0.3V difference between each string, then that is only a 1% difference in Vf requirements. If we had the same 0.1V difference between each series string (same as the parallel string), then that is a difference of only 0.3% in Vf requirements.
Most 48V LED panels using 3030 diodes (or combinations with 3535 diodfes) have series strings of 16-18 diodes (thereabouts) because 3V (average) x 16 (average) = 48V. And most 24V strips have series strings of 8-9. Each of these strings is then placed in parallel – just like your original LED panel – precisely for the reason I've explained.
The more diodes you have in series, the more even the voltage requirements will be for each string, with less chance of thermal runaway if you place each of those strings in parallel. Also, the higher the voltage for each series string, the lower the impact of voltage drop over longer traces of parallel circuits.
And that is how you design a LED PCB without ballast resistors for each string. However, you do need to get your diode voltage bins as close as you can and the thicker the trace (we use 2oz copper instead of 1oz) again, the less voltage drop (and potential difference) there is between strings.