LED Array / String Designer
Supply, Vf, and current → LEDs per string, string count, and the ballast resistor.
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The engineering
Stack as many LEDs in series as the supply allows and the resistor only burns the leftover — that's the whole efficiency game. The headroom field is the resistor's working margin: too little and normal Vf spread (±0.1–0.2 V per LED, times n) swings the current wildly; 15–20% of the supply voltage is a comfortable default for indicator-class strings.
Each string needs its own resistor — never parallel bare LEDs, because the one with the lowest Vf hogs the current and thermal runaway finishes the argument. Above roughly 100 mA per string, trade the resistor for a constant-current driver: the wasted headroom power stops being a rounding error and Vf's temperature drift starts steering the brightness.
Where this math comes from
Electroluminescence was spotted by H. J. Round in 1907 (a cat's-whisker on carborundum, reported in two paragraphs), but the practical visible LED is Nick Holonyak's 1962 red GaAsP diode at General Electric. For three decades LEDs meant indicators — 20 mA, a series resistor, done — and this card's arithmetic was the whole design procedure.
Shuji Nakamura's 1993 high-brightness blue GaN LED at Nichia completed the color triangle and, via phosphor white, turned the indicator into an industry: strings of dozens of one-watt emitters running from mains drivers, with the same series-parallel bookkeeping now deciding luminaires instead of front panels.
- 1907H. J. RoundElectroluminescence observed in silicon carbide.
- 1962Nick Holonyak (GE)First practical visible (red) LED.
- 1993Shuji Nakamura (Nichia)High-brightness blue GaN LED — white lighting unlocked.
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