Voltage drop along an LED strip

Why it is half

A strip is not a resistor with a load on the end. Every pixel takes its share along the way, so the copper at any point only carries the current of what lies beyond it: at the feed it carries everything, at the far tip nothing. Integrating that falling current along the run gives the drop at the tip as r·L·I / 2 — half the lumped I·R, where r is the round-trip resistance of the +V and ground traces together, per metre.

The voltage profile is a parabola, not a line: most of the drop happens in the first third of the run. And the copper loss is r·L·I² / 3, a third rather than a half — real power the supply has to deliver on top of what the pixels use.

A feed cable is different. It carries the full current of its segment along its whole length, so its drop is the plain 2 × ρ × length / cross-section × I. Copper is 0.0172 Ω·mm²/m; copper-clad aluminium, which most cheap “18 AWG” LED wire actually is, about 0.028 — 63 % worse.

Why more feeds help so much

Feeding a run at both ends, or once in the centre, is the same problem: two half-length runs each fed at one end, each with a quarter of the drop. In general, evenly spaced feeds cut the drop with the square of their count — n equal segments give r·L·I / (2·n²). Four interior injection points give one sixty-fourth of the single-end drop.

That square is why one more feed beats thicker wire. Doubling the cable cross-section halves the cable’s drop; adding a second feed quarters the strip’s, and the strip’s is usually the larger.

Evenly spaced is conventional, not optimal. Two feeds at a quarter and three quarters of the run are four times better than two feeds at the ends: every span then drops r·i·L² / 32.

A worked example

Estimated drop at the worst point of a 5 m WS2812B run at 60 LEDs/m — 18.3 A at full white, standard copper — for evenly spaced feeds including both ends. A dash means the estimate is past the point where the model describes a working strip.

Where the model stops

The strip’s resistance is the dominant uncertainty. Real strips measure 0.3–1.5 Ω/m round trip; vendors do not publish it and it does not correlate with price. PixelPower makes it a visible choice — thin, standard or heavy copper — and carries the bracket into every figure rather than pretending to a decimal it does not have.

The load is not resistive. A 5 V pixel holds its current until the rail can no longer drive the blue die, at roughly 3.7 V; then blue drops out, then green, then red. A WS2815 regulator holds until roughly 9–11 V and then stops. Past about 25 % drop the linear model is no longer describing a working installation, so PixelPower reports no figure there. Between 10 % and 25 % the run works and will visibly shift colour. Both thresholds are yours to change; an architectural install holding a white tolerates far less than a party effect.

Not modelled: connectors and solder joints — four JST contacts at 5–30 mΩ each are worth about a metre of strip copper; copper temperature — 16 % more resistance at 60 °C, with positive feedback; and non-uniform content — one bright section at a free end behaves like the lumped I·R.