LED Resistor Calculator: Strings and LED Strip Voltage Drop

For a series string, Kirchhoff's voltage law and Ohm's law give $R_0=(V_s-nV_{f,\mathrm{typ}})/I_d$. The ceiling design uses $R_{\min}=(V_{s,\max}-nV_{f,\min})/[I_d(1-t_R)]$ and rounds upward to an E12 or E24 value. Nearest selection minimizes the absolute resistance difference; a tie selects the lower value. Supply and resistor tolerances are independent inputs. Estimated corner currents use the fixed entered forward voltages, and each of $N$ independent strings contributes its own current.

A voltage range specified at $I_d$ is not an entire I–V curve. Corner current and $P=VI$ results are first-order estimates. If $R\ge R_{\min}$ and the entered lower forward voltage is valid at $I_d$ across the applicable temperatures, monotonic LED I–V behavior limits actual current to $I_d$. Two power bounds are available: $P_I=I_d^2R_{\max}$ when that current ceiling is valid, and the always-applicable zero-forward-drop bound $P_V=V_{s,\max}^2/R_{\min,\mathrm{actual}}$. Use $\min(P_I,P_V)$ when the ceiling is valid, otherwise $P_V$. Divide by 0.5 for the conservative rating recommendation. Likewise PSU current capacity uses $\min[I_d,V_{s,\max}/R_{\min,\mathrm{actual}}]$ when the ceiling is valid, otherwise the zero-forward-drop current bound. These tighter bounds prevent large existing resistors from producing excessive ratings.

The strip equations are derived here from a distributed resistor network, not fitted to a product measurement. Let $V_0$ be the effective segment LED-chain voltage, $H=V_n-V_0$, $g=(p_m/V_n)/H$ in S/m, $r$ the positive-plus-negative rail resistance in Ω/m, and $k=\sqrt{rg}$. For an arm of length $d$, $u(x)=u_f\cosh[k(d-x)]/\cosh(kd)$, where $u=V-V_0$. Open arm ends have zero longitudinal current. With $a=1$ for an end feed or $a=2$ for equal center-fed arms, $G=a(g/k)\tanh(kd)$ and $u_f=H/(1+R_cG)$. Thus darkest-point current/rated current is $1/\{[1+R_cG]\cosh(kd)\}$. Numerically stable exponentials and the exact zero-rail-resistance limit avoid overflow and division by zero.

Copper cable-pair resistance is $R_c=2\rho(T)L_c/A$, with $\rho_{20}=0.017241$ Ω·mm²/m and $\alpha=0.00393$ K⁻¹ (Energypac conductor properties, p.10). The cable area result uses full rated zone current and the entered cable-drop allowance. The injection search finds the largest zone satisfying the current-based brightness target, the full-load cable-drop allowance, manufacturer run limit and entered connection-current limit. It rounds down to whole cut sections, or pairs for center feeds, and balances the total length among zones. Input length must already match those cut quanta. Recommended positions refer to that balanced layout, independent of the installed feed count.

The LED preset uses ams OSRAM LS L296 v1.4, pp.4–5: 1.80/2.00/2.30 V at 20 mA and 25 °C; 60 mA absolute maximum at that temperature. Preferred resistor values use Vishay document 31001, p.1. Strip nameplate values use Waveform CS7041, p.1 and HST's manufacturer product specification. Independent reference cases use Adafruit's 65 Ω and 75 Ω worked values, Waveform's reel/PSU figures and ENTTEC's copper resistance figure.

The strip injection recommendation also enforces the entered cable-drop allowance at full rated zone current: $L_{\mathrm{zone}}\le V_n f_c/(R_c i_m)$. This is separate from the actual cable loss already included in the brightness model. A zero-length cable imposes no cable-drop limit.

Rail heat is calculated independently from downstream arm current $j(x)=\int_x^d g\,u(s)\,ds$: $P_{\mathrm{rail}}=a\int_0^d r\,j(x)^2\,dx$. The rail integral uses adaptive numerical quadrature, not the residual of the other power terms. Supply power is then compared with cable, rail, ballast and LED power. A separate ngspice-36 resistor-ladder benchmark checks center-fed and end-fed cases with nonzero rail and cable resistance. Attached source s10 includes direct solver results, 500/1000/2000-cell refinement results, netlist hashes and reproduction code; it is an authored numerical validation, not measured strip data.

The installed feed count supports 1–2,000 feeds, further limited by the number of complete cut quanta. Requirements above that range are explicitly flagged. The placement table shows the first 20 zones; the feed result gives counts and lengths for every zone so longer plans can be continued.

• The LED and strip sections are independent load cases. Their PSU ratings are not automatically added. Use the rated strip supply voltage; do not raise it to compensate for a dim far end.
• The LED preset is specified at 25 °C, not over an arbitrary junction-temperature range. For another current or temperature, use Custom and enter suitable data-sheet or measured bounds. The absolute maximum is not a recommended design current.
• Higher LED junction temperature generally lowers forward voltage. LS L296 lists a typical −2 mV/K at 20 mA: a 50 K rise would suggest about 0.10 V less per LED, but this is not an automatic temperature correction or a thermal model. Cable temperature is a separate input.
• All strings have the entered number and type of LED, and each has its own resistor. A single common resistor cannot impose equal branch currents. Constant-current drivers offer better current regulation when their compliance voltage is sufficient; no driver circuit is designed here.
• Strip segments are distributed uniformly, with a constant effective LED-chain voltage and linear ballast resistance. The default 25% resistor voltage share and 0.10 Ω/m rail loop resistance are illustrative engineering assumptions, not measured specifications of either preset. They must be replaced or validated for the actual strip.
• Rail resistance includes both strip conductors at operating temperature. Cable resistance includes both copper conductors and a temperature correction; connectors, joints, fuses, controllers and shared supply trunks are omitted. Each zone receives an independent equal-length cable pair. Both rails are cut at zone boundaries; returns join only at the PSU.
• Cut rounding is conservative. A center feed sits at the middle marked cut between equal arms. Cut both strip rails between zones, provide a separate cable pair to each, and feed from the same PSU. Do not parallel independent PSU outputs unless the manufacturer explicitly permits it.
• Current ratio is only a brightness proxy. LED efficacy, optics, color shift, temperature and human perception are not modeled. Manufacturer maximum run is retained even if a center feed would reduce electrical drop.
• Continuous strip rails with multiple cable injections are outside this model; the recommendations use separate strip zones.

For steady DC sizing of low-power LED strings and resistor-limited constant-voltage strips. Fixed-forward-voltage current estimates become less accurate far from the data-sheet test current; use a measured I–V curve or circuit simulation for precise current spread. Current-ceiling and power bounds require valid lower forward voltage at the chosen ceiling, nonnegative LED forward voltage and monotonic I–V behavior. Derate components for actual temperatures.

The continuous strip model is appropriate when the voltage variation over a cut section is small. A warning flags a large per-section decay parameter, large dimming, an unmet brightness target, a manufacturer run limit or an entered connection/cable limit. The zero-rail-resistance limit is supported. Layout positions assume a straight sequence of cut sections; the schematic is illustrative and not a physical routing drawing.

Neither regulated strips, addressable pixels, constant-power loads, PWM transients, RGB channel interactions nor constant-current-driver dropout are covered by the strip brightness calculation. Use the product's load curve and controller limits for those cases. No strip-specific measured brightness validation is claimed.

Waveform CS7041 p.1 is internally inconsistent about copper thickness (4 oz in features; 2 oz in mechanical data). Neither value is used to infer rail resistance. Its SI reel rating is used rather than independently rounded per-foot figures. The published 86 W PSU value at 20% added capacity is rounded; arithmetic gives 86.4 W.

Cable area is a voltage-drop result, not an ampacity or installation approval. No allowance is made for contact resistance or shared trunks; check them separately. Installation work belongs to a qualified person. Verify cable and connector ratings, branch protection, separation of supply zones, thermal mounting, PSU derating and the electrical rules in force.