How to determine PCB trace heating with I^2R, IPC‑2152, and real examples

You determine PCB trace heating by computing I^2R losses and mapping current and cross‑section to temperature rise with IPC‑2152 for the specific layer and environment, then iterating with copper’s temperature coefficient.

What you actually calculate

At DC, power is P = I^2 × R. Trace resistance at 20°C: R20 = ρ × L / A, with ρ(cu) ≈ 1.724e‑8 Ω·m, A = width × copper thickness. Temperature dependence: R(T) = R20 × [1 + α × (T − 20°C)], α(cu) ≈ 0.0039/°C. For cyclic loads, use Irms = sqrt(Σ Ii^2 × ti / T). For high frequency, include AC resistance once thickness exceeds skin depth δ ≈ 66/√f(MHz) µm.

How do watts become temperature rise?

IPC‑2152 provides current‑versus‑ΔT for given copper cross‑section, layer (external vs internal), and environment (still air, airflow, nearby copper). External layers run cooler because convection and radiation are available; inner layers rely on conduction into FR‑4 and copper planes. Soldermask increases external trace ΔT; plane pours tied to the net reduce ΔT via lateral spreading. Use IPC‑2152 for the conversion, not bare convection formulas, which miss board conduction.

External vs internal example with numbers

Assume 1 oz copper (35 µm), width 0.25 mm (10 mil), length 0.10 m, DC current 1.0 A.

• Cross‑section A = 0.25e‑3 × 35e‑6 = 8.75e‑9 m²

• R20 = 1.724e‑8 × 0.10 / 8.75e‑9 ≈ 0.197 Ω

• First‑pass power P ≈ 0.197 W (spread over 0.10 m → 1.97 W/m)

Using IPC‑2152 for an external 1 oz, ~10 mil trace in still air, 1 A typically yields a temperature rise on the order of a few tens of °C; a commonly observed value is about 20°C for bare copper. Iterating resistance with ΔT: R(≈40°C) ≈ 0.197 × [1 + 0.0039 × 20] ≈ 0.212 Ω → P ≈ 0.212 W, increasing ΔT modestly.

Move the same geometry to an internal layer and expect a substantially higher ΔT at the same current per IPC‑2152; it is common to need roughly 2–3× the cross‑section (wider trace or heavier copper) on inner layers to achieve a similar ΔT target. For this case, doubling width to 0.50 mm or moving to 2 oz copper are practical first iterations to bring inner‑layer ΔT back near ~20°C in still air conditions.

Do pulses or RF change heating?

Yes. For pulsed loads, size the trace by Irms over the thermal window of interest. Example: 3.0 A for 10% duty and 0.5 A for 90% gives Irms = sqrt(3²×0.1 + 0.5²×0.9) ≈ 1.06 A; apply that current to IPC‑2152 instead of peak. For high frequency, once δ < copper thickness, AC resistance rises. For 1 oz (35 µm), δ ≈ 21 µm at 10 MHz and ≈ 6.6 µm at 100 MHz; at tens to hundreds of MHz, consider wider traces, parallel routes, or thicker copper if heating or loss is critical.

Quick checks before committing a width

• Gather: layer (external/internal), copper weight (µm), trace length and width, airflow, mask vs bare copper, nearby copper tied to the net

• Compute R20 and Irms, then P = Irms² × R20; do one iteration with R(T)

• Size with IPC‑2152 for your exact cross‑section and layer to hit a ΔT target (many power designs aim for <10–20°C in still air)

• Prefer external layers for high current, add copper pours to the same net for spreading, and use stitched vias to planes alongside long runs

Prototype checks that catch surprises

Measure 4‑wire voltage drop end‑to‑end to get hot resistance and back‑out ΔT via R(T). Cross‑check with a micro‑thermocouple on the trace or IR imaging (use matte black tape to set emissivity). Log ambient, airflow, and load profile so results are reproducible. If external traces are masked, test both masked and exposed cases; mask can raise ΔT.

Fabrication and compliance specifics

If the required width approaches process limits (e.g., fine lines on heavy copper), confirm manufacturability and acceptance criteria early. Boards can be built and inspected to IPC Class 2 or IPC Class 3 acceptance criteria. RoHS and REACH compliance is supported for hazardous substance control. HyperPCB operates an ISO 9001:2015 certified quality management system (certificate no. CN‑2023‑Q1156, issued by SGS, valid until June 2027). Quotes are returned within 24 hours and DFM feedback is provided within 1 business day.