USB PD 3.1 EPR Cable Drop, Heating & Power Budget (48 V)

The circuit equations are derived here from Ohm's law and conservation of energy. Each rail contains its one-way conductor resistance and two mated interfaces:

$R_v=Lr_v(T)+2R_{cv}$, $R_g=Lr_g(T)+2R_{cg}$, and $R_{loop}=R_v+R_g$.

Copper uses $r(T)=r_{20}[1+\alpha_{20}(T-20\,°C)]$, with $\alpha_{20}=0.00393\,K^{-1}$ from NBS Handbook 100 (1966), PDF page 10. The AWG library provides ideal annealed-copper resistance at 20 °C; entered rail resistances include parallel wires before temperature correction.

For a specified current, $V_{sink}=V_s-IR_{loop}$ and $P_{sink}=IV_{sink}$. Wire heat is $I^2(R_{wv}+R_{wg})$; heat at each end is $I^2(R_{cv}+R_{cg})$. Their sum equals $V_sI-P_{sink}$.

For constant sink power, the lower-current root is evaluated as $I=2P/(V_s+\sqrt{V_s^2-4R_{loop}P})$. A negative discriminant has no DC solution. The power budget maximizes $(V_s-IR_{loop})I$ subject to $I\le I_{limit}$, $V_{sink}\ge V_{min}$ and the high-voltage branch $I\le V_s/(2R_{loop})$. Zero resistance is handled explicitly.

The separate 5 A drop screens follow USB Type-C Cable and Connector Specification Release 2.5 (March 2026), §4.4.1, PDF page 151: 0.50 V for VBUS and 0.25 V for ground, including both mated interfaces. These are cable-path screens, not overall compliance verdicts.

Two identical connector interfaces, one at each end; each rail input is the equivalent of all its parallel contacts. Contact resistances are supplied at operating temperature and receive no copper temperature correction. The default 10 mΩ per rail per interface is an illustrative scenario, not a manufacturer's typical value.

Cable conductors are annealed copper at a fixed, user-assumed temperature between 0 and 100 °C. AWG values describe ideal conductors; use measured or manufacturer resistance for stranded or plated copper. Non-copper conductors require a different temperature model and are outside this tool's scope. Equal parallel wires share current equally. No additional VCONN or auxiliary return current, active-cable electronics, source wiring or PCB resistance is included. A shield return is included only if represented in the entered ground equivalent.

The source is a fixed voltage at its port. The negotiated current limit must already account for the actual source and cable capabilities. Constant-power operation uses the high-voltage algebraic solution; this does not establish control-loop stability.

Applies to steady DC cable and contact loss calculations for a negotiated USB PD 3.1 EPR power path, with source voltage entered explicitly. Lower voltages are also accepted for comparison and reference-example verification. Cable-only transfer efficiency excludes source and sink converter losses; at zero load the displayed value is the limiting efficiency.

The power budget imposes electrical limits only. The 5 A drop screens omit VCONN return current and do not assess pin current sharing, allowable temperature rise, insulation, e-marker identity, protocol behavior or USB-IF certification. Temperature rise cannot be inferred from resistance or heat alone. Use measured thermal data and test the actual assembly. No disconnection, arcing, transient or short-circuit model is provided. Check against the standard in force; the cable drop screens here use Release 2.5, March 2026, reviewed 30 October 2026.