Electronics bench reference
The formulas behind the four calculations you keep redoing at the bench — with their sources, so you can check the working instead of trusting a black box.
PCB trace width
Source: IPC-2221
A = ( I / (k · ΔT^0.44) )^(1/0.725) → W = A / (t · 1.378)
A is cross-section in mil², I is current in amperes, ΔT is the permitted temperature rise in °C, and k is 0.048 for external layers or 0.024 for internal ones. t is copper weight in oz; 1 oz ≈ 1.378 mil thick. This is the legacy IPC-2221 estimate — verify against your stack-up and fabrication limits, and consult IPC-2152 before production.
Voltage drop
Source: Ohm's law
V_drop = I · R_path V_delivered = V_supply − V_drop
Resistive loss is I²·R. Voltage retained is V_delivered / V_supply. R_path is the total round-trip resistance of the conductor.
Resistive divider
Source: Ohm's law
V_out = V_in · R2 / (R1 + R2)
Valid while the load draws negligible current compared with the divider. Output impedance is R1 ∥ R2.
Resistor colour code
Source: IEC 60062
4-band: d1 d2 × multiplier ± tolerance 5/6-band: d1 d2 d3 × multiplier ± tolerance (+ tempco)
Multiplier bands are powers of ten; gold is ×0.1 and silver ×0.01. The sixth band gives the temperature coefficient in ppm/K.
