RCSJ model: φ̈ + (1/Q)φ̇ + sin φ = I_bias + I_AC·cos(ω_AC·t). When I_bias < 1: no DC voltage (supercurrent). Above: phase slips, finite voltage. AC drive creates Shapiro steps.
Josephson 1962: Cooper pairs tunnel through insulator. Phase difference φ obeys pendulum equation. Voltage V ∝ dφ/dt. Shapiro steps appear at V = nℏω_AC/2e — DC voltage locked to AC frequency. Used in voltage standards (NIST, PTB).