definition v1 of neper

The neper is the human-made natural-logarithm ratio unit: the level corresponding to one natural-logarithm unit of a ratio, L = ln(P1/P0) nepers. Parameters: (1) ratio kind — a power ratio, expressed ln(P1/P0), or a field-amplitude ratio (voltage, sound pressure, wave amplitude), expressed 2·ln(A1/A0) = ln(A1²/A0²), the factor of two following from power being proportional to the square of the field quantity, so that the neper value is the same under either expression, exactly as the decibel value is the same under 10·log10(P1/P0) and 20·log10(A1/A0); (2) scale relation — one neper corresponds to the power ratio e, the base of the natural logarithm (i.e., to the field-amplitude ratio √e), and converts to the base-10 scale by the fixed factor 1 Np = 10·log10(e) dB ≈ 4.3429 dB, while 1 bel = ln(10) Np ≈ 2.3026 Np; (3) base distinction — where the bel and the decibel apply the base-10 logarithm to the ratio, the neper applies the natural logarithm (base e), so the two families measure the same ratio on different logarithmic scales, with a fixed conversion factor of ln(10) ≈ 2.3026 between them. Persistence mechanism: the neper persists as a named non-SI unit in the IEC system of units (IEC 60027), in the literature of logarithmic transmission and in radio, audio, and control engineering where the natural logarithm is native, and through the fixed conversion constants (1 Np ≈ 4.3429 dB, 1 B ≈ 2.3026 Np) that appear in the standards and the textbooks. Distinct from the decibel (the base-10 practical working unit), from the bel (its base-10 whole-log counterpart), from the natural logarithm (the mathematical function the unit applies to a ratio), and from a plain ratio (a linear two-term quotient needing no logarithmic name). [formal: neper | substrate: mind | horizon: as-long-as-us | explicit: yes | epoch: 0.03]