Inductance Conversion — pH · nH · µH · mH · H

Joseph Henry (1797-1878) was teaching natural philosophy at Albany Academy in upstate New York in 1832 when he discovered the principle of electromagnetic self-induction — independently of Michael Faraday's parallel work at the Royal Institution in London. Henry wound 35 ft of insulated copper wire on an iron horseshoe and observed the spark when the circuit was broken; the back-EMF principle V = -L × dI/dt that governs every transformer, motor, choke and inductor in modern engineering originated in that experiment.

Henry's 1831 demonstration of a long-distance electromagnetic telegraph at Princeton — a mile of wire ringing a remote bell — predates Morse's 1837 patent. Morse used Henry's relay invention without attribution; the resulting dispute shaped 19th-century US patent law. Henry refused to patent the relay, believing scientific discoveries should be open. He became the first Secretary of the Smithsonian Institution in 1846, a co-founder of the National Academy of Sciences (1863), and the second president of the American Association for the Advancement of Science.

The unit henry was adopted at the 1893 International Electrical Congress in Chicago (the same Congress that ratified Tesla's AC system over Edison's DC). The 9th General Conference on Weights and Measures (CGPM) in 1948 codified the henry as an SI derived unit: 1 H = 1 V·s/A = 1 Wb/A — the inductance that produces 1 volt of EMF when current changes at 1 A/s. The 2019 SI redefinition tied the henry to the ampere via the elementary charge e = 1.602176634 × 10⁻¹⁹ C exactly.

Practical inductors span 12 orders of magnitude. PCB via stubs at sub-nH set the upper frequency limit of modern signal integrity — at 56 Gbps PAM-4 SerDes, even 0.3 nH of launch parasitic inductance distorts the eye diagram (IEEE 802.3ck). RF chip inductors at 0402 size hit 100 nH for matching networks at 2.4 GHz Wi-Fi. Power inductors at 22 µH dominate the frequency-conversion crossover region between RF and switch-mode regulation.

Audio crossover coils at 1-10 mH separate woofer from tweeter in passive 2-way speakers (Bruel & Kjaer, KEF, Genelec design rules). Mains line-filter common-mode chokes at 30 mH attenuate the 100 kHz EMI band per CISPR 22 / FCC Part 15 limits. The biggest practical inductors are tube-amp output transformers (5 H primary) and medical-grade isolation transformers (12 H primary, ANSI/AAMI ES60601-1) — both visible at the right edge of the 5-cell coil library.

Inductor saturation is the defining nonlinearity of ferrite and iron-core applications. NEMA MG-1 motor windings operate below saturation flux density B_sat. SMPS manufacturers (TDK, Murata, Coilcraft, Wurth) publish L vs I curves showing 10-30% L-droop at rated I_sat. Air-core coils have no saturation but enormous size for the same inductance: a 1 mH air-core toroid is 10 cm diameter; a ferrite equivalent is the size of a dime. The trade-off is constant L vs compact form factor.

Modern inductance metrology is anchored by quantized magnetic flux: the magnetic flux quantum Φ₀ = h / (2e) = 2.067833848 × 10⁻¹⁵ Wb. The 1980 von Klitzing quantum-Hall standard ties the ohm to fundamental constants; the Josephson junction ties the volt to f and 2e. Since 1 H = 1 V·s/A, every inductance reading on this page traces back through the 2019 SI redefinition to the cesium clock and the elementary charge — from Henry's 1832 Albany horseshoe coil to the BIPM 2019 redefinition, in five decade clicks.