Self-inductance of air-core circular coils with rectangular cross section

Using analytic integration, accurate self-inductance expressions (requiring only single numerical integration) for air-core circular coils with rectangular cross sections (and two special cases, namely thin-wall solenoids and disk (pancake) coils) are derived from the basic mutual-energy formula of two coaxial circular current loops. Based upon these expressions, with integration singularities analytically treated, the self-inductance of any air-core coil can be precisely calculated by use of a microcomputer. Values so computed agreed, to one part in 10⁴, with those reported in the literature.