TX to Ae




Low-frequency effective radius of a single-layer solenoid.
By David W Knight

Main article: Solen_r0.pdf (version 2.06)

+ Open Document spreadsheets:
r0_rect.ods ,
r0_round.ods* ,
r0_numint.ods* ,
r0_round_p.ods* .
*computationally intensive - may be slow to open.

Due to path-length variation and strain, the current distribution in the wire of a solenoid inductor is not uniform at low frequencies. This causes the effective solenoid radius to differ from the physical average, leading to a systematic error in inductance calculations. Formulae and program routines for the effective radius, for coils wound with solid rectangular and round wire, are given.

Principal references:
"Practical Model and Calculation of AC resistance of Long Solenoids". E. Fraga, C Prados, and D.-X Chen. IEEE Transactions on Magnetics, Vol 34, No. 1. Jan 1998.

Formula for the inductance of a helix made with wire of any section. C. Snow. BS Sci. 537, 1926 (5.74MB PDF).