Calculation of high-frequency inductance and current-distribution effects in annular discs

A method is described whereby the inductance of flat disc-shaped conductors having a central hole can be calculated. The calculation has to take into account current distribution, and, for this purpose, the disc is regarded as being divided up into m concentric rings yielding m equations involving the self inductance of each strip and the mutual inductance between them. Digital computation is used to calculate the coefficients of and invert the m × m matrix so formed, giving the current flowing in each strip from which the inductance can be calculated. Errors arising either from the limitation of m or from ill-conditioned sets of equations limit the accuracy to 0.05%. The computed results are compared with those obtained experimentally. A theoretical expression is derived for the limiting case when the width of the conductor is small compared with the radius of the disc, and a formula is suggested from which the inductance of a range of annular discs can be calculated to an accuracy of within 0.5%.