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This paper presents an accurate analytical explicit expression for the self-inductance of a flat pancake round coil made up of concentric turns. The expression is obtained by converting the semi-infinite integral representation for the mutual inductance between two arbitrary turns of the coil into a finite integral, and then by expanding the integrand into a series of Legendre polynomials. As a result, a sum of simpler integrals is obtained, whose analytical evaluation is straightforward. The self inductance is finally expressed as the sum of logarithmic functions, describing the contributions from the self-inductances of the single turns, plus the mutual-inductance terms originating from all the possible pairs of turns of the coil, each one given by a power series of the ratio between the radii of the turns. Numerical simulations are performed to illustrate the advantages of the proposed solution.

AN ACCURATE EXPLICIT EXPRESSION FOR THE SELF INDUCTANCE OF THIN-WIRE ROUND PANCAKE COILS