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RESEARCH PRODUCT
Analytical Solutions for the Self- and Mutual Inductances of Concentric Coplanar Disk Coils
John T. Conwaysubject
PhysicsAssociated Legendre polynomialsPlane (geometry)Electromagnetic coilMathematical analysisElliptic integralAsymptotic formulaElectrical and Electronic EngineeringHypergeometric functionDerivation of self inductanceLegendre polynomialsElectronic Optical and Magnetic Materialsdescription
In this paper, closed-form solutions are presented for the self- and mutual inductances of disk coils which lie concentrically in a plane. The solutions are given as generalized hypergeometric functions which are closely related to elliptic integrals. The method used is a Legendre polynomial expansion of the inductance integral, which renders all integrations straightforward. Excellent numerical agreement with previous studies is obtained. An asymptotic formula for the approach to the ring coil limit is also derived and numerically validated. The methods presented here can be applied to noncoaxial and noncoplanar cases.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2013-03-01 | IEEE Transactions on Magnetics |