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This paper presents an exact expression for the mutual impedance of two coaxial loops located on the surface of a conductive ground. The semi-infinite complete integral representation for the impedance is first converted into a finite integral. Then the spherical Hankel function contained in the integrand is expanded according to Gegenbauer addition theorem. This makes it possible to perform analytical integration and express the mutual impedance as a sum of products of spherical Bessel functions. Since no assumptions are made in the mathematical derivation, the obtained formula is valid in quasi-static as well as non-quasi-static frequency ranges. Numerical examples show how, accuracy being equal, the proposed expression is less computationally expensive than standard GaussKronrod numerical integration technique.

AN EXACT EXPRESSION FOR THE MUTUAL IMPEDANCE BETWEEN COAXIAL CIRCULAR LOOPS ON A HOMOGENEOUS GROUND