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Definition of the inductance of flat (printed) rings at various methods of excitation

Moscow Institute of Physics and Technology (State University)


The paper is received on January 28, 2015


Abstract. The calculation algorithms for inductances, mutual inductances and resistances of the flat rings with arbitrary conductor width are proposed. They are based on definition of three-dimensional distributions of the current density on section of a ring. Calculated distributions of the current density are non-uniformly and considerably changes depending on a way of its excitation. Using the found distributions of current values of the ring’s inductance, mutual inductance and resistance are determined. They essentially differ from results of standard calculations. Relative corrections of our results are increasing with growth of frequency and relative width of a conductor and can exceed 400 %. The submitted calculations have allowed to determine correctly inductance and mutual inductance of printed rings with a wide conductor (the width is close to its radius) in all the frequency range of the quasistatic approximation. Our results for rings with a narrow conductor are converged well to known asymptotic calculations.

Key words: flat ring, inductance, mutual inductance, distribution of the current density.