**
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.