A new general formulation for the entire-domain analysis of an array of arbitrarily oriented circular loop antennas

A general formulation for the entire-domain analysis of arbitrarily oriented coupled circular loops has been presented for the first time. The Eulerian angles are used to unambiguously define the orientation of each loop with respect to another. The formulation gives a solution of the Fourier coefficients of the current on each loop after taking mutual coupling into account. The current coefficients can be used to directly obtain the input impedance and radiation characteristics of a coupled loop array. The formulation has been illustrated by applying it to two scenarios involving a pair of coplanar and coaxial loops. It is seen that the rotation of one loop about each axis could have rather different impacts on the mutual coupling between the loops. Thus the results highlight the necessity for the general formulation presented in this paper for correctly and conveniently analyzing all the various possible orientations in coupled circular loop arrays.