Je. Ross et al., APPROXIMATE INTEGRAL-OPERATOR METHODS FOR ESTIMATING THE NATURAL FREQUENCIES OF COUPLED OBJECTS, Radio science, 29(4), 1994, pp. 677-684
Of central importance to the singularity expansion method (SEM) for an
alysis of conducting objects are the frequencies and currents for the
natural modes of the object. When there is more than one object in pro
ximity, the direct calculation of these quantities becomes difficult,
and it is useful to have approximate methods to simplify the computati
ons. This paper presents two approximate methods for calculating the n
atural frequencies for a group of coupled objects. The first method is
a perturbational one, leading to a transcendental equation for the na
tural frequencies. It assumes weak coupling between objects so that th
e natural mode current distribution is only slightly perturbed from th
at existing on an isolated object. The second method is also perturbat
ional and further assumes that the Green's function can be approximate
d by leading terms of a Taylor series expansion about the natural-mode
frequencies of isolated objects, Results are shown for the case of co
upled thin wires and compared to more rigorous moment-method solutions
as well as experimental results.