A more judicious choice of trial functions to implement the Improved Circuit Theory (ICT) application to multi-element antennas is achieved. These new trial functions, based on Tai's modified variational implementation for single element antennas, leads to an ICT implementation applicable to much longer co-planar dipole arrays. The accuracy of the generalized impedance formulas is in good agreement with the method of moments. Moreover, all these generalized formulas including the radiation pattern expressions are all in closed-form. This leads to an ICT implementation which still requires much shorter CPU time and lesser computer storage compared to method of moments. Thus, for co-planar dipole arrays, the proposed implementation presents a relatively very efficient method and would therefore be found useful in applications such as CAD/CAE systems.

The two variational principles, the Maupertuis' and the Hamilton's principle, are discussed in conjunction with the Fermat's principle. These two principles are shown to describe two different aspects of waves, thus resulting in the different geometry of wave propagation, the treatment of which is thus called the stationary optics or the dynamical optics, respectively. Comparisons for the results obtained from these geometrical optics are given. Another new variational principle valid for the dynamical waves reflected/refracted at the inter-faces, which has not yet been discovered so far, is also derived.