An approximate integral equation for thick slots

The rigorous formulation of the thick aperture problem is first reviewed and cast into a compact and powerful mathematical form. Equivalence principles are used to model the thick slot by a cylindrical cavity, whose associated Green\´s functions play a key role. We then show that the usual formulation cannot provide a smooth transition to the zero-thickness case as the cavity Green\´s functions diverge when the thickness vanishes. To find a way out of this problem and to obtain an improved formulation, we introduce new unknowns and new Green\´s functions, for which we propose analytical approximations. The final result is a new integral equation whose unknown is the average value of the magnetic currents in both sides of the thick slot. This new equation has exactly the same degree of complexity as the zero thickness slot equation, since the only modification is the addition of a corrective "delta" term for the Green\´s functions, that can be analytically approximated and that disappears naturally in the zero-thickness limiting case. Preliminary results for the magnetic currents in both sides of the slots confirm the validity of the approach. The formulation has been applied to a set of slot-based printed antennas.