Mutual admittance between slots on a plane

The exact expression of the mutual admittance between two slots on a plane involves a quadruple [1] integration. The fact that the Green´s function possesses a difference form allows a quadruple integral to be reduced to a double integral. For a narrower slot such as the waveguide fed slot, the mutual admittance expression can be reduced to a single integral instead of a double integral [2] if one ignores the effect of the width. The validity range of the zero width solution and the Illinois´s approximate solution [3] are established by comparing with the exact solution. A flat plate array design process requires a large number of mutual admittance calculations. The above three formulas would greatly reduce the computation effort.