Hallen's method in the problem of a cavity-backed rectangular slot antenna

The integral equation for t he electric fi eld distribut ion in t h e slot which is excited by a current source at its center is solved for t h e longitudinal fi eld variation by Halh~n 's iteration method. The first order solut ion of t he slo t susceptance provides an agreement with computations based on the variat ional method for cavit ie as shallow as "A/20 prov id ed t h e s lot length exceeds "A/2. There is n o agreement for very sha llow cavi t ies, where the fi elds are rapidly attenuated a long t he slot according to t he variational solution . A si mple closed-form a pproximation to t he suscep tance is applicabJe if the slot and the' cavity are of equal lengths. The first-order slot conductance is accurate only for approximately "A/2 long slots which a re backed by deeper cavities ,