Approximate formulas for the complex propagation constant and characteristic field configuration for dielectric-filled traveling wave slot antennas are obtained by a variational procedure. To set up the variational method, the generalized reciprocity theorem for traveling wave line sources is deduced; it differs considerably from the reciprocity theorem for point sources. A perturbation technique for solving the variational equations is given. Formulas are worked out for rectangular wave guides and good agreement with available measurements is obtained.
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V. Rumsey (1953) studied this question.
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