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The problem of a generalised planar transmission line is considered, and a detailed theory of a complete modal solution of the problem is presented. The technique is based on employing the reciprocity theorem in conjunction with the Raleigh-Ritz optimisation procedure. A full solution of both the propagating modes and the field distribution everywhere along the structure is obtained. The technique is then applied to a three-layer structure with conducting strips along each interface. Several configurations are treated and the results presented compare favorably with other results available in the literature.