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The theoretical foundation of a recently proposed reluctance network method for computing the complex series impedance matrix of multi-conductor transmission lines is presented in detail, and the method is extended to more general cross section geometries with gaps of non-constant width between the conductors. It is argued that the method becomes exact in the limit of high frequencies and narrow gaps between the conductors. This limit usually is the most difficult one in alternative approaches, especially when the proximity effect is concerned. The method is verified by comparison with the exact solution of a stacked-slabs geometry, and with finite-element field calculations on a geometry consisting of tightly packed, round wires, surrounded by a shield.