Classes of 4-pole networks having non-linear transfer characteristics but linear iterative impedances

Abstract
The conventional representation of an electric circuit as a pattern of branches, nodes and meshes (topological graph) is historic. The less familiar representation as a set of contiguous rectangles, proposed by the author1 in 1951 from a suggestion made by Hering2 (1927), has many conceptual advantages;* not only does it represent the network pattern topologically but it displays other physical properties: the dual of the circuit is included; the element energies and co-energies (energy duals) are shown; current and voltage magnitudes are represented, etc. This rectangle representation of a planar circuit is briefly reviewed and its special application to non-linear circuits is explained.From simple geometrical symmetry of the rectangle diagrams it becomes immediately obvious that iterative structures (lattices, bridged-T, etc.) may be constructed from dual non-linear resistive elements having linear iterative impedances. If these can be constructed practically, they might be connected in cascade, without mutual interaction, as non-linear equalizers analogous to Zobel's constant-resistance phase-equalizers.The analogy to Zobel's networks is shown to be surprisingly complete, though the author can yet find no physical relation between these and the present non-linear networks.

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