High‐order non‐linear circuit elements: Circuit‐theoretic properties

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Abstract
Highei‐ and mixed‐order non‐linear circuit elements have been introduced to provide a logically complete formulation for non‐linear circuit theory. In this paper, we analyse the circuit‐theoretic properties of these elements, including reciprocity, passivity and losslessness. We have derived necessary and sufficient conditions for a higher‐ or mixed‐order n‐port element to be reciprocal or antireciprocal. We have shown that under very mild assumptions, most non‐linear higher‐order 2‐terminal elements are active and not lossless. Finally, we show that the number of lossless linear higher‐order 2‐terminal elements far exceeds that of the passive linear elements.

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