Adjoint of a Linear Multiport Element Based on Generalized Duality

In this brief, a direct and universal method of finding the adjoint of a multiport element is proposed. This is achieved by expressing the characteristic equations of the element as a hybrid-transmission matrix, which is based on the concept of generalized duality, and deriving a simple relation between the hybrid-transmission matrices of the original and adjoint element. The proposed method unifies the existing transpose relations based on conventional admittance, impedance, and hybrid parameter matrices and can be further generalized to cases which existing methods cannot conveniently deal, or even deal, with. Once the characteristic equations of the element are given, we can obtain the adjoint (if it does exist) immediately by using the proposed method without any additional operations. The proofs of relevant theorems and some applications of the proposed method are given and the sensitivity formula based on the proposed method is also derived.