A New Look at Reciprocity and Energy Conservation Theorems in Electromagnetics

The intimate relationship is discussed between linear vector space concepts, the reciprocity theorem, and the energy conservation theorem in electromagnetics. It shows that these theorems can be derived using nonconventional methods. The reciprocity theorem can be derived by designing symmetric operators. The Lorentz reciprocity theorem can be derived by augmenting the operator with an extra term that generates equivalence surface currents. The energy conservation theorem for the real part of the complex power is derived by designing an operator that becomes Hermitian in the lossless case. The energy conservation theorem for the imaginary part of the complex power is derived by designing an operator which becomes skew Hermitian in the lossless case.