In this paper we prove that it is possible to use techniques specific to electromagnetic field synthesis in the study of some electrical circuits. The definition of a circulant network will be presented. The system matrix of such a network is a circular matrix, which allows an analytical evaluation of all the eigenvalues and all the singular values. Resonance frequencies can then be calculated exactly as will be demonstrated on passive and active circulant networks.

Keywords: Circulant networks, Eigenvalues, Singular values, Condition number