Two Mathematical Comments on the Thevenin Theorem: An “Algebraic Ideal” and the “Affine Nonlinearity”

We discuss the most important and simple concept of basic circuit theory—the concept of the unideal source—or the Thevenin circuit. It is explained firstly how the Thevenin circuit can be interpreted in the algebraic sense. Then, we critically consider the common opinion that it is a linear circuit, showing that linearity (or nonlinearity) depends on the use of the port. The difference between the cases of a source being an input or an internal element (as it is in Thevenin’s circuit) is important here. The distinction in the definition of linear operator in algebra (here in system theory) and in geometry is also important for the subject, and we suggest the wide use of the concept of “affine nonlinearity.” This kind of nonlinearity should be relevant for the development of complicated circuitry (perhaps in a biological modeling context) with nonprescribed definition of subsystems, when the interpretation of a port as input or output can become dependent on the local intensity of a process.