Novel comprehensive feedback theory—Part I: Generalization of the cut-insertion theorem and demonstration of feedback universality

The previous cut-insertion theorem, defined for linear circuits and for particular three-terminal circuits (TTCs) to be inserted into the cut, is here extended to any TTC and, in a simplified form, to non-linear networks. The TTC may include dependent and independent sources and any other passive and/or independent elements, and, together with the remaining part of the circuit, determines a feedback loop for which the "transmission factors" T and T' can be defined and computed. The theorem allows to obtain all the circuit properties: the overall gain, the driving-point immittances, a new properly defined "cut immittance," the sensitivity, and so on. For T'=0, T becomes the "classic" loop gain. As will be shown in Part II of the paper, the new approach, depending on the TTC implementation, includes and unifies all the previous feedback models and enables the creation of new ones. Moreover, starting from the paradigmatic definition of a system with a feedback as a system in which the output quantity is in part an effect of itself, the universal presence of feedback in any system is shown. Finally, the results are highlighted by the application to unilateral non-linear systems, such as digital latches, and to bilateral linear circuits, such as bridged-T networks.