Improved Feedback Theory

A previous cut-insertion theorem for linear circuits and its application to a generalization of the elementary feedback theory are further extended. The new theorem is based on the splitting of an arbitrary node into two nodes and on the insertion between them and another arbitrary ldquoreferencerdquo node, of a three-terminal circuit which keeps the network currents and voltages unchanged. The system analysis is in turn performed on the equivalent cut network by means of the techniques for two-port circuits, using generic variables, i.e., either voltages or currents. The new approach allows one to define a two-port circuit as an open loop around the split and reference nodes, as well to define a new feedback model specifically focused on it. Furthermore, it allows one to retrieve all the results of the previous general feedback theories, as well as several new ones. The obtained expressions of the overall transfer function include, as a particular case, the Blackman formula for the immittances, and relationships without the leakage term, which are useful for circuit synthesis and for dealing with spurious signals. New expressions are proposed for the evaluation of the output and input immittances. The virtual short-circuit method is derived and numerical and design examples are provided. The new approach retains the intuitive feedback vision of the elementary models.