Equivalent Circuits-I

Equivalent circuits have been found valuable in the solution of certain problems in that they simplify the analysis. Furthermore, equivalent circuits provide a means of replacing magnetic coupling with simple impedance links thereby permitting the use of the calculating board for solution. In Part I of this paper, the general equivalent mesh for the n-winding transformer is derived, and other less rigorous transformer circuits are discussed and compared. In Part II the mesh equivalent for the general network having (m + l) points of entry is derived and its application is explained. The generalizations of Parts I and II provide a background for the particular problem treated in Part III in which the study of system networks involving groups of parallel transmission lines is considered. The usually difficult problem of accurately determining ground fault currents in such a system is readily solved by applying the special equivalent circuits developed in Part III to a calculating board set-up of the system. These circuits are particularly valuable in the solution of any problem involving an analysis of the zero phase impedance diagram of a system. The methods and circuits developed in this paper are perfectly general and have many evident applications other than those treated.