The unified nodal approach to circuit analysis

In the Unified Nodal Approach (UNA) to fast switching circuit analysis, transient analysis is not required to simulate the abrupt transition of initial-state response and the long settling time of reaching the steady-state. In this paper, we present the three-graph method of formulating the UNA equations. Generalized from the Reduced Modified Nodal Approach (RMNA), the three-graph method has many advantages over the classical Modified Nodal Approach (MNA) such as eliminating redundant circuit variables, avoiding zero diagonals, and systematically reducing fill-ins generated by the diagonal pivoting condensation. In addition, the UNA equations degenerate into nonsingular systems of equations for one-step generations of the initial-state and steady-state responses. An example is given to illustrate the three-graph method of formulating the UNA equations and the advantages of the UNA over both the MNA and RMNA