An efficient method for RF integrated circuit analysis

The paper presents a new version of the modified nodal method in transient behavior (the semi-state equations) for the analysis of the circuits driven by signals with widely separated time scales. The key idea is to use multiple time variables, which enable signals with widely separated rates of variation to be represented efficiently. The semi-state equation formulation in a partially symbolic form is used in order to obtain a MPDE (multi-time partial differential equation) form with a minimum number of independent variables. Combining an efficient procedure to compute the appropriate boundary conditions of the MPDE, with the semi-state approach, in which only the symbols of the parameters corresponding to the nonlinear circuit elements are considered, a significant efficiency in circuit design accelerating the reaching of the periodic steady state, and an improvement of the accuracy in the numerical calculations are obtained. The algorithm to formulate and to solve the dynamic modified nodal equations was implemented in a computing program, which constitutes a useful tool for steady-state analysis of a very large class of nonlinear analog circuits.