Boundary conditions for multi-tone steady-state analysis of nonlinear integrated analog circuits

Widely-separated time scales appear in many electronic circuits, making traditional analysis difficult even impossible if the circuits are highly nonlinear. The paper presents a new version of the modified nodal method in two time variables for the analysis of the circuit with widely separated time scales. By applying this approach the differential algebraic equations (DAE) describing the nonlinear analog circuits driven by multi-tone signals are transformed into multi-time partial differential equations (MPDEs). In order to solve MPDEs, associated resistive discrete equivalent circuits (companion circuits) for the dynamic circuit elements are used. The boundary conditions are detailed and simulation results are presented.