The application of single-step high order integration methods for periodic steady-state analysis of integrated circuits
The application of conventional transient analysis to find the periodic steady-state solution often results in a long simulation time and hence special purpose means are needed. Unlike the transient analysis the periodic steady-state analysis solves a periodic boundary-value problem. The shooting-Newton method transforms the solution of the periodic boundary-value problem to the solution of sequence of initial value problems on one period of input signal. The initial value problem is solved using transient analysis. The efficiency of the method depends on both the computation of sensitivity matrix and the solution of linear system with dense Jacobian matrix. Another factor that determines the computational cost of the method is a numerical technique used to integrate differential equations on the period of input signal. To perform numerical integration of ordinary differential or differential-algebraic equations the comprehensive variable order and variable time step integration algorithms are used. The most commonly used methods are backward Euler, trapezoidal and backward-differentiation formulas (BDF). The common drawback of BDF methods is the lack of A-stability for order higher than 2. As a result high order methods are not implemented in modern simulators. However the usage of high order and Astable methods allows to improve accuracy and speed up time-domain transient analysis. In this paper the method of periodic steady-state analysis in analog integrated circuits is proposed. The periodic boundary-value problem is solved using shooting-Newton method, in which to solve the initial value problem the single step integration methods based on the Obreshkov formula are suggested to apply. The formulation of methods of order 1 up to 4 are obtained for charge oriented circuit equations. The formulas for computing sensitivity matrix are presented. The numerical examples of steady-state analysis are given which demonstrate the numerical accuracy and efficiency of the proposed method.