The Application of Singlestep High Order Integration Methods for Periodic Steadystate Analysis of Integrated Circuits 
 


Authors 
 Gourary M.M. 
 Zharov M.M. 
 Rusakov S.G. 
 Ulyanov S.L. 
Date of publication 
 2018 
DOI 
 10.31114/2078770720181103109 

Abstract 
 The periodic steady state analysis is one of the most important tool in design of analog and RF integrated circuits. The application of conventional transient analysis to find a periodic steady state solution often results in a long simulation time and hence special purpose means are needed. The method of shootingNewton is used in periodic steady state analysis to solve a periodic boundary value problem. The shootingNewton method transforms the solution of the periodic boundary value problem to the solution of sequence of initial value problems on the 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. The efficient numerical techniques have been proposed. 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 differentialalgebraic equations the comprehensive variable order and variable time step integration algorithms based on implicit multistep integration methods are used. The most commonly used methods are backward Euler, trapezoidal and backwarddifferentiation formulas (BDF). The common drawback of methods is the lack of Astability 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 timedomain transient analysis. In this paper the method of periodic steadystate analysis in analog integrated circuits is proposed. The periodic boundary value problem is solved using shootingNewton 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 steadystate analysis are given which demonstrate the numerical accuracy and efficiency of the proposed method. 
Keywords 
 circuit simulation, periodic steadystate, boundary value problem, shooting method, integration methods 
Library reference 
 Gourary M.M., Zharov M.M., Rusakov S.G., Ulyanov S.L. The Application of Singlestep High Order Integration Methods for Periodic Steadystate Analysis of Integrated Circuits // Problems of Perspective Micro and Nanoelectronic Systems Development  2018. Issue 1. P. 103109. 
URL of paper 
 http://www.mesconference.ru/data/year2018/pdf/D127.pdf 