Some modifications of Newton's method for the determination of the steadystate response of nonlinear oscillatory circuits
Abstract
It is proposed that nondominant states should be eliminated from the Newton algorithm in the steadystate analysis of nonlinear oscillatory systems. This technique not only improves convergence, but also reduces the size of the sensitivity matrix so that less computation is required for each iteration. One or more periods of integration should be performed after each periodic state estimation before the sensitivity computations are made for the next periodic state estimation. These extra periods of integration between Newton iterations are found to allow the fast states due to parasitic effects to settle, which enables the Newton algorithm to make a better prediction. In addition, the reliability of the algorithm is improved in high Q oscillator circuits by both local and global damping in which the amount of damping is proportional to the difference between the initial and final state values.
 Publication:

IEEE Transactions on Computer Aided Design
 Pub Date:
 July 1982
 Bibcode:
 1982ITCAD...1..116G
 Keywords:

 Computer Aided Design;
 Network Analysis;
 Newton Methods;
 NewtonRaphson Method;
 Nonlinear Systems;
 Numerical Stability;
 Stable Oscillations;
 Algorithms;
 Convergence;
 Design Analysis;
 Numerical Integration;
 Q Factors;
 State Estimation;
 State Vectors;
 Steady State;
 Vibration Damping;
 Electronics and Electrical Engineering