Studies on Frequency Response Optimized Integrators Considering Second Order Derivative

Abstract: This paper presents comprehensive studies on frequency response optimized integrators considering second order derivative regarding their numerical error, numerical stability and transient performance. Frequency domain error analysis is conducted on these numerical integrators to reveal their accuracy. Numerical stability of the numerical integrators is investigated. Interesting new types of numerical stability are recognized. Transient performance of the numerical integrators is defined to qualitatively characterize their ability to track fast decaying transients. This property is related to unsatisfactory phenomena such as numerical oscillation which frequently appear in time domain simulation of circuits and systems. Transient performance analysis of the numerical integrators is provided. Theoretical observations from the analysis of the numerical integrators are verified via time domain case studies.