The root-matching method

Abstract

An alternative to the difference equation using the trapezoidal integration developed in Chapter 4 for the solution of the differential equations has been described in this chapter. It involves the exponential form of the difference equation and has been developed using the root-matching technique. The exponential form offers the following advantages: 1) Eliminates truncation errors, and hence numerical oscillations, regardless of the step length used. 2) Can be applied to both electrical networks and control blocks. 3) Can be viewed as a Norton equivalent in exactly the same way as the difference equation developed by the numerical integration substitution (NIS) method. 4) It is perfectly compatible with NIS and the matrix solution technique remains unchanged. 5) Provides highly efficient and accurate time domain simulation. The exponential form can be implemented for all series and parallel RL, RC, LC and RLC combinations, but not arbitrary components and hence is not a replacement for NIS but a supplement.