Indirect numerical integration, difference approximation, and circuit simulation of transmission lines

This dissertation includes three topics in the transient analysis of linear systems: indirect numerical integration, difference approximation, and circuit simulation of transmission lines.Indirect numerical integration is a new class of numerical integration methods with ideal accuracy, convergence and stability properties. The methods are based on a novel time-response invariant discrete synthesis. The foundations and general principles of indirect numerical integration are discussed in detail. The dissertation includes the complete set of indirect numerical integration formulas in the three canonic forms of state-variable representation.Difference approximation is a general method for applying numerical integration to systems characterized by discrete samples of their responses. General principles of the method are analyzed, the set of indirect numerical integration formulas for the difference approximation is given, and novel interpolation-based approximation methods are presented.The above two techniques are applied to the transient simulation of transmission lines. The author attempts to formulate a high-level description of the transmission line simulation method that has maximum efficiency, accuracy and applicability to the transient simulation of high-speed digital circuits. To formulate the approach, most significant aspects of the problem are identified, and alternative approaches in each of the aspects are analyzed and compared to find the combination which results in maximum efficiency, accuracy and applicability for the transient analysis of high-speed digital circuits.The step-by-step implementation of the approach for uniform and nonuniform multiconductor lossy frequency-dependent lines characterized by samples of their responses is presented. The resulting transmission line model can be directly incorporated into a circuit simulator. The implementation includes ac, dc and transient analyses. The method has been adopted in several industrial and commercial circuit simulators, and in numerous real-life simulation exercises proved to be reliable and accurate. It is shown on an extensive set of runtime data that, based on this approach, the accurate line modeling in a circuit simulator is as efficient as the simple replacement of interconnects with lumped resistors.U of I OnlyETDs are only available to UIUC Users without author permissio