Reduced modified nodal approach and its application to circuit simulation

Abstract

Since the early days of semiconductor devices, the dream of the circuit designers has been the use of computers to design newer integrated circuits automatically. This is particularly true for the development of very large scale integrated circuits (VLSI). The complexity of such parts can be handled only with ever improved and extended computer-aided design (CAD). Today, the CAD are recognized as essential to support the VLSI design and manufacture for (I) design turn-around time reduction, (2) elimination of human errors, and, as a result, (3) reduction in design and manufacturing costs. While VLSI-CAD is most widely used and best developed, many talented professionals are presently striving to find solutions to ever increasing problems of the VLSI complexity. This dissertation is mainly concerned with CAD techniques for circuit analysis. We assess the area of circuit simulation. Here, we use circuit simulation to imply that the integrated circuits are simulated by the computer to obtain their electrical performance. An emphasis is on the time-domain transient analysis for VLSI. We will discuss the algorithms and techniques for circuit simulation, which are adequate for VLSI. We first propose a new method of circuit equation formulation, which is called "Reduced Modified Nodal Approach (RMNA)". In the RMNA, a special family of cutset equations as well as the branch relations for voltage sources are formulated in terms of node volatges and controlling currents. The pivoting schemes for avoiding zero diagonals in the RMNA matrix are also discussed. As will be seen, the RMNA retains the simplicity and other advantages of the classical nodal approach and the modified nodal approach, while removing their difficulties. The RMNA is applied to the analysis of switched capacitor networks (SCN``s), which become a popular topic in the area of the signal processing because of its high precision monolithic performance. Four main analysis techniques are discussed for the SC...