Fig. 1: Process of transient analysis
Today the analog simulation of integrated circuits plays an essential role in the chip industry. It serves as a tool for circuit designers to verify the entire design process and to eliminate errors before prototype construction.
As contemporary circuit design becomes increasingly complex, simulation time has continued to grow despite the use of faster computers. The industry is looking for ever more sophisticated and efficient simulation algorithms.
The most important analysis method, the transient analysis, is understood as the calculation of signal versus time. The simulator receives the netlist, the parameters of the modules in use, and various signals as input. The next step is for the necessary tools to interpret the output in order to determine whether the circuit is functional, or to locate any errors in its design.
Fig. 1 illustrates the way a simulator functions. The circuit is considered as a collection of linear and nonlinear devices such as controlled sources, resistors, and capacitors lying on branches connected at nodes. The physical quantities of interest usually are the branch currents and the node voltages. They are related by the branch constitutive equations and Kirchhoff's loop and node laws, creating a differential-algebraic equation (DAE) system.
A linear multistep method (we normally use a backward differentiation formula) determines the approximate solution to the output values at discrete points in time, thus yielding a nonlinear system of equations for every time t. Using Newton's method (the inner loop) reduces this problem to the multiple solving of systems of linear equations. After each iteration step, the equation system must be set up from the element routines which must therefore contain the (nonlinear) v-i characteristics of the devices.
Because of the large number of transistors in contemporary integrated circuits, those equation systems are very big but also very sparse, i.e. most of their coefficients are zero. The pattern of the nonzeros remains the same during the whole simulation process.
[1] Horneber, E.-H.: Simulation elektrischer Schaltungen auf dem Rechner, 1985, Springer Verlag, ISBN 3-540-15735-2
[2] Engl, Walter L.; Laur, Rainer; Dirks, Heinz K.: MEDUSA - A Simulator for Modular Circuits, IEEE Transactions On Computer-aided Design Of Integrated Circuits And Systems, Vol. CAD-1, No. 2, April 1982
[3] Naumann, Ingo: Sortierverfahren und Datenstrukturen in der VLSI-Netzwerksimulation, Shaker Verlag, 2004, ISBN 3-8322-2390-8 (in German) -- Download
[4] Naumann, Ingo; Dirks, Heinz: Efficient Reordering for Direct Methods in Analog Circuit Simulation, Springer, Electrical Engineering (Archiv für Elektrotechnik), Volume 89, Number 4, March 2006, pp. 333-337(5), ISSN: 0948-7921 (Print) 1432-0487 (Online), DOI: 10.1007/s00202-006-0007-5 -- Download