Circuit simulation techniques via generalized Krylov subspaces methods

The increasing trends in industry towards integrating various systems on the same chip is putting enormous demands on CAD tools. Circuit simulation is basically the task of representing general circuit structures in the mathematical domain, and then applying numerical analysis techniques to simulate circuit performance. However, the growing complexity in modern circuit designs and device models is rendering many of the conventional analysis techniques impractical. This thesis tackles the problem of increasing complexity of simulation through using reduction approaches. In general, reduction approaches seek to simulate the huge problem in a much smaller space and then bring the solution to the space of the original problem.; The first problem addressed in the thesis is the problem of high-speed analysis of interconnect circuits. Interconnect circuits represent the dominant factor in assessing the performance of high-speed circuit designs. The difficulty in the analysis of interconnect circuits at high speed stems from the fact that these circuits are naturally described in the frequency-domain, while general circuit simulation is a purely time-domain process. This thesis approaches this problem through using Matrix-Pade approximant to describe the interconnect structure with a macromodel that is amenable to direct time-domain simulation. To increase the efficiency of the time-domain simulation, model-order reduction based on Congruence transform is employed to reduce the size of the total circuit. In addition, a rigorous proof of the passivity of the reduced-order model is presented to guarantee the stability of the numerical simulation process.; The second proposed solution to manage the increasing complexity in modern designs is geared towards the problem of finding the steady-state solution for large nonlinear circuits. Finding the steady-state solution is an essential requirement for the design automation process of analog circuits. However, for large circuits excited by multi-tone inputs, this problem becomes intractably huge. The proposed approach is based on Krylov-subspace projection methods to project the original large problem onto a much smaller subspace. The problem is then solved entirely on the reduced space and the solution obtained is then mapped back to the original space of the problem. The reduction in the size of the problem results in a very significant saving in computational complexity.; time-varying systems into reduced-order macromodels. Linear time-varying systems appear in many contexts during circuit simulation. For example, noise behavior in analog nonlinear circuits is always described by linear time-varying systems. The approach of the proposed algorithm is motivated by the fact that the transfer functions of linear time-varying systems is characterized by short transient response in the right-half plane of the Laplace-domain. Obtaining reduced-order approximation for the transfer function can be achieved easily using simple numerical time-domain integration for a very short period of simulation time. The proposed algorithm therefore avoids completely the need to solve large dense linear systems of equations, which results in saving of several orders-of-magnitude in computational complexity.; Based on the idea of model-reduction of linear time-varying systems, the thesis also tackles the problem of simulating nonuniform transmission lines through Integrated Congruence Transform (ICT). The algorithm proposed describes an orthogonalization procedure for a set of elements related through a differential operator without having to compute these elements explicitly.