Wil H. A. Schilders

Efficient Methods for Large Resistor Networks

Large resistor networks arise during the design of very-large-scale integration chips as a result of parasitic extraction and electro static discharge analysis. Simulating these large parasitic resistor networks is of vital importance, since it gives an insight into the functional and physical performance of the chip. However, due to the increasing amount of interconnect and metal layers, these networks may contain millions of resistors and nodes, making accurate simulation time consuming or even infeasible. We propose efficient algorithms for three types of analysis of large resistor networks: 1) computation of path resistances; 2) computation of resistor currents; and 3) reduction of resistor networks. The algorithms are exact, orders of magnitude faster than conventional approaches, and enable simulation of very large networks.

Adjoint transient sensitivity analysis in circuit simulation

Sensitivity analysis is an important tool that can be used to assess and improve the design and accuracy of a model describing an electronic circuit. Given a model description in the form of a set of differential-algebraic equations it is possible to observe how a circuits output reacts to varying input parameters, which are introduced at the requirements stage of design. In this paper we consider the adjoint method more closely. This method is efficient when the number of parameters is large.We extend the transient sensitivity work of Petzold et al., in particular we take into account the parameter dependency of the dynamic term.We also compare the complexity of the direct and adjoint sensitivity and derive some error estimates. Finally we sketch out how Model Order Reduction techniques could be used to improve the efficiency of adjoint sensitivity analysis.

The Need for Novel Model Order Reduction Techniques in the Electronics Industry

In this paper, we discuss the present and future needs of the electronics industry with regard to model order reduction. The industry has always been one of the main motivating fields for the development of MOR techniques, and continues to play this role. We discuss the search for provably passive methods, as well as passivity enforcement methods that are currently being developed. Structure preservation is another important research topic, for which new concepts are being developed. This also holds for the calculation of delays in long interconnect lines, a topic that leads to an entirely new type of methods. Topics that are still in their infancy are model order reduction for parameterized and nonlinear problems. We will discuss what the needs of the industry are in all of these fields, show specific applications and what has been achieved so far. The paper is meant as a guideline for future research, not as a detailed survey of existing methods.

Parametric structure-preserving model order reduction

Analysis and verification environments for next- generation nano-scale RFIC designs must be able to cope with increasing design complexity and to account for new effects, such as process variations and Electromagnetic (EM) couplings. Designed-in passives, substrate, interconnect and devices can no longer be treated in isolation as the interactions between them are becoming more relevant in the behavior of the complete system. At the same time variations in process parameters lead to small changes in the device characteristics that may directly affect system performance. These two effects, however, can not be treated separately as the process variations that modify the physical parameters of the devices also affect those same EM couplings. Accurately capturing the effects of process variations as well as the relevant EM coupling effects requires detailed models that become very expensive to simulate. Reduction techniques able to handle parametric descriptions of linear systems are necessary in order to obtain better simulation performance. In this work Model Order Reduction techniques able to handle parametric system descriptions are presented. Such techniques are based on Structure-Preserving formulations that are able to exploit the hierarchical system representation of designed- in blocks, substrate and interconnect, in order to obtain more efficient simulation models.

Electromagnetic simulations for nanoscale RF blocks

Next-generation nano-scale RFIC designs have an unprecedented complexity and performance that will inevitably lead to costly re-spins and loss of market opportunities. In order to cope with this, efficient and accurate models of interconnects, integrated inductors, the substrate and devices, together with their mutual interactions, need to be developed. The key idea is that integrated devices can no longer be treated in isolation as the EM interactions due to proximity effects are becoming more relevant in the behavior of the complete system. EM simulations must also address these interactions, so new procedures and models able to be included in coupled simulation must be developed. But these simulations may become very expensive as the complexity of the system increases, so model order reduction techniques able to treat these coupling effects are necessary in order to obtain a better performance. In this work some solutions for efficient simulation of such problems are introduced.