Efficient symbolic computation of approximated small-signal characteristics of analog integrated circuits

A symbolic analysis tool is presented that generates simplified symbolic expressions for the small-signal characteristics of large analog integrated circuits. The expressions are approximated while they are computed, so that only those terms are generated which remain in the final expression. This principle causes drastic savings in CPU time and memory, compared with previous symbolic analysis tools. In this way, the maximum size of circuits that can be analyzed, is largely increased. By taking into account a range for the value of a circuit parameter rather than one single number, the generated expressions are also more generally valid. Mismatch handling is explicitly taken into account in the algorithm. The capabilities of the new tool are illustrated with several experimental result

Symbolic analysis of large analog integrated circuits by approximation during expression generation

A novel algorithm is presented that generates approximate symbolic expressions for small-signal characteristics of large analog integrated circuits. The method is based upon the approximation of an expression while it is being computed. The CPU time and memory requirements are reduced drastically with regard to previous approaches, as only those terms are calculated which will remain in the final expression. As a consequence, the maximum circuit size amenable to symbolic analysis has largely increased. The simplification procedure explicitly takes into account variation ranges of the symbolic parameters to avoid inaccuracies of conventional approaches which use a single value. The new approach is also able to take into account mismatches between the symbolic parameters

An error-controlled methodology for approximate hierarchical symbolic analysis

Limitations of existing approaches for symbolic analysis of large analog circuits are discussed. To address their solution, a new methodology for hierarchical symbolic analysis is introduced. The combination of a hierarchical modeling technique and approximation strategies, comprising circuit reduction, graph-based symbolic solution of circuit equations and matrix-based error control, provides optimum results in terms of speech and quality of results.European Commission ESPRIT 21812Comisión Interministerial de Ciencia y Tecnología TIC97-058

Behavioral modeling of PWL analog circuits using symbolic analysis

Behavioral models are used both for top-down design and for bottom-up verification. During top-down design, models are created that reflect the nominal behavior of the different analog functions, as well as the constraints imposed by the parasitics. In this scenario, the availability of symbolic modeling expressions enable designers to get insight on the circuits, and reduces the computational cost of design space exploration. During bottom-up verification, models are created that capture the topological and constitutive equations of the underlying devices into behavioral descriptions. In this scenario symbolic analysis is useful because it enables to automatically obtain these descriptions in the form of equations. This paper includes an example to illustrate the use of symbolic analysis for top-down design.Comisión Interministerial de Ciencia y Tecnología TIC97-058

Topology Reduction for Approximate Symbolic Analysis

The paper deals with a procedure for approximate symbolic analysis of linear circuits based on simplifying the circuit model. The procedure consists of two main steps. First, network elements whose influence on the circuit function is negligible are completely removed, i.e. their parameters are removed from the resulting symbolic formula. The second step consists in modifying the voltage and current graphs in order to decrease the number of common spanning trees. The influence of each modification of the circuit model is ranked numerically. A fast method based on the use of cofactors is presented. It allows evaluating all the prospective simplifications using at most two matrix inversions per one frequency point

Trends and concerns in digital cartography

CISRG discussion paper ;

Communication Subsystems for Emerging Wireless Technologies

The paper describes a multi-disciplinary design of modern communication systems. The design starts with the analysis of a system in order to define requirements on its individual components. The design exploits proper models of communication channels to adapt the systems to expected transmission conditions. Input filtering of signals both in the frequency domain and in the spatial domain is ensured by a properly designed antenna. Further signal processing (amplification and further filtering) is done by electronics circuits. Finally, signal processing techniques are applied to yield information about current properties of frequency spectrum and to distribute the transmission over free subcarrier channels

The persistent cosmic web and its filamentary structure I: Theory and implementation

We present DisPerSE, a novel approach to the coherent multi-scale identification of all types of astrophysical structures, and in particular the filaments, in the large scale distribution of matter in the Universe. This method and corresponding piece of software allows a genuinely scale free and parameter free identification of the voids, walls, filaments, clusters and their configuration within the cosmic web, directly from the discrete distribution of particles in N-body simulations or galaxies in sparse observational catalogues. To achieve that goal, the method works directly over the Delaunay tessellation of the discrete sample and uses the DTFE density computed at each tracer particle; no further sampling, smoothing or processing of the density field is required. The idea is based on recent advances in distinct sub-domains of computational topology, which allows a rigorous application of topological principles to astrophysical data sets, taking into account uncertainties and Poisson noise. Practically, the user can define a given persistence level in terms of robustness with respect to noise (defined as a "number of sigmas") and the algorithm returns the structures with the corresponding significance as sets of critical points, lines, surfaces and volumes corresponding to the clusters, filaments, walls and voids; filaments, connected at cluster nodes, crawling along the edges of walls bounding the voids. The method is also interesting as it allows for a robust quantification of the topological properties of a discrete distribution in terms of Betti numbers or Euler characteristics, without having to resort to smoothing or having to define a particular scale. In this paper, we introduce the necessary mathematical background and describe the method and implementation, while we address the application to 3D simulated and observed data sets to the companion paper.Comment: A higher resolution version is available at http://www.iap.fr/users/sousbie together with complementary material. Submitted to MNRA

Comparison of the Methods of Graphical Solution of Symbolic Sensitivity

Signal-flow graph (SFG) technique is a very useful tool for a hand analysis of a small and medium-size networks and/or subnetworks of large systems. Last days, the SFG's have been effectively used for the sensitivity solutions, too. This paper describes the comparison between two graph methods for derivation transfer function: the nullor modified Coates flow graph symbolic analysis and the transformation graphs for symbolic analysis. As is given, in some cases the transformation graphs are more useful thanks to their clarity than standard solving methods