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Canonical Symbolic Analysis of Large Analog Circuits with Determinant Decision Diagrams
 IEEE TRANS. ON COMPUTERAIDED DESIGN OF INTEGRATED CIRCUITS AND SYSTEMS
, 2000
"... Symbolic analogcircuit analysis has many applications, and is especially useful for analog synthesis and testability analysis. Existing approaches rely on two forms of symbolic expression representation: expanded sumofproduct form or arbitrarily nested form. Expanded form suffers the problem that ..."
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Cited by 17 (5 self)
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Symbolic analogcircuit analysis has many applications, and is especially useful for analog synthesis and testability analysis. Existing approaches rely on two forms of symbolic expression representation: expanded sumofproduct form or arbitrarily nested form. Expanded form suffers the problem that the number of product terms grows exponentially with the size of a circuit, and approximation has to be used. Nested form is not canonical, i.e., many representations exist for a symbolic expression, and manipulations with the nested form are often complicated. In this paper, we present a new approach to exact and canonical symbolic analysis by exploiting the sparsity and sharing of product terms. It consists of representing the symbolic determinant of a circuit matrix by a graphcalled determinant decision diagram (DDD)and performing symbolic analysis by graph manipulations. We showed that DDD construction, as well as many symbolic analysis algorithms, can be performed in time complex...
Symbolic Analysis of Large Analog Integrated Circuits By Approximation During Expression Generation
, 1994
"... A novel algorithm is presented that generates approximate symbolic expressions for smallsignal 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 wi ..."
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Cited by 9 (1 self)
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A novel algorithm is presented that generates approximate symbolic expressions for smallsignal 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. INTRODUCTION Symbolic circuit analysis refers to the calculation of network functions H(s,x) in the form: (1) where x T ={x 1 , x 2 , . . . x Q } is the vector of circuit parameters which remain as symbols, and the...
Constructing Symbolic Models for the Input/Output Behavior of Periodically TimeVarying Systems Using Harmonic Transfer Matrices
, 2002
"... A new technique is presented for generating symbolic expressions for the harmonic transfer functions of linear periodically timevarying (LPTV) systems, like mixers and PLL's. The algorithm, which we call Symbolic HTM, is based on the organisation of the harmonic transfer functions into a harmonic t ..."
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Cited by 3 (0 self)
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A new technique is presented for generating symbolic expressions for the harmonic transfer functions of linear periodically timevarying (LPTV) systems, like mixers and PLL's. The algorithm, which we call Symbolic HTM, is based on the organisation of the harmonic transfer functions into a harmonic transfer matrix. This representation allows to manipulate LPTV systems in a way that is similar to linear timeinvariant (LTI) systems, making it possible to generate symbolic expressions which relate the overall harmonic transfer functions to the characteristics of the building blocks. These expressions can be used as design equations or as parametrized models for use in simulations. The algorithm is illustrated for a downconversion mixer.
A family of matroid intersection algorithms for the computation of approximated symbolic network functions
 Proc. ISCAS
, 1996
"... In recent years, the technique of simpl$cation during generation has turned out to be very promising for the eficient computation of approximate symbolic network functions for large transistor circuits. In this paper it is shown how symbolic network functions can be simpl$ed during their generati ..."
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Cited by 2 (0 self)
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In recent years, the technique of simpl$cation during generation has turned out to be very promising for the eficient computation of approximate symbolic network functions for large transistor circuits. In this paper it is shown how symbolic network functions can be simpl$ed during their generation with any wellknown symbolic network analysis method. The underlying algorithm for the different techniques is always a matroid intersection algorithm. It is shown that the most eflcient technique is the twograph method. An implementation of the simpltjication during generation technique with the twograph method illustrates its benefits for the symbolic analysis of large analog circuits. 1
Efficient approximation of symbolic expressions for analog behavioral modeling and analysis
 IEEE Trans. ComputerAided Design Integr. Circuits Syst
, 2004
"... Abstract — Efficient algorithms are presented to generate approximate expressions for transfer functions and characteristics of large linear analog circuits. The algorithms are based on a compact determinant decision diagram (DDD) representation of exact transfer functions and characteristics. Sever ..."
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Cited by 1 (1 self)
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Abstract — Efficient algorithms are presented to generate approximate expressions for transfer functions and characteristics of large linear analog circuits. The algorithms are based on a compact determinant decision diagram (DDD) representation of exact transfer functions and characteristics. Several theoretical properties of DDDs are characterized, and three algorithms, namely, based on dynamic programming, based on consecutive kshortest path based, and based on incremental kshortest path, are presented in this paper. We show theoretically that all three algorithms have time complexity linearly proportional to DDD, the number of vertices of a DDD, and that the incremental kshortest path based algorithm is fastest and the most flexible one. Experimental results confirm that the proposed algorithms are the most efficient ones reported so far, and are capable of generating thousands of dominant terms for typical analog blocks in CPU seconds on a modern computer workstation. Index Terms — analog symbolic analysis, circuit simulation, determinant decision diagrams, matrix determinant, behavioral modeling I.
New Algorithms for Reference Generation in Symbolic Analysis or Large Analog Circuits
, 1997
"... This paper addresses the problems arising in the calculation of numerical references (network function coefficients) , essential for an appropriate error control in simplification before and during generation algorithms for symbolic analysis of large analog circuits. The conventional polynomial inte ..."
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Cited by 1 (1 self)
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This paper addresses the problems arising in the calculation of numerical references (network function coefficients) , essential for an appropriate error control in simplification before and during generation algorithms for symbolic analysis of large analog circuits. The conventional polynomial interpolation method reveals to be unable to handle the large circuit sizes needed, mainly due to the dramatic effect of roundoff errors. This paper introduces a new algorithm able to accurately calculate the network function coefficients of large analog circuits in an efficient way. 1. Introduction Symbolic circuit analysis refers to the calculation of network functions where all or part of the circuit parameters are represented by symbols. The applicability of symbolic simulation techniques to the analysis and synthesis of analog integrated circuits has been known for a long time. See for instance [1] for an actualized review of techniques and applications of symbolic analysis. Given the e...
Symbolic Analysis Tools  The StateOfTheArt
, 1996
"... This paper reviews the main last generation symbolic analyzers, comparing them in terms of functionality, pointing out also their shortcomings. The stateoftheart in this field is also studied, pointing out directions for future research. 1. INTRODUCTION Circuit analysis is a basic milestone for ..."
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Cited by 1 (0 self)
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This paper reviews the main last generation symbolic analyzers, comparing them in terms of functionality, pointing out also their shortcomings. The stateoftheart in this field is also studied, pointing out directions for future research. 1. INTRODUCTION Circuit analysis is a basic milestone for efficient design of integrated circuits. Ever since powerful computers have been available, designers have developed programs to analyze circuits automatically. Today, all electrical engineering professionals and students use electrical simulators (such as HSPICE or ELDO). However, electrical simulators do not cover all the analysis tasks required for integrated circuit design. Essentially, they only serve to verify the performance of previously sized circuits. Among other things, designers must be able to predict the behavior of unsized circuits by tracing relationships among performance figures and design parameters. These relationships may be in the form of transfer functions, poles and ...
An Approach To Integrated Numerical And Symbolic Circuit Analysis
 Proc. IEEE Int. Symp. Circuits Syst
, 1994
"... An interface to symbolic circuit analysis has been developed for a SPICElike circuit simulator in order to integrate numerical simulation with an existing program for symbolic circuit analysis. In effect, both numerical and symbolic analyses use the same internal representation of circuits which m ..."
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Cited by 1 (0 self)
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An interface to symbolic circuit analysis has been developed for a SPICElike circuit simulator in order to integrate numerical simulation with an existing program for symbolic circuit analysis. In effect, both numerical and symbolic analyses use the same internal representation of circuits which makes the two approaches truly complementary. This integrated simulation capability is used in simulationbased parameter extraction where all ac smallsignal parameters are fitted through the symbolic analysis rather than numerical one, significantly reducing the execution time of the extraction process. INTRODUCTION Increasing demand for electronic components results in rapidly growing both the scale and the size of electronic circuits. This continuously creates needs for new and more efficient analog methods for circuit analysis. Integration of numerical and symbolic circuit analyses is one of possible improvements than can be used to increase the efficiency of circuit analysis tools. ...
(SEMI)SYMBOLIC MODELING OF LARGE LINEAR SYSTEMS: PENDING ISSUES
"... The paper deals with some open problems from the area of symbolic and semisymbolic modeling of linear systems, focusing on combining the symbolic, semisymbolic and numeric computation. ..."
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Cited by 1 (1 self)
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The paper deals with some open problems from the area of symbolic and semisymbolic modeling of linear systems, focusing on combining the symbolic, semisymbolic and numeric computation.