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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 23 (8 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 Circuits with Determinant Decision Diagrams
, 1997
"... Symbolic analogcircuit analysis has many applications, and is especially useful for analog synthesis and testability analysis. 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 s ..."
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Cited by 16 (10 self)
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Symbolic analogcircuit analysis has many applications, and is especially useful for analog synthesis and testability analysis. 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 and DDDbased symbolic analysis can be performed in time complexity proportional to the number of DDD vertices. We described a vertex ordering heuristic, and showed that the number of DDD vertices can be quite smallusually ordersofmagnitude less than the number of product terms. The algorithm has been implemented. An orderofmagnitude improvement in both CPU time and memory usages over existing symbolic analyzers ISAAC and MapleV has been observed for large analog circuits. 1. Introduction Symbolic a...
Efficient DDDbased term generation algorithm for analog circuit behavioral modeling
 In Pmc. IEEE DATE Conference
, 2003
"... Abstract — An efficient approach to generating symbolic product terms for behavioral modeling of large linear analog circuits is presented. The approach is based on a compact determinant decision diagram (DDD) representation of transfer functions and characteristics of analog circuits. The new algor ..."
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Cited by 6 (1 self)
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Abstract — An efficient approach to generating symbolic product terms for behavioral modeling of large linear analog circuits is presented. The approach is based on a compact determinant decision diagram (DDD) representation of transfer functions and characteristics of analog circuits. The new algorithm is based on the concept that a dominant term in a DDD graph can be found by searching the shortest path in the graph. But instead of traversing a whole DDD graph each time, we show that a shortest path can be found by just updating a small number of the newly added vertices after the first shortest path is found. Experimental results indicate that the new symbolic term generation algorithm outperforms both pure shortest path based algorithm and dynamic programming based algorithm, which is the fastest symbolic term generation algorithm published so far. I.
Interpretable Symbolic SmallSignal Characterization of Large Analog Circuits using Determinant Decision Diagrams
"... A new approach is proposed to generate interpretable symbolic expressions of smallsignal characteristics for large analog circuits. The approach is based on a complete, exact, yet compact representation of symbolic expressions via determinant decision diagrams (DDDs). We show that two key tasks of ..."
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Cited by 4 (3 self)
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A new approach is proposed to generate interpretable symbolic expressions of smallsignal characteristics for large analog circuits. The approach is based on a complete, exact, yet compact representation of symbolic expressions via determinant decision diagrams (DDDs). We show that two key tasks of generating interpretable symbolic expressions — term decancellation and term simplification—can be performed in linear time in terms of the number of DDD vertices. With the number of DDD vertices manyordersofmagnitude less than the number of product terms, the proposed approach has been shown to be much more efficient than other startoftheart approaches.
A family of matroid intersection algorithms for the computation of approximated symbolic network functions
 PROC. ISCAS
, 1996
"... In recent years, the technique of simplification during generation has turned out to be very promising for the efficient computation of approximate symbolic network functions for large transistor circuits. In this paper it is shown how symbolic network functions can be simplified during their genera ..."
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Cited by 2 (0 self)
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In recent years, the technique of simplification during generation has turned out to be very promising for the efficient computation of approximate symbolic network functions for large transistor circuits. In this paper it is shown how symbolic network functions can be simplified 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 efficient technique is the twograph method. An implementation of the simplification during generation technique with the twograph method illustrates its benefits for the symbolic analysis of large analog circuits.
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.
Efficient DDDbased Term Generation Algorithm for Analog Circuit Behavioral Modeling
"... Abstract — An efficient approach to generating symbolic product terms for behavioral modeling of large linear analog circuits is presented. The approach is based on a compact determinant decision diagram (DDD) representation of transfer functions and characteristics of analog circuits. The new algor ..."
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Abstract — An efficient approach to generating symbolic product terms for behavioral modeling of large linear analog circuits is presented. The approach is based on a compact determinant decision diagram (DDD) representation of transfer functions and characteristics of analog circuits. The new algorithm is based on the concept that a dominant term in a DDD graph can be found by searching the shortest path in the graph. But instead of traversing a whole DDD graph each time, we show that a shortest path can be found by just updating a small number of the newly added vertices after the first shortest path is found. Experimental results indicate that the new symbolic term generation algorithm outperforms both pure shortest path based algorithm and dynamic programming based algorithm, which is the fastest symbolic term generation algorithm published so far. I.