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18
MAELSTROM: Efficient simulationbased synthesis for custom analog cells
 Proc. of the 1999 ACM/IEEE Design Automation Conference
, 1999
"... Analog synthesis tools have failed to migrate into mainstream use primarily because of difficulties in reconciling the simplified models required for synthesis with the industrialstrength simulation environments required for validation. MAELSTROM is a new approach that synthesizes a circuit using t ..."
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Cited by 27 (6 self)
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Analog synthesis tools have failed to migrate into mainstream use primarily because of difficulties in reconciling the simplified models required for synthesis with the industrialstrength simulation environments required for validation. MAELSTROM is a new approach that synthesizes a circuit using the same simulation environment created to validate the circuit. We introduce a novel genetic/ annealing optimizer, and leverage network parallelism to achieve efficient simulatorintheloop analog synthesis. ___________________________ Permission to make digital/hardcopy of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage, the copyright notice, the title of the publication and its date appear, and notice is given that copying is by permission of ACM, Inc. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee.
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...
Hierarchical Symbolic Analysis Of Large Analog Circuits With Determinant Decision Diagrams
 IEEE Trans. on ComputerAided Design of Integrated Circuits and Systems
, 1998
"... A novel hierarchical approach is proposed to symbolic analysis of large analog circuits. The key idea is to use a graphbased representation  called Determinant Decision Diagram (DDD)  to represent the symbolic determinant and cofactors associated with the MNA matrix for each subcircuit block. B ..."
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Cited by 14 (4 self)
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A novel hierarchical approach is proposed to symbolic analysis of large analog circuits. The key idea is to use a graphbased representation  called Determinant Decision Diagram (DDD)  to represent the symbolic determinant and cofactors associated with the MNA matrix for each subcircuit block. By exploiting the inherent sharing and sparsity of symbolic expressions, DDD is capable of representing a huge number of symbolic product terms in a canonical and highlycompact manner. Further, it enables cofactoring and sensitivity computation to be performed with time linear in the size of DDD. Experimental results have demonstrated that our method outperforms the bestknown existing hierarchical symbolic analyzer SCAPP, and sometimes even numerical simulator SPICE.
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 13 (8 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...
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 3 (2 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.
Hierarchical Symbolic Analysis of Analog Integrated Circuits via Determinant Decision Diagrams
 IEEE Transactions on ComputerAided Design of Integrated Circuits and Systems, Vol.19, Apr 2000
, 2000
"... A new approach is proposed to hierarchical symbolic analysis of large analog integrated circuits. It consists of performing symbolic suppression of each subcircuit to its terminals in terms of subcircuit matrix determinants and cofactors, and applying Cramer's rule to solve symbolically the set of e ..."
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Cited by 2 (0 self)
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A new approach is proposed to hierarchical symbolic analysis of large analog integrated circuits. It consists of performing symbolic suppression of each subcircuit to its terminals in terms of subcircuit matrix determinants and cofactors, and applying Cramer's rule to solve symbolically the set of equations at the top level of the circuit hierarchy. The novelty of the proposed approach is to use an annotated, directed and acyclic graph, called Determinant Decision Diagram (DDD), to represent symbolic determinants of subcircuit matrices and cofactors used in subcircuit suppression, as well as symbolic determinants of the toplevel circuit matrix and cofactors required in applying Cramer's rule. DDD enables systematically exploiting the inherent sparsity of circuit matrices and the sharing of symbolic expressions. It is capable of representing a huge number of symbolic product terms in a canonical and highly compact manner. The proposed approach is illustrated using a Cauer parameter low...
Hierarchical approach to exact symbolic analysis of large analog circuits
 in Proc. Design Automation Conf. (DAC
, 2004
"... Abstract—This paper proposes a novel approach to the exact symbolic analysis of very large analog circuits. The new method is based on determinant decision diagrams (DDDs) representing symbolic product terms. But instead of constructing DDD graphs directly from a flat circuit matrix, the new method ..."
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Cited by 2 (2 self)
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Abstract—This paper proposes a novel approach to the exact symbolic analysis of very large analog circuits. The new method is based on determinant decision diagrams (DDDs) representing symbolic product terms. But instead of constructing DDD graphs directly from a flat circuit matrix, the new method constructs DDD graphs in a hierarchical way based on hierarchically defined circuit structures. The resulting algorithm can analyze much larger analog circuits exactly than before. The authors show that exact symbolic expressions of a circuit are cancellationfree expressions when the circuit is analyzed hierarchically. With this, the authors propose a novel symbolic decancellation process, which essentially leads to the hierarchical DDD graph constructions. The new algorithm partially avoids the exponential DDD construction time by employing more efficient DDD graph operations during the hierarchical construction. The experimental results show that very large analog circuits, which cannot be analyzed exactly before like UPS and other unstructured circuits up to 100 nodes, can be analyzed by the new approach for the first time. The new approach significantly improves the exact symbolic capacity and promises huge potentials for the applications of exact symbolic analysis. Index Terms—Behavioral modeling, circuit simulation, symbolic analysis. I.
A Hierarchical Approach for the Symbolic Analysis of Large Analog Integrated Circuits
 Proc. IEEE Design Automation and Test in Europe, 2000
, 2000
"... This paper introduces a new hierarchical analysis methodology which incorporates approximation strategies during the analysis process. Consequently, the circuit sizes that can be analyzed increase dramatically, without suffering from the combinatorial explosion of expression complexity. Moreover, th ..."
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Cited by 1 (0 self)
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This paper introduces a new hierarchical analysis methodology which incorporates approximation strategies during the analysis process. Consequently, the circuit sizes that can be analyzed increase dramatically, without suffering from the combinatorial explosion of expression complexity. Moreover, the interpretability and usability in practical applications is enabled by providing analytical models that keep complexity at a minimum with the prescribed accuracy.
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.