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Computeraided design of analog and mixedsignal integrated circuits
 Proceedings of the IEEE
, 2000
"... This survey presents an overview of recent advances in the state of the art for computeraided design (CAD) tools for analog and mixedsignal integrated circuits (ICs). Analog blocks typically constitute only a small fraction of the components on mixedsignal ICs and emerging systemsonachip (SoC ..."
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Cited by 72 (12 self)
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This survey presents an overview of recent advances in the state of the art for computeraided design (CAD) tools for analog and mixedsignal integrated circuits (ICs). Analog blocks typically constitute only a small fraction of the components on mixedsignal ICs and emerging systemsonachip (SoC) designs. But due to the increasing levels of integration available in silicon technology and the growing requirement for digital systems to communicate with the continuousvalued external world, there is a growing need for CAD tools that increase the design productivity and improve the quality of analog integrated circuits. This paper describes the motivation and evolution of these tools and outlines progress on the various design problems involved: simulation and modeling, symbolic analysis, synthesis and optimization, layout generation, yield analysis and design centering, and test. This paper summarizes the problems for which viable solutions are emerging and those which are still unsolved. Keywords—Analog and mixedsignal computeraided design (CAD), analog and mixedsignal integrated circuits, analog circuit and layout synthesis, analog design automation, circuit simulation and modeling. I.
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...
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 15 (5 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.
Compact representation and efficient generation of sexpanded symbolic network functions for computeraided analog circuit design
 IEEE Trans. ComputerAided Design
, 2001
"... Abstract—A graphbased approach is presented for the generation of exact symbolic network functions in the form of rational polynomials of the complex frequency variable for analog integrated circuits. The approach employs determinant decision diagrams (DDDs) to represent the determinant of a cir ..."
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Cited by 8 (2 self)
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Abstract—A graphbased approach is presented for the generation of exact symbolic network functions in the form of rational polynomials of the complex frequency variable for analog integrated circuits. The approach employs determinant decision diagrams (DDDs) to represent the determinant of a circuit matrix and its cofactors. A notion of multiroot DDDs is introduced, where each root represents a symbolic expression for an individual coefficient of the powers of in the numerator and denominator of a network function, and multiple roots share their common subgraphs. A DDDbased algorithm is presented for generatingexpanded network functions. We prove theoretically and validate experimentally that the algorithm constructs in ( DDD) time anexpanded DDD with no more than DDD vertices, where is the degree of the denominator polynomial, is the maximum number of devices that connect to a circuit node, and DDD is
A Fitting Approach to Generate Symbolic Expressions for Linear and Nonlinear Analog Circuit Performance Characteristics
 In Proceedings Design Automation and Test in Europe Conference
, 2002
"... This paper presents a novel method to automatically generate symbolic expressions for both linear and nonlinear circuit characteristics using a templatebased fitting of numerical, simulated data. The aim of the method is to generate convex, interpretable expressions. The posynomiality of the genera ..."
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Cited by 5 (1 self)
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This paper presents a novel method to automatically generate symbolic expressions for both linear and nonlinear circuit characteristics using a templatebased fitting of numerical, simulated data. The aim of the method is to generate convex, interpretable expressions. The posynomiality of the generated expressions enables the use of efficient geometric programming techniques when using these expressions for circuit sizing and optimization. Attention is paid to estimating the relative `goodnessoffit' of the generated expressions. Experimental results illustrate the capabilities of the approach.
Wideband modeling of RF/analog circuits via hierarchical multipoint model order reduction
 in Proc. Asia South Pacific Design Automation Conf. (ASPDAC
, 2005
"... This paper proposes a novel wideband modeling technique for highperformance RF passives and linear(ized) analog circuits. The new method is based on a recently proposed sdomain hierarchical modeling and analysis method [27]. Theoretically, we show that the sdomain hierarchical reduction is equival ..."
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Cited by 4 (4 self)
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This paper proposes a novel wideband modeling technique for highperformance RF passives and linear(ized) analog circuits. The new method is based on a recently proposed sdomain hierarchical modeling and analysis method [27]. Theoretically, we show that the sdomain hierarchical reduction is equivalent to implicit moment matching around s = 0, and that the existing hierarchical reduction method by onepoint expansion is numerically stable for general treestructured circuits. Practically, we propose a hierarchical multipoint reduction scheme for highfidelity, wideband modeling of general passive or active linear circuits. A novel explicit waveform matching algorithm is proposed for searching the dominant poles and residues from different expansion points based on the unique hierarchical reduction framework. Experimental results with large analog circuits, onchip spiral inductors are presented to validate the proposed method. I.
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 3 (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 3 (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.
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 ..."
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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...