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35
A Circuit Representation Technique for Automated Circuit Design
 IEEE Transactions on Evolutionary Computation
"... We present a method of automatically generating circuit designs using evolutionary search and a set of circuitconstructing primitives arranged in a linear sequence. This representation has the desirable property that virtually all sets of circuitconstructing primitives result in valid circuit gr ..."
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Cited by 29 (4 self)
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We present a method of automatically generating circuit designs using evolutionary search and a set of circuitconstructing primitives arranged in a linear sequence. This representation has the desirable property that virtually all sets of circuitconstructing primitives result in valid circuit graphs. While this representation excludes certain circuit topologies, it is capable of generating a rich set of them including many of the useful topologies seen in handdesigned circuits. Our system allows circuit size (number of devices), circuit topology, and device values to be evolved. Using a parallel genetic algorithm and circuit simulation software, we present experimental results as applied to three analog filter and two amplifier design tasks. In all tasks, our system is able to generate circuits that achieve the target specifications. Although the evolved circuits exist as software models, detailed examinations of each suggest that they are electrically well behaved and thus suitable for physical implementation. The modest computational requirements suggest that the ability to evolve complex analog circuit representations in software is becoming more approachable on a single engineering workstation.
Automated Analog Circuit Synthesis Using a Linear Representation
 Proc. of the Second Int’l Conf on Evolvable Systems: From Biology to Hardware
, 1998
"... We present a method of evolving analog electronic circuits using a linear representation and a simple unfolding technique. While this representation excludes a large number of circuit topologies, it is capable of constructing many of the useful topologies seen in handdesigned circuits. Our syst ..."
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Cited by 27 (6 self)
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We present a method of evolving analog electronic circuits using a linear representation and a simple unfolding technique. While this representation excludes a large number of circuit topologies, it is capable of constructing many of the useful topologies seen in handdesigned circuits. Our system allows circuit size, circuit topology, and device values to be evolved. Using a parallel genetic algorithm we present initial results of our system as applied to two analog filter design problems.
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.
A Comparison of Dynamic Fitness Schedules for Evolutionary Design of Amplifiers
 in Proceedings of the First NASA/DoD Workshop on Evolvable Hardware
, 1999
"... Highlevel analog circuit design is a complex problem domain in which evolutionary search has recently produced encouraging results. However, little is known about how to best structure evolution for these tasks. The choices of circuit representation, fitness evaluation technique, and genetic operat ..."
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Cited by 13 (7 self)
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Highlevel analog circuit design is a complex problem domain in which evolutionary search has recently produced encouraging results. However, little is known about how to best structure evolution for these tasks. The choices of circuit representation, fitness evaluation technique, and genetic operators clearly have a profound effect on the search process. In this paper, we examine fitness evaluation by comparing the effectiveness of four fitness schedules. Three fitness schedules are dynamic – the evaluation function changes over the course of the run, and one is static. Coevolutionary search is included, and we present a method of evaluating the problem population that is conducive to multiobjective optimization. Twentyfive runs of an analog amplifier design task using each fitness schedule are presented. The results indicate that solution quality is highest with static and coevolving fitness schedules as compared to the other two dynamic schedules. We discuss these results and offer two possible explanations for the observed behavior: retention of useful information, and alignment of problem difficulty with circuit proficiency. 1
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...
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.
Hierarchical Symbolic Analysis of Analog Circuits Using TwoPort Networks
"... Abstract: This paper presents a method towards hierarchical symbolic analysis of linear analog circuits using twoport networks. The important difference to the ordinary flat symbolic analysis is, that we treat the transistor pairs as blocks and then derive the transfer function with network analyzer ..."
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Cited by 3 (0 self)
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Abstract: This paper presents a method towards hierarchical symbolic analysis of linear analog circuits using twoport networks. The important difference to the ordinary flat symbolic analysis is, that we treat the transistor pairs as blocks and then derive the transfer function with network analyzer without to setup and solve a complicated DAE system for a whole analog circuit. The hierarchical idea can be even used to large circuits in divide and conquer manner. Experimental results obtained with some applications of this method are presented. Key–Words: Symbolic analysis, Twoport network 1
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...