Analog circuit design space description based on ordered clustering of feature uniqueness and similarity Cristian Ferent n , Alex Doboli Q1 Department of Electrical and Computer Engineering, Stony Brook University, Stony Brook, NY 11790, USA article info Article history: Received 22 February 2012 Received in revised form 9 August 2013 Accepted 20 August 2013 Keywords: Analog circuit Feature clustering Computer-aided design (CAD) Design space characterization abstract This paper presents a symbolic technique to create ordered feature clustering schemes that express the main similarities and differences between analog circuits. Four separation scores, based on entropy, item characteristics, category characteristics, and Bayesian classifiers, were studied to produce clustering schemes that offer insight about the uniqueness and importance of specific design features in setting AC performance as well as the limiting factors of the designs. The experiments consider a set of 50 state-of- the-art amplifier circuits. The paper offers a detailed discussion on using the insight obtained from circuit feature clustering for topology synthesis and refinement. & 2013 Elsevier B.V. All rights reserved. 1. Introduction Circuit macromodels express the main characteristics of analog circuits, e.g., the mathematical dependency of voltages and cur- rents at circuit nodes on design variables, e.g., transistor dimen- sions [1,2]. Models also describe the relations between performance attributes and circuit design variables [3,4]. Existing modeling methods successfully address a large variety of perfor- mance attributes, like small-signal AC performance [1,3], weakly nonlinear distortion [5,6], and large-signal analysis [4]. The used techniques include regression analysis [2], symbolic analysis [1], piecewise-linear approximation [7], and model-order reduction [8,9]. Circuit models are used for fast performance evaluation, circuit design and synthesis, and getting insight into circuit operation for verification. There are few modeling methods that characterize a population of circuits to indicate the similarities and differences in their topological and behavioral features as well as their impact on performance. However, descriptions of circuit populations can offer a comprehensive presentation of the design space covered by the design set, the flexibility of design features when used under various constraints, and the uniqueness of features in tackling specific requirements. Such insight results by comparing circuits to find common and unique design features, e.g., the similar and distinct symbolic terms of pole and zero expressions. The comparison helps understanding the performance advantages and limitations of a circuit topology compared to another, the performance impact of circuit nodes and their structural connec- tions to other nodes, the conditions under which alternative circuits offer similar performance, and the design aspects that boost or limit the performance of a circuit compared to alter- natives. The obtained insight is useful to synthesize topologies, or refine existing circuits to incorporate useful features from other designs or to identify common characteristics that can be reused for broad sets of performance requirements. This paper presents a symbolic technique for creating models, called ordered node cluster representations (ONCR), that express the main similarities and differences between a set of analog circuits with common functionality. The insight obtained from the representations are the similar and dissimilar circuit features, including the related topological structures and their symbolic expressions. The modeling method includes three main steps: (i) identifying the possible separation criteria, (ii) analyzing the criteria with respect to their potential of grouping the circuits, and (iii) building ONCRs such that the separation of dissimilar circuits is maximized. In addition, the method performs two initial steps that create the symbolic circuit descriptions used for analysis. The paper studies four separation scores: entropy, item characteristics, category characteristics, and Bayesian classifiers. A preliminary version of the paper was presented in [10]. This paper introduces three new separation scores, and a comprehensive study for two sets of state-of-the-art amplifier circuits: one using ten circuits and the other having fifty circuits. A detailed discussion of the application of ONCRs for topology synthesis and refinement is also offered. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/vlsi INTEGRATION, the VLSI journal 0167-9260/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.vlsi.2013.08.004 n Corresponding author. Tel.: þ1 6316325938. Q3 Q4 Q5 E-mail addresses: Cristian.Ferent@stonybrook.edu, cferent@ece.sunysb.edu (C. Ferent), Alex.Doboli@stonybrook.edu (A. Doboli). Please cite this article as: C. Ferent, A. Doboli, Analog circuit design space description based on ordered clustering of feature uniqueness and similarity, INTEGRATION, the VLSI journal (2013), http://dx.doi.org/10.1016/j.vlsi.2013.08.004i INTEGRATION, the VLSI journal ∎ (∎∎∎∎) ∎∎∎–∎∎∎