## Adaptive Sampling and Modeling of Analog Circuit Performance Parameters (2003)

Venue: | In Proc. VLSI-SOC |

Citations: | 3 - 1 self |

### BibTeX

@INPROCEEDINGS{Wolfe03adaptivesampling,

author = {Glenn Wolfe},

title = {Adaptive Sampling and Modeling of Analog Circuit Performance Parameters},

booktitle = {In Proc. VLSI-SOC},

year = {2003},

pages = {142}

}

### OpenURL

### Abstract

Many approaches to analog performance parameter macro modeling have been investigated by the research community. These models are typically derived from discrete data obtained from circuit simulation using numerous input combinations of component sizes for a given circuit topology. The simulations are computationally intensive, therefore it is advantageous to reduce the number of simulations necessary to build an accurate macro model. We present a new algorithm for adaptively sampling multi-dimensional black box functions based on Duchon pseudo-cubic splines. The splines readily and accurately model high dimensional functions based on discrete unstructured data and require no tuning of parameters as seen in many other interpolation methods. The adaptive sampler, in conjunction with pseudo-cubic splines, is used to accurately model various analog performance parameters for an operational amplifier topology using fewer sample points than traditional gridded and quasi-random sampling methodologies.

### Citations

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(Show Context)
Citation Context ...ance parameter functions. We present a novel algorithm for adaptively sampling multi-dimensional black box functions. This algorithm is coupled to a modeling methodology known as pseudo-cubic splines =-=[3]-=- which readily interpolate multi-dimensional scattered data points. Our methodology is used to guide the exploration of various performance parameter manifolds through selective and adaptive acquisiti... |

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Citation Context ... equations. These coefficients along with the location of the sampled data points completely define the spline interpolate. The details of setting up and solving such a linear system are discussed in =-=[12]-=-. As mentioned earlier, thin-plate splines may also be used to interpolate multi-dimensional scattered data. The mathematical form of thin-plate splines is very similar to that of pseudo-cubic splines... |

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Citation Context ...t the cost of reduced simulation accuracy [10]. Geometric programming and posynomial systems of equations offer the tantalizing promise of “optimal” solutions to the synthesis of large analog systems =-=[5]-=-, [8]. However, the posynomial equations are usually manually created by an expert designer. In addition, the “optimal” solution to the posynomial models and constraints is only as accurate as the tai... |

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Citation Context ...oints via the circuit simulator SPICE. The performance manifolds are also sampled using traditional gridded sampling as well as a quasi-random space filling sampling method known as a Halton sequence =-=[6]-=-. Quasi-random numbers are able to 0-7803-8702-3/04/$20.00 ©2004 IEEE. 931 fill a space more uniformly than uncorrelated pseudo-random generators and are useful for “off-grid” but thorough function ex... |

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Citation Context ...sis of op-amp transistor sizes given a set of user specified constraints. Reuse of simulation data from commercial sizing tools was considered for use in creating analog macro models by Liu et al. in =-=[7]-=-; regression techniques were used to model subsets of a large sets of simulation data to produce models with acceptable accuracies. An adaptive sampling scheme using piecewise linear models was propos... |

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Citation Context ...s have been developed at the expense of human interpretability [11]. Knowledge based, or expert, analog CAD methodologies rely on the acquisition and integration of human analog design expertise [9], =-=[13]-=-. Knowledge based systems typically give very good results but the time and effort needed to encode designer knowledge is considerable. Partial or approximate simulation techniques have been developed... |

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17 |
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Citation Context ... cost of reduced simulation accuracy [10]. Geometric programming and posynomial systems of equations offer the tantalizing promise of “optimal” solutions to the synthesis of large analog systems [5], =-=[8]-=-. However, the posynomial equations are usually manually created by an expert designer. In addition, the “optimal” solution to the posynomial models and constraints is only as accurate as the tailored... |

11 |
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9 |
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(Show Context)
Citation Context ...ade to automate the creation of posynomial models based on SPICE simulation outputs [2], however, accuracy of the models suffers due to the constraining nature of the posynomial equation template. In =-=[14]-=- neural network models were used to map circuit component sizes into various op-amp performance metrics for several different op-amp topologies. The neural network models were embedded in a genetic al... |

5 |
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Citation Context ...nd can be used for any dimension desired. One such class derived by Duchon is the well known thin-plate spline which minimizes the energy of 932 a clamped (via the discrete data points) elastic plate =-=[16]-=-. We will later discuss a problem encountered when using thin plate splines, however, let us first discus the class of splines used in this paper known as pseudo-cubic splines which have the form: k �... |

3 |
Circuit simplification for the symbolic analysis of analog integrated circuits
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(Show Context)
Citation Context ... Section 6 presents conclusions from the paper. 2. RELATED WORK Ranga Vemuri University of Cincinnati ranga@ececs.uc.edu Various methodologies have been proposed for analog modeling. Symbolic methods =-=[1]-=- use linearized device equations to create performance parameter models of analog circuits. This technique has also been expanded to include weakly nonlinear effects. Symbolic circuit equations quickl... |

2 | Macromodeling of the a.c. characteristics of CMOS op-amps
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Citation Context ...rcuits have been developed at the expense of human interpretability [11]. Knowledge based, or expert, analog CAD methodologies rely on the acquisition and integration of human analog design expertise =-=[9]-=-, [13]. Knowledge based systems typically give very good results but the time and effort needed to encode designer knowledge is considerable. Partial or approximate simulation techniques have been dev... |

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(Show Context)
Citation Context ... equations quickly become prohibitively large in expanded form, thus hierarchically methods allowing the analysis of large analog circuits have been developed at the expense of human interpretability =-=[11]-=-. Knowledge based, or expert, analog CAD methodologies rely on the acquisition and integration of human analog design expertise [9], [13]. Knowledge based systems typically give very good results but ... |

1 |
Adaptive Sampling for Macro Modeling of Analog Circuit Performance Parameters
- Wolfe, Ding, et al.
(Show Context)
Citation Context ...ession techniques were used to model subsets of a large sets of simulation data to produce models with acceptable accuracies. An adaptive sampling scheme using piecewise linear models was proposed in =-=[15]-=-. A least squares plane was fit to local areas of discrete data in order to detect regions of nonlinearity. These regions are sampled more densely than linear regions in order to improve maximum model... |