## Efficient DDD-based Symbolic Analysis of Large Linear Analog Circuits (2001)

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Citations: | 8 - 3 self |

### BibTeX

@MISC{Verhaegen01efficientddd-based,

author = {Wim Verhaegen and Georges Gielen},

title = {Efficient DDD-based Symbolic Analysis of Large Linear Analog Circuits},

year = {2001}

}

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### Abstract

A new technique for generating approximate symbolic expressions for network functions in linear(ized) analog circuits is presented. It is based on the compact determinant decision diagram (DDD) representation of the circuit. An implementation of a term generation algorithm is given and its performance is compared to a matroidbased algorithm. Experimental results indicate that our approach is the fastest reported algorithm so far for this application.

### Citations

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Citation Context ...s. These vertices represent zero minors and are removed from the graph in a bottom–up recursive zero–suppression step. A slightly modified version of the algorithm with linear complexity described in =-=[14]-=- is used to this purpose. The zero–suppression leads to a compact graph, which lowers the execution time of many of the algorithms described below. The DDD representation of the determinant is then ob... |

29 |
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Citation Context ...-order RC circuit Many tools have been developed for the automated generation of symbolic network functions, which becomes very cumbersome if not unfeasible to do by hand for increasing circuit sizes =-=[3, 4, 5, 6, 7, 8, 9]-=-. Most of these tools calculate the output of a given circuit in a simplified form based on relative size information of the circuit parameters. The resulting expressions are therefore only valid with... |

22 | Canonical symbolic analysis of large analog circuits with determinant decision diagrams
- Shi, Tan
- 2000
(Show Context)
Citation Context ...e expression–based approach, based on an exact representation of determinants as a graph or determinant decision diagram (DDD), a concept which was introduced to the linear circuit analysis domain in =-=[10, 11, 12]-=-. Instead of calculating the circuit output explicitly, the Laplace expansion of the circuit matrix minor is modeled in a DDD, which is discussed in section 2. This setup needs to be done only once fo... |

16 | Symbolic analysis of large analog circuits with determinant decision diagrams
- Shi, Tan
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(Show Context)
Citation Context ...e expression–based approach, based on an exact representation of determinants as a graph or determinant decision diagram (DDD), a concept which was introduced to the linear circuit analysis domain in =-=[10, 11, 12]-=-. Instead of calculating the circuit output explicitly, the Laplace expansion of the circuit matrix minor is modeled in a DDD, which is discussed in section 2. This setup needs to be done only once fo... |

12 |
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(Show Context)
Citation Context ...hm. Experimental results indicate that our approach is the fastest reported algorithm so far for this application. 1. INTRODUCTION The symbolic analysis of analog circuits has a long standing history =-=[1, 2, 3]-=-. Applications range from the calculation of symbolic expressions of network functions to the simplified behavioral modeling of the circuit in order to trade some accuracy loss for a substantial circu... |

11 | Lazy-expansion of symbolic expression approximation - Seda, DeGrauwe, et al. - 1992 |

11 |
et al., “Equation-Based Symbolic Approximation by Matrix Reduction with Qualitative Error
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(Show Context)
Citation Context ...-order RC circuit Many tools have been developed for the automated generation of symbolic network functions, which becomes very cumbersome if not unfeasible to do by hand for increasing circuit sizes =-=[3, 4, 5, 6, 7, 8, 9]-=-. Most of these tools calculate the output of a given circuit in a simplified form based on relative size information of the circuit parameters. The resulting expressions are therefore only valid with... |

5 |
K.S.: Symbolic analysis of large-scale networks using a hierarchical signal flowgraph approach
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(Show Context)
Citation Context ...-order RC circuit Many tools have been developed for the automated generation of symbolic network functions, which becomes very cumbersome if not unfeasible to do by hand for increasing circuit sizes =-=[3, 4, 5, 6, 7, 8, 9]-=-. Most of these tools calculate the output of a given circuit in a simplified form based on relative size information of the circuit parameters. The resulting expressions are therefore only valid with... |

5 |
Interactive ac modeling and characterization of analog circuits via symbolic analysis
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- 1991
(Show Context)
Citation Context |

3 | Multi-terminal determinant decision diagrams: A new approach to semi-symbolic analysis of analog integrated circuits
- Pi, Shi
- 2000
(Show Context)
Citation Context ...e expression–based approach, based on an exact representation of determinants as a graph or determinant decision diagram (DDD), a concept which was introduced to the linear circuit analysis domain in =-=[10, 11, 12]-=-. Instead of calculating the circuit output explicitly, the Laplace expansion of the circuit matrix minor is modeled in a DDD, which is discussed in section 2. This setup needs to be done only once fo... |

3 |
Evaluation of error-control strategies for the linear symbolic analysis of analog integrated circuits
- Daems, Verhaegen, et al.
- 1999
(Show Context)
Citation Context ...e generated in order of decreasing magnitude, and the number of generated terms per coefficient is controlled by an error control algorithm. An overview of common error control techniques is given in =-=[15]-=-, so we will not go into the details here. A common characteristic of all these algorithms is that individual terms need to be generated per coefficient. DDD’s constructed as explained in section 2 re... |

2 |
Symbolic analysis of large-scale networks by circuit reduction to a two-port
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- 1996
(Show Context)
Citation Context |

1 |
Design tool for symbolic analysis based on the matroid intersection theory
- Dobrovolny
- 1998
(Show Context)
Citation Context ...term–generation tool makes DDD’s a useful data structure for approximative symbolic analysis, and a contender in the symbolic– analysis field for the matroid–based approach, that is presented a.o. in =-=[13]-=-. Section 4 gives a comparison of experimental results for the DDD– based and matroid–based approached, and our new approach turns out to be the fastest term generation algorithm at present. Finally, ... |