## Behavioral Modeling for Analog System-Level Simulation by Wavelet Collocation Method

Citations: | 2 - 2 self |

### BibTeX

@MISC{Li_behavioralmodeling,

author = {Xin Li and Xuan Zeng and Dian Zhou and Xieting Ling and Wei Cai},

title = {Behavioral Modeling for Analog System-Level Simulation by Wavelet Collocation Method},

year = {}

}

### OpenURL

### Abstract

Abstract—In this paper, we propose a wavelet collocation method with nonlinear companding to generate behavioral models for analog circuits at the system level. During the overall process of circuit modeling, nonlinear function approximation is an important issue to accurately capture the nonideal input–output relations of analog circuit blocks. While a great number of previous research works focus on the high-dimensional top-down design/synthesis model, which involves large analog design spaces, this paper primarily concentrates on the bottom-up verification model requiring both simple representation and high accuracy. Taking advantage of the local support of wavelet bases, a nonlinear companding method is developed to control the modeling error distribution based on system-level simulation requirements. It, in turn, significantly improves the simulation efficiency at the system level. To demonstrate the promising features of the proposed method, two circuit examples, a fourth-order switched-current filter and a voltage-controlled oscillator, are employed to build the behavioral models. Index Terms—Analog circuits, behavioral modeling, nonlinear companding, wavelet collocation method. I.

### Citations

2671 | A theory for multiresolution signal decomposition: The wavelet representation
- Mallat
- 1989
(Show Context)
Citation Context ...s error distribution control problem, which has been insufficiently studied in previous research works. Wavelet methods have originally been developed for imaging compression and signal decomposition =-=[15]-=-–[17], and later been employed to compress the integral operator encountered in electromagnetics computations [18]–[20]. The work in [21], [22] is the first one to apply the wavelet collocation method... |

1942 | lectures on wavelets - Daubechies, Ten - 1992 |

1892 |
Sobolev Spaces
- Adams
- 1975
(Show Context)
Citation Context ...e wavelets developed in [24] because they were proved to have a high convergence rate. Let be the Sobolev space, which basically contains all functions with square integrable second order derivatives =-=[26]-=-. We first introduce the following function subspaces: 9 where the definitions of functions , , , , and 9 are given below. is a function set formed by all linear combinations of functions and stands f... |

805 |
An Introduction to Wavelets
- CHUI
- 1992
(Show Context)
Citation Context ...or distribution control problem, which has been insufficiently studied in previous research works. Wavelet methods have originally been developed for imaging compression and signal decomposition [15]–=-=[17]-=-, and later been employed to compress the integral operator encountered in electromagnetics computations [18]–[20]. The work in [21], [22] is the first one to apply the wavelet collocation method to c... |

454 |
Asymptotic Waveform Evaluation for Timing Analysis
- Pillage, Rohrer
- 1990
(Show Context)
Citation Context ... for behavioral modeling of analog circuits. First, for linear systems, there have been a significant body of works originally evolved from the model order reduction problem for interconnect analysis =-=[1]-=-–[4]. These methods are mathematically elegant and are capable of generating reduced-order transfer functions for complicated linear dynamic circuits. Unfortunately, in the community of nonlinear circ... |

443 | Fast wavelet transforms and numerical algorithms - Beylkin, Coifman, et al. - 1992 |

390 |
Analog Integrated Circuit Design
- Johns, Martin
- 1997
(Show Context)
Citation Context ...ital systems. Transistor-level simulation (e.g., by SPICE) of PLL circuit results in impractical run-times, because the acquisition procedure of a PLL circuit will take a large number of clock cycles =-=[33]-=-. In order to improve the simulation speed, it is necessary to extract the behavioral model for each component of the PLL circuit. Based on those behavioral models, high-level simulation can be execut... |

355 |
PRIMA: Passive reducedorder interconnect macromodeling algorithm
- Odabasioglu, Celik, et al.
- 1997
(Show Context)
Citation Context ... behavioral modeling of analog circuits. First, for linear systems, there have been a significant body of works originally evolved from the model order reduction problem for interconnect analysis [1]–=-=[4]-=-. These methods are mathematically elegant and are capable of generating reduced-order transfer functions for complicated linear dynamic circuits. Unfortunately, in the community of nonlinear circuit ... |

261 | Efficient linear circuit analysis by Padè approximation via the Lanczos process - Feldmann, Freund - 1995 |

92 | A trajectory piecewise-linear approach to model order reduction and fast simulation of nonlinear circuits and micromachined devices
- Rewienski, White
- 2003
(Show Context)
Citation Context ...ted linear dynamic circuits. Unfortunately, in the community of nonlinear circuit modeling, no such mature techniques exist, although several theoretical works have been developed in recent years [5]–=-=[7]-=-. Most practical approaches for nonlinear circuit modeling can be classified into three categories. First, the regression models proposed in [8]–[10] map the design space to the performance space dire... |

72 | Coordinatetransformed arnoldi algorithm for generating guarantee stable reducedorder models - Silveira, Kamon, et al. - 1999 |

55 |
Wavelet Analysis: The Scalable Structure of Information, 435 pp
- Resnikoff, Welss
- 1998
(Show Context)
Citation Context ...enotes the operation of transpose. (22) B. Wavelet Approximation for High-Dimensional Functions High-dimensional wavelet basis functions can be generated from tensor products of low-dimensional bases =-=[28]-=-. For example, if are one-dimensional wavelet bases, then functions construct a set of two-dimensional wavelet basis functions. In general, a -dimensional nonlinear function with input variables can b... |

42 | Reduced-order modeling of time-varying systems
- Roychowdhury
- 1999
(Show Context)
Citation Context ...licated linear dynamic circuits. Unfortunately, in the community of nonlinear circuit modeling, no such mature techniques exist, although several theoretical works have been developed in recent years =-=[5]-=-–[7]. Most practical approaches for nonlinear circuit modeling can be classified into three categories. First, the regression models proposed in [8]–[10] map the design space to the performance space ... |

34 | Projection frameworks for model reduction of weakly nonlinear systems - Phillips - 2000 |

34 | A class of bases in L2 for the sparse representation of integral operators - Alpert - 1993 |

30 | Remembrance of circuits past: macromodeling by data mining in large analog design spaces
- Liu, Singhee, et al.
- 2002
(Show Context)
Citation Context ...tical works have been developed in recent years [5]–[7]. Most practical approaches for nonlinear circuit modeling can be classified into three categories. First, the regression models proposed in [8]–=-=[10]-=- map the design space to the performance space directly. These methods construct high-dimensional nonlinear functions to approximate the relation between circuit performances (e.g., gain, area, domina... |

22 |
Adaptive multiresolution collocation methods for initial boundary value problems of nonlinear PDEs
- Cai, Wang
- 1996
(Show Context)
Citation Context ...ed to behavioral modeling of analog circuits in [23]. The purpose of this paper is to further develop and study the behavioral modeling problem using the spline wavelet collocation method proposed in =-=[24]-=-. The rest of this paper is organized as follows. In Section II, we illustrate the importance of error distribution control in behavioral modeling by an example of the switched-current memory cell. In... |

21 |
Externally linear timeinvariant systems and their applications to compandingsignal processors
- Tsividis
- 1997
(Show Context)
Citation Context ... model accuracy is needed. Actually, the idea of nonlinear companding is not a new one, but has already been widely used in communication [29], audio magnetic recording [30] and analog circuit design =-=[31]-=-, [32]. Although the mechanism for those three applications and our analog circuit modeling is different, the motivation for companding is the same, i.e., to improve the signal-to-noise ratio (SNR) at... |

15 |
A fast wavelet collocation method for high-speed circuit simulation
- Zhou, Cai
- 1999
(Show Context)
Citation Context ...een developed for imaging compression and signal decomposition [15]–[17], and later been employed to compress the integral operator encountered in electromagnetics computations [18]–[20]. The work in =-=[21]-=-, [22] is the first one to apply the wavelet collocation method to circuit simulation. That work is extended to behavioral modeling of analog circuits in [23]. The purpose of this paper is to further ... |

14 | Feasibility and Performance Region Modeling of Analog and
- Harjani, Shao
- 1996
(Show Context)
Citation Context ...ce models (e.g., BSIM3 model). Compared with the first modeling approach, the second one is more efficient and flexible. Recently, several new methodologies, including radial basis approximation [8], =-=[9]-=- and data mining [10], etc., have been developed to efficiently approximate the high-dimensional nonlinear functions for analog circuit modeling. These techniques mainly focus on the problem of top-do... |

13 |
Exponential state space filters: A generic current mode design strategy”,IEEE Trans. Circuits Syst
- Frey
- 1996
(Show Context)
Citation Context ... accuracy is needed. Actually, the idea of nonlinear companding is not a new one, but has already been widely used in communication [29], audio magnetic recording [30] and analog circuit design [31], =-=[32]-=-. Although the mechanism for those three applications and our analog circuit modeling is different, the motivation for companding is the same, i.e., to improve the signal-to-noise ratio (SNR) at small... |

11 |
An adaptive wavelet method for nonlinear circuit simulation
- Zhou, Cai, et al.
- 1999
(Show Context)
Citation Context ...veloped for imaging compression and signal decomposition [15]–[17], and later been employed to compress the integral operator encountered in electromagnetics computations [18]–[20]. The work in [21], =-=[22]-=- is the first one to apply the wavelet collocation method to circuit simulation. That work is extended to behavioral modeling of analog circuits in [23]. The purpose of this paper is to further develo... |

9 | Macromodeling of analog circuits for hierarchical circuit design
- Shao, Harjani
(Show Context)
Citation Context ...eoretical works have been developed in recent years [5]–[7]. Most practical approaches for nonlinear circuit modeling can be classified into three categories. First, the regression models proposed in =-=[8]-=-–[10] map the design space to the performance space directly. These methods construct high-dimensional nonlinear functions to approximate the relation between circuit performances (e.g., gain, area, d... |

9 |
Switched currents - a new technique for analog sampled-data signal processing
- Hughes, Bird, et al.
- 1989
(Show Context)
Citation Context ..., are examined to demonstrate the effectiveness of the proposed wavelet collocation method in analog behavioral modeling. A. Switched-Current Filter In the past one decade, switched-current technique =-=[25]-=- has been considered as a promising technique for the monolithic implementation of mixed analog and digital VLSI. Due to the high-speed switching behaviors, general purpose circuit simulators such as ... |

7 |
Studying the Effects of Mismatching and Clock-Feedthrough in Switched-Current Filters Using Behavioral Simulation
- Yufera, Rueda
- 1997
(Show Context)
Citation Context ...ING, VOL. 50, NO. 6, JUNE 2003 There exist two approaches to approximate the nonlinear functions encountered in analog circuit modeling: 1) developing the nonlinear function manually by hand analysis =-=[13]-=- and 2) constructing the nonlinear approximation by data fitting [8]–[10], [12]. The first approach takes into account the internal nonidealities of analog circuits and helps designers to understand t... |

5 |
Simulation of switched-current systems
- Schneider, Fiez
- 1993
(Show Context)
Citation Context ...ilters and delta-sigma converters, the sampled-data operation can be efficiently modeled by a discrete-time system which consists of a number of ideal unit delay blocks and static nonlinear functions =-=[12]-=-–[14]. Clearly, for all these techniques, nonlinear function approximation is a crucial issue within the overall behavioral modeling procedure.s300 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—II: ANALOG... |

4 |
Behavioral modeling of analog circuits by wavelet collocation method
- Li, Zeng, et al.
- 2001
(Show Context)
Citation Context ...etics computations [18]–[20]. The work in [21], [22] is the first one to apply the wavelet collocation method to circuit simulation. That work is extended to behavioral modeling of analog circuits in =-=[23]-=-. The purpose of this paper is to further develop and study the behavioral modeling problem using the spline wavelet collocation method proposed in [24]. The rest of this paper is organized as follows... |

2 |
Non-uniform wavelets on adapted grids for modelling edge singularities
- Oberschmidt, Jacob
- 1997
(Show Context)
Citation Context ... have originally been developed for imaging compression and signal decomposition [15]–[17], and later been employed to compress the integral operator encountered in electromagnetics computations [18]–=-=[20]-=-. The work in [21], [22] is the first one to apply the wavelet collocation method to circuit simulation. That work is extended to behavioral modeling of analog circuits in [23]. The purpose of this pa... |

1 |
Analog behavioral modeling of switched current building block circuits
- Zeng, Wang, et al.
- 2001
(Show Context)
Citation Context ...s and delta-sigma converters, the sampled-data operation can be efficiently modeled by a discrete-time system which consists of a number of ideal unit delay blocks and static nonlinear functions [12]–=-=[14]-=-. Clearly, for all these techniques, nonlinear function approximation is a crucial issue within the overall behavioral modeling procedure.s300 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—II: ANALOG AND ... |

1 |
Numerical Recipes in C The Art of Scientific Computing. city, state/country?: Cambridge Univ
- Press, Flannery, et al.
(Show Context)
Citation Context ...for the switched-current memory cell by SPICE. 15 basis functions are respectively employed and the unknown coefficients for these basis functions are obtained through the least-square error approach =-=[27]-=-. Then, given a sinusoidal input of amplitude 50 A (large signal input), we simulate the switched-current memory cell using these two models and reach the results in Fig. 3. Note that, the behavioral ... |

1 |
Noise reduction system
- Fisher
- 1993
(Show Context)
Citation Context ... of in those regions where high model accuracy is needed. Actually, the idea of nonlinear companding is not a new one, but has already been widely used in communication [29], audio magnetic recording =-=[30]-=- and analog circuit design [31], [32]. Although the mechanism for those three applications and our analog circuit modeling is different, the motivation for companding is the same, i.e., to improve the... |