Wavelet Based Nonlinear Companding Method for Analog Circuit Behavioral Modeling

随着模拟集成电路从早期相对较低的复杂性迅速发展到今天的高度复杂性，对更先进的行为建模技术的需求变得越来越迫切。本计画的目的是研究一种以小波为基础的非线性压扩模拟电路行为模型的方法，并进一步发展一个以所获得的模拟电路行为模型为基础的模拟器，以分析与设计现今射频与高速超大规模积体电路中最重要的电路之一锁相回路电路。提出了一种非线性压扩方法来调节小波的奇异性，使小波与电路函数之间实现“平滑”拟合。这种方法将均匀模型误差分布，并显着提高仿真效率在系统级。本课题为小波理论与应用开辟了一个新的研究方向。所研究的非线性压扩方法将使小波变换成为更有效的工程应用基函数。这将为模拟电路行为建模提供新的方法，并大大提高当今混合信号系统分析的CAD工具的效率。 特别是，它将提高效率的设计和分析的锁相环电路，这是一个最具挑战性和高性能的RF和模拟系统设计的时间消耗的任务。

As analog ICs have rapidly evolved from the relatively low complexity ofthe early days to the high sophistication of today, the need for more advanced behavioral modeling techniques has become increasingly urgent. The objective of this project is to investigate a wavelet based nonlinear companding method for the behavioral modeling of analog circuits, and further develops a simulator based on the obtained behavioral models for the analysis and design of PLL circuit, which is one of the most important circuits in today's RF and high-speed VLSI systems. A nonlinear companding method is proposed to regulate the singularity of the wavelets such that a "smooth" fitting can be achieved between the wavelets and the concerned circuit functions. Such an approach will even the model error distribution and significantly improves the simulation efficiency at the system level. This project opens a new research direction for the wavelet theory and application. The investigated nonlinear companding approach will make wavelet a more effective basis function for engineering application. It will lead to new method for analog circuit behavioral modeling and greatly improve the efficiency of today's CAD tools for the analysis of mixed-signal systems. Particularly, it will improve the efficiency of the design and analysis of PLL circuit which is one of the most challenge and timing consuming tasks in high performance RF and analog system design.