As analog ICs have rapidly evolved from the relatively low complexity of the 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.
