MTL Annual Report

Figure 1: Application example: Low-noise amplifier designed in CMOS technology.

During recent years, a great effort has been made by researchers of the Electronic Design Automation community to develop new techniques for automatically generating accurate compact models of nonlinear system blocks. The majority of the existing methods for creating stable reduced models of nonlinear systems, such as ^[1] , require knowledge of the internal structure of the system, as well as access to the exact model formulation for the original system.  Unfortunately, this information may not be easily available if a designer is using a commercial design tool, or it may not even exist if the system to be modeled is a physical fabricated device.

Figure 2: Comparison of the output response from a commercial circuit simulator (solid blue line) and the output response from a stable nonlinear reduced model created with the proposed approach (green dots).

As an alternative approach to nonlinear model reduction, we have proposed a system-identification procedure.  This procedure requires only data available from simulation or measurement of the original system, such as input-output data pairs. If we enforce incremental stability, as shown in ^[2] , it is possible to formulate a semi-definite optimization problem whose solution is a stable nonlinear model that optimally matches the given data pairs from the original system.  In addition, the proposed optimization formulation, explained in detail in ^[3] , allows us to specify completely the complexity of the identified reduced model through the choice of both model order and nonlinear function complexity.

Applications for the proposed modeling technique include analog circuit building blocks (such as operational amplifiers and power amplifiers), MEMS devices, and individual circuit elements (such as transistors).  The resulting compact models may then be used in a higher-level design optimization process of a larger system.   One such example of an analog circuit block is the low-noise amplifier shown in Figure 1; it contains both nonlinear and parasitic elements.  For this example, input-output training data was generated from a commercial circuit-simulator and used to identify a compact nonlinear model.  The output responses of the original system and the identified model are compared in Figure 2.

1. B. Bond and L. Daniel, “Stabilizing schemes for piecewise-linear reduced order models via projection and weighting functions,” Proc. of the IEEE Conference on Computer-Aided Design, San Jose, CA,  Nov. 2007, pp. 860-867. [↩]
2. A. Megretski, “Convex optimization in robust identification of nonlinear feedback,” Proc. of the IEEE Conference on Decision and Control, Cancun, Mexico, Dec. 2008, pp. 1370-1374. [↩]
3. B. Bond, Z. Mahmood, Y. Li, R. Sredojevic, A. Megretski, V. Stojanovic, Y. Avniel, and L. Daniel, “Compact Modeling of Nonlinear Analog Circuits using System Identification via Semi-Definite Programming and Incremental Stability Certification,” Accepted for publication in IEEE Trans. on CAD of Integrated Circuits and Systems, 2010. [↩]