MTL Annual Research Report 2012

Compact Modeling of “Nonlinear” Analog Circuits using System Identification with Incremental Stability Certification

During recent years, researchers in the Electronic Design Automation community have made great efforts to develop new techniques to automatically generate 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 may not even exist if the system to be modeled is a physical fabricated device.

As an alternative approach to the standard nonlinear model reduction, we propose a system-identification procedure.  This procedure requires only data available from simulation or measurement of the original system, such as input-output training data pairs. However, simply fitting an arbitrary nonlinear model to the training data does not guarantee that the solution is a valid dynamic model. A valid dynamic model must be stable when evaluated in a time domain simulator. The challenge is to search for a nonlinear dynamic model that simultaneously satisfies the stability requirement and optimally matches the training data. We have managed to formulate such problem as a semi-definite convex optimization problem. The proposed optimization formulation, explained in detail in ^[2] as an efficient extension of ^[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, 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. Figure 2 compares the output responses of the original system and the identified model.

1. B. Bond and L. Daniel, “Stabilizing schemes for piecewise-linear reduced order models via projection and weighting functions,” in Proc. of the IEEE Conference on Computer-Aided Design, San Jose, CA, Nov. 2007, pp. 860-867. [↩]
2. 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 demi-definite programming and incremental stability certification,” IEEE Trans. on CAD of Integrated Circuits and Systems, vol. 29, issue 8, pp. 1149-1162, Aug. 2010. [↩]
3. A. Megretski, “Convex optimization in robust identification of nonlinear feedback,” in Proc. of the IEEE Conference on Decision and Control, Cancun, Mexico, Dec. 2008, pp. 1370-1374. [↩]