{"id":3008,"date":"2011-06-27T15:17:28","date_gmt":"2011-06-27T15:17:28","guid":{"rendered":"https:\/\/mtlsites.mit.edu\/annual_reports\/2011\/?p=3008"},"modified":"2011-07-19T19:31:30","modified_gmt":"2011-07-19T19:31:30","slug":"compact-modeling-of-non-linear-analog-circuits-using-system-identification-via-semidefinite-programming-and-incremental-stability-certification","status":"publish","type":"post","link":"https:\/\/mtlsites.mit.edu\/annual_reports\/2011\/compact-modeling-of-non-linear-analog-circuits-using-system-identification-via-semidefinite-programming-and-incremental-stability-certification\/","title":{"rendered":"Compact Modeling of NON-LINEAR Analog Circuits Using System Identification via Semidefinite Programming and Incremental Stability Certification"},"content":{"rendered":"

During recent years, researchers of the Electronic Design Automation community have made a great effort to develop new techniques for automatically generating accurate compact models of NON-LINEAR system blocks. The majority of the existing methods for creating stable reduced models of nonlinear systems, such as [1<\/a>] <\/sup>, require knowledge of the internal structure of the system, as well as access to the exact model formulation for the original system.\u00a0 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.<\/p>\n

As an alternative approach to nonlinear model reduction, we have proposed a system-identification procedure.\u00a0 This procedure requires only data available from simulation or measurement of the original system, such as input-output data pairs.\u00a0 By enforcing incremental stability, as shown in [2<\/a>] <\/sup>, 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.\u00a0 In addition, the proposed optimization formulation, explained in detail in [3<\/a>] <\/sup>, allows users to specify completely the complexity of the identified reduced model through the choice of both model order and nonlinear function complexity.<\/p>\n

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.\u00a0 The resulting compact models may then be used in a higher-level design optimization process of a larger system.\u00a0\u00a0 One such example of an analog circuit block is the low-noise amplifier shown in Figure 1; it contains both nonlinear and parasitic elements.\u00a0 For this example, input-output training data was generated from a commercial circuit-simulator and used to identify a compact nonlinear model.\u00a0 The output responses of the original system and the identified model are compared in Figure 2.<\/p>\n\n\t\t