This paper proposes a novel paradigm to generate a parameterized model of the response of linear circuits with the inclusion of worst case bounds. The methodology leverages the so-called Taylor models and represents parameter-dependent responses in terms of a multivariate Taylor polynomial, in conjunction with an interval remainder accounting for the approximation error. The Taylor model representation is propagated from input parameters to circuit responses through a suitable redefinition of the basic operations, such as addition, multiplication or matrix inversion, that are involved in the circuit solution. Specifically, the remainder is propagated in a conservative way based on the theory of interval analysis. While the polynomial part provides an accurate, analytical and parametric representation of the response as a function of the selected design parameters, the complementary information on the remainder error yields a conservative, yet tight, estimation of the worst case bounds. Specific and novel solutions are proposed to implement complex-valued matrix operations and to overcome well-known issues in the state-of-the-art Taylor model theory, like the determination of the upper and lower bound of the multivariate polynomial part. The proposed framework is applied to the frequency-domain analysis of linear circuits. An in-depth discussion of the fundamental theory is complemented by a selection of relevant examples aimed at illustrating the technique and demonstrating its feasibility and strength.

Combined Parametric and Worst Case Circuit Analysis via Taylor Models / Trinchero, R.; Manfredi, P.; Ding, T.; Stievano, IGOR SIMONE. - In: IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS. I, REGULAR PAPERS. - ISSN 1549-8328. - STAMPA. - 63:7(2016), pp. 1067-1078. [10.1109/TCSI.2016.2546389]

Combined Parametric and Worst Case Circuit Analysis via Taylor Models

Trinchero, R.;Manfredi, P.;STIEVANO, IGOR SIMONE
2016

Abstract

This paper proposes a novel paradigm to generate a parameterized model of the response of linear circuits with the inclusion of worst case bounds. The methodology leverages the so-called Taylor models and represents parameter-dependent responses in terms of a multivariate Taylor polynomial, in conjunction with an interval remainder accounting for the approximation error. The Taylor model representation is propagated from input parameters to circuit responses through a suitable redefinition of the basic operations, such as addition, multiplication or matrix inversion, that are involved in the circuit solution. Specifically, the remainder is propagated in a conservative way based on the theory of interval analysis. While the polynomial part provides an accurate, analytical and parametric representation of the response as a function of the selected design parameters, the complementary information on the remainder error yields a conservative, yet tight, estimation of the worst case bounds. Specific and novel solutions are proposed to implement complex-valued matrix operations and to overcome well-known issues in the state-of-the-art Taylor model theory, like the determination of the upper and lower bound of the multivariate polynomial part. The proposed framework is applied to the frequency-domain analysis of linear circuits. An in-depth discussion of the fundamental theory is complemented by a selection of relevant examples aimed at illustrating the technique and demonstrating its feasibility and strength.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2645588
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