Improving accuracy after stability enforcement in the Loewner matrix framework

The Loewner matrix (LM) is a powerful macromodeling technique that uses sampled data in the frequency domain for representing dynamical systems in a descriptor form. As stability cannot be enforced during the construction process, a postprocessing step is required to ensure a stable macromodel, which reduces its accuracy. In this article, two techniques are incorporated and evaluated with the LM framework in this postprocessing phase. The first one is an efficient sign-pole-flipping technique for stability enforcement. The other one is a matrix updating technique applied after the stability enforcement of the model. The proposed approaches are evaluated using data in the scattering parameter form for printed circuit board via interconnects examples and an electromagnetic shielding structure and compared to the state-of-the-art stability enforcement algorithms. For completeness, we will also compare the results with respect to the macromodels created by the vector fitting algorithm. It was found that by the proposed flipping and matrix updating approaches, an error reduction by a factor between 2 and 20 was achieved with respect to the previously reported methods.

Subjects

Circuit stability

Descriptor systems

Eigenvalues and eigenfunctions

Frequency-domain analysis

Loewner matrix (LM)

macromodeling

Matrix decomposition

passive macromodels

Stability criteria

stability enforcement.

Transfer functions

Transmission line matrix methods

DDC Class

600: Technik

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Improving accuracy after stability enforcement in the Loewner matrix framework