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    Item type:Publication,
    Construction of Reciprocal Macromodels in the Loewner Matrix Framework
    Many of the passive interconnect systems that arise in applications for analysis of power and signal integrity (PI/SI) are reciprocal by nature, and the transfer matrices of such systems are characterized by symmetry constraints. Therefore, it is natural to think in using reciprocal macromodels for the representation of reciprocal systems. Reciprocal macromodels do not only represent in a more faithful way the systems in which they are based upon, but given a reciprocal stable macromodel, it is computationally cheaper to find its passivity violations. This work shows how to construct reciprocal descriptor systems macromodels from black box data using the Loewner matrix (LM) framework, and also, it shows that it is possible to enforce stability and passivity in reciprocal stable macromodels, keeping its size and structure. Various examples of printed circuit board-based high-speed links and power delivery networks described by scattering parameters are used to demonstrate the effectiveness of the proposed approach.
    Publicationtype: Journal Article
      33
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    Item type:Publication,
    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.
    Publicationtype: Journal Article
      49
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    Item type:Publication,
    Efficient construction of interconnect passive macromodels through segmented analysis
    In this article, we propose an efficient methodology to obtain passive macromodels of interconnect systems by previously analyzing the building blocks that are combined to form a full macromodel. Instead of applying vector fitting and then enforcing passivity to the full numerical model, we show that it can be more efficient to obtain and enforce passivity on partial macromodels, and then construct the full macromodel through the concatenation of the respective state-space representation matrices.
    Publicationtype: Conference Paper
      155
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    Item type:Publication,
    Evaluation of vector fitting for compact interconnect model representation
    In this work, we present a study on the utilization of vector fitting as a compression technique for storing passive interconnect model data for multiport systems. A canonical transmission line case and three different modeling examples from the literature are explored, where the error is compared as a function of the number of poles used to extract the rational approximation. The compression ratio for data storage with respect to conventional S-Parameter models is discussed as well. It will be shown that the compression ratio is highly dependent of the electrical length of the configuration and the type of response; however, ratios over 5 could be obtained for all the cases when using a number of poles that guarantees a maximum mean relative error below 1%.
    Publicationtype: Conference Paper
      85
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    Item type:Publication,
    Evaluation of concatenation techniques for state-space interconnect macromodels
    In this work, we show that concatenating inter-connect models represented in state-space (descriptor) form, obtained from either the vector fitting algorithm or the Loewner matrix pencil method, can provide results as accurate as usual concatenation using sampled frequency domain data. A PCB-based interconnect is used as an example.
    Publicationtype: Conference Paper
      209