Rational Function Interpolation of Electromagnetic Transfer Functions of High-Speed Interconnect Systems from Discrete Time-Domain and Frequency-Domain Data

We present new methodologies to generate rational function approximations of broadband electromagnetic responses of linear and passive networks of high-speed interconnects, and to construct SPICE-compatible, equivalent circuit representations of the generated rational functions. These new methodologies are driven by the desire to improve the computational efficiency of the rational function fitting process, and to ensure enhanced accuracy of the generated rational function interpolation and its equivalent circuit representation. Toward this goal, we propose two new methodologies for rational function approximation of high-speed interconnect network responses. The first one relies on the use of both time-domain and frequency-domain data, obtained either through measurement or numerical simulation, to generate a rational function representation that extrapolates the input, early-time transient response data to late-time response while at the same time providing a means to both interpolate and extrapolate the used frequency-domain data. The aforementioned hybrid methodology can be considered as a generalization of the frequency-domain rational function fitting utilizing frequency-domain response data only, and the time-domain rational function fitting utilizing transient response data only. In this context, a guideline is proposed for estimating the order of the rational function approximation from transient data. The availability of such an estimate expedites the time-domain rational function fitting process. The second approach relies on the extraction of the delay associated with causal electromagnetic responses of interconnect systems to provide for a more stable rational function process utilizing a lower-order rational function interpolation. A distinctive feature of the proposed methodology is its utilization of scattering parameters. For both methodologies, the approach of fitting the electromagnetic network matrix one element at a time is applied. It is shown that, with regard to the computational cost of the rational function fitting process, such an element-by-element rational function fitting is more advantageous than full matrix fitting for systems with a large number of ports. Despite the disadvantage that different sets of poles are used in the rational function of different elements in the network matrix, such an approach provides for improved accuracy in the fitting of network matrices of systems characterized by both strongly coupled and weakly coupled ports. Finally, in order to provide a means for enforcing passivity in the adopted element-by-element rational function fitting approach, the methodology for passivity enforcement via quadratic programming is modified appropriately for this purpose and demonstrated in the context of element-by-element rational function fitting of the admittance matrix of an electromagnetic multiport.

Searching for knowledge in the belly of the beast: diversity, social equity and the African graduate student mother's experience in US higher education

Diversity has become a buzz word in public discourse and in educational circles. Higher education institutions in the US have increasingly used this word as a cornerstone of their mission statements and have made increasing efforts to attract students from different backgrounds. As part of the increase in diversity efforts among US colleges, is a significant rise in the number of international students. Attracting international students has become a priority for U.S. universities regardless of size or location. This study examines the intersection between the structure of American educational environment and the blended identities of African Graduate Student Mothers. Within the context of contemporary diversity efforts in US educational institutions, this study examines both the structural environments and the socio-cultural constructs that affect the experiences of African graduate student mothers. Based on a qualitative research interview design, a total of nineteen African graduate student mothers at a Mid-Western University in the US were interviewed individually and in groups over a six weeks period. Results from this study show that apart from the difficult and often dehumanizing treatment African student mothers endure from immigration and consular officials in their various countries and ports of entry, they often find themselves at the margins of their various programs and departments with very little support if any. This is because most of them enroll into graduate programs after arriving as dependants of their spouses; a process that does not allow them to negotiate for departmental commitments and support prior to their arrival. Not only do these women face racial discrimination from white professors, staff and fellow students, but they also experience discrimination and hostilities from African Americans and other minority groups who see them as threats to the limited resources that are often set aside for minority groups in such institutions.