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.

Immune function, gene expression, blood indices and performance in transition dairy cows affected by diet and inflammation

The transition period is associated with the peak incidence of production problems, metabolic disorders and infectious diseases in dairy cows (Drackley, 1999). During this time the cow’s immune system seems to be weakened; it is apparent that metabolic challenges associated with the onset of lactation are factors capable of affecting immune function. However, the reasons for this state are not entirely clear (Goff, 2006). The negative energy balance associated with parturition leads to extensive mobilization of fatty acids stored in adipose tissue, thus, causing marked elevations in blood non-esterified fatty acids (NEFA) and B-hydroxybutyrate (BHBA) concentrations (Drackley et al., 2001). Prepartal level of dietary energy can potentially affect adipose tissue deposition and, thus, the amount of NEFA released into blood and available for metabolism in liver (Drackley et al., 2005). The current feeding practices for pregnant non-lactating cows has been called into question because increasing amounts of moderate-to-high energy diets (i.e. those more similar to lactation diets in the content of energy) during the last 3 wk postpartum have largely failed to overcome peripartal health problems, excessive body condition loss after calving, or declining fertility (Beever, 2006). Current prepartal feeding practices can lead to elevated intakes of energy, which can increase fat deposition in the viscera and upon parturition lead to compromised liver metabolism (Beever, 2006, Drackley et al., 2005). Our general hypothesis was that overfeeding dietary energy during the dry period, accompanied by the metabolic challenges associated with the onset of lactation would render the cow’s immune function less responsive early postpartum. The chapters in this dissertation evaluated neutrophil function, metabolic and inflammation indices and gene expression affected by the plane of dietary energy prepartum and an early post-partum inflammatory challenge in dairy cows. The diet effect in this experiment was transcendental during the transition period and potentially during the entire lactation. Changes in energy balance were observed and provided a good model to study the challenges associated with the onset of lactation. Overall the LPS model provided a consistent response representing an inflammation incident; however the changes in metabolic indices were sudden and hard to detect in most of the cases during the days following the challenge. In general overfeeding dietary energy during the dry period resulted in a less responsive immune function during the early postpartum. In other words, controlling the dietary energy prepartum has more benefits for the dairy cow during transition.