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.

An examination of factors that influence entrepreneurial intention of high school students in Kenya

Abstract Considerable research has been carried out on entrepreneurship in efforts to understand its incidence in order to influence and maximize its benefits. Essentially, researchers and policy makers have sought to understand the link between individuals and business creation: Why some people start businesses while others do not. The research indicates that personality traits, individual background factors and association of entrepreneurship with career choice and small business enterprises, cannot sufficiently explain entrepreneurship. It is recognized that entrepreneurship is an intentional process and based on Ajzen’s Theory of Planned Behavior, the most defining characteristic of entrepreneurship is the intention to start a business. The purpose of this study was, therefore, to examine factors that influence entrepreneurial intention in high school students in Kenya. Specifically, the study aimed at determining if there were relationships between the perceptions of desirability, and feasibility of entrepreneurship with entrepreneurial intention of the students, identifying any difference in these perceptions with students of different backgrounds, and developing a model to predict entrepreneurship in the students. The study, therefore, tested how well Ajzen’s Theory of Planned Behavior applied in the Kenyan situation. A questionnaire was developed and administered to 969 final year high school students at a critical important point in their career decision making. Participants were selected using a combined convenience and random sampling technique, considering gender, rural/urban location, cost, and accessibility. Survey was the major method of data collection. Data analysis methods included descriptive statistics, correlation, ANOVA, factor analysis, effect size, and regression analysis. iii The findings of this study corroborate results from past studies. Attitudes are found to influence intention, and the attitudes to be moderated by individual background factors. Perceived personal desirability of entrepreneurship was found to have the greatest influence on entrepreneurial intention and perceived feasibility the lowest. The study findings also showed that perceived social desirability and feasibility of entrepreneurship contributed to perception of personal desirability, and that the background factors, including gender and prior experience, influenced entrepreneurial intention both directly and indirectly. In addition, based on the literature reviewed, the study finds that entrepreneurship promotion requires reduction of the high small business mortality rate and creation of both entrepreneurs and entrepreneurial opportunities (Kruger, 2000; Shane & Venkataraman, 2000). These findings have theoretical and practical implications for researchers, policy makers, teachers, and other entrepreneurship practitioners in Kenya.