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.

Planning across differences: collaborative planning processes for the California Central Valley's future

This dissertation examines the intersections between difference, participation, and planning processes. Rooted in scholarly conversations about deliberative democracy, collaborative planning, and nonprofit organizations in civil society, this research considers how planning practitioners can better plan across difference. Through case study research, this dissertation examines a collaborative planning process conducted by a nonprofit organization. Unlike more conventional participatory planning processes, the organization utilized scenario planning. Exercising their position in civil society, participation in the process was not open to all community members and the organization carefully selected a diverse set of participants. Findings from this research project indicate that this process, by moving away from a strict definition of rational discourse, focusing on multiple futures as opposed to a single, utopian future, and deliberately bringing together a broad cross-section of community members allowed for participants to speak freely and learn from one another’s perspectives and experiences. Experiences of process participants also demonstrate the degree to which cultural backgrounds shape participation in and expectations of planning processes. While there remains no clear answer in how to represent and respond to cultural differences in planning processes, the experiences of the organization, program staff, and community participants help scholars and practitioners move closer to planning across differences.