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.

Air-coupled ultrasonic tomographic imaging of concrete elements

Ultrasonic tomography is a powerful tool for identifying defects within an object or structure. This method can be applied on structures where x-ray tomography is impractical due to size, low contrast, or safety concerns. By taking many ultrasonic pulse velocity (UPV) readings through the object, an image of the internal velocity variations can be constructed. Air-coupled UPV can allow for more automated and rapid collection of data for tomography of concrete. This research aims to integrate recent developments in air-coupled ultrasonic measurements with advanced tomography technology and apply them to concrete structures. First, non-contact and semi-contact sensor systems are developed for making rapid and accurate UPV measurements through PVC and concrete test samples. A customized tomographic reconstruction program is developed to provide full control over the imaging process including full and reduced spectrum tomographs with percent error and ray density calculations. Finite element models are also used to determine optimal measurement configurations and analysis procedures for efficient data collection and processing. Non-contact UPV is then implemented to image various inclusions within 6 inch (152 mm) PVC and concrete cylinders. Although there is some difficulty in identifying high velocity inclusions, reconstruction error values were in the range of 1.1-1.7% for PVC and 3.6% for concrete. Based upon the success of those tests, further data are collected using non-contact, semi-contact, and full contact measurements to image 12 inch (305 mm) square concrete cross-sections with 1 inch (25 mm) reinforcing bars and 2 inch (51 mm) square embedded damage regions. Due to higher noise levels in collected signals, tomographs of these larger specimens show reconstruction error values in the range of 10-18%. Finally, issues related to the application of these techniques to full-scale concrete structures are discussed.