Unified Formulation for Multiple Vias With or Without Circular Pads in High Speed Interconnects

• Published in: IEEE transactions on components, packaging, and manufacturing technology (2011) Vol. 1; no. 8; pp. 1226 - 1233
• Main Authors: Zhonghai Guo, Pan, G. G., Pan, H. K.
• Format: Journal Article
• Language: English
• Published: Piscataway, NJ IEEE 01-08-2011; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Design. Technologies. Operation analysis. Testing; Electronics; Exact sciences and technology; Galerkin's procedure; Green's function methods; image theory; Insertion loss; Integrated circuits; magnetic frill; Magnetic resonance imaging; Mathematical model; Moment methods; Semiconductor electronics. Microelectronics. Optoelectronics. Solid state devices; Bessel function; magnetic frill; Fourier transformation; Sensitivity analysis; integrated circuits; Magnetic model; Parallel architectures; Cylindrical shape; Galerkin's procedure; Interconnection; Integrated circuit; Analytical method; image theory; Software; Galerkin method; High frequency; Matrix equation; Simulator; Analytical solution; Parallel plate
• ISSN: 2156-3950; 2156-3985
• DOI: 10.1109/TCPMT.2011.2149520

A unified full-wave characterization of massive number of vias with or without circular pads is formulated analytically by means of equivalent magnetic frill array model and Galerkin's procedure. The proposed method takes advantage of the parallel-plate structure and employs image theory and Fourier transform to simplify the problem from 3-D configuration into 2-D frame. Based on the cylindrical symmetry with Bessel's functions and addition theorem, the final matrix equation is formulated analytically which can be used immediately for sensitivity analysis in both via dimensions and pad size. As a result, the new method is simple, efficient, and accurate. Numerical examples demonstrate good agreement between our analytical solution and the results obtained by commercial software (high frequency structure simulator) over a frequency range up to 20 GHz.