Analytical Evaluation of Via-Plate Capacitance for Multilayer Printed Circuit Boards and Packages

• Published in: IEEE transactions on microwave theory and techniques Vol. 56; no. 9; pp. 2118 - 2128
• Main Authors: Yaojiang Zhang, Fan, J., Selli, G., Cocchini, M., de Paulis, F.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.09.2008; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Analytical formula; Applied sciences; Boards; Capacitance; Coaxial components; Conductors; Design. Technologies. Operation analysis. Testing; Diffraction, scattering, reflection; Electronic equipment and fabrication. Passive components, printed wiring boards, connectics; Electronics; Exact sciences and technology; Green's function in a coaxial cavity; Green's function methods; Holes; Integrated circuits; Magnetic analysis; Magnetic multilayers; Mathematical analysis; Mathematical models; multilayer package/printed circuit board (PCB); Multilayers; Nonhomogeneous media; Packaging; Printed circuit boards; Printed circuits; Radiocommunications; Radiowave propagation; Reflection; Semiconductor electronics. Microelectronics. Optoelectronics. Solid state devices; signal integrity; Telecommunications; Telecommunications and information theory; via-holes; via-plate capacitance; Walls; multilayer package/printed circuit board (PCB); Frequency dependence; via-plate capacitance; Analytical formula; Printed circuit board; Quasi static theory; Numerical method; Green function; Wave reflection; via-holes; Perfectly matched layer; Cylindrical wave; Cavity; Electronic packaging; Green's function in a coaxial cavity; Capacitance; Printed circuit; Multilayered printed circuit board; Signal integrity; Reflectance; Parallel plate; Via hole
• ISSN: 0018-9480; 1557-9670
• DOI: 10.1109/TMTT.2008.2002237

The via-plate capacitance for a via transition to a multilayer printed circuit board is evaluated analytically in terms of higher order parallel-plate modes. The Green's function in a bounded coaxial cavity for a concentric magnetic ring current is first derived by introducing reflection coefficients for cylindrical waves at the inner and outer cavity walls. These walls can be perfect electric conductor (PEC)/perfect magnetic conductor(PMC) or a nonreflective perfectly matched layer. By further assuming a magnetic frill current on the via-hole in the metal plate, an analytical formula is derived for the via barrel-plate capacitance by summing the higher order modes in the bounded coaxial cavity. The convergence of the formula with the number of modes, as well as with the radius of the outer PEC/PMC wall is discussed. The analytical formula is validated by both quasi-static numerical methods and measurements. Furthermore, the formula allows the investigation of the frequency dependence of the via-plate capacitance, which is not possible with quasi-static methods.