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.
Y. Zhang et al., "Analytical Evaluation of Via-Plate Capacitance for Multilayer Printed Circuit Boards and Packages," IEEE Transactions on Microwave Theory and Techniques, Institute of Electrical and Electronics Engineers (IEEE), Sep 2008.
The definitive version is available at https://doi.org/10.1109/TMTT.2008.2002237
Electrical and Computer Engineering
Keywords and Phrases
Green's Function in a Coaxial Cavity; Analytical Formula; Multilayer Package/Printed Circuit Board (PCB); Signal Integrity; Via-Holes; Via-Plate Capacitance
Article - Journal
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