Appendix C

Computation of Resonances in the Power Distribution Network of a PCB

This appendix describes three methods for computing resonances in the Power Distribution Network (PDN) of PCBs, which consists of two parallel metallic plates separated by a dielectric substrate, also indicated as power bus. The structure of the PCB used for simulations is the same as that presented in Section 8.2. The first method is based on the cavity model, the second is based on a SPICE equivalent circuit, and the third is based on a 3D model for full-wave numerical electromagnetic codes. The computed results for three points on the PCB are compared for the case of a bare PCB and a PCB populated by decoupling capacitors. It is shown that the three methods provide the same results from a practical viewpoint.

C.1 Cavity Model

The cavity model developed for a microstrip patch antenna can be applied to a PDN having a rectangular power-bus structure, as demonstrated in reference [1]. In this very useful paper, rich in references, it is also demonstrated that the method can be extended to PCBs with arbitrary shape by applying the segmentation method, and a mathematical simplification is given. Herein, the basic mathematical expressions are provided.

The cavity method is based on the following assumptions:

(a) The close proximity between the two ground planes suggests that the E-field has only the z component and the H-field has only the xy components in the region bounded by the power and ground planes. ...

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