Abstract-Mutual external inductance (MEI) associated with fringing magnetic fields in planar transmission lines is a cause of socalled "ground plane noise", which leads to radiation from printed circuit boards in high-speed electronic equipment. Herein, a Method of Edge Currents (MEC) is proposed for calculating the MEI associated with fringing magnetic fields that wrap the ground plane of a microstrip line. This method employs a quasi-magnetostatic approach and direct magnetic field integration, so the resultant MEI is frequencyindependent. It is shown that when infinitely wide ground planes are cut to form ground planes of finite width, the residual surface currents on the tails that are cut off may be redistributed on the edges of the ground planes of finite thickness, forming edge currents. These edge currents shrink to filament currents when the thickness of the ground plane becomes negligible. It is shown that the mutual external inductance is determined by the magnetic flux produced by these edge currents, while the contributions to the magnetic flux by the currents from the signal trace and the finite-size ground plane completely compensate each other. This approach has been applied to estimating the mutual inductance for symmetrical and asymmetrical microstrip lines.

Abstract-The Method of Edge Currents (MEC) proposed in our previous paper [1] is applied herein for calculating the mutual external inductance associated with fringing magnetic fields that wrap ground planes of a stripline structure. This method employs a quasi-static approach, image theory, and direct magnetic field integration. The resultant mutual external inductance is frequency-independent. The approach has been applied to estimating mutual inductance for both symmetrical and asymmetrical stripline structures. Offset of the signal trace from the centered position both in horizontal and vertical directions is taken into account in asymmetrical structures. The results are compared with numerical simulations using the CST Microwave Studio Software.

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PCB-PDN design remains a challenge with the reducing noise margins. One aspect of PDN design is finding the number of decoupling capacitors required for each power rail. As more capacitors are added, the mid frequency equivalent inductance in the impedance of the PCB-PDN converges to a minimum value for each placement pattern. This convergence is studied for different placement patterns to find the least number of capacitors required to satisfy a certain convergence criteria. A first principle method is used resonant cavity model for the analysis.

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