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|Capacitance Calculation for Offset Via Structures using an Integral Approximation Approach Based on Finite Element Method|
|Keywords: offset via structure, via-plane capacitance, integral approximation approach based on 2D FEM|
|Via structures are commonly used in high-speed multilayer printed circuit boards, and can have significant impacts on signal and power integrity. Among various parasitics that a via structure introduces, the via-plane capacitances play a critical role at high frequencies. Thus, it is necessary to calculate the capacitance values accurately and efficiently for high-speed circuit designs. For axially symmetric case, the via-plane capacitances can be extracted using a two-dimensional (2-D) finite element method (FEM) on the ρ-z plane in the cylindrical coordinates. However, in practical manufacturing, an offset from the center of the via drill to the center of the pad and anti-pad can be common due to manufacturing tolerances. The offset makes the via geometry axially asymmetric, which is often modeled using the three-dimensional (3-D) FEM or other similar numerical electromagnetic methods. In this paper, a much simpler and more efficient approach is presented to extract the via-plane capacitances for an offset via structure. In this approach, the via drill, pad, and anti-pad are divided into N segments with equally distributed angles from the origin. The bisector of each segment has a set of the pad-stack parameters such as pad radius, anti-pad radius and drill radius. The 2-D FEM method for the concentric case is used for each segment based on its pad-stack parameters as if it extends to a whole circle. Therefore, N different capacitance values are obtained using the 2D FEM method. Then, the average of these N capacitance values is calculated as the final offset via-plane capacitance. This approach is based on the integral approximation. It is found that, when N equals to 10 or larger, the capacitance value extracted using this proposed integral approximation approach is accurate enough compared to the 3-D full wave simulations. Further, it is much faster and consumes much less memory.|
|Hanfeng Wang, Student
Missouri University of Science and Technology