Efficient DC Analysis of Power Planes Using Contour Integral Method With Circular Elements

Contour integral method, well-known for the analysis of 2-D full-wave effects on power planes, is extended here for the computation of DC resistances of power planes. In particular, circular elements, e.g., vias and antipad holes, are treated using cylindrical modal expansion functions, which leads to a more efficient and accurate calculation than the conventional implementation by the linear discretization. For individual power planes, the method produces a resistor network consisting of only the nodes that are associated with power or ground vias, which can be further employed to formulate solutions for complete multilayer structures. The method is applied to several power plane configurations and results are validated by a 3-D finite element method solver. The efficiency of the extended method is analyzed and a reduction of the number of unknowns by a factor of four for the circular elements can be expected by the modal expansion. Good accuracy can be achieved by including up to the second higher order mode for dense clusters of antipad holes.