S-parameter extraction of passive sub-circuits using computed tomography scans and measured substrate material parameters

Signal Integrity Model Extraction Based on Computed Tomography Scans—Analysis of the Required Voxel Resolution

“…Appropriate methods are methods based on marching cubes [16] or the Canny edge detector [10], [17] or methods based on thinning algorithms [18], which extract the skeleton of thin structures (e.g., bond wires). These methods have different advantages and disadvantages that affect the required computing time and memory consumption for the extraction process.…”

“…The method to extract objects used in [9] and [10] is based on the Canny edge detector [17] and has advantages when extracting planar structures like striplines of multilayer boards. For reconstructing structures of multilayer boards, it is often sufficient to extract the copper layers and substrate layers as 2.5-D objects, which means that not the entire voxel dataset is needed.…”

“…This is because the required transmission lines can be produced on the same panel as the structure to be analyzed and they can be measured without an expensive measurement setup. In [10], the use of the two microstrip line method [24] for measuring the permittivity of the board substrate for simulation model has been shown. Fig.…”

“…Qualitative analyses of the accuracy of the extracted models have already been presented in [13] and [10] for planar transmission lines and bond wires and in [9] for a 90 • hybrid coupler as a more complex RF device. An example of such an analysis, which has been presented in [13], is given in Figs.…”

“…After replacing the uncertainty u(x i ) in (3) by the derived uncertainty for the CT length measurement and u c (y) by the expanded uncertainty of the characteristic impedance U (Z L ), we can use (3) and (9) to obtain Δs by (10). Using this equation, the minimal required voxel resolution for a stripline model can be determined.…”