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36 The PCB Design Magazine • May 2015 The design feedback method [7] , as illus- trated in Figure 3, is another practical way to model conductor roughness and extract mate- rial properties. The idea here is to design and fabricate a test coupon using the dielectric ma- terial and copper foil roughness you plan on using in the final design. After measuring and cross-sectioning a sample, you would bring this data into a circuit simulator, and then fit the simulation to match insertion loss and phase. You would then use the extracted parameters in your real design simulation and finally design- ing the actual product. Although this method is quite practical and accurate, obtaining good measured data requires considerable effort. First a high level of expertise is required to design the test cou- pon. Next expensive test equipment and skill is required in the measurement and de-embed- ding of the fixture. Finally, considerable exper- tise and know-how is needed to tune the right parameters such that the final model fits both insertion loss and phase. All this adds up to increased time and dollars, and is beyond the scope and resources of many companies. Cannonball Model This leads us to the Cannonball model. Us- ing the concept of cubic close-packing of equal spheres, the radius of the spheres (ai) and tile area (A flat ) parameters for the Huray model can now be determined solely by the roughness parameters published in manufacturers' data sheets. This model is a follow-up research to my recent DesignCon2015 paper titled Practi- cal Method for Modeling Conductor Sur- face Roughness Using Close Packing of Equal Spheres [1] . In that paper I presented a similar model using hexagonal close-packing of equal spheres. Since losses are proportional to the surface area of the roughness profile, the Cannonball model can be used to optimally represent the surface roughness. As illustrated in Figure 4, there are three rows of spheres stacked on a Figure 3: Design feedback method to determine material parameters. CANNONBALL STACk FOR CONDuCTOR ROuGHNESS MODELING continues article