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42 DESIGN007 MAGAZINE I JULY 2022 In a uniform cross-section transmission line, a propagating signal sees the same instanta- neous impedance all the way down the line. ere is one value of the instantaneous imped- ance (characteristic impedance) that distin- guishes the transmission line. It depends only on the cross-section of the transmission line and the surrounding material properties. 3D field solvers are not more accurate than 2D field solvers in stackup design. When intercon- nects are uniform transmission lines, a 2D field solver can be more accurate, faster, and much easier to use. Electromagnetic behavior is governed by Maxwell's equations, and all parasitic extrac- tion requires solving some form of these equa- tions. ere are numerous types of field solv- ers but for 2D field solvers, the appropriate form of Maxwell's equations is typically solved by one of two classes of methods. e first uses a differential form of the gov- erning equations and requires the meshing of the entire domain in which the electromag- netic fields reside. Two of the most common approaches in this first class are the finite dif- ference (FD) and finite element (FEM) meth- ods. e resultant linear matrix that must be solved is large but sparse. e second class of methods is integral equation methods which instead require an evaluation of only the sources of the electro- magnetic field. ose sources can be physical quantities, such as the surface charge density or mathematical abstractions resulting from the application of Green's theorem. When the sources exist only on two dimensional surfaces for three dimensional problems, the method is oen called method of moments (MoM), or boundary element method (BEM), as illus- trated in Figure 1. For open boundary condi- tions, the sources of the field exist in a much smaller domain than the fields themselves, and thus the size of the matrix generated by the integral equations methods is much smaller than FEM. Since the BEM results in a smaller solution space, it is considered faster than other 2D solvers. e most effective planning tool for optimiz- ing the stackup of a PCB is a 2D field solver. is tool can be used to predict the character- istic impedance and differential impedance for all topologies, including microstrip, stripline, and dual stripline. e other advantage of a 2D field solver is its ability to include second- order effects such as trace thickness, the influ- ence of solder mask, and mixed prepreg dielec- trics. ese solvers are limited to the numeri- cal accuracy of solving Maxwell's equations, which generally are accurate to better than 1%. erefore a 2D field solver should be used as your design tool of choice. Accuracy is important because of yield. Any inaccuracy in the predicted impedance will shi the center position of the distribution of the PCB fabricators' target impedance. Cus- tomers usually request ±10% tolerance so, with an accuracy of 1%, the field solver is the least of the fabricators' worries. e absolute accuracy of the manufactured product can be evaluated by comparison to measurements on well-characterized test vehicles as well as on production boards. ere are many steps to get the fabrication process right, and the field solver is one of the most reliable links in the chain. For instance, typical results of bet- ter than 3% tolerance (including fabrication variables) are achieved by iCD customers (Figure 2). e field solver is very accurate but if one incorrectly models the structures or incor- When interconnects are uniform transmission lines, a 2D field solver can be more accurate, faster, and much easier to use.