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The Boundary Element Method Quantic’s technology is embedded within the Quantic engine so that engineers can concentrate on their electronics design problems and need not be concerned with the mathematical and algorithmic subtleties. The technology underlying Quantic’s signal integrity (SI) and electromagnetic compatibility (EMC) tools is based upon the integral equation method using Green’s functions. Using this method, conductors and dielectric interfaces are divided into boundary elements over which the free and polarization charges and currents are computed. Quantic uses a higher-order boundary element method (BEM) that yields great accuracy and reliability. Moreover, additional accuracy results because the method directly calculates these surface charges and currents. Parasitic inductance and capacitance is directly related to these surface charges and currents. Finite difference and finite element methods result in fields in space (with artificial boundaries needed to truncate the regions) and numerical differentiation (with significant error introduced) needed to produce the surface charges. It is these charges and currents that are directly related to the computation of these capacitances and inductances that are used for PCB transmission-line modelling. Most competitive SI and EMC tools are based upon the finite element method (FEM). The FEM solves for voltages and currents in the space surrounding the conductor and dielectric structures and requires a calculation grid to be extended well beyond the structures if reasonable accuracy is to be achieved. In order to yield reasonable analysis times, arbitrary limits must be applied to the extension of the grid into space and this results in significant calculation error when the charges and currents are computed. Other FEM techniques – such as “absorbing boundary conditions” – are used in an attempt to compensate for the selection of what is often considered to be an inappropriate technique. Moreover, Quantic appears to be the only supplier to solve the eigen problem to yield modes of propagation with differing velocities. It is for these and for other algorithmic subtleties that Quantic is noted for its robust and accurate algorithms. A recent joint Auburn University/Chrysler Corporation paper (see Appendix) supports the accuracy of Quantic tools. Viz. “ The results of the simulations and measured crosstalk are shown ….. for a line length of 15 inches……. the simulated and measured crosstalk are nearly identical.” “The high accuracy seen in multiple tests was sufficient to conclude that the Quantic Labs tools were reliable.” Some SI tools forsake field analysis altogether and depend entirely on approximate mathematical equations to estimate parasitics. This approach yields very poor accuracy and usually unacceptable results. The boundary element methodologies, used by Quantic, are generally considered to be the most accurate available. Quantic’s PCB Greenfield is acknowledged to provide calculated wave shapes within a few percent of laboratory measurement. Other tools in the market would typically produce errors from 5% to over 10%. While these greater errors may have been acceptable when rise and fall times were of the order of 2 ns to 3 ns, they are not viable with today’s sub-nanosecond rise times and the resulting gigahertz signal harmonic content. The underlying Quantic technology is contained within “The Quantic Engine”. For those mathematically inclined, Quantic uses higher-order boundary elements with the Galerkin method. These methods not only result in excellent accuracy, but also stable matrices and computational efficiency. |
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