Efficient method for the capacitance calculation of circularly symmetric via in multilayered media

Rigorous and simplified models for the capacitance of a circularly symmetric via

“…In addition, simplified approximate formulas for capacitance are developed from the numerical data which account for conductor thickness and cone angle. Use of these simplified formulas allows one to approximate the conical post with a straight cylinder of predetermined radius, thus enabling one to take advantage of more efficient techniques such as those of [8], [9]. Regardless of the method, the accurate modeling of thick conductors increases the number of unknowns and, therefore, the computation time.…”

“…In [7], the via capacitance is determined from an integral-equation method whose Green's function accounts for the dielectric. In [8], [9], Laplace's equation is solved by separation of variables and domain decomposition to account for a multilayered dielectric.…”