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An integral approximation method is proposed to extract the via-plate capacitance of an eccentric via in the via hole (anti-pad). An analytical formula is derived for the coaxial capacitance part, which is used as a benchmark to validate the integral approximation method. Furthermore, numerical simulations are also used to validate the method. It is shown that small eccentricity results in only a few percentage increase of the via-plate capacitance, which is helpful in specifying the manufacturing tolerance of via designs.