Effect of surface perturbations on capacitors

Abstract

Capacitors are fundamental components in electronic and pulsed-power systems. For parallel-plate capacitors, the well-known textbook formula for capacitance is typically used directly in various applications by assuming flat and smooth electrodes for the capacitors. However, real capacitors often exhibit surface perturbations that can significantly affect their performance. In this work, we analytically investigate the effect of a trapezoidal surface perturbation on the electrode surface using Schwarz–Christoffel conformal mapping. This method allows us to compute the modified electric field, the surface charge, and the resulting capacitance. The effect of perturbation properties on the capacitance and their scaling dependences are analyzed systematically. In particular, the subtle effects of the trapezoid angle on capacitance are examined. The theoretical results are validated against finite-element method simulations. The general results show that perturbations that reduce the effective vacuum (or dielectric) region (i.e., minimize the effective gap distance) between the anode and cathode lead to the largest enhancement in capacitance, with important implications for high-energy-density capacitive systems.