Comparison of Analytical and Numerical Methods of Obtaining Coplanar Capacitance of Microelectrodes for Particulate Matter Detection

This work reports a comparative analysis between the analytical and the finite element modelling, for the calculation of the capacitance of microelectrode-based capacitors in both parallel and coplanar architecture. It shows that the inverse-cosine and the Schwartz-Christoffel methods underestimate the capacitance value of the coplanar plate capacitor. It also shows that the parallel architecture closed form solution and the finite element modelling results agree well in all cases. The work finally compares the effects of design parameter change of the microelectrodes on the capacitance obtained from each technique. It shows that finite element modelling provides the best estimate of the capacitance of a coplanar plate capacitor.