Shape sensitivities of capacitances of planar conducting surfaces using the method of moments

In this contribution, a new method is presented to obtain the sensitivities of the capacitance or the charge with respect to a geometrical parameter of planar conducting surfaces. The charge density is found by an integral equation technique. By applying the flux-transport theorem, a new integral equation for the total derivative of the charge with respect to a geometrical parameter is derived from the original electrostatic integral equation for the charge distribution. This new integral equation is solved together with the original integral equation by the method of moments using the same set of basis and test functions. The method is also applied to obtain derivatives for the inductance, impedance and effective dielectric constant. Some simple electrostatic problems are presented, which illustrate the capabilities of our approach. In these examples we also discuss the difference between the geometrical derivatives obtained in this way with geometrical derivatives which are obtained by a central finite difference estimate. Next, some examples of the calculation of geometrical derivatives of capacitance and inductance matrices of multilayer, multiconductor thin microstrip lines are discussed.