Modeling of a metallic truncated cone for electromagnetic capacitive sensors

This paper presents an electromagnetic modeling of a grounded metallic truncated cone to be used for calibration purposes of a microwave imaging system. The basic idea is to demonstrate the equivalence between the cone and a cylinder having a suitable radius, in order to simplify the computation of its capacity with respect to ground. A mathematical expression for the capacitance of the uniform cylinder is presented, and its validity is confirmed by comparing the data provided by this formula with numerical values given by a commercial simulator. Starting from this analytic result, the model of the cone is presented, and a procedure for the choice of the cylinder radius is discussed in detail. This methodology can be applied to calculate the contribution to the stray capacitance of a metallic tip used for scanning probe microscopy, and specifically for microwave sensing applications. In particular, the capacitance due to the conic part of the probe can be quantified, an operation that is usually a difficult task when trying to separate it from contribution of the experimental setup. In our opinion, this issue is very important to improve the accuracy of system calibration in the scanning microwave microscopy technique.