Tianming Chen

Analysis of a concentric coplanar capacitive sensor for nondestructive evaluation of multi-layered dielectric structures

A concentric coplanar capacitive sensor is analyzed for the quantitative characterization of material properties for multi-layered dielectrics. The sensor output signal, transcapacitance CT, is related to the thickness and dielectric constant of each layer of the material under test. Electrostatic Greens functions due to point charges over different dielectric structures are derived utilizing the Hankel transform given the cylindrical symmetry of the proposed sensor. Numerical implementations based on the Greens functions are presented. The sensor electrodes are divided into a number of circular filaments, and the sensor surface charge distribution is then calculated using the method of moments (MoM). From the sensor surface charge, CT is calculated. Numerical calculations on sensor optimization are conducted and show that normalized CT as a function of sensor configuration is determined solely by its own relative dimensions, regardless of the overall dimensions of the sensor. In addition, calculations indicate how the sensor can be optimized for sensitivity to changes in core permittivity of a three-layer test-piece such as an aircraft radome. Benchmark experiment results are provided for one, two-, and three-layer test-pieces and very good agreement with calculated CT is observed. The sensor is also applied to water ingression measurements in a sandwich structure resembling the aircraft radome, in which the water-injected area can be successfully detected from the sensor output signal.

Analysis of Arc-Electrode Capacitive Sensors for Characterization of Dielectric Cylindrical Rods

An arc-electrode capacitive sensor has been developed for quantitative characterization of permittivity of cylindrical dielectric rods. The material property of the cylindrical test piece can be inversely determined from the sensor output capacitance based on a theoretical model. For the modeling process, the electrostatic Greens function due to a point source exterior to a dielectric rod is derived. The sensor output capacitance is numerically calculated using the method of moments (MoM), in which the integral equation is set up based on the electrostatic Greens function. Numerical calculations on sensor configuration optimization are performed. Calculations also demonstrate the quantitative relationship between the sensor output capacitance and the test-piece dielectric and structural properties. Capacitance measurements on different dielectric rods with different sensor configurations have been performed to verify the validity of the numerical model. Very good agreement (to within 3%) between theoretical calculations and measurement results is observed.

Analysis of a capacitive sensor for the evaluation of circular cylinders with a conductive core

A capacitive sensor has been developed for the purpose of measuring the permittivity of a cylindrical dielectric that coats a conductive core cylinder. The capacitive sensor consists of two identical curved patch electrodes that are exterior to and coaxial with the cylindrical test piece. The permittivity of the cylinder is determined from measurements of capacitance by means of a physics-based model. In the model, an electroquasistatic Green function due to a point source exterior to a dielectric-coated conductor is derived, in which the permittivity of the dielectric material may take complex values. The Green function is then used to set up integral equations that relate the unknown sensor surface charge density to the imposed potentials on the electrode surfaces. The method of moments is utilized to discretize the integral equation into a matrix equation that is solved for the sensor surface charge density and eventually the sensor output capacitance. This model enables the complex permittivity of the dielectric coating material, or the geometry of the cylindrical test-piece, to be inferred from the measured sensor capacitance and dissipation factor. Experimental validation of the numerical model has been performed on three different cylindrical test-pieces for two different electrode configurations. Each of the test-pieces has the structure of a dielectric coated brass rod. A good agreement between measured and calculated sensor capacitance (to an average of 7.4%) and dissipation factor (to within 0.002) was observed. Main sources of uncertainty in the measurement include variations in the test-piece geometry, misalignment of sensor electrodes, strain-induced variation in the test-piece permittivity and the existence of unintended air gaps between electrodes and the test-piece. To demonstrate the effectiveness of the sensor, measurements of capacitance have been made on aircraft wires and the permittivity of the insulation inferred. A significant change in permittivity was observed for thermally degraded wires.

Analysis of a concentric coplanar capacitive sensor using a spectral domain approach

Previously, concentric coplanar capacitive sensors have been developed to quantitatively characterize the permittivity or thickness of one layer in multi‐layered dielectrics. Electrostatic Green’s functions due to a point source at the surface of one‐ to three‐layered test‐pieces were first derived in the spectral domain, under the Hankel transform. Green’s functions in the spatial domain were then obtained by using the appropriate inverse transform. Utilizing the spatial domain Green’s functions, the sensor surface charge density was calculated using the method of moments and the sensor capacitance was calculated from its surface charge. In the current work, the spectral domain Green’s functions are used to derive directly the integral equation for the sensor surface charge density in the spectral domain, using Parseval’s theorem. Then the integral equation is discretized to form matrix equations using the method of moments. It is shown that the spatial domain approach is more computationally efficient, ...

Analytical solution for capacitance calculation of a curved patch capacitor that conforms to the curvature of a homogeneous cylindrical dielectric rod

This Letter presents an analytical expression for the capacitance of a curved patch capacitor whose electrodes conform to the curvature of a long, homogeneous, cylindrical dielectric rod. The capacitor is composed of two infinitely long curved electrodes, symmetrically placed about a diameter of the cylinder cross-section. The resulting capacitance per unit length depends on both the dielectric properties of the material under test and the capacitor configuration. A practical capacitance measurement is also presented, with appropriately guarded finite electrodes. Very good agreement between measured and theoretically predicted capacitances were observed, to within 2.4 percent. The analytical result presented in this Letter can be applied for extremely rapid evaluation of rod permittivity from measured capacitance.

Design of interdigital spiral and concentric capacitive sensors for materials evaluation

This paper describes the design of two circular coplanar interdigital sensors with i) a spiral interdigital configuration and ii) a concentric interdigital configuration for the nondestructive evaluation of multilayered dielectric structures. A numerical model accounting for sensor geometry, test-piece geometry and real permittivity, and metal electrode thickness has been developed to calculate the capacitance of the sensors when in contact with a planar test-piece comprising up to four layers. Compared with a disk-and-ring coplanar capacitive sensor developed previously, the interdigital configurations are predicted to have higher signal-to-noise ratio and better accuracy in materials characterization. The disk-and-ring configuration, on the other hand, possesses advantages such as deeper penetration depth and better immunity to lift-off variations.