Physical Construction of the Capacitor Probe

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The parallel-plate capacitor was originally designed at Virginia Tech (Al-Qadi et al., 1994a) to characterize materials based on their dielectric properties and is relatively easy to use because of its simplicity, suitability for low RF frequency range measurements, and the convenience of casting or cutting parallel-faced PCC specimens.  The parallel-plate capacitor induces a uniform electric field over a fairly large volume of space.  Therefore, large specimens can be measured with acceptable accuracy.  The custom made fixture allows measurement of different specimen sizes due an adjustable separation between its plates.  An HP-4195A Network/Spectrum Analyzer (Hewlett-Packard Co., Santa Clara, Calif.) was connected to the fixture to measure the capacitor impedance.  Rectangular-shaped specimens, used for this setup, simplified both the design and the casting mold required.

System Design and Setup

Figure 3.1 shows the experimental setup of the parallel-plate capacitor.  The capacitor plates are mounted in a horizontal direction.  Each stress-relieved plate is approximately 460 x 460 x 13 mm and is made of steel.  A supporting rod at each corner fixes the upper plate.  The lower plate is mounted on a threaded rod located at its center, allowing the lower plate to move vertically.  Fifty-mm-long sleeves on the supporting rods maintain the lower plate in a horizontal position, allowing a range of 50 to 130 mm displacement between the two plates.  The PCC is placed at the center of the parallel-plate capacitor.  Carefully cast rectangular PCC blocks allow for complete surface contact with the plates.

Theoretical Background of the Parallel-Plate Capacitor

The measurement techniques are based on planar transmission line principles. The measuring device assumes a plane transmission line in the form of a parallel-plate capacitor configuration.  The specimen under test forms the dielectric media between the plates.  To ensure a uniform electric field in the middle of the plates where the specimen is placed (see Figure 3.2), the length of each plate should be at least three times the largest dimension of the tested specimen to minimize edge diffraction effects (Al-Qadi, 1992).  Thus, the uniform electric field equation can be used (see Equation 2.8).

Parallel-Plate Calibration Standards

The calibration measurements include open, load (matched impedance), and short standards.

Open Calibration Standard

The open calibration standard is simply an air dielectric between the plates of the parallel-plate system.  It is known, however, that using air as an open calibration standard introduces a small amount of error due to the capacitance that is present between the plates.  This error is taken into consideration with simulation performed to find the average value of this capacitance over different values of spacing between the parallel capacitor plates. It would be very difficult to make a high quality open calibration standard for this system due to the system’s physical attributes.  Therefore, an air dielectric is used for this calibration measurement.  Since the capacitance measurement is dependant on the distance between the plates, the distance for each of the calibration standards must be the same as the distance between the plates when measuring the material with unknown dielectric constant.

Load Calibration Standard

The load standard is a 50Ω resistor.  This calibration standard needs to have the ability to adjust for different distances between the plates for the same reason mentioned in section 3.4.1 Open Calibration Standard.  Shown in Figure 3.4 are the designed load calibration standard and the standard’s dimensions.   The standard is constructed of two solid brass pieces (similar to a piston) with six low tolerance three hundred ohm (300Ω) resistors in series with a dielectric medium separating the plates where the resistors are connected.  A brass spring is used to allow adjustment for different plate separations.

Calibration Schemes

When the developed calibration standards were used as the sole standards in the calibration process, the output was excessively noisy.  This noise could be a result of the estimation of the true value of the standards.  Two methods were developed to optimize the calibration scheme.  These two methods involve calibrating the system up to a certain point using HP calibration standards, and then completing the calibration with the developed standards.  The first scheme used the HP standards to calibrate the vector network analyzer directly at the device.  This scheme was found to decrease the noise, but the imaginary portion of the dielectric constant appears to be negative, Figures 3.14 and 3.15.  The second method was to calibrate the vector network analyzer at the end of the cable that connects the analyzer to the parallel-plate test fixture.  This calibration scheme developed the best measurement results and was used as the calibration scheme for future measurements.


The capacitor probe, in design, resembles a parallel-plate capacitor in the sense that it consists of two conducting plates with a known separation.  However, a parallelplate capacitor does not allow for nondestructive in-situ measurements, whereas the capacitor probe does, because its plates are placed on the surface of the tested specimen or structural element.  The capacitor probe, shown in Figure 4.1, was designed as a surface probe to measure the capacitance properties of materials.  From these capacitance measurements, the dielectric constant of the material under test can be found.  The capacitor probe can be implemented as a field-ready measurement tool to characterize the physical properties of PCC based on the materials dielectric constant.  The capacitor probe, therefore, was designed to be small, lightweight, and durable. The plates are manufactured of “flexible” metal sheet (e.g., copper or brass) that allows complete contact when placed on the PCC structural element.  Rubber backing is used for mechanical strength, handling, and protection purposes.

Physical Construction of the Capacitor Probe

Several probes were constructed during this study with each new design more adaptive to a field environment.  The four types of capacitor probes that have been designed and tested will be discussed in this section.

Capacitor Probe Design

An initial capacitor probe was made using two square brass conducting plates (75 x 75 x 5 mm with a 50 mm separation) mounted on a 12-mm-thick sheet of Plexiglas approximately 600 x 600 mm in size.  These plates were mounted to the Plexiglas with brass screws that were inserted into holes in the Plexiglas and fastened with wing nuts.  This capacitor probe was used with the existing Hewlett-Packard Spectrum/Network Analyzer (Model 4195A).  The outer conductor of the coaxial-type connecting cable connected to one of the plates while the inner conductor connected to the other plate. A 600 x 600 x 300 mm wooden box was constructed (using no metallic connectors) and filled with Ottawa sand.  This measurement box was used to determine if the preliminary capacitor probe design could detect changes in the dielectric properties of sand due to insertion and relative placement of inhomogeneities. No attempts were made to measure the actual dielectric constant of the sand or any inserted inhomogeneities, because a calibration system had not been completed. However, it was determined that changes in the dielectric properties of the sand could be detected.

Rubber-Backed Capacitor Probe

A second capacitor probe was built using two 75 mm square brass sheets (0.04 mm thick with a 50 mm separation) as electrodes and a sheet (250 x 125 x 3 mm) of natural rubber sheet as a backing material.  Initially, computer jumper stands and pins were to be used as connectors to attach the capacitor probe to a cable.  However, after unsuccessful attempts to locate a commercial source, DC power adapter plugs and jacks were used as interface connectors.  Later, it was decided that the DC adapter would not be used in a final design because of questions about its suitability: therefore, a change in the connector was made.  The question of the connectors’ suitability came from the fact that the DC adapter was not designed as a connector for a coaxial fixture. The brass electrodes were affixed to the backing material by means of 1.6 mm thick double-sided tape.  This design was very well suited for field use due to the rubber backing’s high durability and flexibility.  The rubber backing and the doublesided tape on this design, as well as the Plexiglas in the initial design, were found to have a minimal effect on the measurements.  The minimal error effect was achieved using an error parameter inserted into the calibration model to compensate for the space above the probe.

Tape-Backed Capacitor Probe

A third capacitor probe, resembling the rubber-backed capacitor probe in appearance, was built using masking tape as a backing material and similar conducting plates (without the double-sided tape) in the same geometric configuration.  By using the masking tape, intentions were to reduce the effects (if any) of the backing material on the measurements and to have a means of fastening the probe to the material under test.  A RCA connector was used to connect the capacitor probe to a cable since the RCA connector is specifically designed to work with a coaxial-type fixture.  The outer conductor of the RCA plug makes solid contact around the entire connector (which was connected to the network analyzer).

Final Capacitor Probe Design

The final capacitor probe design consisted of the rubber backing also 250 x 125 mm in size, but only 0.6 mm thick.  Along with the natural rubber sheet as a backing, copper tape with a conductive adhesive was used as the conducting plates.  The copper tape was also 75 mm wide; however, it could be cut to any desired length to conform to the previous designs.  Using the tape allows easy change of the electrical conducting plates in the field.  The RCA connectors will also be used in any future designs.

Capacitor Probe Plate Configurations

Several capacitor probes were constructed with varying plate size and plate separations to determine whether a change in plate configuration would yield data indicating a change due to the depth of measurement.  In future experimentation, the spacing between the plates will be used to control the depth of the measurement into a specimen.

1.1 Background
1.2 Problem Statement
1.3 Objectives of Research
1.4 Scope of Research
2.1 Portland Cement Concrete
2.2 Deterioration of PCC
2.3 Dielectric Materials
3.1 System Design and Setup
3.2 Theoretical Background of the Parallel-Plate Capacitor
3.3 Parallel-Plate Capacitor Model
3.4 Parallel-Plate Calibration Standards
3.5 Equations Governing the Parallel-Plate System
3.6 Calibration Schemes
4.1 Physical Construction of the Capacitor Probe
4.2 Capacitor Probe Plate Configurations
4.3 Capacitor Probe Calibration Standards
4.4 Equations Governing the Capacitor Probe System
5.1 Specimen Preparation
5.2 Dielectric Constant Measurements
6.1 Discussion of Dat
6.2 Parallel-Plate Capacitor vs. Capacitor Probe
6.3 Final Remarks
7.1 Findings
7.2 Conclusions
Development and Testing of a Capacitor Probe to Detect Deterioration in Portland Cement Concrete

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