An improved parallel-plate capacitor apparatus for the estimation of dielectric constants of solid materials

Abstract

In this paper, we present the design and implementation of a modified parallel-plate capacitor (PPC) and its mathematical derivation, which may well be incorporated as a challenging problem in physics textbooks covering topics on capacitance and dielectrics. The dielectric material under test (MUT) fills the empty space between the plates of the PPC, and a very thin layer of air is trapped between the uneven surfaces of the metallic capacitor plates and the MUT. It has been reported in the literature (Grove T T et al 2005 Am. J. Phys. 73 52–56; Grove T T and Masters M F 2009 The Physics Teacher 47 312) that these air pockets lead to an error in the measured value of the dielectric constant of the MUT. The present work gives a prescription to estimate this value in a smart way so as to bypass the effect of a trapped thin air layer, and it leads to measured values of the dielectric constant similar to what has been reported in the literature (PLEXIGLAS®, Altuglas International and Arkema Inc., 2006 www.altuglasint.com). To the best of our knowledge, this paper is the first to present the design and implementation of a PPC cell of this kind to study dielectric constants. The topic can reasonably be taught in undergraduate laboratory physics coursework.

Extraction of the Complex Relative Permittivity from the Characteristic Impedance of Transmission Line by Resolving Discontinuities

“…Table 3 shows the excellent contribution of the new approach when Equation ( 36) is used. However, errors can be numerous when utilizing Equation (7). We finally note that the error levels in both techniques (use of the eigenvalue and the new approach) are identical.…”

“…This is because the correction causes the gap observed in the final results in the propagation constant, but not in the characteristic impedance. For instance, taking off Z v in Equation (7), and according to the Brews equation for Q-TEM mode, as mentioned in [47]:…”

“…Six main techniques constitute these two families. Among them are methods using two parallel plates (capacitor method) [7,8], inductors [9,10], free-space [11][12][13][14], probes [15][16][17][18], transmission lines [9,[19][20][21], and resonant cavities [22][23][24]. In these examples, adapting the technique to the material and the scanned frequency seems correct, as each method has its advantages and disadvantages.…”

A modified methodology for dielectric constant measurement of an arbitrary-shaped sheet by using capacitance technique

“…The arrangement of dielectric constant and impedance analyzer measurements can be performed at low frequencies when the wavelength is much larger than the sample dimensions. Recently, Riaz et al [12] reported an idea about a modified capacitor structure that offers a remedy to determine the dielectric constant of a dielectric MUT, placed in between its metal plates, in an elegant way to bypass the effect of a very delicate trapped thin air layer. The general shape of the arrangement that is used in this paper (i.e.…”

“…The general shape of the arrangement that is used in this paper (i.e. parallel plate capacitor with circular electrodes, four screws, and plastic spacers) is similar to the apparatus described by Riaz et al [12]. However, this method does not take the effect of fringing fields into consideration and needs to accurately consider the impact of screws in the calculations.…”