Finite element analysis for complex permittivity measurement of a dielectric plate and its application to inverse problem

Hirayama, Koichi; Hayashi, Yasuhiko

doi:10.1002/ecjb.1024.abs

Cited by 8 publications

(6 citation statements)

References 16 publications

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“…Next, both sides of (14) are multiplied by J 1 (ks m ρ) · ρ and integration is performed at the bonding face. Here, region s is integrated from 0 to b in (14), where 'from 0 to b' represents the entire area of the sample under the condition that the electromagnetic field of the analytical region is the only electrical field.…”

Section: Numerical Analysis Of the Analytical Modelmentioning

confidence: 99%

“…A n U n 2π · a ks m 2 − ku n 2 ku n J 0 (ku n a)J 1 (ks m a)· sin(βu n · L) (20) Based on the above, (14)…”

Section: Numerical Analysis Of the Analytical Modelunclassified

“…However, the scope of most previous reports regarding complex permittivity measurement using the cavity resonator method is limited to application for measurement relating to elemental substrates [7][8][9][10][11][12][13]. A procedure for computation using the finite element method (FEM) for the above structure has also been reported [14]. This technique enables high-accuracy computation of eigenvalues and eigenvectors for an analytical model.…”

Section: Introductionmentioning

confidence: 99%

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Mode‐matching analysis of a spit‐circular cavity resonator for measurement of the dielectric constant for film on a substrate

Shibata

Kobayashi

2017

IEEJ Transactions Elec Engng

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In this paper, we apply the mode‐matching technique (eigenmode expansion) to formulate an analytical model for a split cylindrical cavity resonator with a thick ceramic film layer sandwiched between two‐layer alumina substrates. We then compute the resonant frequencies with the TE011 mode with an eigenvalue problem approach using the model formula. The quality factor (Q‐factor) of the resonator is also calculated by applying the perturbation method to the analytical model. The validity of the proposed analytical technique is confirmed by applying this method to the estimation of permittivity of thick films as an inverse problem. Ceramic films (2 µm thickness) were synthesized using a chemical solution method onto 200‐µm‐thick, 50‐mm‐diameter alumina substrates. The complex permittivity of the films was then determined using the TE011 mode split cylindrical cavity resonator in the 10‐GHz band. The extent of the edge effect at a sample insertion space was evaluated by comparing the estimated results through TE wave analysis using the mode‐matching method when the transverse resonance technique and the perturbation method were applied to calculate the resonant frequency and the dielectric Q‐factor. The results obtained indicate that a difference of 0.153% in the permittivity of the alumina substrate causes differences of 6.10 and 3.75% in the measured permittivity and loss tangent, respectively, of 2‐µm‐thick ceramic film with a permittivity of ∼50. Differences in permittivity and loss tangent were more pronounced with thinner films. It was also confirmed that the estimated results for permittivity and the loss tangent values of these ceramic films were affected by the estimated permittivity value of the alumina substrate. © 2017 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

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Section: Numerical Analysis Of the Analytical Modelmentioning

confidence: 99%

“…A n U n 2π · a ks m 2 − ku n 2 ku n J 0 (ku n a)J 1 (ks m a)· sin(βu n · L) (20) Based on the above, (14)…”

Section: Numerical Analysis Of the Analytical Modelunclassified

Section: Introductionmentioning

confidence: 99%

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Mode‐matching analysis of a spit‐circular cavity resonator for measurement of the dielectric constant for film on a substrate

Shibata

Kobayashi

2017

IEEJ Transactions Elec Engng

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“…On the other hand, for nondestructive measurement of a sample without slicing into a specific shape, a method of finding the complex permittivity has been proposed in which a sheet material is inserted into a cavity resonator and the resonant frequency and Q are measured with the sheet extending from the cavity [4][5][6]. However, the method cannot measure the complex permeability at the same time.…”

Section: Introductionmentioning

confidence: 99%

Application of FEM to measurement of permittivity and permeability of lossy sheet using coaxial line

Hayashi

Oba

Hirayama

2005

Electron. Comm. Jpn. Pt. II

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SUMMARYA method is proposed for simultaneous measurement of the complex permittivity and complex permeability of a sheet material by inserting a lossy sheet between two flanged coaxial lines. The TEM mode is incident from a coaxial line and the axially symmetric scalar finite element method is applied for the electromagnetic field without variation in the circumferential direction, to allow the reflection and transmission coefficients to be calculated. Then, a PML is loaded in order to take account of the electromagnetic field leakage in the gap between the flanges. Also, the inverse problem is formulated by using Newton's method. Further, a measurement system is constructed and an experiment is carried out. In addition to confirming the effectiveness of the present measurement method, the range of applicability of the method is studied.

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“…7, both the complex permittivity and complex permeability can be determined from multiple measurements by using a supplemental sample. In another method, an unprocessed sheet is inserted in a cylindrical resonator or a rectangular resonator, the resonance frequency and the Q value are measured in the state with the sheet protruding from the cavity, and then the complex permittivity [8][9][10][11][12][13] is estimated, but the complex permeability cannot be simultaneously determined.…”

Section: Introductionmentioning

confidence: 99%

Simultaneous measurement of permittivity and permeability of lossy sheet using flanged rectangular waveguide

Hayashi

Mishima

Hirayama

et al. 2003

Electron Comm Jpn Pt II

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SUMMARYWe describe a method for simultaneously measuring the complex permittivity and the complex permeability of a lossy sheet that is inserted between two flanged rectangular waveguides. The equivalence principle of the electromagnetic fields is applied to the boundary surfaces between the sheet and the waveguides to derive the integral equations while taking the high-order modes excited at the boundary surfaces into account. Then the method of moments is used in these equations to formulate the direct problem. Newton's method is applied to the inverse problem, and the convergence performance of the solution is examined. Furthermore, the reflection coefficients and the transmission coefficients are measured for some samples, and their complex permittivities and complex permeabilities are estimated from these coefficients.

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Finite element analysis for complex permittivity measurement of a dielectric plate and its application to inverse problem

Cited by 8 publications

References 16 publications

Mode‐matching analysis of a spit‐circular cavity resonator for measurement of the dielectric constant for film on a substrate

Mode‐matching analysis of a spit‐circular cavity resonator for measurement of the dielectric constant for film on a substrate

Application of FEM to measurement of permittivity and permeability of lossy sheet using coaxial line

Simultaneous measurement of permittivity and permeability of lossy sheet using flanged rectangular waveguide

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