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United States Department of Agriculture

Agricultural Research Service

Research Project: SENSING METHODS & INSTRUMENTATION FOR RAPID DETERMINATION OF MOISTURE CONTENT... AND OTHER QUALITY ATTRIBUTES OF GRAINS, SEEDS, & NUTS

Location: Quality and Safety Assessment Research Unit

Title: Extensions to the quasi-static expressions for the line parameters of coplanar waveguide with relatively thick conductors

Authors
item Roelvink, Jochem
item Trabelsi, Samir

Submitted to: National Radio Science Meeting
Publication Type: Abstract Only
Publication Acceptance Date: March 9, 2012
Publication Date: April 8, 2012
Citation: Roelvink, J.T., Trabelsi, S. 2012. Extensions to the quasi-static expressions for the line parameters of coplanar waveguide with relatively thick conductors. National Radio Science Meeting. Proceedings, p.74.

Interpretive Summary: Co-planar waveguide (CPW) transmission line can be configured as a sensor to measure the complex permittivity of biological materials. By placing a material with unknown permittivity on the CPW and measuring the scattering parameters with a vector network analyzer, the characteristic impedance and effective permittivity of the material/line combination can be determined. In order to calculate the permittivity of the material, expressions that relate the parameters of the CPW to the measured line parameters are necessary. Many techniques have been used to analyze CPW. Some examples of these are:the method-of-moments, the finite-element-method, and quasi-static analyses. In(C. Wen, IEEE Trans. Microwave Theory Tech., 17, 1969) simple closed form expressions for the line parameters of CPW were obtained by a conformal mapping approach, suitable for zero-thickness conductors and quasi-static conditions. It is well known that the quasi-static expressions produce adequate results if both the distance between the two outer conductors and the ratio of the conductor thickness to the gap width are kept small. Furthermore, an approximate extension to the quasi-static analysis for non-zero-thickness conductors has been given in (K. C. Gupta, R. Garg and I. J. Bahl, Microstrip lines and slot-lines, Artech House 1992). While less accurate than full-wave analyses, these approximate expressions are attractive in that they provide a computationally simple means of relating the effective permittivity of the CPW to the permittivity of the material. However, for industrial CPW sensors it is sometimes necessary to use dimensions for which these approximate expressions are not applicable. In this paper, we use a numerical software package based on the finite-elementmethod to compute the line parameters of CPW for a range of practical dimensions. These results are compared to the quasi-static results and it is shown that the approximate extension that accounts for the thickness of the conductors produces considerable error for many practical situations. Using the results from the numerical study and expressions given by (T. Kitazawa and Y. Hayashi, IEE Proc. H, 133, 1986) that relate the non-zero-thickness line parameters to the zerothickness line parameters and the fractional line capacitance of the gap region, we develop simple, empirically derived extensions to the quasi-static expressions that are suitable for CPWs with relatively thick conductors. Results for the line parameters calculated with these expressions are shown to be in good agreement with numerical and experimental results for a wide range of practical CPWdimensions and material permittivities.

Technical Abstract: Co-planar waveguide (CPW) transmission line can be configured as a sensor to measure the complex permittivity of biological materials. By placing a material with unknown permittivity on the CPW and measuring the scattering parameters with a vector network analyzer, the characteristic impedance and effective permittivity of the material/line combination can be determined. In order to calculate the permittivity of the material, expressions that relate the parameters of the CPW to the measured line parameters are necessary. Many techniques have been used to analyze CPW. Some examples of these are:the method-of-moments, the finite-element-method, and quasi-static analyses. In(C. Wen, IEEE Trans. Microwave Theory Tech., 17, 1969) simple closed form expressions for the line parameters of CPW were obtained by a conformal mapping approach, suitable for zero-thickness conductors and quasi-static conditions. It is well known that the quasi-static expressions produce adequate results if both the distance between the two outer conductors and the ratio of the conductor thickness to the gap width are kept small. Furthermore, an approximate extension to the quasi-static analysis for non-zero-thickness conductors has been given in (K. C. Gupta, R. Garg and I. J. Bahl, Microstrip lines and slot-lines, Artech House 1992). While less accurate than full-wave analyses, these approximate expressions are attractive in that they provide a computationally simple means of relating the effective permittivity of the CPW to the permittivity of the material. However, for industrial CPW sensors it is sometimes necessary to use dimensions for which these approximate expressions are not applicable. In this paper, we use a numerical software package based on the finite-elementmethod to compute the line parameters of CPW for a range of practical dimensions. These results are compared to the quasi-static results and it is shown that the approximate extension that accounts for the thickness of the conductors produces considerable error for many practical situations. Using the results from the numerical study and expressions given by (T. Kitazawa and Y. Hayashi, IEE Proc. H, 133, 1986) that relate the non-zero-thickness line parameters to the zerothickness line parameters and the fractional line capacitance of the gap region, we develop simple, empirically derived extensions to the quasi-static expressions that are suitable for CPWs with relatively thick conductors. Results for the line parameters calculated with these expressions are shown to be in good agreement with numerical and experimental results for a wide range of practical CPWdimensions and material permittivities.

Last Modified: 7/22/2014
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