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Title: Extensions to the quasistatic expressions for the line parameters of coplanar waveguide with relatively thick conductors) AuthorRoelvink, Jochem  
Trabelsi, Samir 
Submitted to: National Radio Science Meeting
Publication Type: Abstract only Publication Acceptance Date: 3/9/2012 Publication Date: 4/8/2012 Citation: Roelvink, J.T., Trabelsi, S. 2012. Extensions to the quasistatic expressions for the line parameters of coplanar waveguide with relatively thick conductors. National Radio Science Meeting. Proceedings, p.74. Interpretive Summary: Coplanar 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 methodofmoments, the finiteelementmethod, and quasistatic 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 zerothickness conductors and quasistatic conditions. It is well known that the quasistatic 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 quasistatic analysis for nonzerothickness conductors has been given in (K. C. Gupta, R. Garg and I. J. Bahl, Microstrip lines and slotlines, Artech House 1992). While less accurate than fullwave 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 finiteelementmethod to compute the line parameters of CPW for a range of practical dimensions. These results are compared to the quasistatic 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 nonzerothickness line parameters to the zerothickness line parameters and the fractional line capacitance of the gap region, we develop simple, empirically derived extensions to the quasistatic 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: Coplanar 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 methodofmoments, the finiteelementmethod, and quasistatic 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 zerothickness conductors and quasistatic conditions. It is well known that the quasistatic 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 quasistatic analysis for nonzerothickness conductors has been given in (K. C. Gupta, R. Garg and I. J. Bahl, Microstrip lines and slotlines, Artech House 1992). While less accurate than fullwave 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 finiteelementmethod to compute the line parameters of CPW for a range of practical dimensions. These results are compared to the quasistatic 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 nonzerothickness line parameters to the zerothickness line parameters and the fractional line capacitance of the gap region, we develop simple, empirically derived extensions to the quasistatic 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.
