A Chebyshev Approximation Method for Microstrip Problems
The quasi-static TEM mode of a microstrip line may be obtained approximately from the solution of Laplace's equation subject to certain boundary conditions. The Green's function approach leads to the solution of a Fredholm integral equation with a logarithmic singularity in the kernel. It...
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| Published in | IEEE transactions on microwave theory and techniques Vol. 23; no. 11; pp. 865 - 870 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
IEEE
01.11.1975
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0018-9480 |
| DOI | 10.1109/TMTT.1975.1128704 |
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| Abstract | The quasi-static TEM mode of a microstrip line may be obtained approximately from the solution of Laplace's equation subject to certain boundary conditions. The Green's function approach leads to the solution of a Fredholm integral equation with a logarithmic singularity in the kernel. It is shown that if the charge distribution on the strip is expanded in terms of Chebyshev polynomials then the integrals arising from the logarithmic term may be evaluated in closed from, and the integral equation may be approximated closely by a set of algebraic equations. The method is applied to numerous open and shielded configurations of strips and couple-strips in the presence of dielectrics. Numerical results are compared with exact results whenever possible and with results from previous authors. Design curves are presented for particular shielded couple-strip configurations. |
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| AbstractList | The quasi-static TEM mode of a microstrip line may be obtained approximately from the solution of Laplace's equation subject to certain boundary conditions. The Green's function approach leads to the solution of a Fredholm integral equation with a logarithmic singularity in the kernel. It is shown that if the charge distribution on the strip is expanded in terms of Chebyshev polynomials then the integrals arising from the logarithmic term may be evaluated in closed from, and the integral equation may be approximated closely by a set of algebraic equations. The method is applied to numerous open and shielded configurations of strips and couple-strips in the presence of dielectrics. Numerical results are compared with exact results whenever possible and with results from previous authors. Design curves are presented for particular shielded couple-strip configurations. |
| Author | Gladwell, G.M.L. Coen, S. |
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| Cites_doi | 10.1109/TMTT.1973.1128043 10.1109/TMTT.1968.1126858 10.1109/PROC.1971.8170 10.1109/TMTT.1954.1124875 10.1109/TMTT.1972.1127866 10.1007/978-3-642-52793-7 10.1109/TMTT.1975.1128632 10.1109/TMTT.1970.1127174 10.1109/TMTT.1955.1124973 10.1049/piee.1968.0008 |
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| References | ref13 ref12 ref15 ref14 stroud (ref4) 1966 fox (ref5) 1968 carrier (ref7) 1966 ref11 ref10 sneddon (ref16) 1966 ref1 (ref6) 1954; 2 palmer (ref8) 1937; 56 itoh (ref17) 1971; 59 ref9 ref3 harrington (ref2) 1968 |
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| Snippet | The quasi-static TEM mode of a microstrip line may be obtained approximately from the solution of Laplace's equation subject to certain boundary conditions.... |
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| SubjectTerms | Approximation methods Boundary conditions Chebyshev approximation Green's function methods Integral equations Kernel Laplace equations Microstrip Polynomials Strips |
| Title | A Chebyshev Approximation Method for Microstrip Problems |
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