Explicit Approximations for the Static Capacitance of a Microstrip Patch of Arbitrary Shape

References

• Aleksandrov , V. M. 1964 . The solution of a type of two-dimensional integral equations . [Russian] Priklad. Mat. Mekh. , 28 : 579 – 581 . [Engl. transl. in PMM, Vol. 28, 714-717, 1964]
   Google Scholar
• Aleksandrov , V. M. Asymptotic solution of the contact problem for a thin elastic layer . Russian], Priklad. Mat. Mekh. , 33 61 – 73 . 1969 [Engl. transl. in PMM, Vol. 33, 49-63, 1969]
   Google Scholar
• Alexopoulos , N. G. , Maupin , J. A. and Greiling , P. T. 1980 . Determination of the elec- trode capacitance matrix for GaAs FET's . IEEE Microwave Theory Tech. , MTT-28 : 459 – 466 .
   Google Scholar
• Balaban , P. 1973 . Calculation of the capacitance coefficients of planar conductors on a dielectric surface . IEEE Trans. Circ. Theory , CT-20 : 725 – 731 .
   Google Scholar
• Bedair , S. S. 1985 . Closed form expressions for the static capacitances of some microstrip disk capacitors . Arch. Elek. Ubertragungstech. , 39 : 269 – 272 .
   Google Scholar
• Benedek , P. and Silvester , P. 1972 . Capacitance of parallel rectangular plates separated by a dielectric sheet . IEEE Microwave Theory Tech. , MTT-20 : 504 – 510 .
   Google Scholar
• Bogacheva , L. V. , Budekov , Yu. V. , Krasikova , O. A. , Makhalin , V. N. and Otmakhov , Yu. A. 1985 . Mathematical models of the capacitance of stripline discontinuities. Comparison of calculation methods . [Russian], Radiotekh. Elektron. , 30 : 639 – 646 . [Engl. transl. in Sov. J. Commun. Tech. Electron. , Vol. 30, No. 7, 15-22, 1985]
   Google Scholar
• Borkar , S. and Yang , R. F. H. 1975 . Capacitance of a circular disc for applications in microwave integrated circuits . IEEE Microwave Theory Tech. , MTT-23 : 588 – 591 .
   Google Scholar
• Boulgakov , N. 1904 . Calcul de la capacité électrique d'un condensateur plan de dimen- sions finies . Mem. Acad. Impér. Sci. St.-Pétersbourg , 15 ( 8 ) : 1 – 26 .
   Google Scholar
• Bozdarenko , E. N. , Bublik , V. V. and Simonenko , I. B. 1967 . A method for computing the electrostatic field for a thick layer . [Russian], Izv. VUZ Elektromekhanika , : 503 – 512 .
   Google Scholar
• Braveras , I. , Garbas , H. , Levcenkova , T. and Mejerova , R. 1981 . Capacitance of a circular disk in a microstrip device . [Russian], Litov. Fiz. Sb. , 21 ( No. 2 ) : 61 – 66 . [Engl. transl. in Sov. Phys.-Coll, Vol. 21, No. 2, 42-46, 1981]
   Google Scholar
• Byrd , P. F. and Friedman , M. D. 1971 . Handbook of Elliptic Integrals for Engineers and Scientists , Berlin : Springer-Verlag .
   Google Scholar
• Chew , W. C. and Kong , J. A. 1980 . Effects of fringing fields on the capacitance of a circular microstrip disk . IEEE Microwave Theory Tech. , MTT-28 : 98 – 104 .
   Web of Science ®Google Scholar
• Chew , W. C. and Kong , J. A. 1981 . Asymptotic formula for the capacitance of two oppositely charged discs . Math. Proc. Camb. Phil. Soc. , 89 : 373 – 384 .
   Google Scholar
• Chew , W. C. and Kong , J. A. 1982 . Microstrip capacitance for a circular disk through matched asymptotic expansions . SIAM J. Appl. Math. , 42 : 302 – 317 .
   Web of Science ®Google Scholar
• Clausius , R. 1852 . Ueber die Anordnung der Elektricität auf einer einzelnen sehr dünnen Platte und auf den beiden Belegungen einer Franklin'schen Tafel . Ann. Phys. Chemie , 86 : 161 – 205 .
   Google Scholar
• Clausius , R. 1893 . Théorie Mécanique de la Chaleur, t.2: Théorie Mécanique de l'Electricité , 69 – 70 . Mons : Hector Manceaux .
   Google Scholar
• Coen , S. and Gladwell , G. M. L. 1977 . A Legendre approximation method for the circular microstrip disc problem . IEEE Microwave Theory Tech. , MTT-25 : 1 – 6 .
   Web of Science ®Google Scholar
• Cooke , J. C. 1956 . A solution of Tranter's dual integral equations problem . Quart. J. Mech. Appl. Math. , 9 : 103 – 110 .
   Google Scholar
• Cooke , J. C. 1958 . The circular coaxial disc problem . Z. Angew. Math. Mech. , 38 : 349 – 356 .
   Google Scholar
• Cooke , N. 1963 . Self-inductance of the elliptical loop . Proc. IEE (London) , 110 : 1293 – 1298 .
   Google Scholar
• De Meulenaere , F. and Van Bladel , J. 1977 . Polarizability of some small apertures . IEEE Trans. Antenna Propagat. , AP-25 : 198 – 205 .
   Web of Science ®Google Scholar
• Fabrikant , V. I. 1986 . On the capacity of flat laminae . Electromagnetics , 6 : 117 – 128 .
   Google Scholar
• Farrar , A. and Adams , A. T. 1971 . Computation of lumped microstrip capacities by ma- trix methods-rectangular sections and end effect . IEEE Microwave Theory Tech. , MTT-19 : 495 – 497 .
   Google Scholar
• Farrar , A. and Adams , A. T. 1972 . Matrix methods for microstrip three-dimensional problems . IEEE Microwave Theory Tech. , MTT-20 : 497 – 504 .
   Google Scholar
• Fikhmanas , R. F. and Sh. Fridberg , P. 1974 . Upper and lower bounds on the capacitance of a plane capacitor . [Russian], Zh. Tekh. Fiz. , 44 : 1088 – 1090 . [Engl. transl. in Sov. Phys. Tech. Phys. Vol. 19, 683-684, 1974]
   Google Scholar
• Fuller , J. A. and Chang , D. C. 1970 . On the numerical calculation of capacitance in the presence of edge boundaries . Proc. IEEE , 58 : 490 – 491 .
   Google Scholar
• Gradshteyn , I. S. and Ryzhik , I. M. 1965 . Table of Integrals, Series, and Products , New York : Academic Press .
   Google Scholar
• Grover , F. W. 1946 . Inductance Calculations , New York : Dover .
   Google Scholar
• von Guttenberg , W. 1953 . Uber den genauen Wert der Kapazität des Kreisplattenkon- densators . Ann. Physik , 12 ( 6 ) : 321 – 339 .
   Google Scholar
• Harrington , R. F. 1961 . Time-Harmonic Electromagnetic Fields , New York : McGraw- Hill .
   Google Scholar
• Harrington , R. F. 1968 . Field Computation by Moment Methods , New York : Macmillan .
   Google Scholar
• Hongo , K. and Takahashi , M. 1982 . Evaluation of the integrals occurring in the study of circular microstrip disk . IEEE Microwave Theory Tech. , MTT-30 : 1279 – 1282 .
   Google Scholar
• Hutson , V. 1963 . The circular plate condensor at small separations . Proc. Cambridge Philosophical Society , 59 : 211 – 224 .
   Google Scholar
• von Ignatowsky , W. Kreisscheibenkondensator . Trudy Fiz.-Matem. Inst. Steklov ,
   Google Scholar
• Iossel' , Yu. Ya. , Kochanov , E. S. and Strunskii , M. G. 1969 . Raschet Elektricheskoi Emkosti , Energiya : Leningrad .
   Google Scholar
• Iossel' , Yu. Ya. 1980 . Bounds for the capacitance of isolated conductors . [Russian], Elektrichestvo , No. 8 : 47 – 53 .
   Google Scholar
• Iossel' , Yu. Ya. 1983 . A method for deriving an upper bound for the capacitance of plates . [Russian], Zh. Tekh. Fiz. , 53 : 1665 – 1667 . [Engl. transl. in Soviet Physics Tech. Phys., Vol. 28, 1027-1028, 1983]
   Google Scholar
• Iossel' , Yu. Ya. and Perelman , L. S. 1986 . Calculation of the capacitance of wires . [Russian], Elektrichestvo , No. 9 : 38 – 43 .
   Google Scholar
• Itoh , T. A method for analyzing the characteristics of some lumped elements in microwave integrated circuits . Electron. Common, Japan , 56 ( No. 8 ) 54 – 59 .
   Google Scholar
• Itoh , T. and Mittra , R. 1973 . A new method for calculating the capacitance of a circular disk for microwave integrated circuits . IEEE Microwave Theory Tech. , MTT- 21 : 431 – 432 .
   Google Scholar
• Ivanov , V. N. 1966 . Variational principle for a model of an anisotropically conducting surface . [Russian], Radiotekh. Elektron. , 11 : 1700 – 1702 . [Engl. transl. in Radio Eng. Electron. Phys., Vol. 11, 1491-1493, 1966]
   Google Scholar
• Ivliev , E. A. and Ya. Iossel' , Yu. 1983 . On the computation of capacitance by the sub- area method . [Russian], Elektrichestvo , No. 7 : 65 – 68 . [Engl. transl. in Elec. Technol. USSR, No. 3, 35-43, 1983]
   Google Scholar
• Kazantsev , V. P. 1983 . Variational estimates for the capacitance of conducting plates . [Russian], Zh. Tekh. Fiz. , 53 : 458 – 465 . [Engl. transl. in Soviet Physics Tech. Phys., Vol. 28, 287-290, 1983]
   Google Scholar
• King , R. W. P. 1963 . Fundamental Electromagnetic Theory , New York : Dover .
   Google Scholar
• Kirchhoff , G. 1877 . Zur Theorie des Condensators . Monatsber. Deutsch. Akad. Wiss. Berlin , 42 : 144 – 162 .
   Google Scholar
• Kliot-Dashinskii , M. I. and Minkov , I. M. 1959 . The field of a condenser with circular plates . [Russian], Inxhenerno-Fizich. Zh. , 2 ( No. 6 ) : 104 – 110 .
   Google Scholar
• Kolybel'nikova , O. K. and Simonenko , I. B. 1971 . The capacitance of a conducting disc lying on a dielectric layer . [Russian], Izv. VUZ Elektromekhanika , No. 7 : 720 – 724 .
   Google Scholar
• Kortel , F. 1955 . Contribution á l'etude expérimentale et théorique du champ électro- statique d'un condensateur á armatures rectangularies . Fen Fak. Mec. Istanbul Univ.(ser. C : Astron. Fiz. Kim.) , 20 : 35 – 52 .
   Google Scholar
• Kottler , F. 1927 . “ Elektrostatik der Leiter ” . In Handbuch der Physik , Edited by: Geiger , H. and Scheel , K. Vol. 12 , 349 – 492 . Berlin : Springer .
   Google Scholar
• Kuester , E. F. 1984 . Accurate approximations for a function appearing in the analysis of miccrostrip . IEEE Microwave Theory Tech. , MTT-32 : 131 – 133 .
   Google Scholar
• Kuester , E. F. , Chang , D. C. and Martinson , T. M. 1985; . A note on the edge admit- tance of a wide microstrip patch with electrically thin substrate , Sci. Rept. N. 81 Boulder : Electromagnetics Laboratory, Dept. of Elec. and Comp. Eng., Univ. of Colorado . submitted to IEEE Trans. Antenna Prop. for publication
   Google Scholar
• Lebedev , N. N. 1958 . The electric field at the edge of a plane condenser containing a dielectric . [Russian], Zh. Tekh. Fiz. , 28 : 1330 – 1339 . [Engl. transl. in Soviet Physics Tech. Phys., Vol. 3, 1234-1243, 1958
   Google Scholar
• Leong , M. S. , Kooi , P. S. and Yeo , K. P. 1981a . Determination of circular microstrip disc by Noble's variational method . IEE Proc. , 128 : 306 – 310 . pt. H
   Google Scholar
• Leong , M. S. , Kooi , P. S. and Yeo , K. P. 1981b . Capacitance of a circular disc for ap- plications in microwave integrated circuits . IEE Proc. , 128 : 320 – 332 . pt. H
   Google Scholar
• Leppington , F. and Levine , H. 1970 . On the capacity of the circular disc condenser at small separation . Proc. Cambridge Philosophical Society , 68 : 235 – 254 .
   Google Scholar
• Lewin , L. 1981 . Polylogarithms and Associated Functions , New York : North Holland .
   Google Scholar
• Love , E. R. 1949 . The electrostatic field of two equal circular co-axial conducting discs . Quart. J. Mech. Appl. Math. , 2 : 428 – 451 .
   Web of Science ®Google Scholar
• Magini , R. 1906 . Influenza degli orli sulla capacita elettrostatica di un condensatore . Rend. Accad. Lincei (Cl. Sci. Fis. Mat. Nat.) , 15 ( No. 1 ) : 6 – 14, 270-276, 308- 317,442-450 .
   Google Scholar
• Maxwell , J. C. 1866 . On the viscosity or internal friction of air and other gases . Phil. Trans. Roy. Soc. London , 156 : 249 – 268 .
   Google Scholar
• Maxwell , J. C. 1954 . A Treatise on Electricity and Magnetism , New York : Dover .
   Google Scholar
• Minkov , I. M. 1960 . Electrostatic field of a condenser with a dielectric insert . [Russian], Zh. Tekh. Fiz. , 30 : 1207 – 1209 . [Engl. transl. in Sov. Phys. Tech. Phys., Vol. 5, 1143-1146, 1961]
   Google Scholar
• Mitzner , K. M. 1967 . An integral equation approach to scattering from a body of finite conductivity . Radio Science , 2 : 1459 – 1470 .
   Web of Science ®Google Scholar
• Mosig , J. R. 1977 . Condensateurs circulaires sur microruban . Bull. Assoc. Suisse Electriciens , 68 : 396 – 400 .
   Google Scholar
• Nicholson , J. W. 1924 . The electrification of two parallel circular discs . Phil. Trans. Roy. Soc. London A , 224 : 303 – 369 .
   Google Scholar
• Noble , B. 1958 . The approximate solution of dual integral equations by variational methods . Proc. Edinburgh Math. Soc. , 11 ( 2 ) : 115 – 126 .
   Google Scholar
• Noble , B. 1960 . The numerical solution of the singular integral equation for the charge distribution on a flat rectangular lamina . Symposium on the Numerical Treat- ment of Ordinary Differential Equations, Integral and Integro-differential equations (PICC) . September 20-24 1960 , Rome . pp. 1960 Basel : Birkhauser Verlag .
   Google Scholar
• Nomura , Y. 1941 . The electrostatic problems of two equal parallel circular plates . Proc. Phys. Math. Soc. Japan , 23 ( 3 ) : 168 – 180 .
   Google Scholar
• Okon , E. E. and Harrington , R. F. 1981 . A method of computing the capacitance of flat discs of arbitrary shape . Electromagnetics , 1 : 229 – 241 .
   Google Scholar
• Okoshi , T. 1985 . Planar Circuits for Microwaves and Lightwaves , Berlin : Springer-Verlag .
   Google Scholar
• Ollendorff , F. 1932 . Potentialfelder der Elektrotechnik , Berlin : Springer .
   Google Scholar
• Panych , O. I. 1950 . Approximate boundary conditions in diffraction problems . [Russian], Dokl. Akad. Nauk SSSR , 70 : 589 – 592 .
   Google Scholar
• Panych , O. I. 1953 . Asymptotic expansion of the solution of a boundary problem . [Russian], Matem. Sbornik , 32 : 385 – 406 .
   Google Scholar
• Pólya , G. and Szegö , G. 1951 . Isoperimetric Inequalities in Mathematical Physics , Princeton , NJ : Princeton University Press .
   Google Scholar
• Reitan , D. K. 1959 . Accurate determination of the capacitance of rectangular parallel- plate capacitors . J. Appl. Phys. , 30 : 172 – 176 .
   Web of Science ®Google Scholar
• Reitan , D. K. and Higgins , T. J. 1956 . Accurate determination of the capacitance of a thin rectangular plate . Trans. AIEE, pt. I, Communication and Electronics , 75 : 761 – 766 .
   Google Scholar
• Ruehli , A. E. and Brennan , P. A. 1973 . Efficient capacitance calculations for three- dimensional multiconductor systems . IEEE Microwave Theory Tech. , MTT- 21 : 76 – 82 .
   Google Scholar
• Scott , A. H. and Curtis , H. L. 1939 . Edge correction in the determination of dielectric constant . J. Res. NBS , 22 : 747 – 775 .
   Google Scholar
• Serini , R. 1920 . Teoria del condensatore elettrico a piatti circolari . Rend. Accad. Lincei (Cl. Sci. Fis. Mat. Nat.) , 29 ( No. 2 ) : 34 – 37 . 257 – 261 .
   Google Scholar
• Serini , R. 1922 . Capacita del condensatore a piatti infinitamente sottile . Rend. Accad. Lincei (Cl. Sci. Fis. Mat. Nat.) , 31 ( No. 1 ) : 182 – 184 .
   Google Scholar
• Sharma , A. K. Spectral domain analysis of microstrip resonant structures , New Delhi , , India : Dept. of Electrical Eng., Indian Institute of Technology . Ph.D. Thesis
   Google Scholar
• Sharma , A. K. and Hoefer , W. J. R. 1982 . Spectral domain analysis of hexagonal mi- crostrip resonator . IEEE Microwave Theory Tech. , MTT-30 : 825 – 828 .
   Web of Science ®Google Scholar
• Shaw , S. J. N. 1970 . Circular-disk viscometer and related electrostatic problems . Phys. Fluids , 13 : 1935 – 1947 .
   Google Scholar
• Smythe , W. R. 1968 . Static and Dynamic Electricity , 192 – 194 . McGraw-Hill : New York .
   Google Scholar
• Sneddon , I. N. 1966 . Mixed Boundary Value Problems in Potential Theory , section 8.1 Amsterdam : North-Holland .
   Google Scholar
• Soibel'man , Ya. S. 1981 . An asymptotic formula for the capacitance of a capacitor . [Russian], Dokl. Akad. Nauk SSSR , 258 : 590 – 593 . Engl. transl. in Sov. Phys. Dokl., Vol. 26, 498-500, 1981]
   Google Scholar
• Soibel'man , Ya. S. [summarized in Referativnyi Zhuraal (Matem.), abst. 2B823, 1983]. 1982 . Generalized Leppington-Levine formula for the asymptotic ca- pacitance of a capacitor , [Russian], technical report, Rostov, Gos. Univ., Rostov-na- Donu (VINITI no. 5707-82) [summarized in Referativnyi Zhuraal (Matem.), abst. 2B823, 1983]. ,
   Google Scholar
• Soibel'man , Ya. S. 1984 . Asymptotic capacitance of a condenser with plates of arbitrary shape . [Russian], Sibirsk. Mat. Zh. , 25 ( No. 6 ) : 167 – 181 . [Engl. transl. in Siberian Math. J., Vol. 25, 966-978, 1984]
   Google Scholar
• Tseitlin , L. A. 1946 . On Maxwell's method of geometrical mean distances . C. R. (Dok- lady) Acad.Sci. URSS , 54 : 135 – 136 .
   Google Scholar
• Waldmann , L. 1937 . Zwei Anwendungen der Sommerfeldschen Methode der verzweigten Potentiale . Phys. Z , 38 : 654 – 663 .
   Google Scholar
• Wheeler , H. A. 1982 . A simple formula for the capacitance of a disc on dielectric on a plane . IEEE Microwave Theory Tech. , MTT-30 : 2050 – 2054 .
   Google Scholar
• Wigglesworth , L. A. 1972 . Comments on 'Circular disk viscometer and related electrostatic problems,"' . Phys. Fluids , 15 : 718 – 719 .
   Google Scholar
• Wintle , H. J. and Kurylowicz , S. 1985 . Edge corrections for strip and disc capacitors . IEEE Trans. Instrum. Meas. , IM-34 : 41 – 47 .
   Google Scholar
• Wolff , I. 1973 . Statische Kapazitäten von rechteckigen und kreisförmigen Mikrostrip- Scheibenkondensatoren . Arch. Elek. Ubertragungstech. , 27 : 44 – 47 .
   Google Scholar
• Wolff , I. and Knoppik , N. 1974 . Rectangular and circular microstrip disk capacitors and resonators . IEEE Microwave Theory Tech. , MTT-22 : 857 – 864 .
   Google Scholar