Capacitance of a Circular Disk for Applications in Microwave Integrated Circuits (Short Papers)

Borkar, Samarth; Yang, Ruimin

doi:10.1109/tmtt.1975.1128631

Cited by 31 publications

(10 citation statements)

References 9 publications

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“…This expression, relating the current to just the first of the coefficients in the expansion, is analogous to that obtained in other fields where an expansion has been employed to solve a dual integral equation [27,38,39].…”

Section: /33mentioning

confidence: 82%

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Steady-state currents at inlaid and recessed microdisc electrodes for first-order EC′ reactions

Galceran

Taylor

Bartlett

1999

Journal of Electroanalytical Chemistry

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The analytical solutions, approximate expressions and a Finite Element simulation of the steady-state currents arising from the diffusion of a regenerating electroactive species towards a disc electrode, either inlaid in an insulator or recessed, are discussed. The results are valid for any reversible charge transfer, regardless of the applied potential (i.e. including limiting currents) and for equal or unequal diffusion coefficient of the species. For the inlaid disc, derivation of the exact analytical solution, via a reformulation of the diffusion-reaction problem as a dual integral equation that can then be solved using a series of Bessel functions, allows us to assess and review the accuracy of existing approximate expressions. We present 3 new formulae for the steady state current under these conditions, among which we highlight one with an accuracy better than 0.27% over the entire range of rate constants and we show that the accuracy of a recently presented two point Padé approximation (L. Rajendran and M.V. Sangaranarayanan, J. Phys. Chem. B 103 (1999) 1518) is better than 0.01%. The analytical solution also allows us to show that the accuracy of the simulation of the same problem using the Finite Element Method is better than 0.4%. For the recessed disc the exact analytical solution is derived, as an extension of the solution of the inlaid disc, by matching the series representing the concentration of the electroactive species and its derivative. Two approximate expressions are suggested, one of which yields at least 2% accuracy. Concentration profiles for the electroactive species provide physical insight in to the processes involved

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Section: /33mentioning

confidence: 82%

“…When L > 0, θ(r,L) can be expressed in terms of the new unknown coefficients A s , according to eqn. (38). In order to obtain a relationship between a m and A s , we impose the continuity of the derivative of θ at the mouth of the recess [44][45][46], using the second relationship in (A-6) and (38):…”

Section: Discussionmentioning

confidence: 99%

Steady-state currents at inlaid and recessed microdisc electrodes for first-order EC′ reactions

Galceran

Taylor

Bartlett

1999

Journal of Electroanalytical Chemistry

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“…Itoh and Mittra (1973) (9) first obtained the numerical result to the microstrip disc capacitance using Galerkin's method with one basis function. Borkar and Yang (1975)…”

Section: J (D->0) (1-4)mentioning

confidence: 99%

“…The formula he obtained is valid for small disc separation, and the capacitance C is given by 0 ~ ^f + e o alog ^+ e o a [ l o g 8 7 7 -1 ] (d/a->0), where 2d is the separation of the discs, a the radii of the discs, and e 0 is the free-space permittivity. In 1932, Ignatowsky (8) obtained an approximation for the capacitance given by^ ^J ] (d/a^0), (1)(2) which was later shown by Polya and Szego in 1951 (15) to be an asymptotic lower bound. Both Ignatowsky and Polya and Szego used the basis function expansion 0305-0041/81/0000-7930 $03.50 © 1981 Cambridge Philosophical Society method analogous to Galerkin's method, which is a well-known variational procedure related to the Rayleigh-Ritz method (6).…”

Section: Introductionmentioning

confidence: 98%

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Asymptotic formula for the capacitance of two oppositely charged discs

Chew

Kong

1981

Math. Proc. Camb. Phil. Soc.

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Asymptotic formulae for the capacitances of two oppositely charged, identical, circular, coaxial discs and two identical, infinite parallel strips separated by dielectric slabs are derived from the dual integral equations approach. The formulation in terms of dual integral equations using transforms gives rise to relatively simple Green's functions in the transformed space and renders the derivation of the asymptotic formulae relatively easy. The solution near the edge of the plates, a two-dimensional problem previously thought not solvable by the Wiener-Hopf technique, is solved indirectly using the method. Solution of the Helmholtz wave equation is first sought, and the solution to Laplace's equation is obtained by letting the wavenumber go to zero. The solution away from the edge is obtained by solving the dual integral equations approximately. The total charge on the plate is obtained by matching the solution near the edge and away from the edge giving the capacitance.

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Accurate calculation method for the capacitance of generalized circular structures

Tefiku

Yamashita

1992

Int. J. Microw. Mill.‐Wave Comput.‐Aided Eng.

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Capacitance of a Circular Disk for Applications in Microwave Integrated Circuits (Short Papers)

Cited by 31 publications

References 9 publications

Steady-state currents at inlaid and recessed microdisc electrodes for first-order EC′ reactions

Steady-state currents at inlaid and recessed microdisc electrodes for first-order EC′ reactions

Asymptotic formula for the capacitance of two oppositely charged discs

Accurate calculation method for the capacitance of generalized circular structures

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