Analytical IC Metal-Line Capacitance Formulas (Short Papers)

Chang, W. H.

doi:10.1109/tmtt.1976.1128917

Cited by 113 publications

(25 citation statements)

References 7 publications

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“…Since the numerator and the denominator in l 31 , l 32 , l 33 , and l 34 grow with the same rate with respect to the state variables, those functions are all uniformly bounded. Therefore we have for |z 3 …”

Section: Appendix B: Iss Property Of Closed-loop Error Dynamicsmentioning

confidence: 99%

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A new formulation of fringing capacitance and its application to the control of parallel-plate electrostatic micro actuators

Hosseini

Zhu

Peter

2007

Analog Integr Circ Sig Process

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Though the effect of fringing field in electrostatic parallel-plate actuators is a well-understood phenomenon, the existing formulations often result in complicated mathematical models from which it is difficult to determine the deflection of the moving plate for given voltages and hence, they are not suitable for accurate actuation control. This work presents a new formulation for tackling the fringing field, in which the effect of fringing field is modeled as a variable serial capacitor. Based on this model, a robust control scheme is constructed using the theory of input-to-state stabilization (ISS) and backstepping state feedback design. This method allows loosening the stringent requirements on modeling accuracy without compromising the performance. The stability and the performance of the system using this control scheme are demonstrated through both stability analysis and numerical simulation.Keywords Fringing field effect Á Modeling of electrostatic MEMS Á FEM based simulation Á Input-to-state stabilization Á Robust nonlinear control 1 Introduction

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Section: Appendix B: Iss Property Of Closed-loop Error Dynamicsmentioning

confidence: 99%

“…Assuming zero thicknesses for the plates, several approximate analytical formulae have been developed for the capacitance in the presence of the fringing field, such as Palmer [1] and Elliot [2] models. A number of other formulae have also been recommended assuming finite thicknesses for the electrodes [3][4][5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

A new formulation of fringing capacitance and its application to the control of parallel-plate electrostatic micro actuators

Hosseini

Zhu

Peter

2007

Analog Integr Circ Sig Process

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“…(D/b=.5, s/b=.25) (3) 0 Here h is the ordinate corresponding to the boundary GF, dg is a line increment parallel to the AC boundary, c is the free space permittivity, coo and is presented in the usual normalized form. £ A precise finite difference calculation with the usual relaxation procedure using a stationary integral expression for the capacitance yields a value of 8.801±.001 , i.e.…”

Section: Example: Coupled Bars Of Circular Cross Sectionmentioning

confidence: 99%

“…The closest prior publication appears to be a short paper by Chang [3] but the full implications and wide generality of the method may not be clearly apparant. Chang derives an approximate formula for thick microstrip using conformal transformations where the final parallel plate capacitor has slightly distorted magnetic walls.…”

Section: Example: Coupled Bars Of Circular Cross Sectionmentioning

confidence: 99%

Efficient Computation of Boundary Value Problems using Conformal Transformations Combined with Numerical Techniques

Levy¹

1979

9th European Microwave Conference, 1979

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This paper describes a new approach to the solution of two-dimensional boundary value problems which eliminates the disadvantages and combines the advantages of both conformal transformations and numerical methods. The conformal transformations are used to remove potential gradient singularities, and numerical (e.g. finite difference) methods may then be applied to the resulting almost-regular field problems. Boundary value problems previously regarded as very difficult become tractable, and considerable savings in computer time and storage requirements are achieved. The method is applied to the calculation of the even and odd mode capacitances of cylindrical rods between plane parallel ground planes.

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“…Recently. increased attention has been given to calculate these capacitance which uses either analytical [3]- [4]. or numerical method [MI.…”

Section: Introductionmentioning

confidence: 99%

3-D interconnect capacitance calculation for multi-conductor and its application to a ROM circuit design

Chung

Huang

[1992] Proceedings. Fifth Annual IEEE International ASIC Conference and Exhibit

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The parasitic capacitance associated with interconnection lines has become increasingly important with the scaling down of both device dimension and interconnection line for the present VLSI or ULSI circuit design. A 2-D and a 3-D capacitance simulators have been developed for evaluating the parasitic capacitance in VLSI structures. The coupling capocitancc, cross-wiring capacitance, and thefringing capacitance between wires in a multi-layer structure have been studied. Application of the simulated interconnect capacitance to a ROM circuit shows that good match between simulation and experiments has been achieved. We have made extensions to study the scaling effect of a commercialized ROM circuit design, from which a density of twice the original memory cell size can be obtained by the same design rule.

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Analytical IC Metal-Line Capacitance Formulas (Short Papers)

Cited by 113 publications

References 7 publications

A new formulation of fringing capacitance and its application to the control of parallel-plate electrostatic micro actuators

A new formulation of fringing capacitance and its application to the control of parallel-plate electrostatic micro actuators

Efficient Computation of Boundary Value Problems using Conformal Transformations Combined with Numerical Techniques

3-D interconnect capacitance calculation for multi-conductor and its application to a ROM circuit design

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