Fringing fields in disc capacitors

Sloggett, G. J.; Barton, N. G.; Spencer, Steven J.

doi:10.1088/0305-4470/19/14/012

Cited by 78 publications

(55 citation statements)

References 12 publications

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“…However this situation happens only at this point. It is easy to see that System (8) is stabilizing at this position with an input u = 0. By defining an open ball B e ¼ XjkXk\e f g& X of radius e centered at the origin, where X = (x 1 ,x 2 ,x 3 ) T and |Á| the usual Euclidean norm, a more practical control law can be expressed as…”

Section: Assumptionmentioning

confidence: 98%

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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: Assumptionmentioning

confidence: 98%

“…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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“…Considering the effect of electric fringe field, the electric capacitance to the second order approximation of h/r for h/r < 1 can be expressed as 17 πε π …”

Section: Electrowetting Equationmentioning

confidence: 99%

Analysis of Electrowetting of a Conducting Droplet on a Dielectric Layer

Yang

Zhao

2014

J. Phys. Chem. C

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Electrowetting has been used to actuate and control the motion of droplets on solid surfaces. An analysis based on the theories of thermodynamics and thermal activation processes is presented for the electrowetting of a conducting droplet on a dielectric layer. The concept of release rate of electric energy is proposed. The release rate of electric energy is proportional to the square of the applied electric voltage and the derivative of electric capacitance with respect to the surface area of the corresponding electric system. The velocity of a contact line under the action of an electric voltage is a hyperbolic sine function of the release rate of electric energy. Using the release rate of electric energy and introducing line tension in the analysis, the contact angle of a droplet at a stationary state under the action of a constant electric voltage is found to be a linear function of the release rate of electric energy and the line tension. The line tension introduces the droplet-size effect on the contact angle. A critical contact angle as a function of the applied electric voltage, the thickness of the dielectric layer, and the radius of the contact area is obtained. There exist stable and unstable zones, depending on the relative value of the contact angle and the critical contact angle. There exists an upper bound of electric voltage with the corresponding contact angle of 65.89°between 60 and 70°of the saturated contact angle reported for electrowetting of conducting droplets. This result suggests that the saturation of contact angle likely is related to the condition determining the field-induced stability of the contact line.

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“…Once the probability of electric distortion in internal electrodes reduces, the failing probability of capacitor electrodes decreases, then the electrical breakdown strength of capacitors is specifically improved. Figure 7 indicates capacitance fluctuations of the capacitors under the influence of different internal elec- Figure 6 Weibull plots of electrical breakdown strength for the capacitors using the 850℃ annealed glass-ceramics as dielectrics based on the internal electrode structure of (a) as to Figure 4 Figure 7(a)) in single layer structure seem to have the highest capacitances, because a flat capacitor influenced by the fringe field effects with electrode radius R and dielectric thickness d leads to a simple first-order approximation to actual capacitance C as [16] …”

Section: The Internal Electrodes For Hesdcsmentioning

confidence: 99%