= K, = 1-(16.69 f 1.33) ppm.The uncertainty of 1.33 ppm has the significance of a standard deviation and includes our best estimate of random and known or suspected systematic uncertainties. The mean time of the measurement is May 15, 1988. Combined with the recent measurement of the NBS ohm in SI units: Q N B \ / Q = Ki2 = 1-(1.593 f 0.022) ppm, this leads to a Josephson frequency/voltage quotient of E, = E,[1 + (7.94 f 0.67) ppm] where Eo = 483 594 GHz/V.
Article 690.11 in the 2011 National Electrical Code ® (NEC ® ) requires new photovoltaic (PV) systems on or penetrating a building to include a listed arc fault protection device. Currently there is little experimental or empirical research into the behavior of the arcing frequencies through PV components despite the potential for modules and other PV components to filter or attenuate arcing signatures that could render the arc detector ineffective. To model AC arcing signal propagation along PV strings, the well-studied DC diode models were found to inadequately capture the behavior of high frequency arcing signals. Instead dynamic equivalent circuit models of PV modules were required to describe the impedance for alternating currents in modules. The nonlinearities present in PV cells resulting from irradiance, temperature, frequency, and bias voltage variations make modeling these systems challenging. Linearized dynamic equivalent circuits were created for multiple PV module manufacturers and module technologies. The equivalent resistances and capacitances for the modules were determined using impedance spectroscopy with no bias voltage and no irradiance. The equivalent circuit model was employed to evaluate modules having irradiance conditions that could not be measured directly with the instrumentation. Although there was a wide range of circuit component values, the complex impedance model does not predict filtering of arc fault frequencies in PV strings for any irradiance level. Experimental results with no irradiance agree with the model and show nearly no attenuation for 1 Hz to 100 kHz input frequencies. 4 ACKNOWLEDGMENTSThis work was funded by the US Department of Energy Solar Energy Technologies Program.5
Interconnect lines are thin wires inside microelectronic circuits. The material in an interconnect line is subjected to severe mechanical and electrical loading, which causes voids to nucleate and propagate in the line: microelectronic circuits often fail because an interconnect is severed by a crack. Many of the mechanisms of failure are believed to be associated with diffusion of material through the line; driven by variations in elastic strain energy and stress in the solid, by the flow of electric current, and by variations in the free energy of the solid itself. With a view to modelling interconnect failures, we have developed a finite element method that may be used to compute the effects of diffusion and deformation in an electrically conducting, deformable solid. Our analysis accounts for large changes in the shape of the solid due to surface diffusion, grain boundary diffusion, and elastic or inelastic deformation within the grains. The methods of analysis is reviewed in this paper, and selected examples are used to illustrate the capabilities of the method. We compute the rate of growth of a void in an interconnect by coupled grain boundary diffusion and creep; we investigate void migration and evolution by electromigration‐induced surface diffusion; we study the influence of electromigration and stress on hillock formation in unpassivated interconnects, and compute the distribution of stress and plastic strain induced by electromigration in a passivated, polycrystalline interconnect line.
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