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Topics. Unidentified Flying Objects Alien Abductions Flying Saucers End of the World April 1, 2014. Capacitance and Dielectrics. Capacitance Capacitance examples Energy stored in capacitor Dielectrics Nat’s research (just fun stuff). Capacitance.

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  1. Topics • Unidentified Flying Objects • Alien Abductions • Flying Saucers • End of the World April 1, 2014

  2. Capacitance and Dielectrics • Capacitance • Capacitance examples • Energy stored in capacitor • Dielectrics • Nat’s research (just fun stuff)

  3. Capacitance • Electric potential always proportional to charge • Point • Sheet • Wire • Define capacitance as ratio: • ) • Measure of geometry’s ability to store charge • Charge create a voltage, but voltage requires charge

  4. Capacitance of Parallel Plate Constant electric field between two conducting sheets Potential between sheets Capacitance across sheets With Dielectric between

  5. Capacitance • Typical capacitors

  6. Capacitance examples <<<Huge

  7. Capacitance examples

  8. Capacitance examples

  9. Electrical Properties of Materials Materials can do 2 things: • Polarize • Initial alignment of charge with applied voltage • Charge proportional to voltage • Temporary short-range alignment • Conduct • Continuous flow of charge with applied voltage • Current proportional to voltage • Continuous long-range movement

  10. Dielectrics • Polarizable material increases capacitance • Ability to “cancel” charge on plates draws more charge for given voltage, increases capacitance • Capacitance becomes • Actually k isn’t a “constant”. Can vary with frequency, temperature, orientation, etc.

  11. Dielectric constants

  12. Dielectric Spectroscopy (Nat’s Research) • Most insulators contain polar molecules and free ions • These can align as a function of frequency (up to a point) • Where they fail to align is called “relaxation frequency” • Characteristic spectrum www.msi-sensing.com

  13. TDR Dielectric Spectroscopy • Sensor admittance from incident and reflected Laplace Transforms. • Sample complex permittivity from sensor admittance. • Differential methods • Bilinear calibration methods.1 • Non-uniform sampling.2

  14. Dielectric Permittivity in Epoxy Resin 1 MHz -1 GHz • Aerospace resin Hexcel 8552. • High frequency range 1 MHz – 1 GHz. • Temperature constant 125°C, transition decreases with cure. • TDR measurement method. www.msi-sensing.com

  15. Permittivity in Epoxy Resin during Complete Cure Cycle www.msi-sensing.com

  16. Application to cement hydration • Cement Conductivity - Variation with Cure • Imaginary counterpart of real permittivity (’’). • Multiply by  to remove power law (o’’). • Decrease in ion conductivity, growth of intermediate feature with cure • Frequency of intermediate feature does not match permittivity www.msi-sensing.com

  17. Basic signal evolution in cement paste3 • Permittivity (ε’ ) and conductivity (εoωε’’) from 10 kHz to 3 GHz. • Initial behavior at zero cure time. • Evolution with cure time. • Low, medium, and high (free) relaxations.

  18. Dielectric modeling in cement paste • 1 Cole-Davidson, 2 Debye relaxations4-7 www.msi-sensing.com

  19. Model evolution with cement cure • Free-relaxation decreases as water consumed in reaction. • Bound-water8, grain polarization9 forms with developing microstructure. • Variations in frequency and distribution factor. • Conductivity decrease does not match free-water decrease. www.msi-sensing.com

  20. Energy stored in capacitor • Work to move charge across V • Define • Example 17-11 • Energy Density • Energy Density proportional to field squared! V + 0

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