topics unidentified flying objects alien abductions flying saucers end of the world april 1, 2014
TRANSCRIPT
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Topics
• Unidentified Flying Objects• Alien Abductions• Flying Saucers• End of the World
April 1, 2014
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Capacitance and Dielectrics
• Capacitance• Capacitance examples• Energy stored in capacitor• Dielectrics• Nat’s research (just fun stuff)
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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
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Capacitance of Parallel Plate
Constant electric field between two conducting sheets
Potential between sheets
Capacitance across sheets
With Dielectric between
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Capacitance
• Typical capacitors
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Capacitance examples
<<<Huge
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Capacitance examples
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Capacitance examples
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• 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
Electrical Properties of Materials
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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.
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Dielectric constants
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www.msi-sensing.com
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
2010-12-03
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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
)()(
)()()(
rv
rvGY
oCi
Y
)(
)(
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www.msi-sensing.com
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.
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www.msi-sensing.com
Permittivity in Epoxy Resin during Complete Cure Cycle
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www.msi-sensing.com
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
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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.
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www.msi-sensing.com
Dielectric modeling in cement paste
• 1 Cole-Davidson, 2 Debye relaxations4-7
2010-12-03
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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.2010-12-03 www.msi-sensing.com
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Energy stored in capacitor• Work to move charge across V
• Define
• Example 17-11
• Energy Density
• Energy Density proportional to field squared!
V
0
+